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Special Issue: Celebrating the Nobel Prize Award to 

Richard Ernst in the 50th Year of Magnetic Resonance 

Contents 

Introduction, Another Nobel Prize in Fifty Years of Magnetic Resonance, 

D. G. Gorenstein 3 

Nuclear Magnetic Resonance Fourier Transform Spectroscopy, R. R. Ernst 5 

Reminiscences of My Journey Through a "Nobel" Lab, Anil Kumar 33 

Emphasizing the Role of Time in Quantum Dynamics, J. Jeener 35 

A Novel Contour Plot Algorithm for the Processing of 2D and 3D NMR Spectra, 

J. Weber, F. Herrmann, P. Rosch and A. Wokaun 43 

Selective Rotations Using Non-Selective Pulses and Heteronuclear Couplings, 

O. W. S0rensen 49 

Sensitivity Improvement in Multi-Dimensional NMR Spectroscopy, M. Ranee 54 

Cross Polarization and Dynamic-Angle Spinning of 17 O in L-Alanine, S. L. Gann, 

J. H. Baltisberger, E. W. Wooten, H. Zimmermann, and A. Pines 68 

Influence of Slow Internal Motion in Proteins on Cross-Relaxation Rates Determined 

by Two-Dimensional Exchange Spectroscopy, S. Macura, J. Fejzo, W. M. Westler and 

J. L. Maikley 73 

The Homogeneous Master Equation and the Manipulation of Relaxation Networks, 

M. H. Levitt and L. Di Bari 94 

Effects of Cross-Correlations in 2D NOE Experiments, P. K. Madhu, R. Christy, R. Grace 

and Anil Kumar 115 

Detection of Two-Quantum Nuclear Coherence by Nuclear Quadrupole Induced Electric 

Polarization, D. C. Newitt and E. L. Harm 127 

Calendar of Forthcoming Conferences 134 

Recent Magnetic Resonance Books 136 

Instructions for Authors 143

BULLETIN OF MAGNETIC RESONANCE 

The Quarterly Review Journal of the 

International Society of Magnetic Resonance 

Editor: 

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The Bulletin of Magnetic Resonance is a quarterly review journal by the International Society of 

Magnetic Resonance. Reviews cover all parts of the broad field of magnetic resonance, viz.. the 

theory and practice of nuclear magnetic resonance, electron paramagnetic resonance, and nuclear 

quadrupole resonance spectroscopy including applications in physics, chemistry, biology, and 

medicine. The BULLETIN also acts as a house journal for the International Society of Magnetic 

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Vol. 16, No. 1/2 3 

Introduction, Another Nobel Prize in Fifty Years of Magnetic Resonance 

In this issue of the Bulletin of Magnetic Resonance, 

we celebrate the success of one of the 

leaders of modern magnetic resonance. In 1991, 

Richard R. Ernst received the Nobel Prize in Chemistry 

for his major contributions to the development 

of Fourier transform and multidimensional NMR. 

This year, 1994, represents the 50th anniversary of 

the discovery of electron paramagnetic resonance by 

Zavoisky (1) as reported in his 1944 Thesis (Figure 

1). Next year, 1995, represents the 50th anniversary 

of the discovery of nuclear magnetic resonance 

and the subsequent publication of the results 

in 1946. These experiments of E. M. Purcell, 

H. G. Torrey and T. V. Pound at Harvard (2) and 

F. Bloch, W. Hansen and M. E. Packard (3) at Stanford 

ultimately led to the award of the first Nobel 

Prize in nuclear magnetic resonance to Bloch and 

Purcell in 1952. In fact 1994 also represents the 

50th anniversary of the award of the Nobel Prize to 

another famous researcher in the field, Isidor I. Rabi 

for his groundbreaking molecular-beam experiments 

(4). A very lucid discussion of the early history of 

magnetic resonance can be found in a Bulletin article 

by Norman Ramsey (5). 

In this special issue of the Bulletin, we have reproduced 

the Nobel Prize award lecture of Richard 

Ernst. In addition articles from some of his past 

coworkers and other eminent NMR spectroscopists 

have been included. As noted by Dr. Ernst, both in 

his article and in an ISMAR 1992 Special Plenary 

Lecture, his success rests on the many significant 

contributions of others in the field. 

Unlike almost all other fields of science, the theory 

and application of magnetic resonance has been 

on an exponentially rising curve for the past 50 

years. Normally in science we expect an exciting 

new field to draw initially many new participants to 

it (the "bandwagon" phenomenon) with a resulting 

explosion of new discoveries. However, once many of 

the major questions are answered, an equilibrium in 

the population of top scientists is established. The 

result is an S-shaped curve characterizing the vitality 

of a field with time. Ultimately as the field passes 

from favor (fewer grant funds!), many participants 

David G. Gorenstein, Editor 

Q 

90 

80 

70 

CO 

50 

30\ 

10 

1 

1 

i 

1 

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Figure 1: Electron paramagnetic resonance spectrum 

of CrCl3, from Zavoisky (1). 

migrate to the next exciting development in science. 

This often leads to an actual decrease of scientists 

in the field. The vitality of the field is now better 

characterized by a bell-shaped curve. 

The lifetime of a field in science is often disturbingly 

short, 15 to 25 years. However, this has 

not been the case with magnetic resonance, where 

we find that even after these past five decades we 

still are on the rising exponential portion of the 

curve. The reason for the difference of course is 

that there have been numerous ways of inventing 

new and exciting applications and understanding of 

magnetic resonance. As pointed out by R. Ernst 

(6), "I am not aware of any other field of science 

outside of magnetic resonance that offers so much

freedom and opportunities for a creative mind to 

invent and explore new experimental schemes that 

can be fruitfully applied in a variety of disciplines." 

In the first wave physicists discovered much basic 

magnetic resonance theory. This is still going 

on today as evidenced by the continued strong participation 

of physical scientists in the meetings of 

the International Society of Magnetic Resonance. 

Early on chemists began to recognize the importance 

of the chemical shift and coupling information 

as a way to identify the structure of molecules. 

A new wave of interest developed as commercial 

machines were built and that wave also continues 

to this day. Biochemists followed in turn 

as instruments became more sensitive and applications 

to biomolecular structure and function took 

off. That wave especially continues to expand exponentially 

today following the more recent introduction 

of Fourier transform, 2D and now multidimensional 

NMR spectroscopy - fields richly contributed 

by Richard Ernst. 

I don't believe that any of the early visionaries 

of magnetic resonance would have thought that 

NMR, with such low sensitively, could ever be used 

for 3D imaging. Magnetic resonance imaging and 

spectroscopy now constitute a fourth phase of this 

explosion, and now we are also seeing new developments 

in solid state magnetic resonance and materials 

science that hold much promise as well for the 

future. Each of these waves has brought forth ever 

more diverse and creative scientists into our field. 

In this issue Anil Kumar describes his journey 

through Richard Ernst's laboratory. Jean Jeener, 

the pioneer of the first 2D NMR pulse experiment, 

takes us on a journey through time in quantum dynamics. 

Alexander Wokaun and colleagues describe 

an algorithm that may help lead to automated assignment 

of multidimensional NMR spectra. Ole 

S0rensen describes some novel pulse sequences for 

multidimensional NMR. Mark Ranee again returns 

to multidimensional NMR (clearly a popular field!) 

and methods for improving sensitivity. Alex Pines 

and colleagues describe some of their pioneering developments 

in dynamic-angle spinning. Slobadan 

Macura and colleagues take us back to 2D NMR and 

motional effects in cross-relaxation/exchange spectroscopy. 

Malcolm Levitt and colleague present a 

novel method for treating spin dynamics using the 

homogeneous master equation. Anil Kumar returns 

Bulletin of Magnetic Resonance 

with his colleagues to discuss the importance of 

cross-correlations in 2D NOE experiments. Finally, 

one of the first pioneers of pulsed NMR spectroscopy, 

Erwin Hahn describes with his colleague some 

nuclear electric resonance detection. 

Where is it all going? As pointed out by Richard 

Ernst, following the discovery of X-rays many Nobel 

Prizes have been awarded in that field, including 

medical and biomolecular structure applications. It 

is rather obvious that over the next 50 years we 

will also see many more major magnetic resonance 

discoveries and applications, with numerous other 

Nobel Prizes and awards to come. 

REFERENCES 

X 

E. K. Zavoisky, Ph. D. Thesis (1944) and J. 

Phys. USSR 9, 211 and 245 (1945) and 10, 197 

(1946). 

2 

E. M. Purcell, H. G. Torrey and R. V. Pound, 

Phys. Rev. 69, 37 (1946). 

3 

F. Bloch, W. Hansen and M. E. Packard, Phys. 

Rev. 69, 127 (1946). 

4 I. I. Rabi, Phys. Rev. 51, 652 (1937); J. M. 

B. Kellogg, I. I. Rabi, N. F. Ramsey and J. R. 

Zacharias, Phys. Rev. 57, 677 (1940). 

5 N. F. Ramsey, Bull. Magn. Reson. 7, 94 

(1984). 

6 R. Ernst, Bull. Magn. Reson. 16, 5 (1994); 

following article. 

P.S. The next meeting of ISMAR will be held 

in Sydney, Australia from July 16-21, 1995. The 

council is discussing several possible sites for the 

1998 meeting in Europe. If you are interested in 

hosting the next ISMAR meeting in 2001, please 

contact the president of the society: 

Dr. Alexander Pines 


University of California 

Berkeley, California 94720 USA 

Telephone: 415-642-1220 

Fax: 415-486-5744. 

Clearly the field of magnetic resonance will be 

thriving into the next century.

Vol. 16, No. 1/2 5 

Contents 

Nuclear Magnetic Resonance Fourier Transform 

Spectroscopy (Nobel Lecture) 1 

Richard R. Ernst 

Laboratorium fur Physikalische Chemie, Eidgenossische Technische Hochschule 

ETH-Zentrum 8092 Zurich, Switzerland 

I. Introduction 5 

II. One-Dimensional Fourier Transform Spectroscopy 7 

III. Two-Dimensional Fourier Transform Spectroscopy 9 

IV. Modified Two-Dimensional FT-NMR Experiments 15 

V. Relayed Correlation 15 

VI. Rotating Frame Experiments 15 

VII. Multiple-Quantum Spectroscopy 18 

VIII. Multiple-Quantum Filtering 19 

IX. Spin-Topology Filtration 22 

X. Exclusive Correlation Spectroscopy 22 

XI. Heteronuclear Two-Dimensional Experiments 22 

XII. Three-Dimensional Fourier-Transformation Spectroscopy 23 

XIII. Molecular Dynamics Investigated by NMR 25 

XIV. Magnetic Resonance Fourier Imaging 27 

XV. Conclusion 28 

XVI. References 29 

I. Introduction 

The world of the nuclear spins is a true par- mechanics and quantum statistics, and numerous 

adise for theoretical and experimental physicists. textbook-like examples have emerged. On the other 

It supplies, for example, most simple test systems hand, the ease in handling nuclear spin systems prefor 

demonstrating the basic concepts of quantum destines them for the testing of novel experimental 

concepts. Indeed, the universal procedures of co- 

ôpyright © The Nobel Foundation 1992. - We thank , , 

,. -, . , J? j .. r,, i, , t • • . -4.il.- herent spectroscopy have been developed predomithe 

Nobel Foundation, Stockholm, for permission to print this K KJ . 

lecture. nantly within nuclear magnetic resonance (NMR)

6 Bulletin of Magnetic Resonance 

and have found widespread application in a variety 

of other fields. 

Several key experiments of magnetic resonance 

have already been honored by Nobel prizes in 

physics, starting with the famous molecular-beam 

experiments by Isidor I. Rabi (1-3) acknowledged in 

1944, followed by the classical NMR experiments by 

Edward M. Purcell (4) and Felix Bloch (5,6), honored 

with the 1952 prize, and the optical detection 

schemes by Alfred Kastler (7), leading to a prize in 

1966. Some further Nobel prize winners in Physics 

have been associated in various ways with magnetic 

resonance: John H. Van Vleck developed the theory 

of dia- and paramagnetism and introduced the 

moment method into NMR; Nicolaas Bloembergen 

had a major impact on early relaxation theory and 

measurements; Karl Alex Miiller contributed significantly 

to electron paramagnetic resonance; Norman 

F. Ramsey is responsible for the basic theory 

of chemical shifts and J couplings; and Hans G. 

Dehmelt developed pure nuclear quadrupole resonance. 

But not only for physicists is nuclear magnetic 

resonance of great fascination. More and more 

chemists, biologists and medical doctors discover 

NMR spectroscopy, not so much for its conceptual 

beauty but for its extraordinary usefulness. In this 

context, a great number of magnetic resonance tools 

have been invented to enhance the power of NMR in 

view of a variety of applications (8-15). This Nobel 

lecture provides a glimpse behind the scenes in an 

NMR toolmaker's workshop. 

Nuclear spin systems possess unique properties 

that predestine them for studies of molecules: 

1) The atomic nuclei serving as sensors are extremely 

well localized, with a diameter of a few femtometers, 

and can report on local affairs in their 

immediate vicinity. It is thus possible to explore 

molecules and matter in great detail. 

2) The interaction energy of the sensors with 

the environment is extremely small, less than 0.2 

J mol" 1 , corresponding to the thermal energy at 30 

mK. The monitoring of molecular properties is thus 

virtually perturbation-free. Nevertheless, the interaction 

is highly sensitive to the local environment. 

3) Information on the structure of molecules can 

be obtained from nuclear pair interactions: Magnetic 

dipole-dipole interactions provide distance information, 

while scalar J couplings allow one to de- 

termine dihedral angles. 

At first glance, it may be astonishing that it is 

possible to accurately determine internuclear distances 

by radio frequencies with wavelengths A » 

1 m, since this seemingly violates the quantum mechanical 

uncertainty relation, aq • ap > Ti/2, with 

the linear momentum p = 2nh/X, as it applies to 

scattering experiments or to a microscope. It is 

important that in magnetic resonance the geometric 

information is encoded in the spin Hamiltonian, 

7i = 7i (qi,..., qfc), where q^ is the nuclear coordinates. 

An accurate structure determination, therefore, 

boils down to an accurate energy measurement 

that can be made as precise as desired, provided 

that the observation time t is extended according 

to CTE • t > %/2. An upper limit of t is in practice 

given by the finite lifetime of the energy eigenstates 

due to relaxation processes. Thus, the accuracy of 

NMR measurements is not restricted by the wavelength 

but rather by lifetimes limited by relaxation 

processes. 

The information content of a nuclear spin Hamiltonian 

and the associated relaxation superoperator 

of a large molecule, for example a protein, is immense: 

It is possible to determine the frequencies of 

the chemical shifts of hundreds of spins in a molecule 

to an accuracy of 16-18 bits. Internuclear distances 

for thousands of proton pairs can be measured to 

about 0.1 A. Several hundred dihedral angles in a 

molecule can be determined with an uncertainty of 

less than 10°. 

The weakness of the nuclear spin interactions, so 

far described as an advantage, leads on the other 

hand to severe problems in detection. Large numbers 

of spins are required to discriminate the weak 

signals from noise. Under optimum conditions with 

modern high-field NMR spectrometers, 10 14 -10 15 

spins of one kind are needed to detect a signal within 

a measurement time of one hour. The low signal-tonoise 

ratio is the most limiting handicap of NMR. 

Any increase by technical means would significantly 

extend the possible range of NMR applications. 

This clearly defines the two goals that had to be 

achieved during the past three decades to promote 

NMR as a practical tool for molecular structure determination: 

1) Optimization of the signal-to-noise 

ratio; 2) Development of procedures to cope with 

the enormous amount of inherent information on the 

molecule under investigation.

Vol. 16, No. 1/2 

FT CW 

Figure 1: Schematic representation of pulse FT 

spectroscopy illustrated by the 60 MHz 1 H NMR 

spectrum of 7-ethoxy-4-methylcoumarin (22). An 

initial (7r/2)y rf pulse, represented by the rotation 

superoperator P, excites the transverse magnetization 

with Fy — where Iky is a component angular 

momentum operator of spin k. 7i is the Hamiltonian 

commutator superoperator,7iA = [H, A] and F is 

the relaxation superoperator. The expectation value 

(t) of the observable operator D is then given 

by eqn. 2, where cr$ represents the density operator 

of the spin system in thermal equilibrium. 

< D > (i) = Tr{DE(t)Pcr0} (2) 

The reduction in performance time for one spectrum 

is determined by the number of spectral elements 

N, that is, the number of significant points in 

the spectrum, roughly given by N = F/Af, where 

F is the total width of the frequency range and A/ 

a typical linewidth of a signal. A corresponding increase 

in the signal-to-noise ratio of y/~N per unit 

time can be obtained by coadding an appropriate 

number of FID signals originating from a repeated 

pulse experiment. The gain in signal-to-noise can 

be appreciated from Figure 1. 

It has been known for a long time that the frequency 

response function (spectrum) of a linear system 

is the Fourier transform of the impulse response 

(FID). This was already implicitly evident 

in the work of Jean Baptiste Joseph Fourier who in 

1822 investigated the heat conduction in solid bodies 

(24). In 1957 Lowe and Norberg proved this 

relation to hold also for spin systems despite their 

strongly nonlinear response characteristics (25). 

Stochastic testing of unknown systems by white 

random noise was proposed in the forties by Norbert 

Wiener (26). One could say that the color of 

the output noise carries the spectral information on 

the investigated system. The first applications of 

random noise excitation in NMR spectroscopy were 

proposed independently by Russel H. Varian (27) 

and by Hans Primas (28,29) for broad-band excitation 

and broad-band decoupling, respectively. The 

first successful experiments using random noise irradiation 

led to heteronuclear "noise decoupling" 

(30,31), a method that proved to be essential for 

the practical success of 13 C NMR spectroscopy in 

chemical applications. 

In 1970, Reinhold Kaiser (32) and the author 

(33) independently demonstrated stochastic resonance 

as a means to improve the signal-to-noise 

ratio of NMR experiments by broad-band irradiation. 

Here, the computed cross-correlation function 


(eqn. 3) of the input noise n;(i) and the output noise 

no(t) is equivalent to the FID of pulse FT spectroscopy. 

CI(TT) = no(t)ni(t - T) (3) 

This is illustrated in Figure 2 for fluorine resonance 

of 2,4-difluorotoluene. A binary pseudo-random sequence 

with a maximal white spectrum is used for 

excitation. Its advantages are the predictable spectral 

properties and the constant rf power. The low 

peak-power puts less stringent requirements on the 

electronic equipment. Disadvantages arise from the 

simultaneous irradiation and detection which can 

lead to line-broadening effects absent in pulse FT 

spectroscopy in which perturbation and detection 

are separated in time. A further disadvantage, when 

real random noise is used, is the probabilistic nature 

of the response which requires extensive averaging 

to obtain a stable mean value. Higher order correlation 

functions, such as eqn. 4 allow also the characterization 

of nonlinear transfer properties of the 

investigated system (26). 

= no(t)rii(t - - r2)rij(t - r3) 

(4) 

This has been exploited extensively by Bliimich and 

Ziessow for NMR measurements (34,35). 

A third approach, rapid scan spectroscopy, 

initially proposed by Dadok and Sprecher (36), 

achieves a virtually simultaneous excitation of all 

spins by a rapid sweep through the frequency range 

(37,38). The resulting spectrum is strongly distorted, 

but can be corrected mathematically because 

of the deterministic nature of the distortions. 

Correction amounts to convolution with the signal 

of a single spin measured under identical conditions 

or simulated on a computer. An example is given 

in Figure 3. It is interesting to note how similar 

a rapid scan spectrum is to an FID except for the 

successively increasing oscillation frequency. 

Finally, it is possible by computer synthesis to 

compute an excitation function with a virtually arbitrary 

excitation profile. This was originally utilized 

for decoupling purposes by Tomlinson and Hill 

(39), but is also the basis for composite pulse excitation 

schemes that have proved to be very powerful 

(40,41). 

Among the broad-band excitation techniques, 

pulse excitation is the only one that allows for a rig-

Vol. 16, No. 1/2 

orous analytical treatment irrespective of the complexity 

of the spin system. It does not lead to 

any method-inflicted line broadening as in stochastic 

resonance nor to correction-resistant signal distortions 

as in rapid scan spectroscopy of coupled spin 

systems (38). Pulse FT spectroscopy is conceptually 

and experimentally simple, and last but not least, it 

can easily be expanded and adapted to virtually all 

conceivable experimental situations. Measurements 

of relaxation times, for example, require just a modified 

relaxation-sensitive preparation sequence, such 

as a ir — vr/2 pulse pair for T\ measurements (42) 

and a vr/2 — TT pulse pair for Ti measurements (43). 

Also the extension to the investigation of chemical 

exchange using the saturation-transfer experiment 

of Forsen and Hoffman (44) is easily possible. 

It should be mentioned at this point that pulse 

NMR experiments were suggested already by Felix 

Bloch in 1946 in his famous paper (6), and the 

first time-domain magnetic resonance experiments 

were performed in 1949 by H. C. Torrey (45) and, 

in particular, by Erwin L. Hahn (46-48), who may 

be regarded as the true father of pulse spectroscopy. 

He invented the spin-echo experiment (46) and devised 

extremely important and conceptually beautiful 

solid-state experiments (49,50). 

Pulse FT spectroscopy has not only revolutioned 

high-resolution liquid-state NMR spectroscopy, but 

it has unified NMR methodology across all fields, 

from solid-state resonance, through measurements 

of relaxation times, to high-resolution NMR, with 

numerous spillovers also into other fields such as ion 

cyclotron resonance (51), microwave spectroscopy 

(52), and electron paramagnetic resonance (53). It 

also provided the germ for the development of multidimensional 

NMR spectroscopy. 

III. Two-Dimensional Fourier 

Transform Spectroscopy 

As long as purely spectroscopic measurements are 

made for the determination of the eigenfrequencies 

or normal modes of a system, one-dimensional (ID) 

spectroscopy is fully adequate. In NMR spectroscopy, 

this applies to the measurement of the chemical 

shifts that characterize the local chemical environment 

of the different nuclei. However, no information 

can be obtained in this manner on the 

spatial relationships between the observed nuclei. 

Figure 2: Schematic representation of stochastic 

resonance illustrated by the 56.4 MHz 19 F NMR 

spectrum of 2,4-difluorotoluene (33). Excitation 

with a binary pseudo-random sequence n\(t) 1023 

points in length generates the response no{t). Crosscorrelation 

of the two signals produces ci(r) which, 

after Fourier transformation, delivers the spectrum 

shown. In an alternative procedure, which has actually 

been used in this case, the individual Fourier 

transforms of n\(i) and no(t) are computed, and 

the complex conjugate ^ r {n;(i)}* is multiplied by 

to obtain the same spectrum. 

FREQUENCY SWEEP 

Figure 3: Schematic representation of rapid scan 

spectroscopy. The highly distorted sample spectrum 

obtained by a rapid frequency sweep of the 

frequency during the time t can be corrected by convolution 

with the equally sweep-distorted spectrum 

of a one-line test sample.


i> H^ R O 

a -- - i [ H , a ] - f { cr - a0 } 

COHERENT TRANSFER | | CROSS-RELAXATION "| 

Figure 4: The two pair-interactions relevant in NMR 

spectroscopy. The through-bond scalar 3\.\ coupling 

contributes to the Hamiltonian and leads to a coherent 

transfer (A) of spin order between spins Ik 

and I/. The time-modulated through-space dipoledipole 

interaction Dmn(t) causes multiexponential 

cross relaxation (B) between spins lm and In. The 

two interactions allow a sequential assignment of the 

resonances of neighboring spins in the peptide fragment 

shown and the determination of structure parameters. 

The three-bond J coupling is a measure 

for the dihedral angle about the central bond, the 

dipole-dipole interaction for internuclear distances. 

There are two important pair interactions in 

nuclear spin systems, the scalar through-bond 

electron-mediated spin-spin interaction (J coupling) 

and the through-space magnetic dipole-dipole interaction 

(Figure 4). The J coupling is described by 

the scalar term Tiki = 27rJfc/I/cI; in the spin Hamiltonian. 

It is responsible for the multiplet splittings 

in high-resolution spectra of liquids. Under suitable 

conditions, it can lead to an oscillatory transfer 

of spin order between the two spins Ij, and I;. 

The magnetic dipole-dipole interaction Dmn, on the 

other hand, is represented by a traceless tensor of 

second rank. Its average in isotropic solution is zero, 

and it can lead to signal splitting only in anisotropic 

media. However, its time modulation causes relaxation 

processes also in isotropic solution that are 

responsible for a multiexponential recovery of the 

spins to thermal equilibrium after a perturbation. 

Knowledge of these interactions allows one to deduce 

geometric relations in the molecule in solution 

(54,55) and arrangements of atoms in solids. In the 

optimum case, a complete three-dimensional struc- 

A B C D E F G H 

Figure 5: Schematic correlation diagram for the representation 

of pair interactions of nuclear spins. 

Vol. 16, No. 1/2 11 

contain connectivity information (57). Particularly 

fruitful were double- and triple-resonance experiments 

in which two or three rf fields are applied 

simultaneously, resulting in decoupling and spintickling 

effects (58-60). 

The early multiple-resonance experiments have 

in the meantime been replaced by multidimensional 

experiments. Pair interactions among spins are 

most conveniently represented in terms of a correlation 

diagram as shown in Figure 5. This suggests the 

recording of a "two-dimensional spectrum" that establishes 

such a correlation map of the corresponding 

spectral features. The most straightforward approach 

may be a systematic double-resonance experiment 

whose result can be represented as an amplitude 

S(u>i,u>2) which depends on the frequencies 

u>i and u>2 of the two applied rf fields (8,58). 

A new approach to measuring two-dimensional 

(2D) spectra was proposed by Jean Jeener in 1971 

(61). He suggested a 2D FT experiment consisting 

of two 7r/2 pulses with a variable time t\ between the 

pulses and the time variable £2 measuring the time 

elapsed after the second pulse as shown in Figure 6; 

this is an expansion of the principles illustrated in 

Figure 1 (see also Fig. 10a). Measuring the response 

s{t\,t2) of the two-pulse sequence which is Fouriertransformed 

with respect to both time variables produces 

a two-dimensional spectrum 5(^1,^2) of the 

desired form (62,63). 

This two-pulse experiment by Jean Jeener is the 

progenitor of a whole class of 2D experiments (8,63) 

which can also easily be expanded to multidimensional 

spectroscopy. Each 2D experiment, as shown 

in Figures 6 and 7, starts with a preparation pulse 

sequence P, which excites coherences, that is, coherent 

superpositions represented by the density operator 

(ti, t2) = Tt{DE(*2)RE(ti)P(7o} (5) 

PREPA- EVOLUTION MIXING DETECTION 

RATION ' PERIOD ' PERIOD ' PERIOD 

PERIOD ' ' l 

t, I 1 t, 

Figure 7: Schematic representation of a general 

2D experiment consisting of preparation, evolution, 

mixing, and detection periods. The duration 

t\ of the evolution period is varied systematically 

from experiment to experiment. The resulting 

signal s(£i,*2) oc < D > (£i,*2) is Fouriertransformed 

in two dimensions to produce the 2D 

spectrum 

It is not sufficient to perform a single two-pulse 

experiment. To obtain the necessary data 

(£1,^2) to compute a 2D spectrum S(COI,UJ2), it is 

required to systematically vary £1 in a series of experiments 

and to assemble a 2D data matrix that 

is then Fourier-transformed in two dimensions as is 

indicated schematically in Figure 7. The resulting 

2D spectrum correlates the precession frequencies 

during the evolution period with the precession frequencies 

during the detection period, and is a vivid 

and easily interpretable representation of the mixing 

process. Diagonal and cross peaks are measures 

for the elements of the transfer matrix of the mixing 

pulse sequence in Figure 6. 

Among the numerous transfer processes that can 

be represented in this manner, the most important 

ones (8) are 1) the scalar J coupling leading to 

2D correlation spectroscopy abbreviated as COSY, 

2) internuclear cross relaxation leading to 2D nuclear 

Overhauser effect spectroscopy abbreviated as 

NOESY, and 3) chemical exchange leading to 2D 

exchange spectroscopy abbreviated as EXSY.


7 6 5 4 3 2 1 

~" a>2[ppm] 

©ifppm] 

Figure 8: Phase-sensitive 400 MHz X H COSY spectrum 

of antamanide (1) in chloroform (at 250 K) in 

a contour-line representation. Positive and negative 

contours are not distinguished. The spectrum was 

recorded by Dr. Martin Blackledge. 

Figure 9: Assignment of the protons of the backbone 

of antamanide (1) by the combination of COSY (C) 

and NOESY (N) cross peaks. The missing NH protons 

in the four proline residues break the chain of 

sequential C-N connectivities. 

The COSY transfer, which proceeds through J 

coupling, is truly a quantum mechanical effect that 

does not find a satisfactory classical explanation. By 

means of a single (n/2)x rf mixing pulse, as in Figure 

6, it is possible to transfer coherence of spin 

k, which is antiphase with respect to spin I and 

represented in the density operator by the operator 

term 21^1^ into coherence of spin I, which is 

antiphase with respect to spin k, represented by - 

2IfczIjj/ (eqn. 6), whereby each factor of the product 

spin-operator can be considered to be rotated by 

TT/2 about the a;-axis. 

21*,,! kyi-lz 

~ 2IfczI. 

•fcz% 

Antiphase coherence of the type 21kyIiz is only 

formed during the evolution period when there is 

a direct spin-spin coupling between the spins Ik and 

1/ (eqn. 7). 

+ 2IkyIlzsin 

(7) 

This implies that in a two-dimensional correlation 

spectrum there are cross peaks only between directly 

coupled spins (as long as the approximation of weak 

coupling holds). It is obvious from eqn. 7 that there 

is no net coherence transfer, e.g. I^x —> lix, and 

the cross-peak integral must disappear. In other 

words, there is an equal number of cross-peak multiplet 

lines with positive and negative intensity. 

Pro H 

Phe 10 Val 1 

Pro z 

/ 2 \ 2 i 2 i 2 i i \ 

CH2 CH-CO-NH-CH-CO-NH-CH-CO-NH-CH-CO-N. ^CH, 

^N"^ CH 2 

I I 

CO CO 

I I 

^CHV 

/NN 

CH2 N-CO-CH-NH-CO-CH-NH-CO-CH-NH-CO-CH CH2 

\ / I I i \ I 

CH2-CH2 CH2 

O o 

Pro 7 Phe 6 Phe 5 Ala 4 

CH2-CH2 

Pro J 

A COSY spectrum, such as the one shown in 

Figure 8 for the cyclic decapeptide antamanide (1) 

can be used to find pairs of spins belonging to the 

same coupling network of an amino acid residue in 

(6)

Vol. 16, No. 1/2 13 

COSY 

NOESY j 

EXSY 

RELAY 

TOCSY 

ROESY 

MQS n 

1 

] 

1 

w 

n71 

n n w 

—41—12-^ 

Figure 10: Pulse sequences for some of the most 

useful homonuclear 2D experiments: a) COSY, b) 

NOESY or EXSY, c) relayed COSY, d) TOCSY 

or ROESY in the rotating coordinate system, e) 

multiple-quantum spectroscopy. 

the molecule. All intense cross peaks arise from couplings 

over two and three bonds that allow, first of 

all, the assignment of the pairs of NH and CaH along 

the polypeptide backbone (backbone protons), as 

indicated by C in Figure 9 for the six amino acid 

residues with NH protons. In addition, it is also 

possible to assign the protons in the side chains. 

The transfers of NOESY and EXSY experiments 

involve incoherent, dissipative processes that bring 

the system back to equilibrium in an exponential or 

multiexponential manner after an initial perturbation. 

They require an extended mixing time during 

which the random processes are given a chance 

to occur. Both processes can be investigated with 

the same three-pulse scheme (Figure 10b) (8,64-67). 

The mixing period is bracketed by two TT/2 pulses 

that transform coherence into static spin-order and 

back into coherence. The exchange processes transfer 

the spin order between different spins or between 

different chemical species, respectively. This type 

of transfer can be understood on the basis of classical 

kinetic models. The resulting 2D spectrum 

represents a kinetic matrix with cross-peak intensities 

proportional to the exchange rate constants of 

pseudo-first-order reactions. 

[ 

',lppm] 

Figure 11: 400 MHz 1 H NOESY spectrum of antamanide 

(1) in chloroform (at 250 K) in a contourline 

representation. The spectrum was recorded by 

Dr. Martin Blackledge. 

For the NOESY transfer, the exchange rate constants 

are given by the cross-relaxation rate constants, 

which are due to magnetic dipole-dipole interactions, 

and are proportional to 1/4, for nuclear 

pairs Ifc and I;, and depend on the correlation time 

rc of the tumbling of the molecules in solution. The 

distance dependence can be used to measure relative 

or, if rc is known, absolute distances in molecules. 

The NOESY cross peaks thus allow the identification 

of neighboring protons in a molecule - important, 

for example, in identifying protons that belong 

to adjacent amino acid residues in peptides. 

A NOESY spectrum of antamanide (1) is given 

in Figure 11. The sequential backbone protons of 

adjacent amino acid residues with NOESY cross 

peaks are marked in Figure 9 with N. It is seen 

in Figure 9 that these together with the protons 

with J- cross peaks from the COSY spectrum (Figure 

8) form two unbroken chains of connectivities 

that can be used for the identification of the backbone 

protons. The two chains are not joined because 

of the absence of NH protons in the four proline 

residues. The general assessment procedure of 

proton resonance frequencies based on COSY and 

NOESY spectra has been established by Wiithrich

14 

Figure 12: 2D 13 C EXSY spectrum of a mixture 

of cis- and irans-decalin recorded at 22.5 MHz and 

241 K (76). Top: Three-dimensional representation 

(stacked plot). Bottom: A contour-line representation 

with the assignment of the peaks. 

and his research group (56). 

Based on a complete or partial set of assigned 

resonances, it is then possible to deduce information 

on the molecular structure. Each NOESY crosspeak 

intensity provides an internuclear distance that 

can be used in a manual or computerized process to 

construct a molecular model compatible with the 

experimental data. In this process it is also possible 

to employ scalar coupling constants extracted 

from COSY-type spectra (most conveniently from 

E. COSY spectra, as mentioned later). According 

to the Karplus relations (54), there is a relation between 

vicinal coupling constants and dihedral angles. 

Ingenious computer procedures to determine 

molecular structures based on NMR data were first 

developed by Kurt Wiithrich and his research team 

and tested on a large number of small to mediumsize 

proteins (56, 68-71). At present, mainly two 

a i 

COSY 


RELAY 

E.COSY 

B 

a a 

9 e 

Figure 13: Extensions of the standard COSY experiment. 

Relayed correlation, total correlation spectroscopy 

(TOCSY), and multiple-quantum spectroscopy 

(MQS) increase the information content, while 

exclusive correlation (E. COSY), multiple-quantum 

filtering (MQF), and spin-topology filtration reduce 

the complexity. Both avenues can lead to threedimensional 

spectroscopy. 

computer algorithms for the structure determination 

are in use - the distance-geometry algorithm 

(72,73) and modifications of it, and the restrained 

molecular-dynamics algorithm (74,75), again with 

many variations. The structural problem in antamanide 

(1) will be discussed later, as it involves intramolecular 

dynamic processes that complicate the 

situation. 

Cross peaks in a NOESY-type exchange spectrum 

can also originate from chemical exchange; the 

three-pulse experiment of Figure 10b is indeed well 

suited for the investigation of chemical exchange 

networks (64,65,76). A distinction of the two types 

of signals is not possible by inspection of a single 

2D spectrum. However, variable-temperature studies 

are often conclusive. At sufficiently low temperatures 

at which chemical exchange becomes slow, 

only NOESY cross peaks should remain. The two 

types of signals may also be distinguished in experiments 

with rotating coordinate systems as mentioned 

in the next section. 

The 13 C NMR spectrum of a mixture of cis- and 

irons-decalin in Figure 12 is typical for a spectrum 

. 

4 

©

Vol. 16, No. 1/2 15 

showing chemical exchange. The spectrum gives evidence 

of the well-known conformational stability of 

irans-decalin, whereas for cis-decalin four pairs of 

carbon spins are involved in a conformational exchange 

process, giving raise to two pairs of cross 

peaks (76). 

IV. Modified Two-Dimensional 

FT-NMR Experiments 

Starting from the two prototypical 2D FT NMR 

experiments, numerous modified, expanded, and improved 

experiments have been suggested. Many of 

them have found a place in the arsenal of routine 

methods for the NMR spectroscopist. A first category 

of experiments, represented in the upper part of 

Figure 13, causes extended correlation through two 

or more transfer steps: Relayed correlation experiments 

involve two-step correlation, and total correlation 

spectroscopy (TOCSY) multiple-step correlation. 

The latter experiment leads to the important 

class of rotating frame experiments, including 

rotating frame Overhauser effect spectroscopy 

(ROESY) an alternative to NOESY. Finally also 

multiple-quantum spectroscopy allows one to investigate 

connectivity in spin systems. A second class 

of experiments attempts the simplification of spectra 

by exclusive correlation (E. COSY), multiplequantum 

filtering, and spin-topology filtration. 

V. Relayed Correlation 

In a standard COSY experiment, coherence is 

transfered exclusively between two directly coupled 

spins by means of a single mixing pulse. By a sequence 

of two TT/2 pulses, as in Figure 10c, it is 

possible to effect a transfer of coherence across two 

sequential couplings from spin I& to spin I; through 

the relay spin Ir (77,78). For the relation in eqn. 8, 

Jkrh = Jkr r m = Jri T m = 1/2 is assumed. 

*-kx 

-2L.J 

rzMy 

(8) 

During the extended mixing period rm, it is thus 

necessary to refocus the antiphase character of the 

Ir spin coherences with respect to spin Ij. and create 

antiphase character with respect to spin 1/ to 

allow for a second transfer by the second mixing 

pulse. Relayed correlation is useful whenever the 

resonance of the relay spin Ir cannot be identified 

unambiguously. With a relay experiment it is then 

nevertheless possible to assign spins Ifc and 1/ to the 

same coupling network (e.g. belonging to the same 

amino acid residue in a polypeptide chain). It is 

usually advantageous to refocus the effects of the 

chemical shift precession during the mixing period 

by incorporating a central n pulse as shown in Figure 

10c. 

Relayed coherence transfer is illustrated by 300 

MHz X H NMR spectra of the linear nonapeptide 

buserilin, pyro-Glu-His-Trp-Ser-Tyr-D-Ser-Leu- 

Arg-Pro-NHCH2CH3. Figure 14a shows a (doublequantum 

filtered) COSY spectrum and Figure 14b 

the corresponding relayed COSY spectrum (79). 

In both spectra, the resonance connectivities for 

the leucine residue are marked. It is evident that 

in the COSY spectrum only nearest neighbor protons 

are connected by cross peaks: NH-CaH, CaH- 

C^H 1 - 2 , C^H 1 - 2 -C7H, and C7H-(C^H3) 1 ' 2 . On the 

other hand, in the relayed COSY spectrum, also 

the next-nearest neighbors NH-C^H 1 ' 2 and C/3H 1 ' 2 - 

(C5H3) 1 ' 2 are connected. The third pair of relayed 

cross peaks CaH-C7H, is weak because of the high 

multiplicity of the C7H resonance and is not visible 

in the contour representation of Figure 14b. Similar 

relayed cross peaks can be found for the other amino 

acid residues. 

VI. Rotating Frame Experiments 

By means of an extended mixing pulse sequence, 

transfer of coherence over an arbitrary number 

of steps is possible in principle. In particular, 

continuous wave irradiation leads to the mixing of 

all eigenmodes of a spin system and correspondingly 

to transfers of coherence between all of them. 

This is exploited in total correlation spectroscopy 

(TOCSY) with the sequence shown in Figure lOd. 

All spins belonging to the same J-coupling network 

can be identified with TOCSY (80,81). The accurate 

matching of the precession frequencies of the


8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 

— o)2[ppm] 

Figure 14: 300 MHz correlation spectra of the nonapeptide buserilin in dimethyl sulfoxide (DMSO). Phasesensitive 

spectra with equal representation of positive and negative contours are shown. The resonance 

connectivities and the positions of the NH, CaH, CgH, C7H, and CgH diagonal peaks are indicated for the 

leucine residue (79). a) Double-quantum filtered COSY spectrum with the sequence from Figure 18. b) 

Relayed COSY spectrum with the sequence from Figure 10c and rm = 25 ms. c) TOCSY spectrum with the 

sequence from Figure lOd, rm = 112 ms, and an MLEV-17 pulse sequence applied during rm. 

various spins in the presence of a radio frequency 

field is crucial in enabling an efficient transfer of coherence. 

Either very strong radio-frequency fields 

or specially designed pulse sequences are needed for 

this purpose (81). Coherence transfer is possible 

when the effective average magnetic field strengths 

in the rotating frame are equal to within a J- 

oijlppml 

coupling constant, | 7(B| cor 

ft - Bf 

responding to a strong coupling case in the rotating 

frame. 

The TOCSY experiment is of interest for assignment 

of proton resonances to individual amino acid 

residues in a protein. Of particular value is that its 

transfer rate is enhanced by a factor of 2 in com-

Vol. 16, No. 1/2 17 

parison to COSY or relayed transfer experiments in 

the laboratory frame (80). Another property is that, 

because of the presence of a radio-frequency field, inphase 

coherence transfer is possible (eqn. 9), leading 

to in-phase cross-peak multiplet structures. 

life, Hx (9) 

A TOCSY spectrum of buserilin is included in 

Figure 14c for comparison with the relayed and 

standard COSY spectra depicted. Again three-step 

transfers CoH^CgHs) 1 ' 2 and even four-step transfers 

NH-^C^Hs) 1 ' 2 are visible here. Some expected 

cross peaks involving C7H are missing as before because 

of the extensive multiplet structure of C7H. 

The elimination of the chemical shift precession 

by the rf irradiation leads not only to the coherent 

transfer through the J-coupling network, but 

also to an incoherent transfer of spin order through 

transverse cross-relaxation. The transverse crossrelaxation 

terms are, in principle, always present. 

However, strong differential chemical shift precession 

of spin pairs normally causes a quenching of 

the transfer in the sense of first-order perturbation 

theory. In the presence of a strong rf field, 

this quenching is no longer operative and transverse 

cross-relaxation occurs. This is the transfer mechanism 

of the rotating frame Overhauser effect spectroscopy 

(ROESY) experiment (82). 

ROESY has similar properties as NOESY but 

differs in the dependence of the cross-relaxation rate 

constant Yî on the correlation time TC of the molecular 

rotational motion that modulates the internuclear 

dipole-dipole interaction responsible for crossrelaxation 

(cf. eqns. 10 and 11 where the spectral 

density J is defined by eqn. 12). 

NOE 

MoY 

Air) 

4TT 

3J(2u;o) (10) 

^J(2co0)\ (11) 

(12) 

As usual, coo is the Larmor frequency of the two nuclei 

with the internuclear distance rî- Eqns. 10 and 

12 imply that Fj^ OE changes sign for an intermediate 

correlation time rc of (5/4) l / 2 u0 *; that is, the crossrelaxation 

rate becomes small in the neighborhood 

of this condition. Depending on the viscosity of the 

solvent and the resonance frequency LL>O, this occurs 

for globular molecules within a range of molecular 

mass of 500-2000 Da. F^ OE , on the other hand, 

is less sensitive to rc and remains positive for any 

molecular mass. The ROESY experiment is therefore 

of advantage for molecules of intermediate size. 

- In addition, the different sensitivity of NOE and 

ROE to rc allows one to deduce information on 

intramolecular mobility by comparison of the two 

measurements (83). An advantage of ROESY over 

NOESY experiments is that the cross-peak amplitude 

is negative, while the simultaneously occurring 

cross peaks due to chemical exchange are positive 

and allow for an easy distinction as long as the signals 

do not overlap. 

It should be recognized that in the rotating frame 

coherence transfer through J couplings and cross 

relaxation occur simultaneously, whereby TOCSY 

cross peaks are positive and ROESY cross peaks 

appear with negative amplitude. This complicates 

the 2D spectra and calls for separation procedures. 

The suppression of the coherent transfer through J 

couplings (TOCSY) is easy, because it is only necessary 

to mismatch the condition | 7(B| — Bf) \< 

| 2irJki |, for example by a slight frequency offset in 

the presence of not-too-strong rf fields. The crossrelaxation 

rates are much less sensitive to such a 

mismatch and a clean ROESY spectrum results. 

Obtaining a clean TOCSY spectrum is more demanding 

because relaxation cannot easily be manipulated. 

A technique was proposed by C. Griesinger 

(84), which relies on a combination of eqns. 10 and 

11 to set the average cross-relaxation rate constant 

to zero (eqn. 13). A suitable weighting factor p can 

be found whenever T^[ OE < 0, that is, for sufficiently 

large molecules with rc > (5/4) 1 / 2 w(J" 1 . This 

requires the magnetization to move on a trajectory 

that spends a fraction p of time along the z-axis and 

a fraction (1-p) in the transverse plane. For rc —> oo, 

one finds p = 2/3 for TM — 0. A suitable pulse sequence, 

a modification of an MLEV-17 spin-locking 

sequence, has been proposed in ref. (84). 

Another optimized sequence, called "Clean 

CITY", was developed by J. Briand (85). A clean


10.0 8.0 6.0 

— u>2 Ippm) 

10.0 8.0 6.0 4.0 

o/,[ppm] 

10.0 8.0 6.0 

tt»2 Ippfni 

2.0 

MLEV-17 

ro.o 

2.0 

4.0 

6.0 

8.0 

10.0 

Clean CITY 

>, Ippm] 

Figure 15: Phase-sensitive 300 MHz l R TOCSY 

spectra of 15 mM sample of bovine pancreatic 

trypsin inhibitor in D2O recorded with a mixing 

time of 69 ms (85). a) Mixing process with MLEV- 

17 pulse sequence. Negative peaks are shown bycontours 

filled in black, b) Mixing process with the 

Clean CITY pulse sequence, c) Cross sections along 

LOI through the diagonal peak of Tyr 23 eH at LV2 = 

6.33 ppm in the spectra a) and b) (marked with 

broken lines). 

TOCSY spectrum of bovine pancreatic trypsin inhibitor 

(BPTI) using the Clean CITY sequence is 

compared in Figure 15 with a conventional TOCSY 

spectrum to demonstrate the efficient suppression of 

the (negative) ROESY peaks. 

VII. Multiple-Quantum 

Spectroscopy 

In the spectroscopy, in general, only those transitions 

are directly observable for which the observable 

operator has matrix elements not equal to zero, 

leading to the so-called allowed transitions. For 

«• 

1 

2ft., 

Figure 16: 90 MHz 2D X H correlation spectrum of 

[D3]3-amino-propanol with double-quantum transitions 

along u>\ and single-quantum transitions along 

u>2 • The three types of double-quantum transitions 

mentioned in the text are indicated. Enlargements 

of all cross peaks are shown on the left. The spectrum 

is shown in an absolute value representation 

(from ref. 89). 

magnetic resonance in strong magnetic fields with 

weak cw perturbation or with a free induction decay 

in the absence of rf, the observable operator of 

the transverse magnetization Fx = ]Tfe Ifei has matrix 

elements only between eigenstates of the Hamiltonian 

differing in the magnetic quantum number 

M by ±1. Thus single-quantum transitions are the 

allowed transitions, while multiple-quantum transitions 

with I AM I > 1 are forbidden. Multiplequantum 

transitions can, however, be induced by 

strong cw rf fields that cause a mixing of states 

(8,57) or by a sequence of at least two rf pulses 

(Fig. lOe) (8,63,86,87). Observation is possible again 

in the presence of a strong rf field (8,57) or after a 

further detection pulse (8,63,86,87).

Vol. 16, No. 1/2 19 

For spin systems with 1=1/2, multiple-quantum 

transitions invariably involve several spins, and 

multiple-quantum spectra contain information on 

the connectivity of spins within the J-coupling network 

in analogy to 2D correlation spectra. In particular, 

the highest order transition allows one to 

determine the number of coupled spins. Relaxation 

rate constants of multiple-quantum coherences are 

dependent on the correlation of the random perturbations 

affecting the spins involved and provide information 

on motional processes (88). 

A simple instructive example of a 2D doublequantum 

spectrum is given in Figure 16 to demonstrate 

the use of multiple-quantum transitions for 

the assignment of resonances (89). Along u)\, doublequantum 

transitions and along o>2 single-quantum 

transitions are displayed for the six-spin system of 

[D3]3-aminopropanol DOCH2CH2CH2ND2. In general, 

there are three categories of double-quantum 

transitions: 

1) Double-quantum transitions involving two directly 

coupled spins. They lead to pairs of cross 

peaks displaced symmetrically from the doublequantum 

diagonal (u\ = 2o>2) with u;2 coordinates 

corresponding to the Larmor frequencies of the two 

spins (e.g. uox - OA + $7M, fijvi + ^x)- 

2) Double-quantum transitions involving two 

magnetically equivalent spins. They lead to one or 

more cross peaks at an UJ\ frequency that intersects 

the double-quantum diagonal at the w2 frequency 

corresponding to the common Larmor frequency of 

the two spins (e.g. uj\ = 20,^,20,^, 2QX, although 

the spins are magnetically equivalent only within 

experimental accuracy). 

3) Double-quantum transitions involving two remotely 

coupled spins. They lead to single cross 

peaks at an u>\ frequency that intersects the double 

quantum diagonal at w2 equal to the mean of the 

two Larmor frequencies (e.g. OJI = OA + HX). These 

cross peaks carry information identical to that in 

relayed correlation spectra. 

For the practical application it is essential that 

a multiple-quantum spectrum never contains an 

array of strong diagonal peaks. It should be 

mentioned that a beautiful and useful form of 

a double-quantum experiment is the 2D INADE- 

QUATE spectroscopy proposed by Bax, Freeman, 

and Kempsell (90,91). There, only type 1 peaks can 

arise. 

The methods mentioned so far produce additional 

cross peaks that provide information not accessible 

with the standard COSY and NOESY experiments. 

In the following, techniques are discussed 

that lead to simplified spectra which may 

facilitate their interpretation. 

VIII. Multiple-Quantum Filtering 

Selective filtering can be achieved by exciting 

multiple-quantum coherence, selecting a particular 

quantum order, and reconverting the selected order 

into observable magnetization. Depending on the 

selected order, this leads to multiple-quantum filtering 

of various orders. The spin-system-selective 

effect relies on coherence transfer selection rules that 

limit the allowed transfers for weakly coupled spins 

(8,92): 

1) It is impossible to excite p quantum coherence 

in spin systems with less than p-coupled spins 

1=1/2. 

2) For the appearance of a diagonal peak of spin 

Ifc in a p-quantum-filtered COSY spectrum, the spin 

1^ must be directly coupled to at least p - 1 further 

spins. 

3) For the appearance of the cross peaks between 

spins Ifc and I; in a p-quantum-filtered COSY spectrum, 

both spins must simultaneously be coupled to 

at least p - 2 further spins. 

Violations of these coherence transfer selection 

rules occur for strong coupling and for certain special 

relaxation situations (93). 

In Figure 17, the effect of four-quantum filtering 

on various four-spin systems is demonstrated. The 

sample consists of a mixture of the five compounds 

irans-phenylcyclopropanecarboxylic acid (K4), DLisocitric 

acid-lactone (P3,].), 1,1-dichloroethane (S4), 

2-chloropropionic acid (C4), and D-saccharic acid- 

1,4-lactone (L4) with the coupling topologies indicated 

in Scheme 1 (94). 

Figure 17a shows a conventional (doublequantum-filtered) 

COSY spectrum of the mixture, 

while in Figure 17b the corresponding fourquantum-filtered 

spectrum is reproduced. The filtering 

effect can easily be understood based on the 

given rules and the coupling topologies shown in


2 1 

Figure 17: Multiple-quantum-filtered and spin-topology-filtered 300 MHz 1 H COSY spectra of a mixture of 

the compounds from Scheme 1 containing four-spin systems, a) Double-quantum-filtered spectrum obtained 

with the pulse sequence from Figure 18. b) Four-quantum-filtered spectrum obtained with the pulse sequence 

from Figure 18. c) G4 spin-topology-filtered spectrum obtained with the pulse sequence from Figure 19 (from 

ref. 94). 

Scheme 1. The interpretation is left to the reader. 

Only cross peaks of the molecule with K4 topology 

and diagonal peaks of molecules with P3 1, S4, and 

K4 topologies remain. 

Technically, multiple-quantum filtering exploits 

the characteristic dependence of a multiplequantum 

coherence transfer on the rf phase of the 

acting pulse sequence (8,92,95,96). Let us assume a 

transfer of coherence cpl(t) by a unitary transformation 

U(0), representing a particular pulse sequence, 

to coherence cp2(t), where px and p2 are the orders 

of coherence. 

U(0) 

cp2(t) (14) 

All rf pulses in the sequence are now phase-shifted 

by $, leading to U($). Then it can be shown that 

the resulting coherence Cp2(t) is phase-shifted by 

(15) 

The phase shift is therefore proportional to the 

change in coherence order (Ap = P2—Pi)- After a series 

of experiments are performed in which the phase

Vol. 16, No. 1/2 21 

® ô 

Scheme 1. The compounds used for the spectra in 

Figure 17 and their spin-coupling topologies. 

is incremented systematically in a set of N experiments 

and the resulting experimental results are 

combined according to eqn. 16. 

Figure 19: Pulse sequence for C4 spin-topology filtration 

consisting of TT/2 and TT pulses. The delays 

are adjusted to T = 1/(8J) and A = 1/(2J), where 

J is the uniform J-coupling constant. is phasecycled 

for four-quantum selection and 9 for the suppression 

of axial peaks (94). 

2QF 

• o • o 

o • o • 

o • o • 

3QF 

o»«o 

• oo» 

• oo» 

E.COSY 

• o 

• c) 

— 

J 23 

-M2 

Figure 20: E. COSY experiment to simplify the 

multiplet structure of cross peaks. The doublequantum- 

and the triple-quantum-filtered cross 

peak between spins Ii and I2 of a three-spin system 

are combined to produce an E. COSY pattern. 

Positive and negative multiplet components are distinguished 

by empty and filled circles. 

1


IX. Spin-Topology Filtration 

It may be desirable to enhance the filtering effect 

illustrated in Figure 17 and to select individual 

spin coupling topologies. Indeed it is possible to design 

extended pulse sequences, in combination with 

multiple-quantum nitration, that are tailor-made for 

specific spin coupling topologies (94,97,98). A pulse 

sequence built into a 2D COSY experiment, that 

is selective for cyclic C4 spin coupling topologies is 

depicted schematically in Figure 19. If this pulse sequence 

is applied to the mixture of compounds with 

four-spin systems (Scheme 1), the 2D spectrum of 

Figure 17c is obtained. It shows efficient suppression 

of all other spin systems. It should be noted, however, 

that the situation is here rather ideal. Often, 

these filters do not perform as well because their 

design relies on all non-zero spin couplings being 

equal. In reality, there are weak and strong couplings 

that cannot be characterized by topological 

considerations alone. Often also the intensities of 

signals decrease during the extended pulse sequences 

due to relaxation. This limits the practical usefulness 

of these methods. 

X. Exclusive Correlation Spectroscopy 

Multiple-quantum filtering suppresses not only 

diagonal and cross peaks in 2D spectra but also 

changes the sign pattern in the cross-peak multiplet 

structure. By appropriate combination of differently 

multiple-quantum-filtered 2D spectra, it is 

possible to simplify the multiplet structure by reducing 

the number of multiplet components. Exclusive 

correlation spectroscopy (E. COSY), proposed by 

O.W. S0rensen, eliminates all multiplet components 

from a COSY spectrum except for those belonging 

to pairs of transitions with an energy level in common 

(99-101). In practice, it is not necessary to 

combine multiple-quantum-filtered spectra literally, 

but it is possible to coadd directly the experimental 

results from a phase cycle with the appropriate 

weighting factors. 

Figure 20 shows schematically the combination 

of cross-peak multiplets connecting two spins, Ii and 

I2, in a three-spin system after double- and triplequantum 

filtering. The remaining pattern consists 

of two basic squares with side lengths equal to the 

active coupling constant J\i responsible for the coherence 

transfer. The displacement vector between 

the two squares is given by the two passive couplings 

J13 and J23 to the third (passive) spin. It should be 

mentioned that this multiplet structure is identical 

to the one obtained by a COSY experiment with 

a mixing pulse with an extremely small flip angle 

(102). 

E. COSY is of practical use whenever the crosspeak 

multiplet structure must be analyzed for the 

determination of J-coupling constants. This can be 

done conveniently by hand by measuring the displacement 

of peripheral multiplet components (101) 

or by a recursive contraction procedure on a computer 

(103). 

XI. Heteronuclear Two-Dimensional 

Experiments 

In addition to the homonuclear 2D experiments 

discussed so far, at least as many heteronuclear 

experiments have been proposed and introduced 

to the repertoire of routine spectroscopy methods. 

Of greatest practical importance are heteronuclear 

shift correlation spectra which correlate the chemical 

shifts of directly bonded or remotely connected 

heteronuclei (104,105). In this context, so-called inverse 

detection experiments are of particular interest. 

Here proton I-spin coherence is observed in %2 

while spin coherence of a less sensitive, less abundant 

S nucleus evolves in t\ (104). The most efficient 

pulse sequences create heteronuclear two-spin 

coherence that evolves in t\ and that acquires the 

frequency information of the S-spin resonance (106). 

Also in the heteronuclear environment, relayed coherence 

transfer (78) as well as experiments in the 

rotating frame (107) are important. Spin filtering is 

used for multiplicity selectivity, that is, for distinguishing 

S spins coupled to one, two, or three I spins 

(108), and in the form of J filtering for the distinction 

of one-bond and multiple-bond couplings (109). 

This enumeration of heteronuclear experiments is by 

no means exhaustive.

Vol. 16, No. 1/2 23 

Figure 21: Schematic representation of a 3D NMR experiment as an extension of Figures 1 and 6. Three 

evolution periods with the time variables t\, ti, and £3 are separated by two transfer or mixing processes with 

the transfer matrices Rl and R2. A 3D experiment can be conceived as the contraction of two 2D experiments. 

Figure 22: 3D representation of a 300 MHz 3D 

homonuclear ROESY-TOCSY spectrum of buserilin 

in [De]DMSO photographed from a computer screen 

(116). 

XII. Three-Dimensional Fourier- 

Transformation 

Spectroscopy 

No new principles are required for the development 

of 3D NMR spectroscopy, which is just a 

logical extension of 2D NMR spectroscopy. Instead 

of a single mixing process which relates two frequency 

variables, two sequential mixing processes 

relate three frequencies: the origin frequency u>\, 

the relay frequency u>2, and the detection frequency 

UJ3 (Figure 21). In this sense a 3D experiment can 

be considered as the combination of two 2D experiments. 

Obviously a very large number of possible 

3D experiments can be conceived. However, only 

few of them have proved to be indispensible so far 

(110-118). 

Figure 23: 3D resolution of a 2D X H NMR spectrum 

by 15 N resonance spreading. The NH-CaH 

cross peaks are displaced in a third dimension by 

the corresponding 15 N chemical shifts. 

Two applications of the 3D spectroscopy concept 

have emerged: 1) 3D correlation and 2) 3D 

dispersion spectroscopy (see also Fig. 13). Threedimensional 

correlation is of importance in homonuclear 

experiments. It has been mentioned that 

the assignment procedure in biomolecules requires a 

COSY-type and a NOESY-type 2D spectrum. The 

two 2D experiments could be contracted into one 

3D experiment, combining a J-coupling-mediated 

transfer and a cross-relaxation transfer. A 3D 

COSY-NOESY spectrum possesses the advantage 

that the entire assignment process can be carried 

out with a single homogeneous data set (115,116). 

It also incorporates redundant information that allows 

cross checks of the assignments. For obtaining 

quantitative information, however, 3D spectra are 

less suited, since all peak intensities are products of


two transfer coefficients that are sometimes difficult 

to separate. 

A 3D ROESY-TOCSY spectrum of the linear 

nonapeptide buserilin is shown in Figure 22 (vf. 

Fig. 14)(116). A ROESY instead of a NOESY sequence 

is required for buserilin, as it is a molecule 

of intermediate size for which the NOE intensities 

are small. The TOCSY step has the advantage that 

chains of multiple-step cross peaks extend to nuclei 

in the side chains are obtained thus facilitating the 

identification of the amino acid residues. 

It should be recognized that recording a 3D spectrum 

is considerably more time-consuming than two 

2D spectra, since two time parameters, t\ and £2, 

must be incremented independently, requiring a 2D 

array of experiments. Thus the question arises of 

when it is worth the effort to record a 3D spectrum. 

This question has been discussed in numerous publications 

(116,119,120). 

Let us consider a particular cross peak in a 3D 

spectrum that correlates the coherences {tu} in the 

wi, {rs} in the w2 and {pq} in the U13 dimension. 

Its intensity is determined by the following product 

(eqn. 17) of matrix elements in the eigenbasis of the 

unperturbed Hamiltonian HQ (116). 

Z{pq}{rs}{tu} ~ 

A nonvanishing intensity establishes a two-step correlation 

{tu}-{rs}-{pq}. 

The 3D experiment can be compared with two 

2D experiments that employ the mixing processes 

x(l) x(2) 

R and R , respectively. The corresponding intensities 

are expressed by eqns. 18 and 19. 

Z {rs}{tu} 

~~ 

D 1P R {pq}{rs}( I> 

(18) 

(19) 

If in the 2D spectra the two relevant peaks with 

intensities Z and Z \ can be identified, 

J {rs}{tu} {Pq}{} 

possibly in crowded regions, the two-step correlation, 

represented by a 3D peak, could also be established 

based on the two 2D spectra {tu}-{rs} 

and {rs}-{pq}. Provided that Z{pq}{rs}{tu} / 0 is 

true, the intensities and Z < {Jq}{rs} are de- 

{ 

ferent from zero when in addition Dgr ^ 0 and 

(P

Vol. 16, No. 1/2 25 

In this case, ribonuclease A was grown in an E. coli 

medium containing 15 N-labeled nutrients. The spectrum 

was obtained with the pulse sequence from 

Figure 25. Initially proton coherence is excited and 

precesses during t\ under 15 N refocusing by the applied 

vr pulse. During the mixing time rm, coherence 

transfer from other protons to the NH protons 

is effected in the rotating frame by the application 

of a TOCSY multiple-pulse sequence. The 

NH coherence is then converted into 15 NH heteronuclear 

multiple-quantum coherence (HMQC) which 

precesses during t-i and acquires 15 N resonance information 

(under proton refocusing). After reconversion 

into NH proton coherence, detection follows 

during £3 under 15 N decoupling. For a complete 

assignment of the proton resonances a 15 N-spread 

NOESY spectrum is required in addition. 

The step to 4D spectroscopy (121) is a logical 

one: In 2D experiments, spins are pairwise correlated, 

for example NH and CQH protons. Threedimensional 

dispersion uses either 15 N or 13 Ca resonance 

for spreading the resonances of NH or CQH, 

respectively. In a 4D experiment, both spreading 

processes are applied simultaneously (Scheme 2). 

The order of the frequencies in the actual experiment 

is a matter of convenience. Normally, the detection 

frequency W4 refers to proton spins for sensitivity 

reasons. In most cases, the two spreading 

coordinates are rather coarsely digitized to limit the 

performance time, just enough to achieve separation 

of peaks overlapping in the 2D spectrum. Often 8 

to 32 points in each of the two dimensions are sufficient. 

Scheme 2. Double spreading in 4D experiments. 

XIII. Molecular Dynamics 

vestigated by NMR 

In- 

The molecular structures determined by NMR 

spectroscopy in solution, by X-ray diffraction in single 

crystals, or by other means are invariably motionally 

averaged structures, whereby the averaging 

Figure 24: 3D 15 N-spread 600 MHz X H TOCSY 

spectrum of 15 N-labeled ribonuclease A in water. 

The 3D spectrum shows the 15 N resonances 

along the 102 axis. The spectrum was recorded by 

C. Griesinger with the pulse sequence from Figure 

25 and processed by S. Boentges. The sample 

was provided by Prof. S. Benner of ETH Zurich. 

15 N 

CH 

NH 

TTTTTTT 

TOCSY 

71/2 7T/2 

Figure 25: Pulse sequence for recording a 3D 15 Nspread 

TOCSY spectrum. After presaturation of 

the water resonance (I), the proton resonances are 

excited and precess during t\. After the homonuclear 

TOCSY transfer from CH to the NH protons, 

the coherence is converted into heteronuclear 

multiple-quantum coherence (HMQC) that evolves 

during ti and acquires 15 N shift information. After 

reconversion to proton coherence, the NH resonances 

are detected during £3 under 15 N decoupling.


process is strongly dependent on the measurement 

technique. To interpret experimentally determined 

structures, some knowledge of the motional properties 

of the molecule is in fact indispensible. Molecular 

dynamics is also relevant for its own sake, in 

particular for the understanding of reactivity and 

interaction with other molecules. In many cases, active 

sites in a molecular pocket are only accessible 

due to the flexibility of the molecule itself. 

The characterization of the motional properties 

of a molecule is orders of magnitude more difficult 

than the description of an averaged molecular structure. 

While 3^—6 coordinates are sufficient to fix a 

structure containing N atoms, the characterization 

of molecular dynamics requires 3N-6 variances of 

the intramolecular coordinates, (3JV-6)(3iV-5)/2 covariances, 

and the same number of auto- and crosscorrelation 

functions, respectively. In addition, also 

higher order correlation functions are needed for a 

more refined description of dynamics. In practice, 

a sufficient number of observables is never available 

for a full description of dynamics. In this sense, the 

study of dynamics is an open-ended problem. 

Numerous techniques are available for obtaining 

data on dynamics: Debye-Waller factors in X-ray 

diffraction give hints on the variances of the nuclear 

coordinates, however, without a measure for 

the time scale. Inelastic and quasielastic neutron 

scattering deliver correlation functions, but without 

a reference to the structure. Fluorescence depolarization 

allows one to determine the motional correlation 

function of fluorescent groups, such as tyrosine 

residues in proteins. Ultrasonic absorption gives an 

indication of the frequencies of the dominant motional 

modes, but again without a structural reference. 

NMR spectroscopy is more universally applicable 

to motional studies than most of the other techniques. 

The range of correlation times rc that can 

be covered by various NMR methods is enormous, 

from picoseconds to seconds and more (Scheme 3). 

1 s < rc: Real-time monitoring after initial 

perturbation 

10 ms < rc < 10 s: 2D exchange spectroscopy (EXSY) 

100 fis < TC < 1 s: Lineshape analysis, exchange 

broadening, and exchange narrowing 

1 /xs < TC < 10 ms: Measurements of relaxation time Tje 

in the rotating frame 

30 ps < rc < I/us: Measurements of relaxation time Ti 

in the laboratory frame 

TC < 100 ps: Averaged parameter values 

Scheme 3. NMR methods for the determination of 

motional correlation times rc 

Except for slow motions on a time scale of a 

millisecond or more for which lineshape analysis, 

saturation transfer experiments, and 2D exchange 

studies can be performed, many dynamics studies 

by NMR rely on measurements of relaxation times. 

The various relaxation parameters, such as the longitudinal 

relaxation time Ti, the transverse relaxation 

time T2, the rotating-frame relaxation time 

Tie, and cross-relaxation rate constants TM depend 

on the correlation time rc of the underlying random 

process. 

The following discussion shall be restricted to a 

recent study of the intramolecular dynamics in antamanide 

(1) (83,122,123) (see Figs. 8,9,11). Antamanide 

is an antidote for toxic components of 

the mushroom Amanita phalloides. Astonishingly, 

the antidote is a component of the same mushroom. 

Indications have been found in early ultrasonic 

absorption studies (124) that the peptide 

ring seems to undergo a conformational exchange 

process with a frequency of about 1 MHz. In the 

course of extensive investigations of antamanide by 

Kessler's research group (125), it has also been noticed 

that the distance constraints obtained from 

NMR measurements could not be fitted by a single 

conformation. In our laboratory Martin Blackledge 

performed rotating-frame relaxation measurements 

and localized a hydrogen-bond exchange process 

with an activation energy of about 20 kJ mol" 1 

and a lifetime of 25 fj,s at room temperature (unpublished 

results, see also ref. 126). With a new 

dynamic structure determination procedure called 

MEDUSA (123), the conformational space of antamanide 

was investigated more systematically than 

ever before. 1176 feasible low-energy structures 

were found. They were combined in dynamically

Vol. 16, No. 1/2 27 

interconverting pairs in an attempt to fulfill all experimental 

constraints including NOE distance constraints, 

J-coupling angular constraints, and specific 

information on hydrogen-bond dynamics. A large 

set of feasible structural pairs were constructed. 

Many pairs are compatible with the experimental 

data within experimental accuracy. For a more restrictive 

description of the dynamic system of antamanide, 

additional and more accurate experimental 

data is required. Figure 26 shows, as an example, 

the dynamic pair of structures that fits the 

experimental data best so far. The two interconverting 

structures differ primarily in the hydrogen 

bonds Va^NH-Phe 9 © and Phe 6 NH-Ala 4 0, which 

exist only in one of the two conformations (II), and 

in the torsional angles ^5 and ^10. 

A second study concentrated on the dynamics 

of ring puckering of the four proline residues in antamanide 

(122). The conformation of the five-ring 

systems can be determined from the dihedral angles 

Xi, X2) an d X3 which in turn can be deduced from 

the vicinal proton-proton J-coupling constants using 

the Karplus relations (54). The relevant coupling 

constants (21 per residue) were determined 

from E. COSY spectra. Based on these measurements, 

a model was constructed for each of the proline 

residues by least-squares fitting. It was found 

that for Pro 3 and Pro 8 a good fit can be obtained 

with a single rigid conformation, while for Pro 2 and 

Pro 7 two rapidly exchanging conformations were required 

to reduce the fitting error to within an acceptable 

range. At the same time, measurements 

of the 13 C relaxation time confirmed that Pro 3 and 

Pro 8 are rigid, while Pro 2 and Pro 7 show dynamic 

behavior with correlation times between 30 and 40 

ps. This implies that the dynamics of the peptide 

ring and the proline ring are not correlated and proceed 

on entirely different time scales. The two exchanging 

conformations found for Pro 2 are shown 

in Figure 27. It is seen that the conformational 

changes resemble the up and down movements of 

the "flap of the envelope" (C7). 

XIV. Magnetic Resonance 

Fourier Imaging 

Magnetic resonance imaging (MRI) has had 

an enormous impact on medical diagnosis and has 

rapidly become a powerful routine tool. The basic 

Figure 26: Pairs of conformers of antamanide that 

fulfill the experimentally determined structural constraints. 

The two pairs are shown as stereoplots as 

well as in abstract form. In the former, hydrogen 

bonds are indicated by broken lines, in the latter by 

arrows pointing towards the hydrogen-bonded oxygen 

atom. The C-C. bonds about which the torsion 

angles 5 and 4>§ are defined are indicated by heavy 

lines. 4>5 is in the lower and io in the upper half of 

the stereoplots. (from ref. 123). 

Pro 2 d) 

Pro 2 (2) 

Figure 27: The two experimentally determined conformations 

of the amino acid residue Pro 2 in antamanide 

(1) (see ref. 122).


I 

Figure 28: Schematic representation of Fourier 

NMR imaging, here shown in two dimensions. Two 

orthogonal gradients (gx,9y) are applied during the 

t\ and £2 periods of a 2D experiment. A 2D Fourier 

transformation of the data set s(ti,t2) produces a 

2D image of the investigated subject (R.R.E.). 

procedure for recording a 2D or 3D NMR image of 

an object is attributed to Paul Lauterbur (127). A 

magnetic field gradient, applied along different directions 

in space in a sequence of experiments, produces 

projections of the nuclear spin density of the 

object onto the direction of the gradient. From a 

sufficiently large set of such projections it is possible 

to reconstruct an image of the object, for example, 

by filtered backprojection in analogy to X-ray 

tomography. 

A different approach is directly related to 2D 

and 3D FT spectroscopy. Frequency encoding of 

the three spatial dimensions is achieved by a linear 

magnetic field gradient applied successively along 

three orthogonal directions for the durations £1, £2, 

and £3, respectively, in a pulse FT experiment (128). 

In full analogy to 3D spectroscopy, the time parameters 

t\ and £2 are incremented in regular intervals 

from experiment to experiment. The recorded signal 

s(t\,t2,tz) is Fourier-transformed in three dimensions 

to produce a function S(OJI,0^2,^3) which 

is equivalent to a 3D spatial image when the spatial 

information is decoded using the relations x — 

^l/Sx, V ~ ^2/gy, and z = io^/gz with the three field 

gradients gx, gy, and gz. The procedure is illustrated 

in Figure 28 for two dimensions. 

In a further refinement, proposed by Edelstein et 

al. (129), the time variables £1 and £2 are replaced by 

variable field gradient strengths gx and gy applied 

during a constant evolution time. With regard to 

the accumulated phase, (eqn. 20) it is immaterial 

whether the evolution time or the field gradients are 

varied. 

7 = 

(20) 

However, keeping the time t^ constant eliminates 

undesired relaxation effects. 

In medical imaging, 3D experiments have a natural 

justification, although it is sometimes simpler to 

apply selective excitation techniques to select a 2D 

slice through the object to be imaged (130). Even 

extensions to higher dimensions are quite realistic. 

In a fourth dimension, for example, chemical shift 

information can be accommodated (131). Also 2D 

spectroscopic information could be combined with 

three spatial dimensions, leading to a 5D experiment. 

No limitations seem to exist for human imagination. 

However, the practical limits will soon be 

reached when the required performance times are 

also taken into consideration. 

XV. Conclusion 

I am not aware of any other field of science outside 

of magnetic resonance that offers so much freedom 

and opportunities for a creative mind to invent 

and explore new experimental schemes that can be 

fruitfully applied in a variety of disciplines. NMR 

spectroscopy is intellectually attractive because the 

observed phenomena can be understood based on a 

sound theory, and almost all conceits can also be 

tested by easy experiments. At the same time, the 

practical importance of NMR is enormous and can 

justify much of the playful activities of an addicted 

spectroscopist. 

Most of the credit for the inspiration and execution 

of the work described should go to my teachers 

Hans Primas and Hans H. Giinthard, to my 

supervisor Weston A. Anderson, to the inspirator 

Jean Jeener, and to my co-workers (in more or 

less chronological order): Thomas Baumann, Enrico 

Bartholdi, Robert Morgan, Stefan Schaublin, Anil 

Kumar, Dieter Welti, Luciano Miiller, Alexander

Vol. 16, No. 1/2 29 

Wokaun, Walter P. Aue, Jiri Karhan, Peter Bachmann, 

Geoffrey Bodenhausen, Peter Brunner, Alfred 

Hohener, Andrew A. Maudsley, Kuniaki Nagayama, 

Max Linder, Michael Reinhold, Ronald 

Haberkorn, Thierry Schaffhauser, Douglas Burum, 

Federico Graf, Yongren Huang, Slobodan Macura, 

Beat H. Meier, Dieter Suter, Pablo Caravatti, Ole 

W. S0rensen, Lukas Braunschweiler, Malcolm H. 

Levitt, Rolf Meyer, Mark Ranee, Arthur Schweiger, 

Michael H. Frey, Beat U. Meier, Marcel Miiri, 

Christopher Councell, Herbert Kogler, Roland 

Kreis, Norbert Miiller, Annalisa Pastore, Christian 

Schonenberger, Walter Studer, Christian Radloff, 

Albert Thomas, Rafael Briischweiler, Herman Cho, 

Claudius Gemperle, Christian Griesinger, Zoltan 

L. Madi, Peter Meier, Serge Boentges, Marc Mc- 

Coy, Armin Stockli, Gabriele Aebli, Martin Blackledge, 

Jacques Briand, Matthias Ernst, Tilo Levante, 

Pierre Robyr, Thomas Schulte-Herbriiggen, 

Jxirgen Schmidt and Scott Smith. I would also 

like to thank my technical staff, Hansruedi Hager, 

Alexandra Frei, Janos A. Deli, Jean-Pierre Michot, 

Robert Ritz, Thomas Schneider, Markus Hintermann, 

Gerhard Gucher, Josef Eisenegger, Walter 

Lammler and Martin Neukomm; my secretary Irene 

Miiller; and several research groups with which I 

had the pleasure to collaborate, first of all the research 

group of Kurt Wiithrich and the group of 

Horst Kessler. I am grateful for support in the early 

days from Varian Associates and more recently from 

the Swiss Federal Institute of Technology, the Swiss 

National Science Foundation, the Kommission zur 

Forderung der Wissenschaftlichen Forschung, and 

last but not least to Spectrospin AG. 

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School (Basko Polje, Yugoslavia) 1971, unpublished. 

62 R.R. Ernst, Vlth International Conference on 

Magnetic Resonance in Biological Systems (Kandersteg, 

Switzerland) 1974, unpublished. 

63 W.P. Aue, E. Bartholdi, and R.R. Ernst, J. 

Chem. Phys. 64, 2229 (1976). 

64 J. Jeener, B.H. Meier, and R.R. Ernst, J. 

Chem. Phys. 71, 4546 (1979). 

65 B.H. Meier and R.R. Ernst, J. Am. Chem. 

Soc. 101, 6641 (1979). 

66 S. Macura and R.R. Ernst, Mol. Phys. 41, 95 

(1980). 

67 Anil Kumar, R.R. Ernst, and K. Wiithrich, 

Biochem. Biophys. Res. Commun. 95, 1 (1980). 

68 M.P. Williamson, T.F. Havel, and K. 

Wiithrich, J. Mol. Biol. 182, 295 (1985). 

69 A.D. Kline, W. Braun, and K. Wuthrich, J. 

Mol. Biol. 189, 377 (1986). 

70 B.A. Messerle, A. Schaffer, M. Vasak, J.H.R. 

Kagi, and K. Wuthrich, J. Mol. Biol. 214, 765 

(1990). 

71 G. Otting, Y.Q. Qian, M. Billeter, M. Miiller, 

M. Affolter, W.J. Gehring, and K. Wuthrich, 

EMBO J. 9, 3085 (1990). 

72 T.F. Haveland and K. Wuthrich, Bull. Math. 

Biol. 46, 673 (1984).

Vol. 16, No. 1/2 31 

73 W. Braun and N. Go, J. Mol. Biol. 186, 611 

(1985). 

74 R. Kaptein, E.R.P. Zuiderweg, R.M. Scheek, 

R. Boelens, and W.F. van Gunsteren, J. Mol. Biol. 

182, 179 (1985). 

75 G.M. Clore, A.M. Gronenborn, A.T. Briinger, 

and M. Karplus, J. Mol. Biol. 186, 435 (1985). 

76 Y. Huang, S. Macura, and R.R. Ernst, J. Am. 

Chem. Soc. 103, 5327 (1981). 

77 G.W. Eich, G. Bodenhausen, and R.R. Ernst, 

J. Am. Chem. Soc. 104, 3731 (1982). 

78 P.H. Bolton and G. Bodenhausen, Chem. 

Phys. Lett. 89, 139 (1982). 

79 The spectra were recorded by C. Griesinger, 

see R.R. Ernst, Chimia 41, 323 (1987). 

80 L. Braunschweiler and R.R. Ernst, J. Magn. 

Reson. 53, 521 (1983). 

81 D.G. Davis and A. Bax, J. Am. Chem. Soc. 

107, 2821 (1985). 

82 A.A. Bothner-By, R.L. Stephens, J. Lee, C.O. 

Warren, and R.W. Jeanloz, J. Am. Chem. Soc. 

106, 811 (1984). 

83 R. Briischweiler, B. Roux, M. Blackledge, C. 

Griesinger, M. Karplus, and R.R. Ernst, J. Am. 

Chem. Soc. 114, 2289 (1992). 

84 C. Griesinger, G. Otting, K. Wiithrich, and 

R.R. Ernst, J. Am. Chem. Soc. 110, 7870 (1988). 

85 J. Briand and R.R. Ernst, Chem. Phys. Lett. 

185, 276 (1991). 

86 S. Vega, T.W. Shattuck, and A. Pines, Phys. 

Rev. Lett. 37, 43 (1976). 

87 S. Vega and A. Pines, J. Chem. Phys. 66, 

5624 (1977). 

88 A. Wokaun and R.R. Ernst, Mol. Phys. 36, 

317 (1978). 

89 L. Braunschweiler, G. Bodenhausen, and R.R. 

Ernst, Mol. Phys. 48, 535 (1983). 

90 A. Bax, R. Freeman, and S.P. Kempsell, J. 

Am. Chem. Soc. 102, 4849 (1980). 

91 A. Bax, R. Freeman, and S.P. Kempsell, J. 

Magn. Reson. 41, 349 (1980). 

92 

U. Piantini, O.W. S0rensen, and R.R. Ernst, 

J. Am. Chem. Soc. 104, 6800 (1982). 

93 

N. Miiller, G. Bodenhausen, K. Wiithrich, and 

R.R. Ernst, J. Magn. Reson. 65, 531 (1985). 

94 

C. Radloff and R.R. Ernst, Mol. Phys. 66, 

161 (1989). 

95 

A. Wokaun and R.R. Ernst, Chem. Phys. 

Lett. 52, 407 (1977). 

96 G. Bodenhausen, H. Kogler, and R.R. Ernst, 

J. Magn. Reson. 58, 370 (1984). 

97 M.H. Levitt and R.R, Ernst, Chem. Phys. 

Lett. 100, 119 (1983). 

98 M.H. Levitt and R.R. Ernst, J. Chem. Phys. 

83, 3297 (1985). 

"C. Griesinger, O.W. S0rensen, and R.R. Ernst, 

J. Am. Chem. Soc. 107, 6394 (1985). 

100 

C. Griesinger, O.W. S0rensen, and R.R. 

Ernst, J. Chem. Phys. 85, 6837 (1986). 

101 

C. Griesinger, O.W. S0rensen, and R.R. 

Ernst, J. Magn. Reson. 75, 474 (1987). 

102 

A. Bax and R. Freeman, J. Magn. Reson. 44, 

542 (1981). 

103 

B.U. Meier and R.R. Ernst, J. Magn. Reson. 

79, 540 (1988). 

104 A.A. Maudsley and R.R. Ernst, Chem. Phys. 

Lett. 50, 368 (1977). 

105 G. Bodenhausen and R. Freeman, J. Magn. 

Reson. 28, 471 (1977). 

106 L. Miiller, J. Am. Chem. Soc. 101, 4481 

(1979). 

107 M. Ernst, C. Griesinger, R.R. Ernst, and W. 

Bermel, Mol. Phys. 74, 219 (1991). 

108 M.H. Levitt, O.W. S0rensen, and R.R. Ernst, 

Chem. Phys. Lett. 94, 540 (1983). 

109 H. Kogler, O.W. S0rensen, G. Bodenhausen, 

and R.R. Ernst, J. Magn. Reson. 55, 157 (1983). 

110 H.D. Plant, T.H. Mareci, M.D. Cockman, 

and W.S. Brey, 27th Experimental NMR Conference 

(Baltimore, MA, USA) 1986. 

111 G.W. Vuister and R. Boelens, J. Magn. Re- 

son. 73, 328 (1987). 

112 C. Griesinger, O.W. S0rensen, and R.R. 



Ernst, J. Am. Chem. Soc. 109, 7227 (1987). 

U4 H. Oschkinat, C. Griesinger, P. Kraulis, O.W. 

S0rensen, R.R. Ernst, A.M. Gronenborn, and G.M. 

Clore, Nature (London) 332, 374 (1988). 

115 G.W. Vuister, R. Boelens, and R. Kaptein, J. 

Magn. Reson. 80, 176 (1988). 



117 E.R.P. Zuiderweg and S.W. Fesik, Biochem- 

istry 28, 2387 (1989). 

U8 D. Marion, P.C. Driscoll, L.E. Kay, P.T. 

Wingfield, A. Bax, A.M. Gronenborn, and G.M. 

Clore, Biochemistry 28, 6150 (1989).


119 S. Boentges, B.U. Meier, C. Griesinger, and 

R.R. Ernst, J. Magn. Reson. 85, 337 (1989). 

120 O.W. S0rensen, J. Magn. Reson. 89, 210 

(1990). 

121 L.E. Kay, G.M. Clore, A. Bax, and A.M. Gro 

nenborn, Science 249, 411 (1990). 

122 Z.L. Madi, C. Griesinger, and R.R. Ernst, J. 

Am. Chem. Soc. 112, 2908 (1990). 

123 R. Briischweiler, M. Blackledge, and R.R. 

Ernst, J. Biomol. NMR 1, 3 (1991). 

124 W. Burgermeister, T. Wieland, and R. Winkler, 

Eur. J. Biochem. 44, 311 (1974). 

125 H. Kessler, M. Klein, A. Miiller, K. Wagner, 

J.W. Bats, K. Ziegler, and M. Frimmer, Angew. 

Chem. 98, 1030 (1986); Angew. Chem. Int. Ed. 

Engl. 25, 997 (1986); H. Kessler, A. Miiller, and 

K.H. Pook, Liebigs Ann. Chem., 903 (1989); H. 

Kessler, J.W. Bats, J. Lautz, and A. Miiller, Liebigs 

Ann. Chem., 913 (1989); J. Lautz, H. Kessler, W.F. 

van Gunsteren, H.J. Berendsen, R.M. Scheek, R. 

Kaptein, and J. Blaney, Proc. 20th Eur. Pept. 

Symp., (Eds.: G. Jung, E. Bayer), 438 (1989). 

126 R.R. Ernst, M. Blackledge, S. Boentges, J. 

Briand, R. Briischweiler, M. Ernst, C. Griesinger, 

Z.L. Madi, T. Schulte-Herbriiggen, and O.W. 

S0rensen, in "Proteins, Structure, Dynamics, Design" 

(Eds.: V. Renugopalakrishnan, P.R. Carey, 

I.C.P. Smith, S.G. Huang, and A.C. Storer), ES- 

COM, Leiden, 1991. 

127 P.C. Lauterbur, Nature 242, 190 (1973). 

128 Anil Kumar, D. Welti, and R.R. Ernst, J. 

Magn. Reson. 18, 69 (1975). 

129 W.A. Edelstein, J.M.S. Hutchison, G. Johnson, 

and T.W. Redpath, Phys. Med. Biol. 25, 751 

(1980). 

130 P. Mansfield, A.A. Maudsley, and T. Baines, 

J. Phys. E9, 271 (1976). 

131 P.C. Lauterbur, D.M. Kramer, W.V. House, 

and C.-N. Chen, J. Am. Chem. Soc. 97, 6866 

(1975).

Vol. 16, No. 1/2 33 

Reminiscences of My Journey Through a "Nobel" Lab 

Anil Kumar 

Indian Institute of Science, Bangalore - 560 012, INDIA 

It was the Christmas of 1972 when I received 

an exciting offer - the possibility of working with 

Richard Ernst of Switzerland. I had just returned 

to India from U.S.A. after completing three years of 

Post-doctoral work after a Ph.D. in 1969 from the 

Indian Institute of Technology, Kanpur. I was looking 

for openings and immediately grabbed it. An old 

friend from Kanpur days, who was already working 

in E.T.H., met me at Zurich airport (Feb., 1973) and 

we immediately launched into the bylanes of Zurich 

looking for the best places to eat and drink. Ernst, 

a junior faculty member in the Physical Chemistry 

Laboratory of E.T.H., was occupying a small office 

at the top landing of a flight of stairs. I was the 

only post-doc and he had 4 Ph.D. students, one of 

which (Dieter Welti) was busy working through a 

paper I had published from Kanpur. With the help 

of another (Enrico Bartholdi) I soon found living 

quarters, a two bedroom apartment at Roetel Str., 

which I shared with a Swiss architect, who still is 

a good friend. The other lab mates were Thomas 

Baumann and Stefan Schaublin. Soon Alexander 

Wokaun and Geoffrey Bodenhausen came to do their 

diploma work. While Alexander stayed on to do his 

Ph.D., Geoffrey decided to go to England. 

Lab consisted of three crammed rooms full of 

people and equipment half of it home made. I got 

involved into doing, - which in those days was somewhat 

of a tricky experiment - cross polarization in 

solids - which did not work till we moved into a 

more spacious laboratory in a new building, allowing 

more elbow space. We switched transmitters and 

suddenly the experiment worked. Ernst was quite 

pleased and gave me a small raise. Around that 

time a young student, Luciano Miiller, joined our 

group for his Ph.D. and I initiated him into crosspolarization 

experiments. He grew a fine crystal of 

ferrocene and we observed oscillations in the crosspolarization 

dynamics which was later published in 

Physical Review Letters. Dedicated minicomputers 

attached to experimental set-ups were novelties 

those days and it was fun programming them 

into their little languages and then making modifi- 

cations directly into machine language - you could 

almost see how computers worked and interpreted 

your commands. Using these, I did a series of pulsed 

cross-polarization experiments, and presented the 

results in a conference in England in the summer 

of 1974. 

During February 1974, I received an urgent message 

from my father asking me to make a quick trip 

to India. I told Ernst, "I am going for two weeks", 

but returned three weeks later after getting married. 

Ernst and all members of the group had hearty 

laughs at the idea of getting married to someone 

you have hardly seen. Visa for my wife took some 

bother, as Switzerland was in the midst of another of 

their many referendums on controlling the number 

of foreigners. I remember Ernst making a special 

trip to foreigner's office in Zurich convincing them 

that it was important that I stayed in Switzerland. I 

had been to Ernst's home in Winterthur for a group 

party, but had another exclusive one after Padma's 

arrival in May 1974. 

Jean Jeener of Belgium in a summer school held 

in Pule, Yugoslavia in 1971 had proposed an esotoric 

looking idea of two-dimensional NMR and, it 

seems, promptly forgot about it. I remember Ernst 

discussing with me sometimes during 1973 that he 

would like to continue on the theme but did not 

want to step-toe on Jeener if he is continuing on 

it - a case of high and these days rare scientific 

ethics. I was of the opinion that a two year period 

is long enough. However, Ernst is made of finer 

stuff. He used the idea in an experiment which is 

completely different from what Jeener had in mind. 

The story is as follows. Paul Lauterbur of USA had 

in 1972 described a technique of obtaining images of 

small objects using steady field gradients and NMR. 

Ernst thought of doing imaging using pulsed gradients 

and two-dimensional Fourier analysis. Dieter 

Welti wrote some subroutines and I did the experiment. 

I still remember the little teletype tick-ticking 

printing blanks, dots, numbers and a few alphabets, 

spitting out a crude image of two tubes of water 

placed in a magnet. We laughed at the experiment,


thought nothing will ever come out of it and decided 

that it was not worth patenting. What shortsightedness? 

In fact not only we but many others 

did not think much about the idea and the Swiss National 

Science Foundation turned down a proposal 

from Ernst for further work on NMR imaging. 

We then turned all our attention to twodimensional 

NMR spectroscopy. Luciano and I did 

the first experiment, which was a simple one, resolving 

a complex spectrum into components. I remember 

a visit to our lab by Kurt Wiithrich. On seeing 

the spectrum he took his head in his hands and sat 

down. The potential of the technique seem to have 

hit him. He later collaborated with Ernst in exploiting 

the applications of it in biomolecules and revolutionized 

the applications. Enrico Bartholdi worked 

on the theory, Walter Aue on protons and Luciano 

and myself on carbon-proton two-dimensional experiments. 

Many developments were made and a 

quiet revolution was taking place without our ever 

realizing it. Perhaps I should add, without fear of 

contradiction, that the work looked nothing different 

from extremely routine laboratory work, full of 

frustrations and slow progress, without any special 

excitement and anxiety - except for some occasional 

worry such as a visit by a couple, both scientists. 

We had observed some unexpected modulations of 

carbon echoes and after a lot of explaining we convinced 

them of our observations. As soon as they 

left Ernst and myself exchanged worried glances and 

we immediately wrote-up a short account for Chemical 

Physics Letters. Four months later Ernst received 

a preprint from the couple saying they have 

also observed the effect. 

During our stay in Europe we travelled extensively. 

Padma insisted that I take her back to all the 

places I had visited before her arrival. In addition 

we visited many places including a skiing trip with 

research-mates in the Swiss Alps. Many places were 

visited for attending conferences. In one of these 

(Colloque Ampere in Heidelberg, Germany, 1976) 

Ernst was invited to give a plenary lecture on Twodimensional 

NMR. For some reason he was not able 

to go and instead asked me to give the talk. It was 

my first major lecture and I was a bit nervous but 

it went off well. During this conference a boat ride 

down the Necker river with many famous scientists 

was particularly memorable. During a conference in 

Kenderstag, a town in Swiss mountains, Ernst was 

the expert tracking guide. 

Although Ernst had told me that I could stay 

in his research group as long as I wanted, I had 

to look for a position of my own. I therefore put 

an ad in Physics Today with a box number. Ernst 

noticed it and remarked that this is the person he 

wants in his lab, but soon realized that he already 

had him. Ernst recommonded my name to several 

places and I went for an exploratory lecture trip to 

University of Lausanne. Though a beautiful city, my 

lack of knowledge of French must have upset me and 

I showed little interest in that position (presently 

occupied by Geoffrey Bodenhausen). When the offer 

of a position came from Bangalore I accepted it 

without even looking at the details. We returned to 

India in late 1976 and I joined the Indian Institute of 

Science in January 1977. Two and a half years later, 

after the birth of our daughter, we went back to 

Zurich for one more year to apply two-dimensional 

NMR to biomolecules, in a joint project of Ernst and 

Wiithrich. The work carried out during that period 

proved to be a turning point in the application and 

growth of two-dimensional NMR. 

Life has many turning points which are often recognized 

years later. It is always possible to go and 

work with a famous person - a nobel laurate - but 

to do so before he becomes famous and to take part 

in some of the exciting things are the more pleasant 

parts of life. It becomes more so when the person 

is a thorough gentleman and highly cultured. 

Ernst enjoys western classical music and is a lover 

of fine arts. He has a large collection of Tibetan 

Tankas (hand made religious scroll paintings). His 

wife once remarked, when they did not own a car 

in early seventies, that whenever they had enough 

money he goes out and buys a painting. I wonder 

what he did with the Nobel money!

Vol. 16, No. 1/2 35 

Contents 

Emphasizing the Role of Time 

in Quantum Dynamics 

J. Jeener 

Universite Libre de Bruxelles (CP-232) 

Campus Plaine, B-1050 Brussels, Belgium 


II. Bases and Representations 36 

1. Single basis, single date 36 

2. Single basis, two dates (or more) 37 

3. Two bases, two dates (or more) 37 

III. Time Derivatives As Seen From Different Bases 38 

IV. Quantum Dynamics As Seen From Different Bases 39 

1. Laboratory frame 39 

2. Rotating frame 40 

3. Interaction representation 41 

V. Acknowledgments 

VI. References 


Richard Ernst begins his Nobel Lecture entitled 

"Nuclear Magnetic Resonance Fourier Transform 

Spectroscopy" (1) with the remark that NMR 

is one of the first fields in which quantum theory 

and experiments have been discussed with time (and 

not energy or frequency) as the essential explicit 

variable, eventually leading to the general concept 

of "coherent spectroscopy." Again and again, when 

teaching the elementary aspects of quantum dynamics 

and pulsed NMR, I felt dissatisfied with the traditional 

way of handling the time-related variables 

and transformations, and I progressively developed 

an alternative presentation which leads to the same 

conclusions in a somewhat different way. It is a real 

pleasure to present these ideas in this issue of the 

Bulletin of Magnetic Resonance as a tribute to a 

very good friend, Richard Ernst. 

One customary weakness is to use the same name 

("time"), and similar typographic symbols, for dates 

and for durations (i.e. time intervals). Of course, 

this does not disturb or confuse the experts, but it 

is inconvenient and misleading for beginners, and 

intolerable if one tries to get systematic help from a 

symbolic manipulation program. Solving this problem 

is just a matter of care in the choice of words, 

symbols and notation. 

Another, more subtle, traditional weakness has 

to do with the comparison or combination of quantum 

objects defined at different dates, as involved 

in the definition of time-derivatives for instance. To 

illustrate this point, let us examine the seemingly 

obvious notion of a constant ket, taking as a prototype 

one of the kets forming the basis b in current 

use in ket space. If we should be taking the 

ideas of "rotating frame" or "toggling frame" literally, 

we would be using different bases in ket space 

associated with the different "frames", and these 

bases would be moving with respect to each other. 

Clearly, a ket which appears as immobile or con- 

41 

42


stant with respect to one of these bases will, in 

general, appear as time-dependent with respect to 

other bases. "Absolute rest" is not a valid concept 

in quantum state space any more than in ordinary 

configuration space. With this situation in mind, 

the traditional presentation of quantum dynamics 

appears as strongly tied to a particular choice of 

basis in ket space, a choice on which attention is 

usually not drawn explicitly. If we want to avoid 

this limitation, for the sake of generality and uniformity, 

or in order to retain full freedom in the 

final choice of basis for the evaluation of traces, we 

should mention the reference basis explicitly, whenever 

relevant, and formulate quantum dynamics in 

such a way that the reference basis can be changed 

at will, while keeping the same abstract quantum 

objects for the description of the physical situation 

under investigation. As we shall see, this does not 

require any major change in notation or logic, and 

tends to make the quantum engineering more systematic 

and transparent [see, for instance, ref. (2)]. 

Consequences of dropping the tacit notion of absolute 

rest are that, for instance, 

(a) all kets will carry a date tag and operations 

on kets like linear combination or scalar product will 

be meaningful only if the kets involved are all defined 

at the same date, 

(b) changing the date tag(s) of a quantum object 

will appear as an important transformation in itself, 

(c) time-derivatives of quantum objects will be 

labelled by the basis in which they are evaluated, 

(d) c-number objects, like matrix elements or 

traces, have a date-dependence which is not related 

to any particular choice of basis, hence providing 

a convenient tool for linking objects with different 

basis labels. 

The ideas and techniques which are discussed in 

the present paper for the "ket-bra-operator" presentation 

of quantum mechanics can be extended to 

the "Liouville" presentation in a particularly simple 

way if Liouville space objects are introduced, 

which are the direct counterparts of kets, bras and 

operators [see, for instance, ref. (3)]. The resulting 

limitation to superkets and superbras which do 

not change the date, hence to superoperators which 

involve two dates at most, does not seem to be a 

hindrance, at least for NMR applications. 

For simplicity, the discussion will be limited to 

non-relativistic problems which can be described in 

terms of discrete bases in ket space. No attempt will 

be made towards more generality. 

II. Bases and Representations 

For clarity in the present paper, we shall write 

explicitly, for each quantum object, all the arguments 

which are date tags, and no other. If other 

arguments were necessary, the typography should 

clearly separate date tag(s) from other arguments. 

As a starting point, we choose a basis b in ket 

space, which is a collection of kets \h(t)) which, at 

any date t, satisfies the orthonormality condition 

and the closure relation 

= 6j 

jtk 

where 1 denotes the unit or identity operator (note 

that this operator is denned without reference to 

any specific basis or date, hence a date tag would 

be irrelevant). 

1. Single basis, single date 

As long as a single date t is involved, no deviation 

from the traditional procedures is necessary: 

Any ket \ip(t)) can be expressed ("represented") as a 

linear combination of the kets of the basis {\bi(t))} 

by the usual multiplication from the left with the 

closure relation eqn. 2 

This procedure is easily extended to linear operators 

Aft) involving a single date, which are defined 

by the linear relation between \i/)(t)) and \

Vol. 16, No. 1/2 37 

2. Single basis, two dates (or more) 

As a first example involving two dates, let us 

consider the operator Pb,i(ti,t0) = |6j(ti))(&j(io)|, 

which has the obvious property Pb,i(ti,to)\bi(ta)) = 

\bi(ti)) whenever \bi(to)) is normalized. The action 

of this operator to its right on a ket |a) is denned 

only if the date tag of this ket is i0, and the result 

is then the ket |/3) = Pb,i{ti,to)\a(to)) with date tag 

t\. Of course, \Q(t\)) may also depend implicitly on 

to- 

Conversely, the action of P;))i(ti,io) to its left on 

a bra is defined only if the date tag of the bra is t\, 

and the result is then a bra with date tag £ Summarizing, 

the operator Pb,i(ti,to) has date tags t\ 

on its left and to on its right, as indicated explicitly 

by the typography (t\, to) of the pair of date tags. 

Clearly, such date-changing operators can be 

added together (only) if they have the same pair 

of date tags, and they can be multiplied together 

(only) if the sides which are in contact have the 

same date tag. For instance, one can easily verify 

that Pbti(t2,t0) = A,i(t2,*i)^,i(ti,to). 

The ket \ip(t)) will be called immobile as seen 

from basis b if all its projections on this basis are 

independent of the date t, hence 

E i 

E bi(t))(bi(t0 (5) 

where to is some fixed date, and the unitary date 

displacement operator associated with basis 6, 

Ub(t,tQ) = (6) 

has all the usual properties of evolution operators, 

including the group property for connected date 

pairs 

Ub(t2,t0) = 

and the relations 

Ub(t,t) = l 

and 

(7) 

= Ub(tQ,t). (8) 

Note that the definition of the inverse, as the solu- 

/ N - 1 

tion of the equation \Ub(t,t0)\ Ub(t,t0) = 1 with 

a unit operator involving a single date, implies that 

the inverse has the date tags t on the right and t0 on 

the left, hence the unit operator has the tacit date 

tag t0. 

The operator B{t) involving a single date will 

be called immobile as seen from basis b if all its 

matrix elements (&j(t)|i?(t)|£>fc(t)) in this basis are 

independent of t. Such an operator can be expressed 

for any date t in terms of the operator at a fixed date 

to and the characteristic evolution operator Ub(to, t) 

of basis b as 

= Ub{t,t0)B{t0)Ub{t0,t). (9) 

After introducing the explicit notion of datechanging 

operator, in contrast to operators involving 

a single date, it is worth stressing that "taking 

the trace" is a valid operation only when applied to 

operators which do not change the date, for instance 

Tr[^4ftj]. Of course, A may be expressed as a product 

involving a number of date-changing operators, 

but this product itself must have the same date tag 

on either side. . 

3. Two bases, two dates (or more) 

Let us now consider a second basis {|cj(i))} with 

characteristic evolution operator Uc(t,to). At any 

single date t, basis c is related to basis b by the 

unitary transformation Wcb(t), such that, for any i, 

where 

has the usual properties 

and 

Wbb(t) = 1 

(10) 

(11) 

Wcb{t)) ] = (Wcb(t)) X = Wbc{t). (12) 

Of course, basis kets are immobile as seen from their 

own basis, so that we can use eqn. 5 to obtain 

the relations \ck(t))= Uc(t,t0)\ck(t0)) and (bk(t)\ = 

(bk(to)\Ub(to,t), which we can insert in eqn. 11 to 

derive the useful transformation rules


and 

Uc(t,t0) = Wcb{t)Ub(t,t0)Wbc(t0) 

Wcb(t) = Uc{t, to)Wcb(to)Ub(tQ, t). (13) 

If more than two bases are involved, (11) immediately 

leads to the relation 

Wdc(t)Wcb(t) = Wdb(t). (14) 

Consider now the particular case of a basis c 

such that all its basis kets |cj(t)) are immobile with 

respect to basis b, hence |cj(t)) = Ub(t,to)\ci(to)) 

for all i. Combining this with the definition eqn. 5 

for Uc(t,to), we conclude that Ub(t,to) = Uc(t,to). 

Hence, two bases which are immobile with respect 

to each other have exactly the same characteristic 

evolution operator. 

III. Time Derivatives As 

Prom Different Bases 

Seen 

In the present perspective, the naive definition of 

the time derivative of an arbitrary ket (not necessarily 

mobile or immobile with respect to any specified 

basis) as the limit of [\ip(t + At)) - \ 0 has to be supplemented with a procedure 

for comparing (subtracting) kets defined at different 

dates. With basis b chosen as reference, a natural 

way out of this problem is to interpret |

Vol. 16, No. 1/2 39 

ih {^) Mt) = i*[ : k) A(t)-\Dcbit),Ait)\. 

dt dt) 

(19) 

Permuting the roles of the bases, and using eqns. 12, 

14, 17 and 19 in the perspective of multiple bases, 

one can easily verify that 

and 

IV. 

Dbc(t) = - 

(20) 

Quantum Dynamics As Seen 

From Different Bases 

1. Laboratory frame 

We choose basis b as the conventional reference 

basis in which the equation of motion for the density 

operator p(t), which describes the state of the 

physical system, is the usual von Neumann equation 

(21) 

where the Hermitian operator H(t) is the Hamiltonian 

of the system. We shall assume, as usual, that 

the Hamiltonian and all other relevant observables 

of the system are well known in terms of their action 

on the basis kets of the reference basis b. In general, 

basis b and the "basic" observables are introduced, 

according to the standard quantization rules, starting 

from classical quantities denned in a particular 

classical frame of reference (called "laboratory 

frame" in the NMR literature). If this frame is inertial, 

then H(t) is both the generator of motion with 

respect to basis b, as shown by eqn. 21, and the 

energy observable suitable for discussing thermodynamics 

in this classical frame. 

Combining eqns. 19 and 21, we see immediately 

that pit) is immobile in any basis d such that 

Ddbit) = Hit), hence, using eqn. 9, we have 

The characteristic evolution operator Udit, to) of basis 

d can be evaluated by solving its equation of motion 

(23) 

directly, with the initial condition Ud(to,to) = 1, or 

by solving the equation of motion for the unitary 

transformation Wdb{t), 

= Hit)Wdbit), (24) 

with a suitable unitary initial condition and using 

eqn. 13. 

A useful step towards approximate solutions of 

eqns. 23 or 24 for short delays is to reformulate the 

problem as an equivalent integral equation. For instance, 

we can use the version of eqn. 15 for operators 

to cast eqn. 24 under the form 

+ At) = Ub{t + At, t)Wdbit)Ubit, t + At) 

+ At Hit)Wdbit) 

(25) 

in the limit of At —>• 0. This process of infinitesimal 

date change can be iterated, leading to the simple 

integral equation version of eqn. 24, including the 

initial condition: 

= Ubit,to)Wdb(to)Ubito,t) 

to 

(26) 

Eqn. 26 can be used recursively to derive the usual 

formal series expansion 

Wait) = Ubit,to)Waito)UbitQ,t) 

-\ / dtiUbi 

in Jto 

^ ( 2 , ) ( f l , ( ) ^ ( ) 

(27) 

In the case of Udit, to), similar calculations lead from 

eqn. 23 to 

in t0 

/ i \ 2 A 

— 

dt2Ubit,ti)Hiti)x 

\inj Jt0 Ubit1,t2)Hit2)Ub(t2,t0) + ... 

(28)


The analogous expression for pit) in terms of p(to) 

involves nested commutators with the Hamiltonian 

taken at different dates, also with Uf, operators 

bridging the "gaps" between different date tags. 

As usual, the difficulties involved in deriving a 

compact version of these formal series expansions 

depend crucially on the commutation properties of 

H(t) with itself taken at different dates. In the 

present formalism, the simple case is when 

H(ti),J7b(ti,t2)H(t2)l76(t2,ti) =0 (29) 

for any pair of dates ti and t

Vol. 16, No. 1/2 41 

hence 

= {wcb(t)B(t)Wbc(t)} 

= {uc(t,to)B(to)Uc(tQ,t)}, 

B{t) = Wbc(t){wcb(t)B(t)Wbc(t)}wcb(t) 

= Wbc(t)BW(t)Wcb(t). 

(36) 

(37) 

Pursuing in the same direction, we shall find that 

the final evaluation of the trace in eqn. 31 will also 

be simplified by the use of basis c or some basis 

immobile with respect to basis c. 

The procedure indicated in this section is perfectly 

practical and has the major advantages of being 

the exact analogue of the general idea of one 

same experiment (involving the system under investigation, 

"external actions," and measuring instruments) 

being examined and discussed by various observers 

who try to choose the most convenient point 

of view. Of course, this procedure has the minor 

drawback of an unusual typography: time derivatives 

are indexed by the relevant basis, a new set of 

basic operators is introduced for each new basis,... 

If we are willing to drop the major advantage of 

physical clarity mentioned above, we can very easily 

translate the many-bases procedure into the conventional 

single-basis "interaction representation" technique. 

3. Interaction representation 

In the rotating frame procedure outlined above, 

the "original" operators (density operator, Hamiltonian, 

observables, evolution operator,...) are discussed 

with reference to the "not-original" basis c. 

If we apply the transformation Wbc(t) to all these 

quantum objects, basis c is transformed into basis 

b, each operator is transformed into its l 6c l transform 

(note the rule for date changing operators), 

= Wbc(t)A{t)Wcb(t), 

= Wbc(t)K(t,t0)Wcb(t0), 

(38) 

time derivatives with respect to basis c are transformed 

into time derivatives with respect to basis 

b, hence eqn. 34 is transformed into an equation of 

motion for p^ bc \t), formulated in basis 6, 

The solution of eqn. 39 can be written as 

where 

and 

(39) 

(40) 

i(t,t0) = W (41) 

(42) 

Of course, average values can be evaluated from the 

transformed versions of the relevant operators: 

A(t))=Tr{A(t)p(t)}=Tr )}• (43) 

As far as practical calculations are concerned, including 

the introduction of suitable approximations, 

the interaction representation method described by 

eqns. 32-33 and eqns. 38-43, and the rotating frame 

method described by eqns. 32-37, are equivalent because 

they only differ by minor details of notation, 

as shown above. The purpose of the rather clumsy 

notation used in this paragraph is to clarify the relation 

between the quantum objects which describe 

the same physical object in the two methods, hence 

helping to combine the more intuitive visualisation 

provided by the rotating frame with the traditional 

convenience of interaction representations. 


Discussions with P. Broekaert and F. Henin 

helped to clarify many aspects of the present text. 

This work was supported, in part, by "Loterie 

Nationale" and FRSM, and by "Communaute 

Frangaise de Belgique" (contrat ARC 91/96-149).



1 

see, for instance, R. R. Ernst, Bull. Magn. 

Reson. 16, 5-32 (1994). 

2 

J. Jeener and F. Henin, Phys. Rev. A34, 4897 

(1986), Appendix D. In this reference, (D33) must 

be corrected by replacing 1 by Ui,(t,to). 

3 

J. Jeener, Adv. Magn. Reson. 10, 1 (1982).

Vol. 16, No. 1/2 43 

Contents 

A Novel Contour Plot Algorithm 

for the Processing of 2D and 3D NMR Spectra 

J. Weber 1 , F. Herrmann 2 , P. Rosch 2 and A. Wokaun 1 

1 Physikalische Chemie II and 2 Lehrstuhl fur Biopolymere 

University of Bayreuth, D - W - 8580 Bayreuth, Germany 


II. The 'ribbon' contour plot algorithm 43 

1. Peak identification 44 

2. The contour 44 

III. Discussion 46 

IV. Environment for the reduction and representation of data from 2D and 3D NMR 

experiments—the 'NDEE' program package 46 

V. References 48 


Elucidation of the conformation of peptides and 

proteins in solution by NMR (nuclear magnetic resonance) 

methods requires efficient and versatile data 

processing capabilities. Especially for the handling 

and for a convenient display of large two- or threedimensional 

data matrices, sophisticated codes are 

being developed. 

A conventional 2D NMR spectrum typically consists 

of 512 * 4096 4 byte floating point data values, 

equivalent to 8 MByte. An impressive variety of 3D 

NMR experiments has been conceived and realized 

to this date (1-7). The introduction of the third 

dimension considerably increases the data size. At 

present, data matrices consisting of 256 * 256 * 512 

or of 128 * 128 * 2048 floating point data values, 

i.e. 134 MByte, can be handled with medium-sized 

work stations (8). 

Provided that highly resolved spectra of the 

molecule can be recorded, the next decisive step 

in structural investigation is the assignment of the 

spectra. In this process, a major task consists in 

identification of NOE connectivities. Short range 

connectivity information is required for the sequential 

assignment, while the long-range NOE contacts 

serve as the crucial input for the distance geometry 

and restrained molecular dynamics calculations 

(9-14). 

Several efforts have been reported (15-19) to automate 

the assignment of 2D spectra. However, neither 

for 2D nor for 3D spectra of proteins, a decisive 

breakthrough in this computational problem 

has been made yet. As a prerequisite for any assignment 

algorithm, be it by eye or by computer, 

several requirements must be met, i.e. the capability 

of handling large data matrices, the identification 

of cross peaks, and the extraction of their specific 

coordinates. As a tool for the solution of this 

problem, a new contour plot algorithm, called the 

'ribbon' method, is reported in this communication, 

which provides several advantages as compared to 

conventional grid search methods. 

II. The 'ribbon' contour plot algorithm 

The algorithm extracts all pixels belonging to a 

contour, and stores the coordinates of the contour


in a sequence proceeding around the circumference 

of the peak. Furthermore, the peak volume and the 

center of mass coordinates are computed. 

1. Peak identification 

At the onset, the process of drawing a contour in 

the two-dimensional data matrix representing a 2D 

spectrum is reviewed. Once the intensity level has 

been set, a peak is defined as a set of data points 

fulfilling the condition that all points with intensities 

higher than the predetermined level are immediately 

adjacent along rows and/or columns of 

the 2D matrix. First, the original data matrix is 

searched for 'transitions' across the preset contour 

level. To avoid border problems, the data matrix is 

extended by one row and one column of zeroes on either 

side of the data. Starting from coordinates (0, 

0), the 2D spectrum is searched for up-transitions 

(preceding point has a lower intensity than the contour, 

while intensity of the next point is higher than 

the contour level) and for down-transitions, both in 

horizontal and vertical direction. The two types of 

transition are stored as distinct flags. 

All points belonging to one peak are extracted 

from the 'transition matrix.' This might be envisaged 

as a 'flood fill' were the peaks are protruding 

from an ocean of constant height, corresponding 

to the contour level. In a search along the rows, 

all points between the first up-transition and the 

corresponding down-transition are marked as 'horizontally 

connected' and stored as 'to be searched 

vertically.' Starting from these points, a vertical 

search along the columns is performed, and 'vertically 

connected' points are marked and stored as 

'to be searched horizontally.' This procedure is repeated 

until no more points remain 'to be searched.' 

The connected points identified in this manner are 

written into a peak matrix. 

2. The contour 

The coordinates of the peak contour are collected 

in an ordered array (i.e., sequentially along 

the contour line starting at any point) by means of 

a virtual 'ribbon' that surrounds the peak in the corresponding 

matrix. First, the band is placed at the 

smallest rectangle surrounding the peak. The idea, 

illustrated in Figure 1, is to shrink the ribbon until 

it touches the contours of the peak everywhere. For 

this purpose one has to define, for every segment of 

the elastic ribbon, the direction in which it is going 

to contract. With all other segments fixed, one 

point of the ribbon is moved inwards until a transition 

is found. If more than one step is required, 

new points are inserted into the ribbon from which 

a search perpendicular to the original one has to be 

performed subsequently. 

Once the searching tip has arrived at a transition, 

it is anchored there, and develops sprouts in 

the two perpendicular directions. At this point it is 

important to test immediately whether it is possible 

to go 'around the corner' from the present contour 

point (Figure 2). Staying with the image of a flood 

fill, this test ensures that one reaches the inside of 

any lagoons or coves around the borders of the peak. 

If, in the course of the search, any two points 

of the ribbon meet with opposite search directions, 

a connection is made, the points in between are 

deleted, and the rubber band shrinks accordingly. 

When all points with their specific search directions 

have been anchored in this manner, the ribbon adheres 

correctly around the contour of the peak, and 

the points in the contour are connected sequentially, 

which is of advantage for the graphical output. 

One has to consider the case illustrated in Figure 

3 that there might be a 'lake' hidden within 

the peak. If transitions are indeed found within 

the peak, the outer contour is stored and then removed, 

and the sign of the inner transitions is inverted 

(down becomes up and vice versa). Thereafter, 

a restart of the ribbon search method will correctly 

yield the inner contour. 

Evidently one might think of a peak surrounded 

by another peak (an island within the lake in the 

picture of the flood fill, cf. Figure 3). This case is 

treated by storing and deleting the contour of the 

'lake,' such that every interior peak is consequently 

found. Of course, the entire procedure must now 

be repeated over the entire integer matrix of 'transitions,' 

until all contours have been drawn. 

Thus far the points of the contours are associated 

with the indices of the data points. Finally the 

accurate coordinates of every point of the contour 

are calculated by interpolation.

Vol. 16, No. 1/2 

-1 .-1 

\ 

Figure 1: Principle of the 'ribbon' method used to define the contour of a peak. In (a), the fully expanded 

ribbon surrounds the 'peak' as represented by the integer 'transition matrix.' The search directions of the 

ribbon elements are indicated by horizontal or vertical dashes. After a two-step search (b), four new ribbon 

elements with perpendicular search directions have been inserted. 

V 

Figure 2: 'Corner test' used to reach the inside of a 'cove.' A triple of new ribbon elements is inserted after 

every successful step around a corner (a). The triple inside the cove shown in (b) serves to attach the ribbon 

to the inner wall (c). 

V 

45


Figure 3: Complex peak structures. In the model of a flood fill, a peak may contain a 'lake' (a), or even a 

second peak ('island') within the lake (b). 

III. Discussion 

A conventional grid search results in pairs of 

points to be connected, i.e. the individual elements 

of a line. In contrast, the present contour plot algorithm 

yields all the points contributing to the contour 

of a given peak in sequential order. These contours 

are easily stored, and can be conveniently displayed 

with graphics standards such as X-Windows 

(20), GL (21) or PEX (22). 

As a consequence of this graphic advantage, it 

is possible to overlay the results of several different 

experiments on the screen or display device. Of particular 

interest is the option for a visual or graphical 

comparison of the spectra resulting from different 

types of experiments (i.e., pulse sequences). 

Such spectra will, in general, have been acquired 

using different spectrometer frequencies, carrier offsets, 

and sweep widths. Prior to a direct overlay, 

the various spectra must therefore be scaled individually; 

this option has been implemented in our 

program. 

As an example a comparison of TOCSY and 

NOESY type experiments is shown in Figure 4. 

With the present algorithm, an exact calculation 

of the peak volume (integral) is straightforward, as 

all points inside the contour are clearly identified. 

At the same time, the center of mass coordinates of 

the peak may be obtained. By comparison, several 

programs in current use (23 - 26) calculate the integral 

over the smallest rectangle surrounding the 

peak; the coordinates of the peak, set equal to the 

center of the rectangle, consequently do not precisely 

correspond to the center of mass. The accuracy 

gained with the present algorithm is a promising 

starting point for automated data evaluation. 

The amount of data is considerably reduced to a list 

of coordinates and integrals of the peaks. Again, 

complementary information from various types of 

experiments may be used as an input. This possibility 

is being explored in ongoing work in our laboratories. 

IV. Environment for the reduction 

and representation of 

data from 2D and 3D NMR 

experiments - the 'NDEE 9 

program package 

The contour plot algorithm described is part 

of a program system that manages all operations 

which need to be performed during the reduction 

of a two- or three-dimensional NMR spectrum, i.e. 

baseline subtraction, fast Fourier transformation, 

2D or 3D phase correction, and graphical display. 

These operations have been implemented in a program 

package termed 'NDEE.' The code was developed 

to meet the requirements of NMR research 

groups, i.e. processing of 2D and 3D data files, fast 

performance, portability, and ease of handling via 

a self-explanatory user interface. Particular attention 

was paid to the problems and needs met in the 

structural determination of biopolymers.

Vol. 16, No. 1/2 

;:


Figure 5: A 3D data cube from a 15 N-HMQC 

TOCSY experiment performed on EIAV-Tat (30). 

nient interface to standard molecular dynamics programs 

has been realized. The on-screen edited NOE 

and J constraints are converted, by a single menuprompted 

switch, into a formatted file for use with 

codes such as XPLOR (27) or GROMOS (28). 

The contour plot algorithm implemented in the 

NDEE program package is a promising platform for 

tackling the problem of pattern recognition and automated 

assignment of protein spectra. 

A demo version of the program is available from 

the author (F. Herrmann) and via the anonymous 

ftp of Bayreuth University (132.180.8.29). 

V. References 

1 G.W. Vuister, R. Boelens, J. 

1987, 73, 328. 

2 C. Griesinger, O.W. S0rensen, 

J. Magn. Reson. 1987, 73, 574. 

3 H. Oschkinat, C. Griesinger, 

O.W. S0rensen, R.R. Ernst, A.M. 

G.M. Clore, Nature 1988, 332, 374. 

4 C. Griesinger, O.W. S0rensen, 

J. Magn. Reson. 1989, 84, 14. 

5 S.W. Fesik, E.R.P. Zuiderweg, J. 

1988, 78, 588. 

6 L.E. Kay, D. Marion, A. Bax, J. 

1989, 84, 72. 

Magn. Reson. 

R.R. Ernst, 

P.J. Kraulis, 

Gronenborn, 

R.R. Ernst, 

Magn. Reson. 

Magn. Reson. 

7 M. Ikura, L.E. Kay, A. Bax, Biochemistry 1990, 

29 4659. 

8 R.E. Hoffman, G.C. Levy, Prog. NMR Spect. 

1991, 23, 211. 

9 T. Havel, I.D. Kuntz, G.M. Crippen, 

Bull. Math. Biol. 1983, 45, 665. 

10 W. Braun, N. Go, J. Mol. Biol. 1985, 186, 

611 . U T.F. Havel, K. Wuthrich, Bull. Math. Biol. 

1984, 46, 673 . 12 J.A. McCammon, S.H. Harvey, 

Dynamics of proteins and nucleic acids Cambridge 

University Press, New York 1987. 

13 M. Karplus, G.A. Petsko, Nature 1990, 347, 

631 . 14 W.F. van Gunsteren, A.E. Mark, Eur. J. 

Biochem. 1992, 204, 947. 

15 B.U. Meier, Z.L, Madi, R.R. Ernst, 

J. Magn. Reson. 1987, 74, 565 . 16 H. Grahn, F. Delaglio, 

M.A. Delsuc, G.C. Levy, J. Magn. Reson. 

1988, 77, 294 . 17 L. Emsley, G. Bodenhausen, J. 

Am. Chem. Soc. 1991, 113, 3309. 

18 D.S. Garret, R. Powers, A.M. Gronenborn, 

G.M. Clore, J. Magn. Reson. 1991, 95, 214. 

19 M. Kjaer, F.M. Poulsen, J. Magn. Reson. 

1991, 94, 659 . 20 The X Window System Series, 

Vol. 1-7, O'Reilly & Associates, Inc., Sebastopol, 

1988. 

21 Graphics Library, Silicon Graphics, Inc.; Cali- 

fornia. 

22 PHIGS Extension to X, Evans k Sutherland 

Workstations Reference Manual. 

23 NMRZ, Tripos Inc. 

24 FELIX, Biosym Technologies Inc. 

25 UXNMR and AURELIA, Bruker Analytische 

Mefitechnik, Karlsruhe. 

26 EASY, J. Biomol. NMR 1991, 1, 111. 

27 A.T. Briinger, Methods and Applications in 

Crystallographic Computing (N. Isaacs, ed.) Oxford 

Press, Oxford, Great Britain, 1987, 613. 

28 W.F. Van Gunsteren, R. Kaptein, 

E.R.P. Zuiderweg, Nucleic acid conformation and 

dynamics (W.K. Olson, ed.) pp. 79-92, Report of 

NATO/CECAM Workshop, Orsay, France, 1983. 

29 U. Marx, S. Austermann, W.-G. Forssmann, 

F. Herrmann, P. Rosch, to be published. 

30 D. Willbold, P. Bayer, Rosin-Ardesfeld, 

A. Gazit, A. Yaniv, F. Herrmann, P. Rosch, to be 

published.

Vol. 16, No. 1/2 49 

Contents 


Selective Rotations Using Non-Selective 

Pulses and Heteronuclear Couplings 

Ole Winneche S0rensen 

Novo Nordisk, 2880 Bagsvterd, Denmark 

II. Heteronuclear Bilinear ir/2 and -K Rotations in Spin Systems with a Single 

III. Selective Rotations where None are Possible 

IV. Discussion and Conclusions 

V. References 


The pulse sequence kit for construction of multidimensional 

NMR pulse sequences contains many 

elements for effecting selective or seemingly selective 

rotations. They are employed for suppression of entire 

cross or diagonal peak multiplets or for blocking 

certain coherence transfers with the purpose of obtaining 

simplified multiplet patterns. 

This paper will describe some known and some 

novel pulse sequence elements within multidimensional 

liquid state NMR. In general, the optimum 

choice of element depends on several conditions related 

to the exact application as for example (i) 

whether the element shall be part of a preparation or 

a mixing sequence, (ii) whether relevant spins are active 

or passive or both, (iii) whether there are orders 

of magnitude differences between the sizes of pertinent 

J coupling constants that can be exploited, and 

(iv) whether the selectivity must be obtained in a 

single step or a linear combination of experiments is 

acceptable. 

II. Heteronuclear Bilinear TT/2 

and TT Rotations in Spin Systems 

with a Single 1 Ji$ 

In this section we consider selective rotations 

in the presence of only one large one-bond coupling, 

1 Jls, per molecule. That would apply for S = 13 C or 

15 N at the natural abundance level but also for S = 

15 N in fully 13 C, 15 N-labeled proteins since 1 JCH can 

be suppressed. A thesis written in a local dialect (1) 

suggested the following two sequences for broadband 

selective excitation of S satellites in I = 1 H spectra: 

A:m -^- 

— — T — 

- r - 

with r = (2Jis) 1 - In addition, sequence B with 

r = (2Jcc)^ X an d exclusively 13 C pulses throughout 

was proposed as a "poor mans" INADEQUATE 

for observation of 13 C satellites in 13 C spectra (1). 

Nowadays sequence B is known as TANGO (2) and 

sequence A has been referred to as a purging sandwich 

in 13 C editing experiments (3,4). 

The rationale behind sequence A is to apply the 

equivalent of y and —y rotations to the satellites corresponding 

to spin S in a and (3 spin state, respectively. 

This is illustrated in Figure la, which shows 

that the parent signal is not excited at all since it 

occurs at the zero crossing of positive and negative 

rotations. That, of course, also follows from the 

propagator behind the sequence: 

371- 

49 

49 

51 

53 

53


(a) (b) 

Figure 1: Graphical illustration of the basic ideas behind the excitation profiles for discrimination between 

IS and isolated I spin systems. 6 is the rotation angle and the zero on the abscissa represents the refocused 

chemical shifts: (a) sequence A; (b) sequence B. Note that these diagrams only illustrate the ideas and that 

in practice J-dependent phases and amplitudes occur using sequence B and its derived sequences. 

-i02IySz 

_ e = eif I -if Ix 

(1) 

where insertion of two ir pulses results in sequence 

A. The idea of formulating the aim of a pulse sequence 

in terms of selective rotations and then expanding 

the propagator to end up with a sequence 

employing only non-selective pulses has been used 

in refs. (5,6) and exploited extensively in ref. (7). 

For the rare occasions where the antiphase character 

of the signals resulting from sequence A is not 

acceptable the sequence can be extended with the 

spin echo 

and possibly terminated by a 7r/2 purging pulse (8) 

on the S channel. The same effect can be obtained 

with less pulses using sequence B. 

That sequence corresponds to the profile in Figure 

lb. However, an expansion procedure equivalent 

to eqn. 1 is not immediately possible because 

the propagator for the selective rotations is equal to 

the propagator for a non-selective excitation: 

6 — 6 { £ J 

Hence a simple "expansion" like eqn. 2 does not 

have a built-in guarantee for zero excitation of the 

parent signals as did sequence A. It is necessary to 

add another idea that exploits an interaction present 

only in the IS spin system and not in the isolated I 

spin system. Obviously this interaction can only be 

the Jis coupling: 

(3) 

where \J/ is a parameter explained below. In analogy 

to sequence A the parent signal is at the zero 

crossing for the z rotation. 

A (\P + TX)X pulse followed by a ixz rotation is 

equivalent to a — (^ + TT)X pulse. Thus for an overall 

(TT/2)X rotation ^f must be set according to 

0 = - 

J7T 

= — (4a) 

4t 

Sequence B in fact corresponds to a (n/2)-x rotation: 

6 = -(* + TT) + (TT -*) = _- =>* = - (46) 

The it refocusing pulse is pulled out of (\? + ir)x to 

yield 

B' : - r - 

So far we have implied TT/2 rotations but the general 

sequence B' also allows an easy derivation of a 

IT rotation according to a modified version of eqn. 4:

Vol. 16, No. 1/2 51 

= - 2 * = 7T 

That leads to the sequence 

C: ~\ - T - 

7T 

= ± 2 

which is commonly referred to as BIRD (9). Note 

that the only difference between sequences A and C 

is the interpulse delay resulting in TT/2 and n rotations, 

respectively. 

The opposite situation of rotating isolated I spin 

systems while not affecting or doing something different 

to IS systems also occurs. Sequences for that 

purpose can easily be derived from those above. 

Sequence A corresponds to a 2TT rotation for isolated 

I spins so, for example, a (ir/2)y pulse can be 

appended for excitation. That turns the antiphase 

IS magnetization to the z axis; this antiphase character 

of the IS z magnetization is normally of no 

concern. 

The resulting sequence may be simplified according 

to 

e 2 x e 2 ye 2 = e~ "2 y 

(5) 

(6) 

where the z rotation was added for simplification 

purposes. Combined with sequence A we obtain: 

W * ~ 2 - Ujv 

A 7r rotation of the isolated I spin is obtained by 

adding a (7r)_x I pulse to sequence A: 

E:m -1- 

This sequence results in transverse antiphase IS 

magnetization (as does sequence A) which might or 

might not represent a problem depending on the application. 

The IS spin systems can be left invariant if the 

opposite sequences are based on sequence B and C 

instead of sequence A. Then TT/2 and ir rotations are 

and 

respectively. Another sequence related to F acts as 

a (n) 1 pulse in IS systems: 

F': - ~r- 

Sequence G is used as part of the preparation 

sequence in multidimensional NMR experiments 

where a subsequent delay ensures that the magnetization 

of non-hetero-labeled molecules largely vanishes 

at the starting point of the actual experiment 

(10). It has also been used as a refocusing pulse in 

evolution periods (11, 12). 

For selective excitation of isolated I spin systems 

as part of a preparation period sequence D offers 

itself. However, a better approach is based on lowpass 

J filtering (13) because the spins of interest 

experience less pulses. Simple first order low-pass J 

filters are 

V2') S 

2/ ±x 

G' : - - A - (n) b 

where the two experiments indicated for G are coadded 

while G' requires coaddition of two experiments 

with A = r = (2Jis)~ x and A = 0, respectively. 

Alternatively, pulsed field gradients can be 

combined with sequence G in order to effect the filter 

in a single step. 

In connection with mixing processes in multidimensional 

experiments the most useful sequence is 

A. It can, for example, be employed for coherence 

transfer from 15 N to the directly bonded protons 

while leaving the a protons unperturbed (14), a 

crucial feature in experiments for measurement of J 

coupling constants via E.COSY type multiplet patterns 

(15-17). 

We return to the sequences of this section in Section 

III covering small-angle bilinear rotations. 

III. Selective Rotations where 

None are Possible 

This self-contradictory title covers the situations 

where no J couplings can be exploited to different i-


ate between spins that consequently all experience 

the same perturbation. Nevertheless it is still possible 

to obtain an apparent selectivity by employing a 

small-angle rotation or by suppressing the spectral 

traces of lack of selectivity. These tricks are only 

of interest in connection with mixing processes and 

are completely irrelevant for preparation sequences. 

The concept of small-angle rotations is intimately 

connected with the notion of active and passive 

spins. For given coherences, active spins are 

those that are transverse before or after (including 

before and after) the mixing process whereas passive 

spins are longitudinal in both periods surrounding 

the pertinent mixing sequence. 

As far as active spins are concerned, variation in 

the rotation angle fundamentally causes an amplitude 

modulation. On the other hand, passive spins 

either stay in the spin state they are in or get inverted 

which is expressed by the intensity distribution 

within multidimensional multiplets. Small 

rotation angles leave passive spins largely unperturbed 

(18,19) thus emphasizing the multiplet components 

corresponding to preserved spin states of 

passive spins. However, perfect preservation of spin 

states only occurs in the limit of a vanishing perturbation 

where also the amplitude factor from the 

active spins vanishes except for the trivial case of 

diagonal peaks. 

The E.COSY and TR (20) techniques are the 

outcome of the challenge to obtain multiplets corresponding 

to 100% preservation of passive spin states 

while maintaining significant amplitude factors for 

the active ones. However, in particular in connection 

with heteronuclear NMR satisfactory performance 

is obtained by just applying a small-angle 

pulse. 

Small-angle bilinear rotations have been employed 

in homonuclear proton NMR (21,22) but so 

far only one application (23) of small-angle heteronuclear 

bilinear rotations based on sequences of 

the type described in the preceding section has appeared. 

They are relevant in connection with molecules 

containing more than one heteronuclear spin 

isotope of the same type, like for example 13 Clabeled 

proteins. 

A small-angle version of sequence A is 

where the small angle comes from a short delay rg. 

Sequence A^ does not have an opposite equivalent 

because the major part of IS spin systems behave 

as isolated I spin systems for short TQ delays. 

In contrast, both versions are possible by modifications 

of sequence B because here the interpulse 

delay must be constant and the small angles j3 are 

obtained by adjustment of pulse angles. 

Analytical derivations are possible based on the 

equivalents of eqns. 3 and 4: 

That results in the sequence 

- (7) 

which effects a j3 pulse in the IS spin systems while 

leaving the isolated I spins invariant. Another sequence 

that rotates by (TT — j3) in IS spin systems 

but inverts isolated I spins follows immediately from 

sequence H: 

P P 

The opposite sequences where the isolated I spins 

experience a (3 pulse can in analogy to eqn. 3 and 

sequence B' be written on the general form 

Because the flip angle for the isolated I spins is invariant 

to ^ the flip angle in the IS spin systems 

can be selected independently in analogy to eqn. 4: 

= /?-2* (8) 

For 6 = 0 and TT, respectively, we obtain the sequences 

and 

- 7T

Vol. 16, No. 1/2 53 

All sequences with a total interpulse delay 2r = 

(Jis)" 1 described so far in the paper are special 

cases of sequence I and could have been derived from 

that one using eqn. 8. It should also be mentioned 

that phase shifts have been ignored because they 

normally are immaterial; for example sequence J is 

not an invariant operation in IS spin systems but 

rather a (TT)Z rotation. Finally, we suggest that the 

small angle or /?-TANGO sequences be referred to 

as BANGO. 

IV. Discussion and Conclusions 

The paper has described pulse sequences for selective 

rotations where dominant one-bond heteronuclear 

coupling constants are responsible for the selectivity. 

It has been shown how such sequences 

are derived; originally the simple vector model with 

rotations of vectors in three-dimensional space was 

employed and this level of sophistication is still completely 

adequate for all sequences above. 

A novel general class of pulse sequences were introduced: 

f} 1 and /3 IS are the desired flip angles for isolated I 

spin systems and IS spin systems, respectively, and 

r is (2JIS)- 1 . 

Selective pulse sequences of the type described in 

this paper have been used mainly as part of preparation 

periods in multidimensional experiments but 

it seems that their potential in mixing sequences has 

not been fully exploited in particular in connection 

with experiments generating E.COSY type multiplet 

patterns. 

V. References 

X 

O. W. S0rensen, Thesis, University of Aarhus, 

1981. 

2 

S. Wimperis and R. Freeman, J. Magn. Reson. 

58, 348 (1984). 

3 

O. W. S0rensen, S. D0nstrup, H. Bilds0e, and 

H. J. Jakobsen, J. Magn. Reson. 55, 347 (1983). 

4 

U. B. S0rensen, H. Bilds0e, H. J. Jakobsen, and 

O. W. S0rensen, J. Magn. Reson. 65, 222 (1985). 

5 H. Hatanaka and C. S. Yannoni, J. Magn. Re- 

son. 42, 330 (1981). 

6 O. W. S0rensen, G. W. Eich, M. H. Levitt, G. 

Bodenhausen, and R. R. Ernst, Prog. NMR Spectrosc. 

16, 163 (1983). 

7 O. W. S0rensen, Prog. NMR Spectrosc. 21, 503 

(1989). 

8 O. W. S0rensen and R. R. Ernst, J. Magn. Re- 

son. 51, 477 (1983). 

9 J. R. Garbow, D. P. Weitekamp, and A. Pines, 

Chem. Phys. Lett. 93, 504 (1982). 

10 A. Bax and S. Subramanian, J. Magn. Reson. 

67, 565 (1986). 

U A. Bax, J. Magn. Reson. 53, 517 (1983). 

12 V. Rutar, J. Magn. Reson. 56, 87 (1984). 

13 H. Kogler, O. W. S0rensen, G. Bodenhausen, 

and R. R. Ernst, J. Magn. Reson. 55, 157 (1983). 

14 O. W. S0rensen, J. Magn. Reson. 90, 433 

(1990). 

15 C. Griesinger, O. W. S0rensen, and R. R. 






18 W. P. Aue, E. Bartholdi, and R. R. Ernst, J. 

Chem. Phys. 64, 2229 (1976). 

19 A. Bax and R. Freeman, J. Magn. Reson. 44, 

542 (1981). 



21 M. H. Levitt, C. Radloff, and R. R. Ernst, 

Chem. Phys. Lett. 114, 435 (1985). 

22 T. Schulte-Herbruggen, Z. L. Madi, O. W. 

S0rensen, and R. R. Ernst, Mol. Phys. 72, 847 

(1991). 

23 H. B. Olsen, S. Ludvigsen, and O. W. S0rensen, 

J. Magn. Reson. 104, 226 (1993).


Contents 


II. Theory 

Sensitivity Improvement in Multi-Dimensional 

NMR Spectroscopy 

Mark Ranee 

Department of Molecular Biology 

The Scripps Research Institute 

10666 North Torrey Pines Road 

La Jolla, California 92037 U.S.A. 

III. Applications 60 

1. TOCSY Experiments 61 

2. 3D TOCSY-HMQC Experiment 61 

3. 3D NOESY-HMQC Experiment 61 

4. Heteronuclear Relaxation Experiments ...... 62 

5. Additional Applications 64 

IV. Conclusion 




A critical concern in many applications of nuclear 

magnetic resonance spectroscopy is the sensitivity 

of the measurements, as determined by the 

achievable signal-to-noise ratio for a given experiment 

duration. The sensitivity of a NMR measurement 

is affected by many factors (1-3), and numerous 

schemes have been described over the years for 

improving the sensitivity. These schemes can generally 

be categorized into one or more of three broad 

areas: (i) modification of experimental techniques 

(i.e. spin physics); (ii) advancements in spectrometer 

hardware; and (iii) utilization of new data processing 

procedures. The present paper describes a 

novel methodology, falling under category (i), for 

providing a factor of up to y/2 improvement in sensitivity 

for a variety of multi-dimensional NMR experiments. 

The principle upon which this new method- 

54 

54 

65 

66 

ology is based will be reviewed below, followed by a 

brief description of a few practical applications. 

II. Theory 

In order to explain the basis of the sensitivity improvement 

scheme for multi-dimensional NMR spectroscopy, 

it would perhaps be useful first to mention 

a somewhat analogous method which involves 

a hardware modification rather than a direct manipulation 

of the spin system, and is applicable in 

any NMR experiment. Some time ago Hoult and coworkers 

(4) pointed out that, at least in principle, 

a y/2 improvement in sensitivity can be achieved in 

NMR measurements by using two orthogonal detection 

coils rather than the single coil normally 

employed. If the two rf coils are orthogonally positioned 

but otherwise identical, the NMR signals 

66

Vol. 16, No. 1/2 55 

+2 

-2 

\\\\\\\\\\\\\\\\\\\\\\\v\>\\\\v< 

'ss/rsssssssss/s/ss/sssss/sssssss/j 

Ix 

Y: 

Sx 

Iz 

\ 

Sz 

Ix, 

Figure 1: Pulse sequence, a diagram of the coherence 

transfer pathway, and the relevant density operator 

terms for a sensitivity-enhanced 2D TOCSY 

experiment (34). The pulse sequence itself is identical 

to the z-filtered TOCSY experiment in common 

use (8,9); the sensitivity enhancement is achieved by 

separating the conventional phase-cycling into two 

halves and recording the data separately. 

detected in each will be identical except for a relative 

phase shift of 90°; thus, after correcting for 

the relative phase shift, the two NMR signals can 

be combined to double the size of the detected signal. 

On the other hand, the thermal noise generated 

in the two receiver circuits (probe coils plus 

preamplifiers) will be statistically independent, and 

thus when combined will increase the rms noise voltage 

by only a factor of \/2- The net result of this 

scheme therefore is a \[2 improvement in the overall 

sensitivity of the NMR experiment. Unfortunately, 

this concept has been difficult to implement due to 

practical problems in designing an efficient, crossedcoil 

probe. The sensitivity improvement scheme described 

below is essentially an analogue of crosscoil 

detection for evolution periods (5) in multidimensional 

NMR experiments. 

To explain the basic principle underlying the sensitivity 

enhancement scheme, the response of an isolated 

spin-1/2 nucleus to the pulse sequence shown 

in Figure 1 will be described; application of this 

pulse sequence to a coupled spin system produces 

a 2D TOCSY spectrum (6-9), but for present purposes 

it can be viewed as simply producing a 2D 

chemical shift-resolved spectrum of the uncoupled 

spin-1/2 nuclei. All relaxation effects are ignored. 

Starting from the equilibrium magnetization of the 

spin-1/2, the first 90° pulse creates transverse magnetization 

which then evolves under the influence of 

the chemical shift/resonance offset, O, to: 

a{t\) = Ix sin — Iy (1) 

where for convenience the single spin angular momentum 

operators are used to indicate the relevant 

state of the spin system, and constants of proportionality 

have been omitted. The 90°^ pulse at the 

beginning of the mixing period produces the following: 


Ix[(fx(Tm) cos Qt2 + fz(Tm) sin Qt2) sin Qti 

+a(gx(T~m) cos Qt2 + gz( T m) sin Qt2) cos Qt 

+Iy[(fx(Tm) sinttt2 - fz(Tm) cosQt2) sin fl 

+a.(gx(Tm)s'mQt2 - gz(rm) cos9,t2) cosfii (5) 

Inspection of eqn. 5 indicates that for some arbitrary 

mixing sequence, a 2D Fourier transformation of the 

time-domain NMR signal will result in complicated 

lineshapes in the 2D spectrum. 

To proceed, assume that instead of some arbitrary 

mixing sequence being applied, a so-called 

'isotropic' sequence is employed (6). One of the 

properties of an isotropic mixing sequence is that 

the total spin angular momentum Ia (a= x,y or z) 

is conserved (10). Thus, eqn. 5 simplifies to: 

0a(*l> T m,*2) = 

Ix[fx{Tm) sin fiii cos 9,t2 + agz(Tm) cos Qti sin Q,t2] 

+Iy[fx(Tm) sin Clti sin Q,t2 — agz(Tm) cos Vtt\ cos Ut2] 

2D Fourier transformation of the NMR signal represented 

by eqn. 6 will still produce spectral peaks 

with a highly undesirable phase-twist (11,12). This 

phase twist can be removed, however, if either an additive 

or subtractive combination is made of the two 

data sets collected separately for

Vol. 16, No. 1/2 57 

detected dimension does not affect the conclusion 

regarding signal intensity. To determine whether 

or not a sensitivity improvement is realized by the 

modified experimental procedures it is necessary to 

consider the behaviour of the spectral noise when 

making the combination indicated by eqn. 10; it 

will be shown below that the random noise in a + 

is uncorrelated to that in CT~, and thus the combination 

which doubles the NMR signal intensity only 

increases the noise by a factor of \/2, resulting therefore 

in a \/2 improvement in sensitivity. 

As illustrated by the trivial example described 

above, the general procedure and requisite conditions 

for implementing the sensitivity enhanced 

scheme in a 2D NMR experiment can be stated as 

follows. The pulse sequence must be designed to 

retain the signals originating from both of the orthogonal 

magnetization components, or higher order 

spin operator terms, generated during the evolution 

period by the chemical shift interaction; in conventional 

experiments one of these two components is 

eliminated either as an inherent feature of the pulse 

sequence or by specific design to purge the 2D spectrum 

of undesirable features (12,13). The sensitivity 

enhancement scheme is applicable only to experiments 

in which the mixing sequence causes the relevant, 

orthogonal spin operator terms generated during 

the evolution period to have sufficiently similar 

transfer functions to observable magnetization components 

during the detection period; in the example 

above this would require that /x(rm) & gz(Tm) so 

that the data in eqn. 11 would combine constructively 

to enhance the signal strength. Some experiments 

are easily adapted to incorporate the sensitivity 

improvement scheme, such as the z-filtered 

TOCSY sequence discussed above, while other experiments 

can be modified to fulfill the necessary 

conditions. Some pulse techniques, however, have 

segments which inherently require a unique coherence 

transfer pathway (20,21), such as 2D labframe 

(22) or rotating-frame (23) NOE experiments 

(NOESY or ROESY, respectively), and thus the 

sensitivity enhancement scheme is inapplicable for 

the evolution periods preceding the 'bottleneck'. 

Since the sensitivity enhancement scheme relies 

on the ability to retain and combine essentially 

equivalent information from two orthogonal, coherence 

transfer pathways in a suitable NMR experiment, 

it will for convenience be referred to below 

as PEP (Preservation of Equivalent Pathways) technology. 

Also for convenience much of the discussion 

will refer to 2D experiments, but it should be realized 

that the PEP methodology is applicable in 

experiments of higher dimensionality as well (vide 

infra). 

To implement the sensitivity enhancement 

scheme for a suitable NMR experiment, it is first 

necessary to ensure that the propagator for the relevant 

portion of the pulse sequence, i.e. the portion 

between the relevant evolution period and the detection 

period, transforms the appropriate, orthogonal 

spin operator terms present at the end of the 

evolution period to observable magnetization terms 

with approximately equal efficiency (but not necessarily 

along exactly equivalent coherence transfer 

pathways). To accomplish this it may be necessary 

to re-design part of the pulse sequence; in a 2D experiment 

this part consists of just the mixing period, 

while in experiments of higher dimensionality it is 

necessary to consider all the intervening mixing and 

evolution periods. In addition, the PEP scheme requires 

the elimination of the phase-cycling normally 

employed to select one of the two relevant, orthogonal 

spin operator terms at the end of the appropriate 

evolution period; instead, two experiments are 

run in which the appropriate selection pulse (e.g. 

the second 90° pulse in the example above) is inverted 

in phase between the two experiments and 

the data sets are accumulated separately. After the 

acquisition is completed, additive and subtractive 

combinations of the two raw data sets are made to 

generate the sine and cosine, amplitude-modulated 

data sets, as in eqns. 8. These two new data sets 

can be treated in either of two ways. First, the two 

data sets can be independently processed to produce 

separate 2D (or higher dimensional) spectra; as indicated 

above, there will be a relative phase shift 

of 90° in both frequency dimensions (detection dimension 

and relevant, indirect dimension), and it is 

therefore necessary to correct for this relative phase 

shift. The two spectra can then be added together 

to enhance the signal intensity. While this first procedure 

for handling the data provides the ability for 

spectral editing in some heteronuclear experiments 

(vide infra), it is often more convenient to do all of 

the required data manipulation on the time domain 

data. The 90° phase shift in the detection dimension 

of either the additive or subtractive data set is


trivially accomplished by simply interchanging the 

real and imaginary parts of the complex free induction 

decays. If the data has been collected using 

the so-called 'hypercomplex' (12-15) method for sign 

discrimination in the relevant, indirectly detected 

frequency dimension, then the necessary 90° phase 

shift in this dimension is trivially accomplished by 

swapping the two free induction decays collected for 

each time increment (i.e. t\ point in a 2D experiment) 

as part of the 'hypercomplex' procedure; this 

swap is usually done on the same data set, either 

additive or subtractive, as was subjected to the 90° 

phase shift in the detection dimension. The doubly 

phase-shifted time domain data set is then combined 

with the second, unshifted data set (whether added 

to or subtracted from is best determined by trial and 

error) to produce a single, signal enhanced data set 

which is then processed to a 2D spectrum as desired. 

As implied in the above discussion, performing the 

phase shifts in the time domain requires that the x 

and y components of the free induction decays be 

digitized at simultaneous time points and that the 

hypercomplex method, not TPPI, be used for sign 

discrimination in the relevant, indirect dimension. 

To summarize in brief form, the PEP data handling 

procedure is as follows, assuming hypercomplex 

data collection: 

(la) Collect two separate data sets ux(ti,t2) and 

vx{ti, *2) which are identically recorded except 

for an inversion of the relevant phase selection 

pulse for the PEP scheme. 

(lb) Collect a second pair of data sets uy(ti,t2) and 

vy(ti,t2) similarly to the first, as part of the 

hypercomplex procedure (12-15). (The acquisition 

of the four data sets ux, vx, uy and vy is 

normally interleaved so that four FIDs are collected 

before the parameter t% is incremented). 

(2) Make the combinations ax = ux + vx, sx = 

ux - vx, ay = uy + vy and sy = uy - vy. 

(3) Effect a 90° phase shift in the detection dimension 

to create a new data set sx, sy: 

real(sx)=imag(s:c), imag(sx)=real(sa;), and 

the same for sy (sx and sy were arbitrarily 

chosen over ax and ay). 

(4) Effect a 90° phase shift in the indirect dimension 

to create a new data set sx, sy: sx=sy 

and sy=-sx. 

(5) Make the combinations cx = ax + sx and 

cy = ay + sy (subtractive combination may 

be necessary instead, the uncertainty is due 

to hardware and pulse sequence details). 

(6) Process the data cx(ti,t2), cy(t\,t2) as appropriate 

for a hypercomplex data set. If the 

TPPI procedure is used for uj\ sign discrimination 

or if certain spectral editing capabilities 

need to be retained, then it is necessary to 

process the two data sets a{ti,t2) and s(ti, £2) 

separately and combine them afterward if desired. 

In order to determine the sensitivity enhancement 

achievable using PEP methodology, it is necessary 

to analyze the behaviour of the signal noise 

(24) in these experiments. A general analysis of the 

noise behaviour can be performed by considering the 

consequences of the PEP procedure in the frequency 

domain. The additive and subtractive combinations 

of the raw, time domain data sets are made as indicated 

in step (2) above; no assumption is necessary 

regarding how the data is digitized or LO\ frequency 

discrimination is achieved. The resulting two data 

sets are then processed separately but identically to 

produce two, 2D spectra, A{u>i,u>2) and S(OJI,OJ2) 

(assume that only the real data has been retained 

and that A(UJI,OJ2) is phased as desired). According 

to the PEP protocol it is necessary to perform a 90° 

phase shift in each of the two frequency dimensions 

of one of the spectra before combining the spectra. 

As Ernst has pointed out (25,26), a 90° phase shift 

is equivalent to performing a Hilbert transformation 

of the data, due to the causality principle. Thus, the 

combined spectrum C{LUI,OJ2) can be written as: 

C(wi,w2) = i4(a;i,a;2)+5(a;i,W2) (12) 

Eqn. 12 can be rewritten in expanded terms as: 

C(u1,UJ2) = [U(iOi,0J2) +V(ujX,uJ2)} 

+ {U{cul,uj2)-V(io1,uJ2)} (13) 

where U(u)\,LO2) and V{w\,oj2) are the 2D spectra 

produced by identical processing of the original, raw 

data sets u[t\, t2) and v{t\, t2). Rearranging eqn. 13 

gives 

(14)

Vol. 16, No. 1/2 59 

Assume that the raw data consists only of random 

noise. In order to determine the behaviour of the 

spectral noise when combined according to eqn. 14, 

it is sufficient to calculate the cross-correlation function 

Ruty(ai,a2), where 

(15) 

and £ represents the mean value of the function in 

brackets, averaged over io\ and UJ2, and it is assumed 

that the spectral noise is stationary. The 2D Hilbert 

transform of U(u>i,uj2) is given by (19): 

oo oc 

_ l r da r 

n 2 J fa - a) J 

fa -a) J fa - P) 

U(P,*) 

dj3 (16) 

where for simplicity it is assumed that U(UJI,LJ2) is a 

continuous function and that the integration limits 

can be extended to infinity. Inserting eqn. 16 into 

eqn. 15 gives: 

Making the substitutions r\ = (3 — 

leads to 

and 7 = a — OJ2 

Assuming that the order of integrations can be interchanged, 

eqn. 18 can be expressed as: 

oo oo 

1 f C?7 f 

^ J (a2-7)/ 

d7 

^dr, 

- 7) - V) 

dr] 

(19) 

Eqn. 19 indicates that the cross-correlation function 

of U(uiiiU)2) and its 2D Hilbert transform U(UJI,U>2) 

is equal to the Hilbert transform of the autocorrelation 

function of U(001,0)2); this relationship is well 

known for functions of one variable (27,28). It is 

trivial to prove that Ruu(^1,^2) is an odd function 

in both 2) and its 

2D Hilbert transform are uncorrelated, as is well 

known for ID Hilbert transform pairs (27,29). Thus, 

in making the combination U + 0 in eqn. 17 the 

rms noise level increases only by a factor of y/2, 

and the same of course is true for V — V. The net 

result therefore is that the PEP procedure increases 

the spectral rms noise level by a factor of y/2 over 

that for a conventional spectrum (corresponding to 

either the U + V or U — V combinations in eqn. 13); 

if the NMR signal is doubled in a PEP-modified 

experiment, then an improvement in sensitivity by 

a factor of y/2 will be realized. 

Perhaps the earliest example of PEP methodology 

was in the work of Bachmann et al. (12) 

on phase separation in two-dimensional spectroscopy. 

Two techniques were described for obtaining 

pure phase, 2D resolved spectra; the first technique 

achieved phase separation by reversed precession, 

while the second relied on the use of phase selection 

pulses between the evolution and detection periods. 

The reversed precession technique is really a PEP 

scheme, and as mentioned by Bachmann et al., provides 

a factor of y/2 sensitivity enhancement over 

the phase selection method. 

Before proceeding on to describe some recent applications 

of PEP methodology, it would perhaps be 

useful to point out the existence of somewhat related 

experiments. The PEP scheme is based on designing 

a pulse sequence so that the two orthogonal 

magnetization components present during the evolution 

period follow more or less equivalent coherence 

transfer pathways to the detection period and therefore 

provide essentially identical information. Other 

schemes have been proposed in the past which also


H 

2 

3 

=X,-X 

= X, X, X, X / -X, -X, -X, -X (collect data separately) 

= x, x, -x, -x 

Figure 2: Pulse sequence for recording 3D 

sensitivity-enhanced TOCSY-HMQC spectra (38). 

The isotropic mixing is performed using the DIPSI- 

2 pulse sequence (35) or other, suitable sequences. 

The thin and thick vertical lines represent 90° and 

180° pulses, respectively, applied to the H (proton) 

or X (heteronucleus) spins. The delay r is set to 

1/(2JHX)- Decoupling of the X spins during acquisition 

is accomplished using GARP-1 (54) or other 

appropriate composite pulse sequences. Quadrature 

detection in the OJ\ and cu2 dimensions can be 

achieved via either the TPPI (13,16-18) or hypercomplex 

(12-15) methods. After the data is collected 

with the basic four step phase cycle (plus any 

additional cycling desired), the phase fo is inverted 

and the resulting data set is stored separately from 

the first. 

retain signals originating from the two orthogonal 

components in the evolution period; the difference 

in these schemes is that the information provided 

by the two signals is not the same, and thus cannot 

be combined to achieve a sensitivity enhancement 

as it is normally denned. However, when the techniques 

are applicable they can provide a substantial 

increase in the information recorded per unit 

measuring time. One example of such techniques 

is the COSY-NOESY (30) or COCONOSY (31) experiment, 

in which a COSY data set is recorded 

during the mixing time of a NOESY experiment. 

H 

•, x 

*! =X,-X 

x y 

2 = X, X, -X, -X / -X, -X, X, X (collect data 

separately) 

% = y,y,-y,-y 

rec = x, -x, -x, x 

Figure 3: Pulse sequence for recording 3D 

sensitivity-enhanced NOESY-HMQC spectra (38). 

The thin and thick vertical lines represent 90° and 

180° pulses, respectively, applied to the H (proton) 

or X (heteronucleus) spins. The delay r is set to 

1/(2JHX), while rm is the NOE mixing period. Decoupling 

of the X spins during acquisition is accomplished 

using GARP-1 (54) or other appropriate 

composite pulse sequences. Quadrature detection in 

the toi and o>2 dimensions can be achieved via either 

the TPPI (13,16-18) or hypercomplex (12-15) 

methods. After the data is collected with the basic 

four step phase cycle (plus any additional cycling 

desired), the phase 2 is inverted and the resulting 

data set is stored separately from the first. 

Another, closely related example is the combined 

relayed NOESY-TOCSY experiment (32). 

III. Applications 

PEP technology can be applied to a wide variety 

of experiments (33). Brief descriptions will be given 

in the following sections for some representative examples 

of sensitivity-enhanced, solution-state NMR 

experiments.

Vol. 16, No. 1/2 61 

1. TOCSY Experiments 

Aside from the trivial case of a 2D chemical 

shift-resolved experiment, perhaps the simplest 

example of the application of PEP technology is 

a sensitivity-enhanced, 2D homonuclear TOCSY 

experiment (34). The pulse sequence for the 

sensitivity-enhanced TOCSY experiment is shown 

in Fig. 1; this sequence is just the z-filtered TOCSY 

experiment proposed some time ago (8,9), but with 

modified phase-cycling and data acquisition. Instead 

of phase-cycling the second 90° pulse to select 

for the z magnetization during the isotropic mixing 

period, both the z and x magnetization components 

are retained by performing two experiments with 

the phase-cycle of fa inverted between them and the 

data collected separately. The two data sets are then 

processed according to the PEP procedure, as described 

above. The key to achieving sensitivity enhancement 

in the TOCSY experiment is to employ a 

mixing sequence which promotes coherence transfer 

with equal efficiency for the z and x magnetization 

components present at the beginning of the mixing 

period. A so-called 'isotropic' mixing sequence, 

such as the DIPSI-2 sequence described by Shaka et 

al. (35), is ideal for use in the sensitivity-enhanced 

TOCSY experiment; the defining characteristic of 

an isotropic mixing sequence is that it creates an effective 

Hamiltonian consisting only of the isotropic 

scalar coupling terms. Under such a Hamiltonian 

each of the orthogonal magnetization components 

is conserved (neglecting relaxation), since they commute 

with the effective Hamiltonian; thus, there is 

no mixing of the terms arising from the z and x 

magnetization present at the beginning of the mixing 

period. As indicated schematically in Fig. 1, 

z magnetization starting on one spin can be transferred 

to z magnetization of another spin belonging 

to the same coupling network, and likewise for x 

magnetization. In a conventional TOCSY experiment 

(6-9), one of these two components is intentionally 

destroyed in order to purge the 2D spectra 

of undesirable phase characteristics. With the PEP 

procedure, however, it has been demonstrated (34) 

that pure phase TOCSY spectra can be recorded 

with an improvement in sensitivity by a factor of 

2. 3D TOCSY-HMQC Experiment 

The PEP sensitivity enhancement scheme can be 

applied in principle to a NMR experiment of any dimensionality. 

For example, by concatenating the 2D 

sensitivity-enhanced TOCSY pulse sequence with a 

conventional heteronuclear HMQC sequence (36,37) 

it is possible to create a 3D, sensitivity-enhanced 

TOCSY-HMQC experiment (38); this pulse sequence 

is shown in Fig. 2. An analysis of this relatively 

simple experiment shows that the two, orthogonal 

magnetization components created by evolution 

under the chemical shift interaction during the 

t\ period undergo essentially identical transformations 

during the rest of the pulse sequence, and lead 

to observable signals containing equivalent information. 

According to the PEP prescription, two data 

sets are collected for each increment of t\, with fa 

being inverted between the two experiments. Data 

reduction is most conveniently accomplished in the 

time domain as the data is being accumulated. 

3. 3D NOESY-HMQC Experiment 

The 2D TOCSY experiment shown in Fig. 1 

and the 3D TOCSY-HMQC experiment presented 

in Fig. 2 are examples of PEP applications in which 

no change in the actual pulse sequences of the corresponding, 

conventional experiments are required; in 

these cases the only changes necessary in the experimental 

protocol are to the phase-cycling and to the 

data collection procedure. This simplicity is largely 

due to the inherent characteristic of an isotropic 

mixing sequence to act on orthogonal magnetization 

components with equal efficiency and identical 

effect; in the TOCSY experiments the two equivalent 

coherence transfer pathways required for the 

PEP scheme come as a natural part of the conventional 

pulse sequence. However, most other multidimensional 

NMR experiments have one or more 

segments which normally treat differently the orthogonal 

components present at the end of a given 

evolution period. For example, in a 2D NOESY experiment 

only one of the orthogonal magnetization 

components present at the end of the evolution period 

can be converted to the longitudinal magnetization 

required during the NOE mixing period; the 

second, transverse component must be eliminated 

to remove coherence transfer artifacts. Thus, it is 

not possible to apply the PEP scheme for any evolu-


tion period which precedes a NOESY mixing period 

or, by analogy, a ROESY spin-lock period; however, 

it may be possible to apply the PEP technique to 

subsequent evolution periods. 

Fig. 3 shows a pulse sequence for a sensitivityenhanced, 

3D NOESY-HMQC experiment (38). 

Unlike the TOCSY experiments, it is necessary 

in this case to modify the conventional sequence 

for this popular experiment. A detailed analysis 

(39,40) of the conventional HMQC experiment indicates 

that the two relevant, orthogonal spin operator 

terms present at the end of the evolution period 

(*2 period in Fig. 3) are not transformed equivalently 

following the evolution period; one term is converted 

to anti-phase proton coherence which evolves into 

in-phase magnetization observable during the detection 

period, while the second term is left as unobservable 

multi-spin coherence and is therefore lost. 

However, by modifying the pulse sequence (39,40) 

(adding the pulses after the 90^2 pulse in Fig. 3), it 

is possible to have both of the relevant spin operator 

terms from the evolution period transformed to observable 

magnetization for IS spin systems. While 

the resulting propagator does not cause the orthogonal 

terms to follow exactly equivalent pathways, 

under suitable conditions a substantial sensitivity 

enhancement can be achieved (39); the degree of 

non-equivalence is dependent on various relaxation 

rates. A modification analogous to that shown in 

Fig. 3 has also been described (39,40) for the HSQC 

experiment (41). 

The modifications to the HMQC and HSQC experiments 

only allow sensitivity enhancement for 

IS spin systems, i.e. heteronuclear spin systems in 

which only one proton is directly coupled to the heteronucleus. 

In applications where both IS and InS 

(n>l) spin systems are present, it is sometimes useful 

to process separately the two data sets recorded 

as part of the PEP procedure; by doing so one of 

the two spectra will only contain resonances from 

the IS spin systems, while the other will contain all 

the resonances, thus allowing easy distinction of IS 

from InS spin systems. 

4. Heteronuclear Relaxation Experiments 

Over the past several years there has been 

a resurgence of interest in measuring heteronuclear 

relaxation rate constants and heteronuclear 

NOEs for use in studying the internal dynamics of 

biomolecules (42). This renaissance is due partly 

to the availability of methods for biosynthetically 

enriching biomolecules with 13 C and/or 15 N nuclei 

and partly due to the development of methods 

for indirectly measuring the heteronuclear relaxation 

rate constants and { 1 H}-X NOEs with proton 

signal detection. The general scheme of the proton 

detection methods is to concatenate a conventional 

heteronuclear relaxation experiment with a 

HSQC experiment. For example, an experiment for 

measuring heteronuclear spin-spin relaxation rate 

constants (43,44) consists of a refocussed-INEPT 

(45,46) segment to enhance the sensitivity by transferring 

the larger proton equilibrium magnetization 

to the heteronuclei, a CPMG sequence (47,48) with 

a parametrically varied length T, and a HSQC type 

2D sequence (omitting the initial INEPT segment 

since the desired heteronuclear coherence has already 

been created) to record the data. A series 

of 2D experiments are collected as T is varied, and 

a plot of the cross-peak intensities in the 2D spectra 

as a function of T can be analyzed as usual for 

CPMG experiments. If the improved resolution of a 

2D correlation spectrum is unnecessary, then a simple 

reverse, refocussed-INEPT sequence can be used 

in place of the HSQC segment. 

Multi-dimensional, heteronuclear NMR experiments 

which contain a reverse polarization transfer 

step lend themselves well for application of the 

PEP scheme (39,40). An example of a sensitivityenhanced 

pulse sequence for measuring heteronuclear 

spin-spin relaxation rate constants is shown 

in Fig. 4. The section leading up to and including 

the t\ evolution period is a conventional sequence, 

with the initial refocussed-INEPT segment, 

the CPMG sequence modified so that dipolar-CSA 

cross-correlation effects are eliminated (43,44), and 

the t\ evolution period for frequency labelling the 

X nucleus coherences. In a conventional experiment 

the evolution period would be followed by a reverse 

polarization transfer sequence such as refocussed- 

INEPT or DEPT (49); these sequences transfer only 

one of the two, orthogonal magnetization components 

present at the end of the evolution period to 

observable proton signals. However, with relatively 

simple modifications (39,50), these sequences can 

be made to transfer both components with approximately 

equal efficiency to observable proton magne-

Vol. 16, No. 1/2 

H 

X 

) c 

-e- 

1 

A A A A 

X 

^ =X,-X 

T 

_ ^_ 

) ( ) 

X T 

—T- 

: 

X 

^ 

n 

t 

1 

A A A A A A 

2 

> 

y 

X 

y 

t2 

I GARP i 


4.8 4.0 

1 H (ppm) 

3.2 4.8 4.0 

1 H (ppm) 

Figure 5: Contour plots of the Ca-Ha region of 13 C- 1 H 2D correlation spectra for a sample of 15% fractionally 

13 C-enriched calbindin Dgk, recorded using the sensitivity-enhanced pulse sequence of Figure 4 for measuring 

13 C spin-spin relaxation time constants. The two sets of data recorded during the experiment were added 

together to produce plot (a) and subtracted to produce plot (b); all processing and plotting parameters were 

identical for the two plots except for a 90° relative phase shift in both frequency dimensions (i.e. the zeroth 

order phase corrections necessary for spectrum (b) were shifted by 90° from the parameters used for spectrum 

(a)). The length of the CPMG cycle employed in this experiment was 4 ms. All data processing was done 

using the FTNMR software from Hare Research. 

for all slices, which required that the combined data 

be reduced in size by a factor of v 2 before plotting 

with the same scaling factors as the additive and 

subtractive data. The sensitivity enhancement expected 

for the PEP scheme is clearly demonstrated 

by the data in Fig. 6. 

5. Additional Applications 

The PEP scheme is a general concept, not a specific 

design. In addition to the examples described 

above and presented in detail elsewhere (33,34,38- 

40), many other applications are possible. Kay and 

coworkers (51) have recently reported the use of 

PEP technology in pulsed field gradient versions 

of the HSQC experiment. Their new method allows 

pure absorption heteronuclear correlation spec- 

3.2 

tra to be recorded with the use of pulsed field gradients 

for eliminating undesired coherence transfer 

pathways. PEP technology is employed in the 

gradient-enhanced experiment to extract separate 

signals which are cosine- and sine-modulated as a 

function of the evolution time t\\ this data can then 

be processed with a hypercomplex Fourier transformation 

to yield a pure absorption spectrum with 

u>i frequency discrimination. Madsen and S0rensen 

(52) have recently described very useful modifications 

to a variety of constant-time experiments for 

achieving optimal spectral resolution; PEP technology 

was incorporated into these experiments to enhance 

the sensitivity. Similarly, Madsen et al. (53) 

have employed the PEP scheme in designing new 

pulse sequences for measuring coupling constants in 

13 C, 15 N-labelled proteins.

Vol. 16, No. 1/2 65 

ppm 

Figure 6: One-dimensional slices taken parallel to the w2 frequency axis (proton chemical shift) from 13 C- 

X H 2D correlation spectra for the 15% fractionally 13 C-enriched calbindin D9k; the 2D spectra were recorded 

using the sensitivity-enhanced pulse sequence of Figure 4 for measuring heteronuclear spin-spin relaxation 

time constants. The length of the CPMG cycle employed in this experiment was 108 ms. The two data sets 

recorded during the experiment were added together to produce the 2D spectrum from which slice (a) was 

taken; slice (b) is from the 2D spectrum resulting from the subtractive combination; and slice (c) is the result 

of co-adding slices (a) and (b). The data are plotted such that the rms noise level appears the same for all 

slices; this required slice (c) to be reduced in absolute terms by a factor of A/2- The slices intersect peaks for 

the Ca-HQ correlations of Val 61 (5.10 ppm), Thr 45 (4.43 ppm), Tyr 13 (4.00 ppm), and Lys 25 (3.46 ppm). 

IV. Conclusion 

The general scheme of the PEP methodology 

for obtaining sensitivity improvements in multidimensional 

NMR experiments is simple. However, 

its implementation in practice may or may not be 

straightforward. The basic requirement which must 

be satisfied in order to exploit PEP technology is 

that the relevant, orthogonal spin operator components 

generated by the chemical shift/resonance offset 

precession during an evolution period be transformed 

to observable NMR signals along suitably 

equivalent coherence transfer pathways with approximately 

equal efficiency. In some applications 

no change in the actual pulse sequence is necessary 

in order to implement the PEP scheme, while other 

applications require some segments of the conven- 

add 

sub 

com 

tional pulse sequence to be re-engineered to meet 

the requisite conditions. It should be anticipated 

that PEP technology will be applicable in additional 

classes of experiments not specifically addressed in 

this paper. The maximum achievable sensitivity enhancement 

factor for PEP technology applied to one 

evolution period of a multi-dimensional NMR experiment 

is V2) which of course translates to a reduction 

by a factor of two in the measuring time 

required to record a data set with a given S/N ratio. 

Such improvement is extremely important in 

applications where the sensitivity is limited by practical 

factors such as low sample concentrations or 

inherent features such as the requirement for large 

numbers of individual free induction decays in 3D 

or 4D experiments or in relaxation rate measurements. 

Sensitivity improvements are also extremely


useful in experiments which require the data to be 

collected in a limited period of time. 


I would like to acknowledge the fundamental 

contributions of Dr. John Cavanagh and Prof. 

Arthur Palmer to the development of the sensitivityenhanced 

NMR experiments and the collaboration 

with Dr. R. Andrew Byrd on extending the original 

techniques to 3D applications. Helpful discussions 

during the course of the research with Dr. 

Malcolm Levitt, Prof. Geoffrey Bodenhausen and 

Dr. Ole S0rensen are also gratefully acknowledged. 

This work was supported by the National Institutes 

of Health (RO1-GM40089). 


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Magn. Reson. 64, 547 (1985).


Cross Polarization and Dynamic-Angle 

Spinning of 17 O in L-Alanine 

S. L. Gann, J. H. Baltisberger,* E. W. Wooten,^ H. Zimmermann, 0 and A. Pines 

Materials Sciences Division, Lawrence Berkeley Laboratory and 

Department of Chemistry, University of California, Berkeley, CA 94720 

* Current address: Department of Chemistry, Berea College, Berea, KY 40404 

'Current address: Biophysics Research Division, The University of Michigan, Ann Arbor, MI 4.8109 

°Permanent Address: Max-Planck-Institut Fur Medizinische Forschung, 

Arbeitsgruppe Molekulkristalle, Jahnstrasse 29, D-6900 Heidelberg, Germany 

Contents 


II. Experimental 

III. Results and Discussion 

IV. Acknowledgments 

V. References 


The study of biologically active and other organic 

compounds by solid-state NMR has for the 

most part been limited to spin-1/2 nuclei such as 

1 H, 13 C, 15 N, 19 F, and 31 P. The study of 17 O, a 

quadrupolar nucleus (S = 5/2), in solid organic compounds 

has been limited due to its low natural abundance, 

low magnetogyric ratio, and strong secondorder 

quadrupolar interactions. The first two difficulties 

can be alleviated to some extent through isotopic 

substitution, the use of high magnetic fields, 

and through cross polarization (CP) (1) from 1 H 

to the central (1/2 —1/2) 17 O transition. For a 

static sample, it is theoretically possible to achieve 

a one-shot sensitivity enhancement of 7.3 (assuming 

a large excess of *H compared to 17 O). An alternative 

approach involving adiabatic slow passage 

to transfer magnetization from the satellite transitions 

to the central transition of 17 O could be used 

to generate an enhancement factor of 5.0 (2). However, 

when the sample is spun about an axis inclined 

with respect to the magnetic field, there can be a 

significant decrease in CP efficiency (3) because the 

time dependence of the first-order quadrupolar interaction 

interferes with Hartmann-Hahn matching. 

Cross polarization while spinning the sample at an 

angle of 0° (parallel) with respect to the magnetic 

field is tantamount to operating under static conditions 

and maximum CP efficiency can be achieved. 

As shown recently (4,5), the effects of strong 

quadrupolar interactions can also be averaged coherently 

by spinning the sample about two axes. 

For the central transition of quadrupolar nuclei of 

half-integer spin, the chemical shift anisotropy and 

the second-order quadrupolar interactions are generally 

the dominant broadening mechanisms; the 

quadrupolar coupling constant, e 2 qQ/h, of 17 O in 

organic molecules typically ranges from 5 to 12 

MHz. Solid-state line narrowing techniques such 

as magic-angle spinning (MAS) do not fully average 

second-order interactions and, therefore, generally 

do not give sufficiently narrowed spectra, unless 

the coupling constant is less than about 0.5 

MHz. However, in dynamic-angle spinning, the ef- 

68 

69 

70 

71 

72

Vol. 16, No. 1/2 69 

'H 

X 

0(t) 

90* 9O.A 90, 

J -* 

90x 90. nx 

CP t,/6 40ms 2xr 51,/6 

0 u 

SLV 

63.43 U 

v v 

2 Y X Y X X Y X Y Y X Y X X Y X Y 

4>3 X X X X Y Y Y Y X X X X Y Y Y Y 


CP efficiency per scan (signal compared to a single 

pulse FID on oxygen with hydrogen spin decoupling) 

of approximately 200%. The theoretical maximum 

was not achieved because of short rotating frame relaxation 

times. Ti relaxation times were 750 ms for 

l R and 2.5 s for 17 O. 

DAS experiments at a field strength of 11.7 T 

(67.797 MHz) were performed on a CMX spectrometer 

using the single-tuned DAS probe described in 

ref. (10). No decoupling or cross-polarization was 

performed at this field. 

III. Results and Discussion 

The structure of this amino acid, shown in Figure 

2, has been determined previously by x-ray crystallography 

and neutron diffraction (8,12) and indicates 

two inequivalent O sites due to a difference in 

hydrogen bonding of the two oxygen atoms (12), so 

the spectrum should consist of two overlapping powder 

patterns. Figure 3 shows the 17 O MAS and DAS 

spectra of L-alanine taken at 11.7 T, both without 

spin decoupling. The MAS spectrum shows a broad 

powder pattern with a number of singularities. In 

addition, sidebands complicate the powder pattern, 

resulting in a spectrum that is difficult to simulate. 

In contrast, the DAS spectrum shows a separated 

isotropic peak and sideband pattern. The two sites 

in alanine are not clearly resolved in this spectrum 

and appear as one peak. The isotropic position is 

assigned to 200±7 ppm by comparison with a spectrum 

taken at a different spinning speed. 

Figure 4 shows the 2D-CP/DAS spectrum of alanine, 

along with the projection of the isotropic shift 

dimension, recorded at 7.0 T. Spin decoupling of 

X H resulted in lines significantly narrower than that 

of the experiment without decoupling in Figure 3. 

The two sites are clearly resolved and are assigned 

to 51±4 and 80±4 ppm by comparison to a spectrum 

taken at a different spinning speed. The advantages 

of using cross polarization are, first of all, 

that the signal intensity per scan is approximately 

twice that seen in an experiment without cross polarization. 

Secondly, the recycle time is determined 

by the Ti of 1 H rather than that of 17 O, resulting 

in an increase in the signal-to-noise ratio by a factor 

of two, giving an overall four-fold increase in the 

signal-to-noise ratio. As mentioned above, cross polarizing 

from X H to 17 O can result in an increase in 

Figure 2: Structure of L-alanine showing differences 

in hydrogen bonding of the two oxygen sites. 

MAS 

100 200 300 400 

17/ 

Frequency (ppm from H2 O) 

and 

Figure 3: Magic-angle spinning (MAS) auu 

dynamic-angle spinning (DAS) spectra of 17 O in Lalanine 

at 11.7 T (67.797 MHz), without proton spin 

decoupling. The spectra are referenced to 17 O labeled 

H2O.

Vol. 16, No. 1/2 

-600 

-400 

-200 

200 

400 

•400 200 0 -200 -400 

Frequency (ppm from H2 17 O) 

-600 

Figure 4: Two-dimensional DAS with cross polarization 

(CP/DAS) and proton spin decoupling spectrum 

of 17 O in L-alanine at 7.04 T. The projection 

of the isotropic shift dimension is shown at the top. 

The spectrum is referenced to 17 O labeled H2O. 

intensity by a factor of 7.3, so with favorable relaxation 

times the enhancement of the signal-to-noise 

ratio can be considerable and in fact could be crucial 

in rendering an experiment feasible. 

Using the results of the experiments at the two 

different fields, the isotropic chemical shifts and 

quadrupolar coupling products can be calculated 

(13) by solving a system of simultaneous linear equations, 

with the results given in Table 1. The observed 

isotropic shift (in ppm), 6obs, is related to 

the isotropic chemical shifts, 6iSOtCS, and quadrupolar 

coupling product, PQ, by 

&obs — 

Hso,cs 

3 x 10 6 41(1 + 1) - 3 

(1) 

The quadrupolar coupling product, PQ, is given by 

h 

where I is the spin, LOQ is the Larmor frequency, and 

T]Q is the quadrupolar asymmetry parameter. The 

values for the quadrupolar coupling product are in 

good agreement with the quadrupolar coupling constant 

measured for the carboxyl oxygen atoms in 

similar compounds using NQR (14). Due to the 

similarities of the sites, it is not possible to assign 

the spectra to particular 17 O sites. However, further 

work on amino acids might reveal trends in isotropic 

chemical shift and quadrupolar coupling products 

which allow for the assignment of sites. 

NMR of 17 O in L-alanine has been performed 

previously by Goc, et al. (15), in which the static 

lineshape of a polycrystalline sample was simulated. 

Their simulation assumed that there was only a single 

17 O site, while our work and the crystal structure 

are consistent with two inequivalent sites. The reported 

values for e 2 qQ/h of 6.6 MHz and for TJQ of 

0.55, which were reported to be precise to 20% (15), 

give a PQ from their data of 6.9 MHz, which agrees 

(to within 20%) with our calculations for either site. 

Both Figures 3 and 4 show the disadvantages of 

insufficient spinning speeds. While the sidebands 

are clearly separated from the isotropic peaks in 

these spectra, in general, the large number of sidebands 

normally present in 17 O NMR of organic compounds 

can be a considerable problem. The types of 

compounds one would like to study with solid-state 

NMR, such as small peptides or carbohydrates, will 

typically have numerous inequivalent sites. However, 

fast spinning speeds are becoming easier to 

achieve in DAS experiments resulting in fewer sidebands. 

In addition, such techniques as dynamicangle 

hopping (DAH) (16) can eliminate sidebands 

altogether in cases where adequate spinning speeds 

cannot be obtained. 

IV. Acknowledgments 

This work was supported by the Director of 

the Office of Energy Research, Office of Basic Energy 

Sciences, Materials Sciences Division of the U. 

S. Department of Energy under Contract No. DE- 

AC03-76SF00098. J.H.B. was supported by a NSF 

71 

(2)


Table 1: Isotropic shifts and quadrupolar coupling products for L-alanine. 

Site ^ T fll.7T 

°obs 

graduate fellowship. E.W.W. was supported by a 

NIH postdoctoral fellowship. 

V. References 

U ISO,CS 

1 51±4 ppm 200±7 ppm 8.1±0.3 MHz 285±8 ppm 

2 80±4 ppm 200±7 ppm 7.2±0.3 MHz 268±8 ppm 

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15 R. Goc, E. Ponnusamy, J. Tritt-Goc, and D. 

Fiat, Int. J. Peptide Protein Res. 31, 130-136 

(1988). 

16 S. L. Gann, J. H. Baltisberger, and A. Pines, 

Chem. Phys. Lett. 210, 405-410 (1993).

Vol. 16, No. 1/2 73 

Influence of Slow Internal Motion in Proteins on Cross-Relaxation 

Rates Determined by Two-Dimensional Exchange Spectroscopy 

Contents 

Slobodan Macura* 1 , Jasna Fejzo* 2 , William M. Westler # , and John L. Markley* 

* Department of Biochemistry and Molecular Biology, 

Mayo Graduate School 

Mayo Foundation, 

Rochester, MN 55905 

and 

& Department of Biochemistry, 

University of Wisconsin, 

420 Henry Mall, Madison, WI 53706 


II. Theory 74 

1. Two Groups of Equivalent Spins 76 

2. Three-Spin Systems 78 

3. Four-Spin Systems 80 

III. Internal Motions and Full Matrix Analysis 85 

IV. Internal Motion and Initial-build-up Rate Analysis 86 

V. Experimental Examples 87 

VI. Conclusions 89 

VII. Acknowledgments 92 

VIII. References 92 


Two-dimensional exchange spectroscopy (1-4) has 

become a very popular tool for the study of dynamic 

processes in liquids. Originally, chemical exchange 

(1,5) and cross-relaxation (6,7) were considered to 

be separate processes. Interference between the two 

processes (chemical exchange and cross-relaxation) 

was recognized early (7), but active treatment of 

the problem (8) was possible only following the development 

of exchange spectroscopy in the rotating 

1 Author to whom correspondence should be sent. 

Present address: Harvard Medical School, Department of 

Biological Chemistry and Molecular Pharmacology, Boston, 

MA 02115 

frame (9,10). Subsequently, a full class of exchange 

experiments has been developed that enable the two 

processes to be identified and separated (11-13). 

Two-dimensional cross-relaxation spectroscopy 

in the laboratory frame (NOESY) and in the rotating 

frame (ROESY) have taken experimental precedence 

over 2D chemical exchange spectroscopy because 

information from cross-relaxation provides the 

basis for the determination of structures of macromolecules 

in solution (14). The basic tenet of the 

original method for structure determination from 

NOE data is that the macromolecule is rigid. How-


ever, many macromolecules have internal mobility 

in forms that produce chemical exchange artifacts 

in cross-relaxation spectra. 

If misinterpreted, chemical exchange effects can 

degrade calculated structures by distorting input 

distances. When chemical exchange rates are commensurate 

with cross-relaxation rates, then they can 

only be recognized and evaluated from their direct 

effects on cross-peak volumes. Chemical exchange 

effects contribute to the volumes of corresponding 

cross peaks, and, if not identified, lead to underestimation 

of interproton distances. This direct effect, 

however, is easy to identify. Whenever chemical 

exchange is much faster than cross-relaxation, 

the indirect effects of chemical exchange also must 

be considered (15). When k >> o (where k is the 

chemical-exchange rate constant, and a is the crossrelaxation 

rate constant) chemical exchange acts 

as a short-circuiting device for magnetization exchange. 

It transfers magnetization between chemically 

exchanging spins instantly, compared to crossrelaxation. 

Chemically exchanging spins become involved 

in cross-relaxation with their spatial neighbors; 

thus chemical exchange partners can enter into 

cross-relaxation networks that are spatially distant. 

In NOESY spectra, a chemical exchange pathway 

acts like any other cross-relaxation pathway. An 

important difference, however, is that chemical exchange 

is physically unrelated to cross-relaxation 

and, therefore, chemical exchange rates can easily 

exceed cross-relaxation rates by orders of magnitude. 

This possibility that a competing magnetization 

exchange pathway can occur at a rate up to two 

orders of magnitude faster than the one one wishes 

to measure, drastically changes the way the system 

can be approximated in the analysis. Except for full 

matrix analysis (FMA), all approaches use (implicitly 

or explicitly) some degree of approximation. 

The most widely used approach for structural 

studies of proteins is the initial-build-up rate approximation. 

Chemical exchange effects can lead to 

serious problems in such an analysis. For example, 

when k ^> a the initial-build-up rate approximation 

may be valid only for extremely short mixing 

times (krm < 1). However, under these conditions, 

the intensities of regular cross-relaxation cross peaks 

become vanishingly small. The initial-build-up rate 

approximation holds for cross-relaxation magnetization 

transfer rates such that arm < 1. If chemical 

exchange is rapid, however, this approximation will 

break down for spins involved in chemical exchange 

since then krm > 1. Ignorance of this breakdown 

in the initial-build-up rate approximation can introduce 

serious errors in the determination of interproton 

distances. 

Full matrix analysis (FMA) theoretically does 

not depend on the magnitude of dynamic matrix 

elements. However, when the nature of experimental 

errors is taken into account, one recognizes that 

FMA is as vulnerable as any other method. For example, 

when krm > 1 the cross and diagonal peaks 

corresponding to direct processes are of similar magnitude, 

and, if their difference is within experimental 

error, k cannot be determined properly. Chemical 

exchange leads to the equalization of the intensities 

of cross peaks affected by the exchange process. 

If the intensity (volume) differences are less than 

the experimental errors, full matrix analysis fails 

(16,17). Another difficulty with full matrix analysis 

is that it requires the knowledge of the intensities 

of all cross and diagonal peaks, which in many 

instances are unavailable. Another disadvantage is 

that FMA does not allow partial analysis of the exchange 

network. 

The similar effects of fast magnetization transfer 

that arise from strong cross-relaxation (spin 

diffusion) are already well recognized (16,18-20). 

The combined effects of cross-relaxation and chemical 

exchange have been described theoretically 

and demonstrated experimentally in relation to 

the transferred nuclear Overhauser effect (TRNOE) 

(21-26). Also, the influence of internal mobility on 

the accuracy of a protein structure determination 

has been demonstrated experimentally (15). 

II. Theory 

Chemical exchange and cross relaxation are incoherent 

magnetization transfer processes driven by 

random molecular motion. The transfer can be described 

by a system of N coupled linear differential 

equations (3,27) 

dm(rm) 

drm 

with the formal solution 

= Lm(rn 

m(rm) = exp(Lrm)m(0) 

(1) 

(2)

Vol. 16, No. 1/2 75 

(a) 

(c) 

2.5- 

1.5 

0.5- 

m L12 

1 ^ 2 

O 1 O 

n2L21 

"-—-—— 

^--— 

0.5 

31 

32 

33 

21 

22 

23 

11 

12 

13 

1 

0.9 

0.8 

0.7 

(b) 

}/ 

(d) 

\21 

0.6 

H 

0.5 

/ s 'W 9? 

\31,22\/ 

C/^32. 

0.4 

\32\. "/// 

Figure 1: Two-spin systems composed of two groups of equivalent spins: 

a) The magnetization exchange network consists of two spin groups with populations (ni = na, n2 = nt,) and 

exchange rates (niLi2 = n2L2i). 

•b) An experimental example: water protons in chemical exchange and/or cross relaxation with a hydroxyl 

proton of a protein. 

c) Build-up curves for ni = 1, 2, 3 and n2 = 1, 2, 3. Diagonals start from the integer equal to nx- The 

numbers indicate the values of ni and 112. Cross-peaks start from zero with slopes proportional to nix n2d) 

Two ways of normalizing cross- and/or diagonal-peak volumes provide useful means of obtaining magnetization 

exchange rate constants per single spin, Lo- In the first 

an 12 

0.3 

0.2 

0.1 - 

\1 

"V 

\ 

0.5 

(nx+ n2)(an- 2n1n2 

the initial linear slope extends to much longer mixing times than that of ai2 itself (Figure lc) and is proportional 

to Lo, irrespective of the number of spins involved. In the second, 

an 11 2 

h 

n2 

112 

the curves start from different levels, a"1(0) = 2/(ni + n2), but have the same initial slope —Lo. 

H-O 

11 /


The vector m has elements niXjirii, where rii is the 

number of equivalent spins, x; is the mole fraction, 

and m; is the deviation from thermal equilibrium 

of magnetization at site i. The dynamic matrix L 

contains all information about exchange rates in a 

given system. In general, L is a linear combination 

of the kinetic matrix, K, and the relaxation matrix, 

R 

or, in scalar form, 

L = K-R 

Ly — ky 2 is the same as the rate 

2 -> 1, i.e.: 

= n2L 2i 

(3) 

(4) 

or in other words, the exchange rates per single spin 

are equal: 

The exchange matrix is 

or with regard to eqn. 6 

L12 _ L21 

n2 ni = Lo (6) 

L = ( ~ki2 L21 

\ L12 — L21 

The population matrix is 

-n2 

n2 

0 

m(0) = m0 

V 0 n2 

Eqn. 1 can be solved easily, and one obtains (7) 

(7) 

(8) 

(9) 

an(rm) = —~~\~ + exp[-(ni+n2)Lorm]> 

ni+n2tn2 

J 

(10a) 

, v nin2 fn2 r , . ,1 

a22(rm) = —-—

Vol. 16, No. 1/2 77 

0.5 1 

CJi2Tm 

Figure 2: Three-spin systems: 

a) Magnetization exchange networks. Single lines indicate cross-relaxation and double lines chemical exchange 

pathways. 

b) Typical example - (doubly deuterated) tyrosine ring and arbitrarily placed third proton. 

c) Build-up curves, a23(rm), a33(rm) according to eqns. 14c and 14f. Numbers represent the ratio 012/^23 with 

O"13 = 0. 

d) Build-up curves for ai2(Tm) and ai3(rm), according to eqns. 14a and 14b (solid lines). Dotted lines represent 

build-up curves of cross peaks in the limit where 0, according to eqns. 18. Again, numbers on 

each solid line represent the ratio 012^23. With increases in either the chemical exchange rate constant or 

the mixing time, cross-peak volumes ai2(rm) and ai3(rm) converge toward their average value l/2[a^2(Tm) + 

(a^3(Tm)], as shown by eqn. 18a. 

frame (NOESY) and in the rotating frame (ROESY) 

(8). Cross-relaxation can be eliminated from chemical 

exchange by a modified NOESY experiment 

(clean-EXCSY) (11,12). The clean-EXCSY spectrum 

contains contributions from only chemical exchange 

while cross-relaxation is completely eliminated. 

Then, the cross-relaxation can be evaluated 

by "subtraction" of the chemical exchange part from 

a normal exchange (NOESY) spectrum. An alternative 

experiment, which directly eliminates the effects 

of a selected chemical exchange pathway, has been 

proposed recently (17). Its main limitation is that it 

eliminates chemical exchange paths originating from 

one selected spin only. In spite of this, the exper-

78 

iment can be of great value for the study of crossrelaxation 

between water and protein protons (34- 

37). With exchangeable protein protons (OH, NH) 

water protons exhibit cross-relaxation and chemical 

exchange simultaneously. Separation of the two effects 

is crucial for the proper placement of water 

molecules in and around a protein molecule. 

2. Three-Spin Systems 

A three-spin system is the simplest system 

that exhibits the problem of indirect magnetization 

transfer. This effect has been studied extensively 

by quadratic approximation (7), full matrix simulations 

(18,20), or partial analytical solution (16). 

Here we give explicit expressions for magnetization 

exchange in a three-spin system as revealed by 2D 

exchange spectroscopy. 

Representative magnetization exchange networks 

in a three-spin system are depicted in Figure 

2a. The exchange matrix for a general three-spin 

system with magnetization exchange rate constants 

L12, L13, and L23 is 

It has the general solutions 

au(rm) = - 

where 

L12 

— (L12 + L23) 

L23 

A3 

exp(A2rm) 

A2 — A3 

'Lij + A2 

exp( A3rn 

\ 7 

A3 — A2 

(12a) 

ij + Lik) + 2A3 

, \ 

exp(A2rm) 

A3 — A2 

3(Lij + La) + 2A2 

.[exp(A 3r m) (12b) 

A2 - A3 J 

J [ 

Ao 3= - L12 + L13 + L23 

±\ '(L12 - L13) 2 + (L13 - L23) 2 + (L23 - L12)2 


= 1,2,3, (13) 

Again, overall relaxation has been neglected. If 

all the spins have the same (external) relaxation 

rate, p, then this can easily be taken into account 

by multiplying each aij with exp(—prm). 

Eqns. 12 describe magnetization transfer in an 

arbitrary three spin system. However, these equations 

are complicated, and many relevant properties 

are not immediately obvious from them. For 

the sake of clarity, we consider a special three-spin 

system where L12 =

Vol. 16, No. 1/2 79 

(b) 

(c) (d) 

Figure 3: Four-spin system G^: 

a) Magnetization exchange network consisting of four nodes and six paths. Double lines indicate chemical 

exchange, and single lines denote cross-relaxation pathways. The system is highly symmetric; the exchange 

rates are pairwise equal, i.e., u\2 = 034;


Their dependence on the ratio crn/^-23 is relatively 

complex, but the fast-exchange limit, where 

CT i2/k23 —> 0, can be easily assessed analytically. In 

this case, the system of eqns. 14 simplifies to: 

H2\ 

a 22V T m) — 

l-expl-3-—rm)| (16a) 

, 1 

2 

- - 

~ 2 

-3^rm 

-exp(-2k23Tm) 

(16b) 

o °l2 .)] (16d) 

The superscript k denotes that eqns. 16 are valid in 

the fast-exchange limit. 

Fast chemical exchange quickly equilibrates magnetization 

between spins 2 and 3, rendering their 

diagonal and mutual cross peaks equal, even at the 

shortest mixing times r^ for which cross-relaxation 

can be measured. When CT^T^ < 1 1 then the 

individual exchange rates (Lik, Ljk) cannot be determined. 

Instead, one can find their average by 

full matrix analysis by replacing the original groups 

i,j by a new group ij with population ny = n; + n.j: 

3. Four-Spin Systems 

(njL ik (20) 

Magnetization exchange in a symmetric fourspin 

system can be expressed in a relatively compact 

form. We have chosen two simple cases, which 

we label according to their magnetization exchange 

graphs: GP)qjtl represents a graph with p-nodes and 

q-lines; n is the index of the p,q graph if more than 

one such exists (38). 

A G^fi system comprises four nodes and six lines, 

i.e., four spins with six magnetization-exchange 

paths (Figure 3a). The symmetry of the system renders 

ki4 = k4i = k23 = k32,

Vol. 16, No. 1/2 81 

where 

an(rm) = 

L = (21) 

= O\2 + CT13 + ki4 (22) 

+exp[-2(ai2 + ki4)rm 

= ^ 11 - exp[-2(cr12 -f al3)rm] 

k14)r 

(23a) 

+exp[-2(

82 


Figure 4: Four-spin system G^^ 

a) Magnetization exchange network consisting of four nodes and three paths. Cross-relaxation rates oX2 = 

a 3 4 ~ a ' i • -j-i, 

b) Experimental example: ring protons of a partially deuterated rotating tyrosine ring in cross relaxation with 

two equally distant neighbors. 

c) Build-up curves according to eqns. 27a, 27b, and 27f, at different ratios a/k as indicated beside the curves; 

a22(Tm), a23(rm) - full lines; an(rm) - dashed lines. Since it is only remotely related to chemical exchange, 

an(rm) changes only slightly with a hundred-fold change in k. 

d) Build-up curves ai2(rm), ai3(Tm) (full lines) and ai4(rm) (dashed lines) according to eqns. 27c, 27d and 27e. 

With increases in either the chemical exchange rate constant or the mixing time, curves ai2(rm) and ai3(rm) 

converge toward their average value; ai4(rm) also rises but much more slowly since it is of second order with 

respect to cross-relaxation. Dotted lines represent linear combinations, according to eqns. 29a and 29b, that 

are invariant to chemical exchange. 

A second specialized four-spin system, G4]3i2, depicted 

in Fig. 4a, has two spin pairs with identical 

cross-relaxation rates (012 = C34 = a ) tnat are con " 

nected by a single chemical exchange path (k23 = 

k). The interaction of a rotating tyrosine ring with 

its neighbors can be approximated by such a system 

as is indicated in Fig. 4b. This system has been analyzed 

numerically (40). To get better insight into 

the interplay between the two processes, we present 

an analytical solution:

Vol. 16, No. 1/2 83 

The dynamic matrix is 

with solutions of the system 

where 

an (Tin) = a44(rm) 

a33(rm) 

a34(rm) 

ai3(rm) 

ai4(rm) 

a23(rm) 

A2 = -2cr 

A3j4 = -(a 

(26) 

1 + exp(A2rm) + (1 - - ) exp(A3rm) + (1 + - ) exp(A4rm) 

( 

k\ / k\ 

1 + - exp(A3rm) + I 1 - -r I exp(A4rm) 

V) V & J 

1 - exp(A2rm) - -exp(A3rm) + -exp(A4rm) 

u u 

1 - exp(A2rm) + êxp(A3rm) - -exp(A4rm) 

(28) 

Build-up curves, according to eqns. 27, are shown 

in Figure 4 c,d. As in the previous cases, an increase 

in the chemical exchange rate equalizes two 

unrelated processes. Here, when krm 3> 1, cross 

peak volumes ai2(rm) and ai3(rm) become very similar, 

although the respective cross-relaxation rates 

are quite different: a 12 = &, ^13 = 0. This is also 

evident from eqns. 27c and 27d, where the terms 

with A3 and A4 vanish when kr^ S> 1. Then, 

ai2(7"in) ~ a i3(r,^). As with the G46 system, the 

same linear combinations of cross-peak volumes are 

invariant with regard to chemical exchange due to 

the symmetry of the system: 

ai2(rm 

an(r 

a13(rm) = - 

ai4(rm) = 

- exp(-2crrm) 

+ exp(-2


0k = 

(b) 

0k = 

024 + 034 0°+ 0 + 0+0° 00 

= = _ 

0k 

n2=2 

014 + 024 + 023 °23 0° 

Figure 5: Reduction of the four-spin system G^^ 

into a three- group and a two-group system by fast 

(chemical) exchange: 

a) Fast (chemical) exchange between spins 2 and 3 

equalizes magnetization in the respective sites and 

makes spins 2 and 3 equivalent in their exchange 

with surrounding spins, even if they have different 

individual exchange rates. Their own cross peaks 

are practically equal to the diagonal peaks, indicating 

that krm ^> 1. If the difference between the cross 

and the diagonal peaks is no larger than experimental 

error, then k cannot be determined. Spins 2 and 

3 behave like components of a group of two equivalent 

spins. Although they are distinct, fast chemical 

exchange makes them apparently equivalent; see 

eqn. 34. In the system G^^, symmetry makes spins 

1 and 3 equivalent, and the system reduces further 

to two groups of two equivalent spins. 

b) If fast (chemical) exchange equalizes spins (1, 2) 

and (3, 4) then eqns. 27 reduce directly to those for 

a system of two groups of two equivalent spins, as 

given by eqns. 10, where ni = n2 = 2 and L° = cr°/4. 

= Jim [a14(rm)] (33) 

Finding limits from eqns. 30-33 one obtains: 

a 12( r m) — a 23( T m) — ~^ 

a k 3«) = 7 

+exp(-2a

Vol. 16, No. 1/2 85 

III. Internal Motions and Full 

Matrix Analysis 

Solution of the master equation, eqn. 1, yields 

the time dependence of various magnetization components 

(cross and diagonal peaks) which are also 

a function of exchange rate constants, eqn. 2. Full 

matrix analysis expresses exchange rate constants 

(matrix L) as a function of cross- and diagonal-peak 

volumes at a given mixing time. Since we are dealing 

with systems for which solutions of the master 

equation can be expressed explicitly in terms of exchange 

rate constants, we can also explicitly perform 

a full matrix analysis on them. For the sake of simplicity 

we restrict our analysis to four spin systems 

G4)6 and G4i3)2. 

From eqns. 23, one easily finds exchange rate constants 

in the G4i6 system: 

47V, 

•In (an + ai2 + a13 + 

! - ai3 - ai4) 

(an - 

(an - a12 

(an 

•In 

(an 

-a14) 

- ax4) 

111 ""12 **13 ~ 

(an + ai2 — ai3 — aj4) 

(an - - ai4) 

ai4) 

(37a) 

(37b) 

Owing to the symmetry of the system (Fig 3a), 

similar expressions can be derived for other cross 

and diagonal peaks: 

k=l 

an — a22 = a33 = a44 

ai4 = a4x = a23 = a32 

a-12 = a 2i = a34 = a43 

a i3 = a3i = a24 = a42 

i = 1,2,3,4 (38) 

As far as the values

exchange rate constant. This comes from the fact 

that peak volumes a^ and ai4 (also ai2 and ai3) 

are added in eqn. 40a, contrary to eqn. 37b where 

they are subtracted. An increase in the chemical exchange 

rate constant changes their difference quickly 

(for k —> oo, (an—au) ~* 0) but does not influence 

their sum at all. The price for increased stability of 

the value for the cross-relaxation rate is paid by the 

loss of the individual values of

Figure 6: Part of the x-ray structure (43) of turkey 

ovomucoid third domain (0MTKY3) showing the 

Tyr 31 ring and its immediate neighbors. Ring protons 

1 H* 1 and iH* 2 (and also x H £l and X H £2 ) exchange 

magnetization by ring rotation about the 

C^-C 7 bond. Owing to close proximity, direct 

cross-relaxation can be observed among the protons 

(Tyr 31 1 H* 1 , Tyr 31 1 E El ), (Tyr 31 H 52 , Tyr 31 

(Ala 40 1 H^, Tyr 31 1 E sl ), and (Lys 29 

X H £2 ). 

rate constant shortens the useful mixing time range 

accordingly. Since a lower limit of the mixing time 

is predetermined by the existing signal-to-noise level 

(or peak volume error Aa), fast chemical exchange 

can render build-up rate analysis useless. Again, 

if build-up rate analysis is performed over suitably 

combined cross peaks, then a linear combination of 

the respective exchange rates can be obtained. In 

that case, the build-up curves are independent of 

the chemical exchange rate constant as can easily 

be derived from eqns. 18, 25, and 34. 

V. Experimental Examples 

As an experimental demonstration of the effects 

of fast chemical exchange on 2D exchange spectra 

and on the determination of cross-relaxation 

rates, we have chosen internal rotation of a tyrosine 

ring in turkey ovomucoid third domain (0MTKY3). 

The x-ray and NMR structures of the protein are 

known (43,44), and internal rotation of the Tyr 31 

ring is well documented (11,15). The relevant part 

of the 0MTKY3 x-ray structure (43) is shown in 

Figure 6. Tyrosine ring (Tyr 31 ) rotates around its 

C@ — C 7 bond with a rate which can be controlled 

by the sample temperature. In a 2D exchange spectrum, 

ring rotation generates cross-peaks (Tyr 31 

1 R S1 , Tyr 31 l E 62 ) and (Tyr 31 1 H el , Tyr 31 l E e2 ). 

Because of the proximity of residues Ala 40 and 

Lys 29 to the Tyr 31 ring, direct cross-relaxation peaks 

(Tyr 31 x H £l , Ala 40 l YiP) and (Tyr 31 1 W 2 , Lys 29 

*EP 2 ) can be observed as well. Also, cross relaxation 

peaks (Tyr 31 l E 6 \ Tyr 31 1 E El ) and (Tyr 31 

l E 62 , Tyr 31 1 W 2 ) are present. This simple picture 

(superposition of direct cross peaks) exists only at 

short mixing times and at temperatures low enough 

(T < 265K) to slow down the ring rotation so that 

k < a (Figure 7a). At higher temperatures, where 

k ^> a, fast chemical exchange gives rise to additional 

chemical-exchange-mediated spin-diffusion 

peaks (Figure 7b,c). For example, at T = 278 K 

(Figure 7c), cross peaks (Tyr 31 1 H E2 , Tyr 31 1 1T 51 ), 

and (Tyr 31 1 H e2 , Ala 40 1 H /3 ) are brought up by 

two-step magnetization transfer: Cross-relaxation 

+ chemical exchange (Tyr 31 X W 2 - a -> Tyr 31 

- k -> Tyr 31 l E 61 ) and (Tyr - k 

Tyr 31 x H £l - a -> Tyr 31 1 H (5i ). Since chemical exchange 

is the much faster process, two-step magnetization 

transfer mediated by chemical exchange 

could not be distinguished from a single-step process 

(cf. ai3(rm) in eqns. 14b and 16a). In eqn. 16a, 

due to fast chemical exchange, a^3(rm) has all the 

properties of a direct driven process, although 1^3 

= 0. 

In addition to creating new spin diffusion crosspeaks, 

fast chemical exchange also reduces the volumes 

of peaks originating from direct magnetization 

transfer. This reduction of peak volumes comes 

from the redistribution of magnetization by fast exchange. 

Instead of having one strong peak (direct 

exchange) and one weak peak (or no peak at all because 

of the absence of direct exchange) fast chemical 

exchange redistributes magnetization, creating 

two almost identical cross peaks with a total volume 

identical to the volume of the single peak in the absence 

of the exchange. For example, fast chemical 

r 31 

87

(a) T=265 K (b) T=273 K (c) T=278 K 

Y31 € 2 Y31 € 2 Y31 €1 Y31 € 2 

G)2 /ppm 


Figure 7: Low temperature 2D exchange spectra of turkey ovomucoid third domain (0MTKY3) at 500 MHz: 

a) In 30% glycerol-d6/70% 2 H2O, pH* = 8.1, T = 265 K, rm = 20 ms; cr61e2/kel£2 « 2. The low temperature 

and short mixing time keep chemically-mediated spin diffusion low. One should notice the absence of cross 

peaks (A40^, Y31 e2 ) in accordance with their relatively long distance. 

b) OMTKY3 in 30% glycerol-d6/70% 2 H2O, pH* = 8.1, T = 273 K, rm = 50 ms; aSi,ei/Kie2 « 0.3. At this 

increased temperature the cross-relaxation rates are reduced (shortened correlation time) and the chemical 

exchange rate is increased. With the increase in the k/a ratio, indirect magnetization transfer becomes 

noticeable. Indirect cross-peaks (A40^, Y31 E2 ) and (Y31 51 , Y31 £2 ) are comparable to direct cross peaks 

(A40^, Y31 e2 ). 

c) OMTKY3 in 2 H2O, pH* = 8.1, T = 278 K, rm - 50 ms; a6iei/Kie2 ~ 0.1. Here chemical exchange is much 

faster than cross-relaxation and indirect transfer cross peaks are of the same intensity as the corresponding 

direct peaks. For example, indirect peak (Y31 51 , Y31 e2 ) is of the same intensity as the direct peak (Y31 52 , 

Y31 e2 ). 

exchange (Tyr 31 1 H fil , Tyr 31 1 H 52 ) and (Tyr 31 1 H el , 

Tyr 31 1 H e2 ) gives rise to peaks (Tyr 31 X H 61 , Tyr 31 

X H E2 ) and (Tyr 31 1 H 62 , Tyr 31 l R £l ) even if a61}£2 is 

negligibly small (a6he2 = • oo to the one half of the actual volume) may 

not be noticeable if a spectrum is inspected qualitatively. 

In a quantitative interpretation of 2D exchange 

spectra, however, the volume reduction can 

be easily observed. If not taken into account, it 

can lead to the apparent increase of the interproton 

distance derived from the (reduced) cross-peak 

volume. Although the distance increase is not very 

large (10% for a 50% volume reduction) it may be 

important, for example, if the distorted distance is 

used for calibration purposes. (Ring protons are 

suitable for distance calibrations since their geometry 

is fixed (r = 2.49 A) and because their chemical 

shifts often are well resolved). In the present example, 

fast chemical exchange (Tyr 31 1 H 61 , Tyr 31 1 H 52 )

Vol. 16, No. 1/2 89 

and (Tyr 31 1 H el , Tyr 31 1 H e2 ) reduces the volumes 

of peaks (Tyr 31 X H 51 , Tyr 31 1 H el ) and (Tyr 31 1 H 52 , 

Tyr 31 1 H e2 ) which otherwise might be used for distance 

calibration. However, as indicated in eqn. 24, 

the sum of the cross-peaks [(Tyr 31 1 H e2 , Tyr 31 X H 52 ) 

plus (Tyr 31 x H e2 , Tyr 31 1 E S1 )} does not depend on 

the exchange rate constant and may well serve the 

calibration purpose. 

The effects of fast chemical exchange can be best 

illustrated on experimental systems to which some 

of derived equations can be applied. Suitable threeand 

four-spin systems are seldom isolated as required 

by all the equations derived above. As a good 

approximation, one can take desired groups of three 

or four spins from a multispin system and treat their 

interaction with the spins outside the groups as "external" 

. Then these interactions and the real relaxation 

of the magnetization are taken into account 

by the hybrid relaxation rate, p*. The value of p* 

is determined empirically in the following manner. 

The sum of magnetization components of the spin 

at one site (diagonal and all cross peaks from that 

diagonal) is multiplied by exp (+/?*rm) at all mixing 

times. The p* value is chosen such that the total 

magnetization of the chosen spin does not change as 

a function of mixing time. Experimental data modified 

in this fashion are suitable for analysis by the 

equations derived in this paper. 

As a three-spin system we have chosen a group 

of protons Ala 40 1 E^- Tyr 31 iff 1 - Tyr 31 1 H e2 ; 

and, as a four-spin system, we have selected protons 

of the Tyr 31 ring: 

Their build-up curves and experimental peak volumes 

(multiplied by exp(+p*Tm) are shown in Figures 

8 and 9. All the parameters are given in the 

figure captions. No attempt has been made to fit 

experimental data to the analytical curves owing to 

the large scattering of the low-temperature data. 

However, all parameters common to the two systems 

(for example, the chemical exchange rate constants) 

are the same, except p*, which depends on 

the system itself as well as on the temperature. (In 

the four-spin system, spins Tyr 31 1 H 51 and 1 H 52 are 

internal, and in the three-spin system, they are external. 

Therefore, at the same temperature p* is not 

the same for the two systems). 

At low temperature, T = 265K, both systems 

(Fig. 8a, 9a) have distinct peak volumes for different 

processes. Chemical exchange is relatively slow 

so that direct and indirect cross peaks have different 

volumes. The systems, within the limits of experimental 

error, can be well described by either fullmatrix 

analysis or build-up analysis. At a higher 

temperature (T = 278K, Figs. 8b and 9b) chemical 

exchange is the dominant dynamic process. It 

effectively short-circuits the exchanging spin sites 

making them equivalent as seen from the surrounding 

spins. Thus, direct and indirect peaks (o\2 and 

CT13) become equal within experimental error. The 

individual cross-relaxation rates (a 12 and a\z) cannot 

be recovered. However, their arithmetic mean 

can be determined from the build-up curves of the 

combined peaks (ai2 + &i3)- 

VI. Conclusions 

We have used analytical descriptions of a few 

simple multispin systems to clarify general properties 

of multispin systems that are not obvious from 

a matrix treatment of the problem. For example, 

from consideration of the explicit expressions for exchange 

rate constants in different systems, eqns. 37, 

40 and 41, one can depict how full matrix analysis 

(FMA) works. As seen from these equations, 

in the FMA approach magnetization exchange rates 

are calculated from the logarithm of various combinations 

of cross- and diagonal-peak volumes. FMA 

fails if the argument of the logarithmic function is 

equal to or less than zero. In the ideal case, this 

happens only when the difference between peak volumes 

is close to the precision of the computer. In 

real cases, however, this condition occurs whenever 

the difference between peak volumes is close to or 

less than the error in experimental peak volumes. 

Since, during the mixing time, cross- and 

diagonal-peak volumes converge toward common 

values before decaying to zero by relaxation, this 

happens at increasing values of rm. At the other extreme, 

where rm is short, the diagonal peaks dominate; 

linear combinations of cross peak volumes are 

always positive; and FMA is stable. Further shortening 

of the mixing time makes second- and higherorder 

cross-peak volumes disappear and makes firstorder 

peaks become vanishingly small. Then the 

product in the argument of the logarithmic function 

tends to unity, and the function itself toward 

zero; here the logarithmic function can be safely replaced 

by its linear approximation, (ln(l+x) ft* x),


T=265 K T=278 K 

1* 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

1 P 

oA40 

2 A n3 

a33 Y31 £1 Y31 £2 

ai3 . 

a-i2 '. J • 

! >£ 

0.2 0.4 

Figure 8: Build-up curves for the three-spin system (Ala 40 1 H' 3 - Tyr 31 x H el - Tyr 31 1 H e2 ) of 0MTKY3 at 

two different temperatures. Solid lines are drawn according to eqns. 14a-14f. Dotted lines represents the sum, 

a i2( r m)+ a i3( T m)- The horizontal axis is set dimensionless by multiplying the mixing time by ag£. Then, all 

exchange processes are normalized to the cross-relaxation rate between the 1 H S and X H £ ring protons and can 

be compared irrespective of the temperature. Experimental points (cross-peak volumes) are multiplied by 

exp(+p*Tm) to take into account the fact that the observed spins are not isolated. The rate constant p* was 

chosen so as to make the sum of the cross and diagonal peaks independent of the mixing time, ^j aij = 1: 

+ -ai2(rm) 

° -ai3(rm),a33(rm) 

* - a23(rm). 

•- [ai2(rm) + ai3(rm)]; 

since the sum is almost independent of k23, points from both temperatures are displayed along with the 

build-up curve. 

a) At T = 265 K in 30% glycerol-d6/70% 2 H2O; rm = 10,15,17,20 ms; aSe = 20 

10 s" 1 ; p* = 19 s" 1 = 6.7 s" 

; rc = 87 ns. Chemical exchange is relatively slow; ai2(rm) 

1 ; k23 = 

ai3(rm) indicates close 

proximity of the protons (Ala 40 1 H /3 , Tyr 31 1 H el ), but not that of (Ala 40 1 H /3 , Tyr 31 1 H e2 ) 

b) At T = 278 K in 2 H2O; rm = 20,40,60 ms; aSe = 3 s" 1 ; a12 = 1 s" 1 ; k23 = 30 s" 1 ; p* = 5 s" 1 ; rc = 13 

ns. Fast chemical exchange mixes magnetization between sites 2 and 3 (Tyr 31 1 H el , Tyr 31 x H e2 ) so that their 

interactions with a third spin, 1, (Ala 40 X H^) appear almost identical. Cross peaks ai2(rm) and ai3(rm) have 

similar intensities. The first one is smaller than it would be in the absence of chemical exchange whereas the 

second one is larger. If chemical exchange is not taken into account, the similarity of their cross-peaks may 

lead to the erroneous conclusion that protons Tyr 31 x H el and Tyr 31 1 H e2 are at the same distance from Ala 40

Vol. 16, No. 1/2 91 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

(a) T=265 K T=278 K 

Figure 9: Build-up curves for the four-spin system, Tyr 31 ( 1 H


stants are proportional to average errors in peak volumes 

and inversely proportional to the mixing time. 

In addition, the error is proportional to the sum of 

positive exponentials of the mixing time and all the 

exchange rate constants related to the observed spin 

(the constants for all exchange processes found on 

the same row and column of the exchange matrix). 

Whenever at least one exchange rate constant fulfills 

the condition, LijTm > 1, the respective exponential 

term may become dominant and the error 

increases exponentially with the mixing time. The 

larger the Ly term, the earlier the error starts to 

increase. Therefore, the largest element in the magnetization 

exchange network determines the upper 

limit to the mixing time. In addition, the largest exchange 

rate constant determines the error limit for 

all the other constants in the same network. 

At the other extreme, when rm —» 0, all exponential 

terms become independent of the actual exchange 

rate constants. Absolute errors in the exchange 

rate constants are proportional to errors in 

peak volumes and inversely proportional to the mixing 

time. Therefore, the lower limit of the mixing 

time is determined only by errors in peak volumes, 

i.e., by the background noise level. The important 

conclusion with regard to its application is that 

FMA can be utilized safely only in a range of mixing 

times longer than the lower limit imposed by experimental 

conditions (noise) and shorter than the 

upper limit imposed by the system itself (LyTm). 

Finally, comparison of eqns. 37 and 40 provides 

a clue as to how the influence of fast chemical exchange 

can be eliminated by linear combination of 

the corresponding cross and diagonal peaks. Fast 

chemical exchange tends to equalize the peak volumes 

of direct and indirect processes taking place 

among chemically exchanging spins and their surrounding 

spins. In the direct approach, the exchange 

rate constant is calculated from the difference 

in intensities of peaks that are equalized by 

fast chemical exchange. In the linear combination 

approach, however, peaks that are equalized by the 

fast exchange process are added. Since their sum 

is invariant to the chemical exchange rate they produce 

a good value for the average cross-relaxation 

rates irrespective of the rate of chemical exchange. 

In summary, by explicit calculations of magnetization 

exchange in two-, three-, and some fourspin 

systems, we have analyzed the influence of fast 

chemical exchange processes on strategies for determining 

cross-relaxation rates and have shown that 

in the extreme cases when even full matrix analysis 

cannot be performed, by suitable data manipulation, 

one can obtain average values of the crossrelaxation 

rates. 

VII. Acknowledgments 

This study was carried out at the National Magnetic 

Resonance Facility at Madison under support 

from NIH grants LM04958 and RR02301. Equipment 

in the Facility was purchased with funds from 

the University of Wisconsin, the NSF Biological 

Instrumentation Program (grant DMB-8415048), 

the NIH Biomedical Research Technology Program 

(grant RR02301), NIH Shared Instrumentation Program 

(grant RR02781), and the U. S. Department 

of Agriculture. 

The authors are thankful to Mr. V. Likic for help 

in calculations, Mr. C. G. Hoogstraten for critical 

reading and Ms. S. van Hook and Mrs. K. Ivanovic- 

Likic for careful preparation of the manuscript. 

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Krezel, A.M., Ph.D. Thesis; University of Wis- 

consin, Madison 1991.


Contents 

The Homogeneous Master Equation and 

the Manipulation of Relaxation Networks 1 

Malcolm H. Levitt" and Lorenzo Di Bari 6 

a Physical Chemistry Division, Arrhenius Laboratory, Stockholm University, SI0691 Sweden 

b Dipartimento di Chimica, via Risorgimento 35, 1-56126 Pisa, Italy 


II. The Inhomogeneous Master Equation (IME) 95 

III. The Homogeneous Master Equation (HME) 97 

IV. Application A: vr pulses on the I-spins 98 

1. Dynamics in the gerade subspace 100 

2. Dynamics in the ungerade subspace 100 

V. Application B: n pulses on both I and S-spins 101 

1. Dynamics in the ungerade subspace 104 

2. Dynamics in the gerade subspace 104 

VI. Discussion 105 

VII. Acknowledgments 108 

VIII. Appendix A: The HME in the rotating frame 108 

IX. Appendix B: The thermal correction 0 109 

X. Appendix C: Continuous rf fields 110 

XI. Appendix D: Numerical calculations with the HME 111 

XII. Appendix E: The HME and phase cycling 111 

XIII. References 112 


Recently, we presented a novel method for calculating 

NMR spin dynamics (1). This involves a 

homogenous master equation (HME) and is particularly 

suitable for treating the interplay of incoherent 

relaxation processes and coherent effects such 

as those involving applied rf fields. The new theory 

1 Presented in part at 5th Chianti Workshop, San Miniato, 

Italy, May 1993. 

provides a unified framework within which a very 

wide range of magnetic resonance experiments may 

be described. A point of special interest is the treatment 

of the long-term behavior of the spin system, 

such as the steady-state established under extensive 

repetition of some pulse sequence. In reference 

(1), we demonstrated an unusual effect: If 

a two-spin system is exposed to a repetitive se-

Vol. 16, No. 1/2 95 

quence of non-selective IT pulses, correlations between 

the nuclear spin polarizations are gradually 

established even where none existed before. This 

is manifested as a build-up of two-spin longitudinal 

order < 2IZSZ >. The creation of two-spin order is 

the result of cross-correlated relaxation mechanisms, 

and is unconnected with the J-coupling between the 

spins. It runs counter to the naive expectation that 

a closely-spaced sequence of n pulses should saturate 

the spin system (destroying all order) if applied for 

long enough. 

In this article, we re-examine the HME and its 

consequences in a more physical and less formal 

light. We also emphasize another consequence of 

the HME: Carefully-chosen sequences of rf pulses 

may be used to simplify interconnected relaxation 

pathways. This is important in a number of situations 

(2-13): An example is the suppression of unwanted 

"spin diffusion" pathways in the relaxation 

of many-spin systems, as demonstrated by a number 

of groups (4,7-12). We show results here for 

the analogous problem of the selection of weak relaxation 

pathways driven by weak cross-correlation 

effects, in the presence of stronger autocorrelation 

effects. Although such experiments may also be 

treated within the framework of the ordinary master 

equation, we hope to demonstrate that the HME 

gives a more general and powerful insight. 

II. The Inhomogeneous Master 

Equation (IME) 

The ordinary "master equation" for the evolution 

of the spin density operator a has the following form: 

—a = - aeq) (1) 

The spin Hamiltonian Hcoh contains the "coherent" 

influences on the spin ensemble, i.e. those which are 

the same for all ensemble members. This includes 

external magnetic fields as well as the time-average 

of microscopic spin interactions such as chemical 

shifts and spin-spin couplings. The relaxation superoperator 

F encodes the incoherent interactions 

which are inhomogeneous over the spin ensemble 

and fluctuate in time. The master equation is valid 

in the "Redfield regime" of rapid fmctations (14) 

(assumed for the rest of this article). The elements 

of F can be written in terms of the spectral densities 

of the fluctuating incoherent interactions. 

The term aeq is of particular concern. It does 

not appear in the unmodified Redfield theory, which 

uses a clean division between spin system and environment, 

with the states of the environment or bath 

implicitly uncorrelated with the nuclear spin states. 

As is well-known, this approximation leads to disagreement 

with experiment, predicting that the nuclear 

spin order tends to zero at long times. In fact 

the nuclear spin system is polarized by the contact 

with the environment, which has a finite temperature. 

The master equation is patched up by including 

the phenomonological correction term ae

96 

(CHCI3). The X H spin will be denoted I and the 13 C 

spin 5. Each spin has a chemical shift anisotropy 

(CSA), and the two spins have a through-space magnetic 

dipole-dipole interaction (DD). Relaxation of 

the spin-pair system results from a combination of 

fluctuations in the three interactions WQSA' ^CSA 

and TipD (19-22). Since all have a molecular origin, 

all are modulated in synchrony as the molecule rotates, 

resulting in a finite cross-correlation between 

pairs of interactions (19,20,23-29). At any given 

time t, ensemble averages such as 

) (5) 

do not vanish in general. The relaxation of the spin 

system is characterized by autocorrelation functions 

of the individual interactions, for example 

D(0) (6) 

and cross-correlation functions between pairs of interactions, 

for example 

») CO 

In the absence of applied rf fields, the IME leads 

to three coupled differential equations for the singlespin 

Zeeman polarizations : 

A 

-\ A 

at » A 

aIS - / A 

A 

-prs J \ A 

(8)' 

where A< fi > indicates the deviation of the expectation 

value of a spin operator Q from its thermal 

equilibrium value: 

- eq 

f2} - Tr{creqO} . (9) 

These are known as the extended Solomon equations 

(20,27,29); explicit expressions for the equilibration 

rate constants pj, ps, pis, the cross-relaxation rate 

constant pis, and the CSA/DD cross-correlation 

transfer rate constants 6j and 63 can be found, for 

example, in ref.(29). 

This equation indicates a dynamic coupling of 

the expectation values of the three Cartesian product 

operators Iz, Sz and 2IZSZ. The system may 

be pictured as three coupled "reservoirs," each containing 

"difference order" (deviation of the expectation 

value from thermal equilibrium). The difference 

reservoirs "leak" with rate constants pi, ps 


Figure 1: Physical interpretation of the extended 

Solomon equations for a heteronuclear 2-spin system 

Eqn. 8. The deviations from thermal equilibrium of 

the expectation values of the three spin operators 

form a set of coupled reservoirs. 

and pis, and are connected by "pipes" corresponding 

to the cross-relaxation rate constants 075, Si 

and 8s (Figure 1). This picture should, however, be 

used cautiously: The "liquid" in each reservoir may 

have either sign, and the cross-relaxation rate constants 

may be negative, indicating that the "liquid" 

is changed in sign on transferring from one reservoir 

to another. 

Nevertheless, the "reservoir" picture does give 

a clear image of the dynamic interdependence of 

the three expectation values. By a careful study 

of the trajectories of all three expectation values after 

some initial perturbation, it is possible in principle 

to derive all the various rate constants (20). 

However, this is not very accurate for small rate 

constants, which have only a minor influence on the 

dynamics of the system. This problem is of course 

much worse for larger spin systems, where the interconnections 

between the expectation values are 

more complex still. 

The measurement of small rate constants (for example, 

the 6 terms in the above system), would be 

facilitated if the relaxation dynamics could be simplified, 

isolating selected "subnetworks." It is nat-

Vol. 16, No. 1/2 97 

ural to try to accomplish this using rf pulse sequences. 

Analogous techniques are well-established 

for the simplification of spin Hamiltonians. For example, 

in decoupling experiments, large couplings 

between different spin species are effectively removed 

by applying a suitably modulated rf field to 

one of the species (30-33): small interactions of the 

non-irradiated spins are revealed even in the presence 

of much larger heteronuclear spin couplings. 

The problem of observing weak relaxation processes 

in the presence of stronger ones seems related. 

There is, however, a theoretical difficulty in describing 

experiments in which rf pulses (coherent 

perturbations) interfere with relaxation networks 

(incoherent processes). In the inhomogeneous master 

equation, the rf fields act on the full spin density 

operator a, while the relaxation applies to the 

difference from thermal equilibrium a — aeq. It is 

not obvious how to mix these two worlds. In the 

framework of the IME, it is difficult to construct an 

average Liouvillian analogous to the average Hamiltonian 

(30-35) so successful in treating the coherent 

response. 

III. The Homogeneous Master 

Equation (HME) 

The awkward aeq term is avoided by using a 

homogeneous master equation (HME). This was 

first suggested by Jeener (36). A slightly different 

derivation, and some interesting applications, were 

sketched in (1). In this article we will concentrate 

on the consequences of the HME. 

The rotating-frame HME (see Appendix A) has 

the form 

—a = -i[HCoh, cr] + To- , 

at 

(10) 

where the thermally-corrected relaxation superoperator 

T is given by 

T=f+0, (11) 

and Ti-coh ls the ordinary rotating-frame Hamiltonian. 

Instead of including aeq, the ordinary relaxation 

superoperator F is adjusted by adding a "thermal 

correction" ©. Eqn. 10 has the mathematical 

form of a homogeneous first-order differential equation. 

This is best illustrated by example. The HME 

for the relaxing 2-spin system, in the absence of rf 

fields, looks like 

0 0 0 

Qi —pi — a is —Si 

0s -vis -Ps -6s 

'is SI - of this operator represents 

the amount of spin disorder. The other expectation 

values < Iz > ... are much smaller by a 

factor ~ LJJTQ (assuming ordinary thermal nuclear 

spin polarization). Nevertheless, all interesting experimental 

observations are associated with these 

small quantities. 

Since the top row of the new relaxation matrix 

contains only zeros, < |1 > remains constant independent 

of the other expectation values. From 

Eqn. 4, the constant value is 

(14) 

The dynamic independence of < ^ 1 > is an approximation 

valid for weak spin polarization. In addition, 

Eqn. 11 assumes a high nuclear spin temperature, 

and the expressions for the elements of © (Eqn. 13) 

assume that the interaction with the static field is 

much larger than the other spin interactions (strong 

field limit). These approximations are discussed in 

Appendix B and are well-satisfied under ordinary 

circumstances. 

The eigenvalues of T are the same as F, although 

the eigenvectors are different. This means that the 

thermal correction terms do not change the characteristic 

relaxation rates, only the position of the 

eventual equilibrium. 

In Appendix B, it is shown that the elements of 

© in Eqn. 13 may be written down by the following 

procedure:


1. Write down the usual Redfield relaxation matrix 

in a basis of Cartesian product operators 

(in the above case, this corresponds to the extended 

Solomon equations). 

2. For columns corresponding to the Zeeman polarization 

< Ijz > of the spin Ij, multiply all 

elements by the factor ^LU^TQ, where LO°- is the 

Larmor frequency of spin Ij. 

3. Multiply columns .corresponding to other polarizations 

(such as < 2IjzIkz > ... < Ijx > ...) 

by zero. 

4. Sum the elements in each row to get the corresponding 

element of O. 

For example, in the current case, the second row 

of the Solomon matrix reads 

 

 

-ps 

(15) 

After multiplying by the appropriate factors, we get 

 

\ -l \psu o sTd 0 (16) 

Summing the row gives the correct thermal correction 

(17) 

This procedure is general for spin-1/2 systems 

within the approximations mentioned above. 

A pictorial representation of Eqn. 12 is shown in 

Figure 2. The relaxation dynamics appears as a unidirectional 

flow from left to right in the picture. The 

physical significance of this "flow" is as follows: The 

three "reservoirs" enclosed by a dotted line contain 

the "spin order," which can be redistributed internally 

by the a and 6 terms. The object on the left 

contains the large < ^1 > term, i.e. the disorder 

of the spin system. The three arrows labelled #/, 

6s and Qi$ indicate the conversion of spin disorder 

into spin order, i.e. a decrease in spin entropy due 

to the polarizing influence of the finite-temperature 

molecular environment. These three terms therefore 

take into account the spin-bath correlations. The 

three wiggly arrows marked pi, ps and pjs indicate 

the dissipation of spin order, i.e. the creation of 

spin entropy. These arrows do not need to "go anywhere" 

: The destruction of order is an irreversible 

process which need not be balanced out somewhere 

else. Figure 2 is an authentic representation of the 

spin system as an open system, acting as a channel 

for the creation of entropy in the universe. Thermal 

equilibrium is established when the expectation values 

, and < 2IZSZ > have values such 

that a steady flow is maintained, and as much spin 

entropy is created as is destroyed. 

IV. Application A: IT pulses on 

the I-spins 

So far the HME does not appear to be much of a 

simplification. Its power is only revealed when relaxation 

and pulses are mixed together. Since the HME 

relaxation superoperator T applies to the complete 

spin density operator, not just to the deviation from 

thermal equilibrium, pulse superoperators and relaxation 

superoperators may be combined at will. 

The interaction between them may be elucidated 

using well-known techniques. 

As an example, consider a sequence of evenlyspaced 

strong n pulses, separated by an interval r/2, 

applied to the I-spins. The relevant pulse sequence 

segment 

T 

- 

T 

7T, - •£ 

(18) 

has total duration r. 

If each iK pulse is short and ideal, it transforms 

the four spin operators as follows: 

1 

Sz 

2IZSZ 

1 

-I* 

(19) 

These equations refer to transformation properties 

such as 

exp{-mlx}lz 

(20)

Vol. 16, No. 1/2 99 

Figure 2: Physical interpretation of the HME for the 2-spin system Eqn. 12. The expectation values of the 

four spin operators |1, Iz, Sz and 2IZSZ constitute reservoirs. The three terms #/, 6 s and 9is represent the 

creation of spin order by polarization from the environment. 

In superoperator form, the pulse can be written 

11/= 

'I 

-1/ 

\ 

(21) 

The four spin operators are classified according to 

their parity under 11/: The two operators |1 and 

Sz are unchanged in sign under ft/, and are termed 

gerade. The two operators Iz and 2IZSZ are changed 

in sign, and are termed ungerade. 

In the absence of rf fields, the evolution of the 

spin density operator from time to to time t\ is given 

by 

= exp{(ti - t0) T}cr(t0) (22) 

It follows that the evolution of the density operator 

over the entire sequence CA can be written 

where 

= CAa(t0) (23) 

CA = exp{T ~T} 11/ exp{f ^ ft/ exp{f U 

(24) 

This corresponds to 

where 

CA = exp{f ~T} exp{f 'K) exp{f K] (25) 

f' = ft/f ft/ . (26) 

The matrix representation of the transformed superoperator 

T' is the same as that of T, except that 

elements connecting operators of opposite parity are 

changed in sign: 

f' = 

0 

-0i 

0s 

•Ois 

0 

-Pi 

O~IS 

-Si 

0 

CIS 

-ps 

Ss 

0 > 

-Si 

Ss 

-Pis) 

(27) 

It is convenient (but not essential) to take the 

limit of a cycle duration r short compared to the 

relaxation time constants. An approximation to 

Eqn. 25 is then: 

(28) 

(This is equivalent to taking the first term in a Magnus 

expansion of the interaction frame Liouvillian;


by symmetry, the second term in the Magnus expansion 

vanishes (30-35)). The propagator for the entire 

sequence, including both relaxation and pulses, 

is therefore 

^ exp{TAr} , (29) 

where the effective relaxation superoperator TA has 

a matrix representation 

0 

0 

0 

0 

-pi 

0 

-Si 

0 

0 

-Ps 

0 

0 

-Si 

0 

-pis 

(30) 

Thus, for rapid pulsing, the system separates dynamically 

into independent gerade and ungerade 

subspaces: 

with 

and 

TA = f 9 A 

(31) 

(32) 

(33) 

This is shown visually in Figure 3. 

We now consider individually the dynamics in 

the two subspaces. 

1. Dynamics in the gerade subspace 

The dynamics in the gerade subspace are very 

simple. The expectation value < Sz> is polarized 

at the constant rate 9 s < |1 > and dissipates at 

the rate ps < Sz >. There is a single exponential 

approach to a steady-state value of S-spin polarization. 

If pulse cycles are CA are repeated one after 

the other, the value of S-spin polarization after N 

repetitions is 

(NT)= SS 

+ (0 - SS ) exp{-psNr} 

(34) 

where the initial S-spin polarization is < Sz >o and 

its steady-state value is 

This evaluates to 

«=li!^ = iL. (35) 

< 5. > ec i 

PS 

= 1 + 

using the thermal equilibrium expectation value 

(36) 

< Sz > ef *= Tr{aeqSz } = - \ (37) 

4 

Eqn. 36 describes the steady-state nuclear Overhauser 

enhancement of the S-spin magnetization on 

applying radio-frequency fields to the I-spin (22,37). 

Although this effect is well-known, its interpretation 

in the HME formalism is unusual and revealing. 

The NOE arises because the rf fields are able 

to stem the leakage of S-spin polarization into the Ispin-order 

and two-spin-order terms. The applied 

fields merely turn off unwanted relaxation pathways, 

allowing a build-up of S-spin order under the 

favourable $s term. 

2. Dynamics in the ungerade subspace 

The dynamics in the ungerade subspace are also 

of interest. The central feature is that transfer of order 

takes place between I-spin Zeeman polarization 

and 2-spin order within a dynamically 

simple two-dimensional subsystem. The weak 

cross-correlation pathway connecting the two terms 

is isolated, allowing a more accurate experimental 

measurement. 

We have examined dynamic isolation of the 

cross-correlation pathway using the pulse sequences 

shown in Figure 4. The sequence in Figure 4a is 

used to examine the unmanipulated transfer of order 

from < Iz> into < Sz> and < 2IZSZ >. Initial 

thermal equilibrium is disturbed by two TT/2 pulses 

applied to the I-spins, which can have different relative 

phases. After a time T, a TT/2 pulse is applied 

to the S-spins and the signal detected. Signal from 

experiments in which the two I-spin TT/2 pulses have 

the same phase are subtracted from those in which 

the two I-spin 7r/2 pulses have opposite phase. As 

discussed in Appendix E, thermal polarization effects 

in the subsequent evolution may then be ignored. 

The contributions to < Sz> and < 2IZSZ >

Vol. 16, No. 1/2 101 

Figure 3: Relaxation dynamics in the presence of rapid vr pulses on the I-spins. The effective relaxation superoperator 

is factored into a gerade subspace \,\ and an ungerade subspace {, }. 

through cross-relaxation from < Iz > over the interval 

r are deduced by Fourier transforming the 

signal and manipulating the intensities of the two 

lines in the J-coupled multiplet in the usual way 

(38,39). The experiment is repeated for a range of 

cross-relaxation intervals r. 

The r-dependence of < Sz > and < 2IZSZ > 

are shown in Figure 5a. The predominant process, 

as expected, is the rapid creation of < Sz > 

under the dominant autocorrelation ajs pathway. 

< Sz > is negative since the cross-relaxation rate 

constant ajs is positive for this small molecule. 

< 2IZSZ > is also created, but in this experiment 

it is not easy to tell how much of this is due to direct 

< Iz >—>< 2IZSZ > transfer and how much to a 

two-step process —>—>. 

With one n pulse on the I-spins in the middle of 

the mixing time (Figure 4b), the < Iz >—>< Sz > 

transfer is greatly suppressed (Figure 5b). The 

< Iz >—>< 2IZSZ > transfer is also attenuated at 

long times, indicating the removal of two-step contributions 

(the change in sign on the right-hand side 

of Figure 5b is due to the inverting effect of the single 

TT pulse on the ungerade spin operators). 

By placing two n pulses at times r/4 and 3r/4, 

the autocorrelation pathway — j > is elim- 

inated and the observed polarization of < 2IZSZ > 

can be attributed to an essentially uncontaminated 

6j cross-correlation term. The r-dependences of 

< 2IZSZ > in Figure 5(b,c) are essentially mirrorimages, 

indicating that pulse imperfections are negligible. 

In Figure 6 we show the difference between 

the curves in Figure 5a and Figure 5c on 

an expanded scale. This curve indicates the influence 

of multiple-step transfers in the unmanipulated 

experiment. Although in principle the derivative of 

the curve is zero at r = 0, the steep rise would make 

an "initial rate" analysis problematic. 

The transfer curves could be analyzed to obtain 

the value 6j = —1.65 x 10~ 2 s" 1 . We have strong evidence 

(not discussed here) that this result is more 

accurate than that obtained from a previous dynamical 

analysis of the full relaxation network, performed 

with the aid of two-dimensional spectroscopy 

(28). 

V. Application B: ir pulses on 

both I and S-spins 

Interesting results are also obtained if the HME 

is used to analyze an experiment in which simulta-

102 

b 

T/2 T/2 

II 

1 

T/4 T/2 T/4 

1 


Figure 4: Pulse sequence for exploring the dynamics in the ungerade subspace. The experiments begin with 

two phase-cycled TT/2 pulses on the I-spins: These select the contribution from initial polarization at the 

beginning of the mixing period r. A TT/2 pulse on the S-spins at the end of r and observation of the J-coupled 

multiplet allows detection of cross-relaxed < Sz > and < 2IZSZ > at the end of r. (a) No manipulations of the 

relaxation network, (b) One I-spin vr pulse at the centre of r (c) Two I-spin vr pulses at r/4 and 3r/4. The 

relative pulse lengths are greatly exaggerated with respect to the delays. In practice, composite TT pulses were 

used. 

neous (or nearly simultaneous) vr pulses are applied 

to both I- and S-spin species. The relevant pulse 

sequence is 

T T T 

CB = - - 7T/7TS - - - 7T/7TS - - (38) 

which again has a total duration r. 

The operators are re-classified according to their 

parity under the two TT rotations: 

sz 

2IZSZ 

~sz 

(39) 

indicating transformation properties such as 

exp{-i7r (Ix + SX)}2IZSZ expjivr (Ix + Sx)} = 2IZSZ. 

(40) 

The simultaneous TT pulse pair can therefore be represented 

by a rotating-frame superoperator 

/I 

-1 

-1 

1/ 

(41) 

This time both one-spin Zeeman operators Iz and 

Sz are ungerade, while the two-spin-order operator 

2IZSZ and the normalized unit operator |1 are gerade.

Vol. 16, No. 1/2 103 

< 2lzSz > 

T/S 

Figure 5: Experimental results for 13 C-labelled chloroform at a proton frequency of 200 MHz. Rows a, b 

and c correspond to the experiments in Figure 4. Left column: Cross-relaxed . Right column: Crossrelaxed 

< 2IZSZ >. Vertical axes normalized to < Sz > eq . Note the different scales. In c, the suppression of 

cross-relaxed indicates the isolation of the ungerade subspace. 

shown in Figure 5a and Figure 5c, on an 

expanded scale. The solid line has no theoretical significance. The curve has zero derivative at r = 0, but 

rises steeply.


If the arguments given above are repeated, we 

get an overall superoperator for the pulse sequence 

= exp{Tsr} , (42) 

where the effective relaxation superoperator, as 

modified by the rf fields, is 

tB = f % + f B . (43) 

The matrix representations of the gerade and ungerade 

subspace relaxation superoperators are 

and 

T u R — 

0 0 0 0 

0 0 0 0 

0 0 0 0 

Jis 0 0 -PIS, 

0 

-pi 

0 

0 0\ 

-vis 0 

-ps 0 

0 0/ 

A visual representation is shown in Figure 7. 

1. Dynamics in the ungerade subspace 

(44) 

(45) 

The dynamics in the ungerade subspace are, as 

before, purely dissipative: order is transferred from 

< Iz > to < Sz > with the autocorrelation crossrelaxation 

rate constant cris, accompanied by dissipation 

of the Zeeman orders with rate constants 

pi and ps- This describes a normal transient nuclear 

Overhauser effect experiment (20), with the 

minor difference that the participation of crosscorrelation 

pathways is eliminated. This experiment 

could therefore be used to avoid potential errors 

in distance estimation due to non-negligible crosscorrelation 

effects (40,41), as demonstrated elsewhere 

(42). The method is analogous to the suppression 

of cross-correlation effects in measurements 

of relaxation time constants (3,43). 

2. Dynamics in the gerade subspace 

The gerade subspace in this experiment throws 

up a real surprise. It is naively expected that longterm 

irradiation by non-selective vr pulses should 

saturate the spin system, equalizing all populations 

and destroying all spin order. The HME analysis 

shows that on the contrary a dense sequence of nonselective 

7T pulses polarizes the multiple-spin-order 

terms, providing the relaxation mechanisms display 

suitable cross-correlation (1). By repeating the arguments 

used in the previous section, a steady-state 

of 2-spin-order can be predicted: 

(46) 

sz 

It should be emphasized that the vr pulses do 

not merely preserve any existing two-spin order, but 

establish the conditions for its creation. Two-spin 

order develops even when the ir pulses are applied 

to a spin system which is totally saturated. 

The effect is demonstrated by the sequence 

shown in Figure 8a. N repetitions of the cycle 

CB (Eqn. 38) are applied to the 13 C- 1 H system, 

starting from thermal equilibrium. The total irradiation 

time is T — NT. Composite n pulses 

(TT/2)Q (2vr)27r/3 (vr/2)0 were used throughout in order 

to reduce pulse imperfections (44). At the end 

of the long vr pulse train, a TT/2 pulse was applied to 

either the I-spins or the S-spins, and the free induction 

decays recorded. Fourier transformation gives 

J-coupled doublets in the I-spin or S-spin spectra, 

from which the values of < Iz > (T), < Sz > (T) 

and < 2IZSZ > (T) may be extracted (20,38,39). 

The trajectories of the three expectation values under 

the TT pulse train are shown in Figure 9. As 

expected, the one-spin Zeeman orders < Iz > and 

< Sz > saturate under the n pulse sequence, while 

negative two-spin-order grows in, eventually attaining 

a steady state of around —18% of the thermal 

equilibrium S-spin Zeeman polarization. The magnitude 

of the steady-state agrees quantitatively with 

the cross-correlation rate constants derived by the 

experiment in the previous section. 

It is also possible to demonstrate this effect in 

homonuclear spin systems, using the pulse sequence 

shown in Figure 8b. Strong non-selective TT pulses 

are used, affecting all spins in the sample. At the 

end of the TT pulse train, a strong vr/4 pulse is applied 

and the spectrum recorded. (A TT/2 pulse 

would be unsuitable, since two-spin order would 

be completely converted into unobservable multiplequantum 

coherence). The TT/4 pulse partially converts 

two-spin Zeeman order into observable singlequantum 

coherence, with the lines appearing in a 

characteristic antiphase pattern.

Vol. 16, No. 1/2 

\ 

J 

r IS 

Figure 7: Relaxation dynamics in the presence of rapid ir pulses on both I and S-spins. The effective relaxation 

superoperator is factored into a gerade subspace j,\ and an ungerade subspace 

{} 

Figure 10 shows a series of experimental X H spectra 

for a sample of exifone, 

HO 9 H 

a system already used by the Lausanne group for 

studying cross-correlation effects (45). The normal 

X H spectrum (lowest plot) shows a four-line AX pattern 

from the ortho and meta protons on one of the 

aromatic rings and a strong singlet from the two 

equivalent ortho protons on the other ring. When a 

long series of vr pulses is applied, the singlet gradually 

saturates, while the four AX lines eventually 

assume an antiphase character. The topmost spectrum 

is in the steady-state, after the application of 

many hundreds of vr pulses. The two-spin order is 

105 

small but certainly not negligible. We report elsewhere 

a quantitative analysis at a set of different 

magnetic fields, including a treatment of pulse imperfections. 

These results indicate that the steadystate 

provides a reliable estimate of CSA-DD crosscorrelation, 

possibly superior to the usual methods. 

Burghardt et al. (46) previously observed 

steady-state two-spin order effects in simulations of 

synchronous nutation experiments (5,6) using the 

conventional master equation. 

VI. Discussion 

In the above discussion, the HME was written 

implicitly in the rotating reference frame. The use 

of the rotating frame in the context of the HME, 

and spin-lattice relaxation in general, is discussed 

in Appendix A. 

The theory of the thermal correction to the relaxation 

superoperator is given in Appendix B. 

The above treatment was restricted to situations 

in which the rf fields implemented perfect, short, 

7T pulses. The treatment could then be restricted 

to a small Liouville subspace, making for a simple 

physical situation amenable to physical insight.

106 

1 VW////W/A 

V//////////M 

T=Nx 

71/4 


Figure 8: Pulse sequences for exploring steady-state effects in the gerade subspace, in the presence of nonselective 

7T pulses, (a) Heteronuclear experiment. 2N simultaneous TT pulses are applied over a time T = NT. 

A TT/2 pulse on one of the spin species generates the signal, (b) Homonuclear experiment. 2N non-selective vr 

pulses are applied over a time T = NT before a TT/4 pulse is used to convert the polarizations into observable 

signals. 

0.4 

o 

o 

< ^ 0 JL T « QiO 

> A 

Z > * 

A A 

Figure 9: Experimental results for 13 C-labelled chloroform at a proton frequency of 200 MHz, using the 

experimental sequence in Figure 8a. Composite vr pulses were actually used. The cycle period was r = 200 ms. 

The horizontal axis is the total irradiation time T. The vertical axis is normalized to < Sz > eq . Note the 

build-up of .

Vol. 16, No. 1/2 107 

Figure 10: Experimental 1 H spectra for exifone at a frequency of 300 MHz, using the sequence in Figure 8b. 

The cycle period was r = 50 ms. 

Another simple case is when frequency-selective 

vr pulses are used. Providing the pulses operate perfectly, 

and relaxation during the pulse is neglected, 

the spin operators may be classified as ungerade or 

gerade with respect to the selective spin inversions. 

There is considerable freedom in the classification 

of the operators, limited only by the ease of experimental 

implementation on the required timescale. 

The interposition of selective ?r pulses in the mixing 

period can therefore be used to restrict relaxation to 

an almost freely-chosen group of one-spin or multispin 

operators. For example, cross-relaxation pathways 

involving spins falling in a given spectral range 

may be suppressed (10), or cross-relaxation may only 

be allowed between spins falling within two freelychosen 

spectral ranges (4,12). 

Similar results may also be obtained using continuous 

rf fields, rather than selective n pulses (5- 

8). Such experiments are also amenable to HME 

analysis, although a larger Liouville subspace of orthogonal 

spin operators must be used. This involves 

no particular difficulties, although calculations can 

become cumbersome. A simple example is given in 

Appendix C. 

The HME is well-suited for numerical simulation 

(47). It provides an attractive alternative to 

the methods developed by Ravikumar et al. (48), 

who took into account thermal polarization effects 

in a different way. Their method involves a separate 

estimation of the steady-state during each element 

of the pulse sequence, using the conventional master 

equation. In contrast, HME calculations simply 

require the usual numerical diagonalization of the 

matrix representation of T. The asymmetry of the 

matrix representation involves no special problems. 

A short cut is available for periods where rf fields 

are absent, as discussed in Appendix D. 

Griesinger et al. (49) developed a technique 

known as "invariant trajectories" to analyze the averaging 

of relaxation rates under general multiplepulse 

trains. The same results follow from a 

straightforward HME calculation in the interaction 

frame, followed by the average Liouvillian approximation. 

Such calculations are useful for deriving 

"average relaxation rates" in the presence of rf fields, 

for example in the manipulation of spin diffusion


(4,7-12). The HME includes thermal polarization 

and nuclear Overhauser effects omitted from most 

other analyses. 

Many results arising from the HME can also be 

derived from the conventional master equation, albeit 

with more trouble. For many experiments involving 

phase cycling or difference spectroscopy, the 

thermal correction term © may actually be omitted, 

without generating incorrect results. This property 

is extremely important, since otherwise, a great 

body of NMR experiments would have to be reinterpreted. 

This is discussed in Appendix E. 

In summary, the HME establishes a much needed 

link between incoherent and coherent averaging experiments. 

The simplification of relaxation networks 

may be treated on an equal footing with the 

simplification of spin-spin coupling networks (i.e. 

decoupling experiments). The extensive literature 

on coherent averaging (30-35) becomes directly applicable 

to incoherent averaging experiments. The 

HME provides a strong physical insight, representing 

the spin ensemble as an open system, exchanging 

energy and entropy with the surrounding molecular 

environment. 

VII. Acknowledgments 

M.H.L. acknowledges support from the Swedish 

Natural Science Foundation. We would like to thank 

J. Kowalewski, J. Jeener, L. Maler, A. Vega and 

D. Sodickson for communications, help and discussions. 

We would also like to thank I. Burghardt for 

a copy of her doctoral thesis, and G. Bodenhausen 

for discussions and the sample of Exifone.. 

VIII. Appendix A: The HME in 

the rotating frame 

The HME is normally used in the rotating frame, 

where the dynamics under radio-frequency fields appear 

particularly simple. However, there is scope for 

confusion as to the correct expression for the relaxation 

equations in the rotating frame, and numerous 

errors in the literature can be found. The problem is 

that the spin system exchanges energy with the lattice, 

which is indifferent to the rotating frame used 

to analyze the spins. The comment of Abragam may 

be recalled (15): "spin and lattice temperatures are 

defined in two different frames of reference and there 

is danger of being led astray by intuitive physical arguments 

in this unfamiliar situation." 

The main problems center around the use of the 

term "rotating-frame Hamiltonian," i.e. the operator 

which generates the spin dynamics, as corrected 

for illusory forces arising from the motion of the 

frame (50). For example the equation of motion (neglecting 

relaxation) of a rotating-frame spin density 

operator defined by 

is 

a R (t) = a(t) 

dt a = ~ 1 t Wc °h' CT 1 

with the "rotating-frame Hamiltonian" 

(48) 

(49) 

Hfoh = exp{iu)tlz} Hcoh exp{-iutlz} -LOIZ . (50) 

This type of "rotating-frame Hamiltonian" is so 

familiar in NMR theory that it is often forgotten 

that it is not a real Hamiltonian at all. It is a sort 

of "pseudo-Hamiltonian" which fulfils the dynamic 

but not the energetic function of a true Hamiltonian. 

In particular, < Hôh > is not the energy of the spin 

system (51), and W^,h cannot be used in statistical 

thermodynamical expressions involving the spin system 

energy. For example, the steady-state density 

operator in the presence of a field has no relationship 

with the "rotating-frame Hamiltonian": 

a* + Z- 1 exp{-Wfohr4 . (51) 

Erroneous statements to the contrary can unfortunately 

be found in many textbooks and papers. 

A false impression is also left by the unfortunate 

terminology "spin-lattice relaxation in the rotating 

frame" and "rotating-frame nuclear Overhauser effect." 

These phenomena involve relaxation dynamics 

in the presence of rf fields, and have no particular 

connection with the use of a rotating frame. 

To elucidate the role of the rotating frame, consider 

the (lab frame!) HME in the presence of an 

applied rf field: 

a(t) = f (*)) a(t) , (52) 

dt 

where 7Ycoh is the commutation superoperator with 

the time-dependent coherent Hamiltonian 

, ft] , 

(53)

Vol. 16, No. 1/2 109 

and the coherent Hamiltonian is assumed to have a 

large, time-independent, component Ho and a small, 

time-dependent component Hi: 

= Ho + H\(t) (54) 

In principle, the relaxation superoperator is also 

time-dependent, since the eigenstates and energies 

of the spin system are affected by the modulation 

of Ticoh- However, if H\ is much smaller than Ho, 

and the fluctuations in the incoherent interactions 

are rapid compared to the magnitude of Hi, the 

effect of Hi on Y may be ignored and the HME 

approximated as 

to) (55) 

where To is the relaxation superoperator in the absence 

of the rf field. 

By using a transformed density operator of the 

form Eqn. 48, the HME becomes 

dt aR (t)= I - (56) 

where, for a proper choice of frame, the "pseudo- 

Hamiltonian" Hôh in Eqn. 50 can be made timeindependent. 

This is the most useful form of the 

HME: Normally the rotating-frame is assumed and 

the superscripts "R" and subscript "0" dropped. 

IX. Appendix B: The thermal 

correction © 

Since the lattice has a finite temperature, the 

probability of the nuclear spin system making a 

transition \r> —• \s> differs slightly from that for 

the reverse transition \s> —• \r> according to the 

relative energy of the two states. Elementary considerations 

of this kind lead to an "improved" relaxation 

superoperator of the form 

f = f exp{wr4 (57) 

where the superoperator Co has the property 

= ]T uirttrr\r> of the main part 

of the coherent (lab frame!) Hamiltonian 

Ho r > = u>r\r> . (59) 

Thus CJ projects out the "secular" components of 

an operator Q, weighting each component with the 

energy of the corresponding spin state. 

For high nuclear spin temperature, the exponential 

in Eqn. 57 can be approximated by the first two 

terms in a series, giving 

with 

(60) 

(61) 

This looks simple but gives rise to rather complicated 

expressions. 

Consider therefore the projection superoperator 

P-j which removes all traceless components of its 

argument operator: 

= n~ l Tr{0} 1 . (62) 

This can be used to decompose the density operator 

into a non-traceless and a traceless component: 

The HME can therefore be written 

d 

—a = ( —1 

h + f J a + TUJP^ are 

Yd) I 1 — Pj ) (JTg. 

(63) 

(64) 

Since the traceless part of the density operator is 

much smaller than the non-traceless part, by a factor 

of the order of ||(Dr^||, the last term is proportional 

to ||O)T^|| 2 and can be ignored. The thermal 

correction is 

(65) 

which proves easier to handle. 

An expression for the elements of 6 in a 

base of normalized Cartesian product operators 

(38,39) can be derived as follows: Consider a 

spin system with n eigenstates. A suitable set 

of product operators is denned by {Q11Q2 • • •} = 

271" 1 / 2 { § 1, Ilz, I2z • • • *hzhz •••}• The operators 

are normalized such that 

Tr{QjQk} = 6j (66) 

Now all elements 9jk = Tv{QjQQk} with k ^ 1 vanish 

since Qk>i are traceless. Similarly, all elements


Oik vanish since f is symmetrical and f 1 = 0. We 

are left with the elements in the first column, 9j\ 

with j ^ 1. These may be written as follows: 

9jX= 

Since P-jQi = Qi, this becomes 

(67) 

(68) 

Using the definition of a), and Qi = n" 1 ' 2 ^, we get 

rk 

(69) 

introducing the elements of the ordinary relaxation 

matrix in the Cartesian product basis 

= Tr{QjtQk} , (70) 

and the matrix elements of spin operators 

Qk, in the eigenbase of the coherent Hamiltonian. 

Now in high field, the energies uir are very 

close to the eigenvalues of the pure Zeeman Hamiltonian 

defined by 

T/0 V^ 0 T /rr-i \ 

where uf^ is the Larmor frequency of spin /^, ignoring 

chemical shifts and spin-spin couplings. Hence 

the thermal correction elements can be written 

rk 

(72) 

Since 7i°z is diagonal for a spin system in high field 

(this is true even for strongly-coupled systems), this 

can be written in turn 

or more explicitly 

(73) 

(74) 

Since for spins-1/2, Tr{/^} = n/4, this equation 

encodes the simple step-by-step procedure given in 

the text for the thermal correction elements (Eqns. 

15-17). 

X. Appendix C: Continuous rf 

fields 

We give one example of the HME in a situation 

where additional operators must be included in the 

relevant Liouville subspace. Consider a heteronuclear 

two-spin system with continuous, on-resonance 

rf irradiation of the S-spin. This has been treated 

by Boulat and Bodenhausen (52) who showed that 

a naive application of the Solomon equations for the 

spin state populations fails. It is necessary to take 

into account the full spin dynamics, including the 

creation of spin coherences by the rf field. 

The rotating-frame HME in the presence of the 

rf field is 

where p^ is the transverse relaxation rate constant 

of S-spin coherences, and cross-correlation effects 

are neglected this time. The rf field is considered 

to have magnitude oj\ in frequency units and phase 

vr/2. The Liouville subspace is extended by one row 

and one column, in order to encompass the mixing 

of the rotating-frame expectation values and 

< Sx > by the rf field. 

Eqn. 75 contains the full dynamical behaviour of 

the system, which could in principle be extracted 

by diagonalizing the 4x4 matrix A in the equation 

above. Let us just concentrate on the steady-state 

behaviour. The steady-state expectation values of 

the spin system form a vector vs which lies in the 

nullspace of A i.e. 

Avw = 0 . 

(76) 

The nullspace is the set of eigenvectors with zero 

eigenvalue (53). 

In the present case, the actual steady state is 

that nullspace vector with < |1 >= ^. Explicit calculation, 

or computer algebra (54) gives the result 

immediately: 

X (A 2 p t sL0°ITe 

X 

/ + OISU)%) 

\ 

(77)

Vol. 16, No. 1/2 111 

where 

and 

= pips - 

-i 

(78) 

(79) 

In the limit of UJ\ much greater than the relaxation 

rates, and neglecting second-order effects, the 

expression reduces to 

\ 

Since the thermal equilibrium value of S-spin Zeeman 

polarization is given by 

\ 

(80) 

(81) 

the steady-state value of the transverse S-spin polarization 

in the presence of the rf field is 

SS , A 2 

(82) 

and the steady-state nuclear Overhauser enhancement 

of the longitudinal I-spin polarization is described 

by 

>eq 

(83) 

i.e. the same as when TT pulses are used. These 

results are in agreement with the calculation by 

Boulat and Bodenhausen (52). 

XI. Appendix D: Numerical calculations 

with the HME 

The HME may be used for numerical spindynamical 

calculations involving simultaneous relaxation 

and rf fields. In general, this can be done 

one pulse sequence element at a time. The evolution 

superoperator under a pulse sequence element 

B has the form 

B= (84) 

where r is the pulse sequence element duration and 

C is the effect of rf fields and relaxation, without the 

thermal correction: 

c = -mcoh + r 

(85) 

The exponential in Eqn. 84 can be calculated numerically 

in the usual way, by forming a matrix representation 

of the superoperator and diagonalizing. 

The asymmetry of the matrix representation generates 

no particular problems. 

We point out here a special feature of Eqn. 84. 

Since £1 = 0, we have €>£ = G 2 = 6. Hence 

£ + e) = £ 2 + £6 

(86) 

and so on. It follows that the exponent can be written 

e (87) 

The evolution superoperator is itself the sum of a 

"normal" superoperator and a thermal correction 

term. This has important consequences (see Appendix 

E). Furthermore, in the special case of "free 

precession periods" where no rf fields are applied, 

Eqn. 87 may be set in the form 

exp{(£0 

= exp{£or} 

For free precession, the thermally corrected evolution 

superoperator may be derived from the nonthermally 

corrected superoperator, in just the same 

way as T can be derived from F. 

XII. Appendix E: The HME and 

phase cycling 

Many magnetic resonance experiments involve 

taking a linear combination of results from related 

but slightly different experiments. A typical example 

is phase cycling, in which the experiments only 

differ in the relative phase of some of the pulses. 

The signals from the phase-shifted experiments are 

multiplied by complex phase factors and combined 

in the processing device.

112 

For many experiments of this kind the thermal 

correction terms 0 may be omitted from at least 

part of the calculation. This is fortunate, since it 

has been common practice to disregard the thermal 

polarization effects when convenient. A formal justification 

in the context of the HME may be useful. 

In the treatment by Ernst and co-workers (38), 

phase cycling is represented by an instantaneous 

projection of the density operator onto a subspace 

of operators with particular rotational properties, 

i.e. coherences of particular orders. This is very 

convenient for calculations. All elements of the density 

operator which do not belong to coherences of 

a given order are simply removed and the calculation 

carried further using only the elements which 

do have the "right" order. 

The basis for this procedure is awkward in terms 

of the ordinary master equation since the aeq terms 

get in the way (55). It also not obvious what happens 

in the case of extended rf fields. In the HME, 

the treatment of phase cycling is more straightforward. 

Suppose a pulse sequence consists of two 

parts, A and B. The B part is performed in two 

versions, B\ and _B2, and the NMR signals s\ and 

s-2 combined with complex factors c\ and c2. In the 

HME, the individual NMR signals can be written 

Sl(t) = 

s2(t) = > ( 89 ) 

where O is the observable operator and UQ the initial 

density operator, assumed identical in the two 

experiments. The combined signal c\S\(t) + 

can be written 

where 

s(t) = Tr{Q+ exp{C0t}BAa0} 

B = + c2B2 . 

(90) 

(91) 

Thus the superoperators of different pulse sequences 

are combined linearly. In phase cycling, the experiments 

are selected such that the averaged superoperator 

behaves according to: 

= BPM 

(92) 

where PM projects out operator terms belonging to 

spin coherences of a particular order M, or set of 

orders. 


From Eqn. 87, the superoperator including phase 

cycling, for ¥/0, is 

exp{(£ + 6) T}PM = exp{£r}PM • (93) 

The "thermal correction" vanishes since P-j PM = 0. 

It follows that if phase cycling is used to select 

coherences of some non-zero order M at a particular 

point in a pulse sequence, the thermal correction 

terms may safely be omitted from all subsequent 

pulse sequence elements. Similar conclusions apply 

to other forms of difference spectroscopy. 

XIII. References 

*M. H. Levitt and L. Di Bari, Phys. Rev. Lett. 

69, 3124 (1992). 

2 

T. E. Bull, J. Magn. Reson. 93, 596 (1991). 

3 

L. E. Kay, L. K. Nicholson, F. Delaglio, A. Bax 

and D. A. Torchia, J. Magn. Reson. 97, 359 

(1992). 

4 

G. Bodenhausen, 5th Chianti Workshop, San 

Miniato, Italy, May 1993. 

5 

B. Boulat, I. Burghardt and G. Bodenhausen, 

J. Am. Chem. Soc. 114, 10679 (1992). 

6 

I. Burghardt, R. Konrat, B. Boulat, S. J. F. 

Vincent and G. Bodenhausen, J. Chem. Phys. 98, 

1721 (1993). 

7 

E. T. Olejniczak, R. T. Gampe and S. W. Fesik, 

J. Magn. Reson. 67, 28 (1986). 

8 

W. Massefski and A. G. Redfleld, J. Magn. 

Reson. 78, 150 (1988). 

9 

J. Fejzo, W. M. Westler, S. Macura and 

J. L. Markley, J. Magn. Reson. 92, 20 (1991). 

10 

J. Fejzo, W. M. Westler, S. Macura and 

J. L. Markley, J. Magn. Reson. 92, 195 (1991). 

11 

J. Fejzo, W. M. Westler, J. L. Markley and 

S. Macura, J. Am. Chem. Soc. 114, 1523(1992). 

12 

C. Zwahlen, S. J. F. Vincent, L. Di Bari, 

M. H. Levitt and G. Bodenhausen, J. Am. Chem. 

Soc., in press. 

13 

I. Burghardt, R. Konrat and G. Bodenhausen, 

Mol. Phys. 75, 467 (1992). 

14 

A. G. Redfield, Adv. Magn. Reson. 1, 1 

(1965). 

15 

A. Abragam, "The Principles of Nuclear Magnetism", 

(Clarendon Press, Oxford, 1961). 

16 

A. J. Vega and D. Fiat, Pure. Appl. Chem. 

40, 181 (1974);

Vol. 16, No. 1/2 113 

A. J. Vega and D. Fiat, J. Magn. Reson. 13, 260 

(1974); 

A. J. Vega and D. Fiat, J. Chem. Phys. 60, 579 

(1974); 

A. J. Vega and D. Fiat, J. Magn. Reson. 19, 21 

(1975). 

17 D. H. Jones, N. D. Kurur and D. P. Weitekamp, 

Bull. Magn. Reson. 14, 214 (1992). 

18 F. A. L. Anet and D. I. Freedberg, Chem. 

Phys. Lett. 208, 187 (1993). 

19 L. G. Werbelow and D. M. Grant, Adv. Magn. 

Reson. 9, 189 (1977). 

20 D. Canet, Prog. NMR Spectrosc. 21, 237 

(1989). 

21 J. McConnell, "The theory of NMR Spin Relaxation 

in Liquids", (Cambridge University Press, 

Cambridge, 1987). 

22 D. Neuhaus and M. P. Williamson, "The Nuclear 

Overhauser Effect in Structural k, Conformational 

Analysis", (VCH, Cambridge, 1989). 

23 M. Gue'ron, J. L. Leroy and R. H. Griffey, 

J. Am. Chem. Soc. 105, 7262 (1983). 

24 M. Goldman, J. Magn. Reson. 60, 437 

(1984). 

25 R. Bruschweiler, C. Griesinger and R. R. 

Ernst, J. Am. Chem. Soc. Ill, 8034 (1989). 

26 R. Bruschweiler and R. R. Ernst, J. Chem. 

Phys. 96, 1758 (1992). 

27 C. Dalvit and G. Bodenhausen, Adv. Magn. 

Reson. 14, 1 (1990). 

28 L. Maler and J. Kowalewski, Chem. Phys. 

Lett. 190, 241 (1992). 

29 C. Dalvit and G. Bodenhausen, Chem. Phys. 

Lett. 161, 554 (1989). 

30 M. H. Levitt and R. Freeman, J. Magn. Re- 

son. 43, 502 (1981). 

31 J. S. Waugh, J. Magn. Reson. 50, 30 

(1982). 

32 J. S. Waugh, J. Magn. Reson. 49, 517 

(1982). 

33 A. J. Shaka and J. Keeler, Prog. Nucl. Magn. 

Reson. Spectrosc. 19, 47 (1987). 

34 U. Haeberlen and J. S. Waugh, Phys. Rev. 

175, 453 (1968). 

35 U. Haeberlen, "High Resolution NMR in 

Solids. Selective Averaging", (Academic, New York, 

1976). 

36 J. Jeener, Adv. Magn. Reson. 10, 1 

(1982). 

37 I. Solomon, Phys. Rev. 99, 559 (1955). 

38 R. R. Ernst, G. Bodenhausen and A. Wokaun, 

"Principles of Nuclear Magnetic Resonance in One 

and Two Dimensions", (Clarendon Press, Oxford, 

1987). 

39 O. W. S0rensen, G. W. Eich, M. H. Levitt, 

G. Bodenhausen and R. R. Ernst, Prog. NMR Spectrosc. 

16, 163 (1983). 

40 V. V. Krishnan and Anil Kumar, J. Magn. 

Reson. 92, 293 (1991). 

41 Anil Kumar, 5th Chianti Workshop, San 

Miniato, Italy, May 1993. 

42 L. Di Bari and M. H. Levitt, to be published. 

43 A. G. Palmer III, N. J. Skelton, W. J. Chazin, 

P. E. Wright and M. Ranee, Mol. Phys. 75, 699 

(1992). 

44 M. H. Levitt, Prog. NMR Spectrosc. 18, 61 

(1986). 

45 L. Di Bari, J. Kowalewski and G. Bodenhausen, 

J. Chem. Phys. 93, 7698 (1990). 

46 I. Burghardt, Doctoral Thesis, University of 

Lausanne, 1991. 

47 S. Szymanski, A. M. Gryff-Keller and G. Binsch, 

J. Magn. Reson. 68, 399 (1986). 

48 M. Ravikumar, R. Shukla and A. A. Bothner- 

By, J. Chem. Phys. 95, 3092 (1991). 

49 C. Griesinger and R. R. Ernst, Chem. Phys. 

Lett. 152, 239 (1988). 

50 A lucid description of the rotating frame transformation 

can be found in Appendix D of J. Jeener 

and F. Henin, Phys. Rev. A 34, 4897 (1986). 

51 A. G. Redfield, Phys. Rev. 98, 1787 (1955), 

note 29. In this influential early paper, Redfield indicates 

that Eqn. 51 is incorrect because "the electrons, 

which are responsible for the relaxation are almost 

completely unaffected by the rf field" (p.1796) 

[this is the case of nuclear relaxation by metallic 

conduction electrons]. This argument is too weak. 

A much stronger justification is that < 7~tôh > is not 

the spin energy, and cannot be used in statistical calculations 

involving combinations of lattice and spin 

energies. A truly energetic role of the "rotatingframe 

Hamiltonian" is inadmissable in principle. 

52 B. Boulat and G. Bodenhausen, J. Chem. 

Phys. 97, 6040 (1992). 

53 G. Strang, "Linear Algebra and its Applications", 

(Harcourt Brace Jovanovich, San Diego, 

1988). 

54 S. Wolfram, "Mathematical A System for Do-


ing Mathematics by Computer", (Addison-Wesley, 

New York, 1991). 

55 see ref. (38), p.288.

Vol. 16, No. 1/2 115 

Contents 


Effects of Cross-Correlations in 2D NOE Experiments 1 

P.K. Madhu*, R. Christy Rani Grace* and Anil Kumar* 1 

* Department of Physics and ^Sophisticated Instruments Facility 

Indian Institute of Science, Bangalore - 560 012, INDIA 

II. Theory 

1. Net effect due to dipolar cross-correlations in a homonuclear three spin system 

III. Conclusions 

IV. References 


The development of two dimensional Fourier 

transform NMR techniques by Professor Ernst during 

the Seventies and Eighties created a revolution 

in the study of biomolecules by NMR. The ubiquitous 

COSY experiment and its many variants, especially 

the DQFC and TOCSY experiments made 

it possible to obtain assignments of resonances of 

molecules containing several hundreds of protons - a 

task which was considered "impossible" before the 

development of 2D NMR. Similarly the impact of 

the 2D NOE experiment was "electrifying". It made 

it possible to obtain the structures of biomolecules 

in solution, a task which was considered "very difficult" 

before the application of this experiment (1-5). 

The revolutionary developments of Fourier transform 

NMR spectroscopy in one and multidimensions 

by Professor Ernst, with literally hundreds of 

new experiments developed by him during these two 

decades, leading to an explosion of research in this 

area by many workers, have culminated in his receiving 

the 1991 Nobel Prize in Chemistry. 

The success of the 2D NOE experiment has made 

it an "object-la-focus" on which much attention has 

been paid. In order to extract as much information 

as possible from this experiment, it is performed in 

the realm of the initial-rate approximation, build-up 

1 Presented in part at 5 th Chianti workshop on Magnetic 

Resonance Nuclear and Electron Relaxation, held at San 

Miniato, Italy, June 1993. 

115 

116 

. 118 

122 

123 

curves and long mixing times, subjecting the data 

respectively to the two-spin approximation, buildup 

rates and full relaxation-matrix analyses. Several 

attempts are underway to obtain "accuratedistances" 

(not just distance estimates) from the 2D 

NOE data. Simultaneously there have been many 

concerns regarding the systematic errors in the distance 

estimates from 2D NOE data. These are, effects 

of internal motions (6-9), anisotropy of motion 

(10-13), spin diffusion (14-19), sources of relaxation 

other than intra-molecular dipolar interactions, 

and cross-correlations between different pathways 

of relaxation of a spin. While many attempts 

are underway to include the effects of internal motions, 

anisotropy of reorientation, spin diffusion 

and other relaxation processes, cross-correlations 

present somewhat of an insurmountable problem. 

The problem, as succinctly pointed out by Bull (20), 

is that if one wants to include cross-correlations for 

N number of relaxation coupled spins, the dimension 

of the relaxation matrix goes up exponentially 

to 2^ x 2 N as against a linear N x N increase if 

one neglects cross-correlations. For example, for 10 

relaxation coupled spins one needs a 1024 x 1024 relaxation 

matrix with cross-correlations and a 10 x 10 

matrix without cross-correlations. Therefore the 

question, whether one can discard cross-correlations 

without making much error, becomes very pertinent. 

In this paper the effects of cross-correlations

d 

"dt 


and their influence in the 2D NOE experiments are 

examined in some detail, especially with respect to 

their influence on the net NOE. 

II. Theory 

The longitudinal relaxation of N relaxation coupled 

spins is in general described by the rate equation 

(4) 

dP(t) 

dt = W(P(t) - (1) 

where P(t) is a vector of populations of various levels 

at a time 't' and P° is their equilibrium value. 

W is the longitudinal relaxation rate matrix. The 

dimension of P is 2 iV and that of W is 2 W x2. 

If one neglects the cross-correlations a simpler rate 

equation describing the magnetization of each spin 

is obtained as (14,21) 

dlz(t) 

dt 

= R(£(*) - (2) 

This later equation is the generalized Solomon's 

equation in which Iz(t) describes the longitudinal 

magnetization of various spins at time 't', their equilibrium 

values 1^ and the rate matrix R whose diagonal 

elements describe the self relaxation of a spin 

and the off-diagonal elements the cross-relaxation 

Az 

Mz 

Xz 

2AZMZ 

2AZXZ 

2MZXZ 

4AZMZXZ 

PA O~AX 

0 

SA 

PM 

&AX &MX PX 

AM A AM 

fix 

AAM 

0 

PAM 

+ *MX 

Vol. 16, No. 1/2 117 

Figure 1. 

Az(r) Mz(r) Xz(r) 

The presence of multispin modes creates unequal 

intensities for the various transitions of a spin. For 

example, the intensities of the four transitions of 

spin A in an AMX spin system are given by 

Ax = (1/4)[AZ + 2AZMZ + 2AZXZ + 4AZMZXZ] 

A2 = (1/4){AZ-2AZMZ + 2AZXZ-4AZMZXZ\ 

A3 = (1/4)[AZ + 2AZMZ-2AZXZ~4AZMZXZ] 

A4 = (l/4)[Az~2AzMz-2AzXz+4AzMzXz\ 

(4) 

The net intensity of the spin is the sum of all 

four transitions, and is given by the single spin mode 

Az. If the four transitions are not resolved (J=0) or 

if one uses a 90° measuring pulse (which does not 

measure the multispin modes) one only sees the net 

effect. However, the net effect will be different, when 

cross-correlations are present, from that predicted 

by eqn. 2. The net effect is independent of the value 

of J, within the weak coupling limit. 

In a 2D NOE experiment on uncoupled or weakly 

coupled spins using the [90 — t\ — 90 — rm — a] sequence, 

each cross-section parallel to Fi is equivalent 

to a ID transient NOE experiment in which 

the spin (or all the transitions of the spin) on the 

diagonal, is inverted at rm = 0 (27-29). This means 

that in each cross-section, a single spin mode is created 

and all the other modes are zero at rTO = 0. 

From eqn. 3 it is seen that this single spin mode 

then evolves, in the initial rate approximation, into 

single spin modes of other spins (NOE) through 

cross-relaxation (


15 sec 

.0 sec 

3.8 sec 

0 0 

***v 

x8 

x8 

.4 sec *«*»*?+*, x8 

3.0sec 

0 -01 sec- 

Figure 2: The AX part of the inversion-recovery 

spectra of coumarine dissolved in CDCI3, recorded 

with a measuring pulse of 20°, for recovery times 

indicated in the diagram. Some of the spectra are 

multiplied 4 or 8 times as indicated. The spectra 

were recorded on an AMX-400 spectrometer. 

This paper, on the other hand, concentrates on 

the net effect arising from the cross-correlations. For 

this purpose a three spin system is considered, the 

discussion being restricted to dipole-dipole crosscorrelations. 

It has been earlier shown that there 

is a significant multiplet effect in such a spin system 

especially in a linear geometry and that the NOE 

and the multiplet effect are sensitive to the geometric 

disposition of the three spins (39). 

1. Net effect due to dipolar crosscorrelations 

in a homonuclear three 

spin system 

Three geometries of the relaxation coupled 

three spin system, without or with weak J couplings 

(AMX ) considered are, (i) equilateral triangle (ii) 

isosceles triangle with a right angle and (iii) a linear 

arrangement of the three spins, keeping the distance 

between 'AM' and' MX' equal. The magnitude of 

the geometric factor of the AM-MX dipole-dipole 

cross-correlation compared to AM-AM auto correlation 

for the homonuclear system is given by 

r(3cos 2 f9-l) (5) 

where ri is the distance between A and M spins, 

i2 the distance between M and X spins and 9 is the 

angle between these two vectors (Figure 3). For ri = 

r2, this ratio is —1/8, —1/2, and 1 respectively for 

equilateral triangle, isosceles triangle and a linear 

arrangement of the spins. Thus the cross-correlation 

is extremely sensitive to the geometric disposition of 

the three spins with the linear arrangement having 

maximum cross-correlation.

Vol. 16, No. 1/2 119 

-60 

[A (T 

u z v m 

io SEC go 

Figure 4: Calculated net NOE in percentage on spin A, after selective inversion of spin M at rm = 0 is shown 

as a function of rm for three geometries; (a) equilateral (b) isosceles and (c) linear, for three values of LUTC 

in each case. In the left hand diagrams the dashed curves represent the calculated net NOE without crosscorrelations 

and the solid curves with cross-correlations. In the right hand diagrams the difference between 

these two calculated NOE's are shown by solid curves. 

The calculated net NOE on spin A [Az(Tm)] for 

the selective inversion of spin M (equal to the intensity 

of AM cross peak in a cross-section parallel 

to i


-30 - 

-60 

Figure 4: continued. 0 

[Afr-J/A ]% 

NOE calculated with and without cross-correlations 

has a direct consequence in the distance estimation 

from the 2D NOE data. The neglect of crosscorrelations 

causes a systematic error in the distance 

measurement. However, the error builds-up at large 

mixing times since it is due to the second-order effect 

of cross-correlations. One redeeming factor is 

that these mixing times are much larger than the 

mixing times usually employed in 2D NOE experiments. 

Never-the-less these errors are significant, 

and are due to opening up of additional relaxation 

pathways of the spin by the cross-correlations. This 

is discussed in more detail in the following. 

SEC 10 0 T m 10 SEC 20 

The cross-correlation 6M transfers some of 

M magnetization to the three spin order term 

(AAZMZXZ) which then leaks to Az or Xz via 8A 

or 8x respectively or comes back to Mz via 6M- 

These additional pathways cause the changes in the 

net NOE. In equilateral and isosceles triangle cases 

all the 6's are small. As a result these additional 

pathways are insignificant. However in the linear 

case the geometric factor of the AM-MX crosscorrelation 

is as significant as AM-AM or MX-MX 

auto-correlation. Thus in the linear case the dominant 

additional pathway is (8M, &M) (Figure 5). 

The NOE from spin M to spin A is affected by two

Vol. 16, No. 1/2 121 

Figure 4: continued. 

15 - 

0 - 

-5 4 

-30 -I 

-60 

/ \ \ 

/ x \ 

1 WTC=O. 

pathways one involving (6M, 8M, &AM) path and 

the other involving (8M, 8A) path (Figure 6). In the 

UTC = 1.118 limit (JAM ~ 0 and the net NOE to A 

spin comes only through cross-correlations using the 

path (8M, 8A)- Since 8A is small this NOE is small 

(Figure 4c). However when U>TC ^> 1 (urc = 10), 

&AM is large along with 8M and the path (8M, 8M, 

a AM) contributes significantly to the net NOE on 

A and the difference in net NOE calculated with or 

without cross-correlation is significant (Figure 4c). 

Identical results are obtained for the X spin in this 

case due to symmetry and are not shown. 

The self-relaxation of spin M is also affected by 

\ 

I 

10 

io SEC 20 

the presence of cross-correlations (Figure 7). The 

self-relaxation of a spin can be monitored as the decay 

of the diagonal peak in the 2D NOE experiment 

or by a selective-inversion-recovery experiment. The 

self-relaxation of spin M shows a very large effect of 

cross-correlations as has also been pointed out by 

early workers in this field (40-42). The pathways 

affecting the self relaxation of spin M are indicated 

in Figure 8. Of these the dominant path due to 

cross-correlations is again the path (8M, 8M)- For 

UITC = 1.118 the other paths are cut off and this is 

the only path left. 

The NOE from spin A to M and X and its self-


Figure 5. 

Figure 6. 

AAZMZXZ 

8M 8M 

=> 4AZMZXZ 

&AM 

relaxation is considered next. Since 8A is small 

the conversion of Az to 4AZMZX- is weak. Figure 

9 shows the net NOE from spin A to M and 

X for various correlation times. This figure shows 

that the differences are smaller than Figure 4 but 

are not negligible. In the short correlation limit 

(UJTC < 1) the net NOE to X is small and the difference 

with and without cross-correlation is also 

small. The calculated net NOE on M and X spins 

without cross-correlations is zero for U>TC = 1.118. 

The pathways contributing to the net NOE on M 

and X spins are shown in Figure 10. For WTC = 

1.118 when

Vol. 16, No. 1/2 123 

-100 - 

-200 

-100 - 

-200 

-100 - 

-200 

[Mz(rm)/M ]% 

SEC 20 

Figure 7: The calculated net magnetization in percentage of spin M is shown as a function of rm, after a 

selective inversion of spin M at rm=0 for the linear geometry of the three spins AMX for three different values 

of WTC. In the left hand diagrams, the dashed curves represent the calculated magnetization without crosscorrelations 

and the solid curves with cross-correlations. In the right hand diagrams the differences between 

these two calculated magnetizations are shown by solid curves. 

correlations are small. The CSA-dipole crosscorrelation 

for protons are also usually small and 

perhaps can be ignored. The CSA-dipole crosscorrelation 

is significant for other spin 1/2 nuclei 

such as 19 F, 13 C, 31 P and 15 N and may 

not be ignored. More work is required to assess 

whether proton-proton dipole-dipole crosscorrelations 

should be included in biomolecular 

NOE studies of large molecules. 


P. Aue, E. Bartholdi and R. R. Ernst, J. 

Chem. Phys. 64, 2229-2245 (1976). 

2 Anil Kumar, R. R. Ernst and K. Wiithrich, 

Biochem. Biophys. Res. Commun. 95, 1-6 (1980). 

3 K. Wiithrich, "NMR of Proteins and Nucleic 

Acids", John Wiley and Sons, New York (1986).

124 

Figure 8. 

-60 

[M( 

GAM &AX 

4AZMZXZ 

u - 

5 - 

0 - 

-20 - 

Xz 

M s- 

1 «Tc=0 

-^ 

X 


.1 

\ . 

. • 

10 20 

0 T m 5 SEC io 0 T m 10 SEC 20 

Figure 9: Calculated net NOE in percentage on spins M and X, after a selective inversion of spin A at 

rm — 0, for the linear geometry. The remaining details are same as in Figure 4.

Vol. 16, No. 1/2 125 

Figure 10. 

&AX 

4 

R. R. Ernst, G. Bodenhausen and A. Wokaun, 


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5 

R. R. Ernst, Angew. Chem. Int. Ed. Engl. 31, 

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D. E. Woessner, J. Chem. Phys. 42, 1855-1859 

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J. W. Keepers and T. L. James, J. Magn. Re- 

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9 

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10 

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Anil Kumar, G. Wagner, R. R. Ernst and K. 

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16 

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17 

V. V. Krishnan, N. Murali and Anil Kumar, J. 

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18 

A. Majumdar and R. V. Hosur, J. Magn. Reson. 

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Mz 

23 

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Lett, 161, 554-560 (1989). 

32 

H. Oschkinat, D. Limat, L. Emsley and G. Bodenhausen, 

J. Magn. Reson. 81, 13-42 (1989). 

33 

C. Dalvitt, J. Magn. Reson. 95, 410-416 

(1991). 

34 

V. A. Daragan and K. H. Mayo, Chem. Phys. 

Lett. 206, 393-400 (1993). 

35 

R. Bruschweiler, C. Griesinger and R. R. Ernst, 

J. Am. Chem. Soc. 111,8034-8035 (1984). 

36 

C. Dalvitt and G. Bodenhausen, J. Am. Chem. 

Soc. 110,7924 (1988). 

37 

S. Wimperis, J. M. Bohlen and G. Bodenhausen, 

J. Magn. Reson. 77, 589-595 (1988). 

38 

M. Ernst and R. R. Ernst, Fifth Chianti Workshop 

on Magnetic Resonance, San Miniato, Italy, 

June, 1993. 

39 

V. V. Krishnan and Anil Kumar, J. Magn. Reson. 

92, 293-311 (1991). 

40 

V. A. Daragan, T. N. Khazanovich and A. U. 

Stepanyants, Chem. Phys. Lett. 26, 89-92 (1974).

126 

41 

L. G. Werbelow and D. M. Grant, J. Chem. 

Phys. 63, 544-556 (1975). 

42 

J. Courtieu, P. E. Fagerness, D. M. Grant, J. 

Chem. Phys. 65, 1202-1205 (1976). 

43 

L. Di. Bari, J. Kowaleswski and G. Bodenhausen, 

J. Chem. Phys. 93, 7698-7705 (1990). 

44 

I. Burghardt, R. Konrat and G. Bodenhausen, 

Mol. Phys. 75, 467-486 (1992). 

Bulletin of Magnetic Resonance

Vol. 16, No. 1/2 127 

Contents 

Detection of Two-Quantum Nuclear Coherence by Nuclear 

Quadrupole Induced Electric Polarization 


II. Nuclear Electric Resonance Detection 

III. Experimental Results 

IV. Conclusions 




The Nobel Prize in Chemistry for 1991 was conferred 

upon Richard Ernst for his development of 

elegant NMR techniques and fundamental theory 

applicable to various types of physical and chemical 

analysis. These include in particular specific 

innovations and extensions of pulse Fourier transform 

methods for NMR high resolution spectroscopy 

and MRI. We of the NMR community especially 

salute and congratulate Ernst because the 

Prize brings honor as well upon all of us who have 

had so much fun in a field that has yielded many innovations 

over a time period much longer than many 

of us expected. The field of NMR in its development 

reached a stage where one could hardly distinguish 

whether chemists or physicists were doing NMR. 

Now the chemists, or rather the physical chemists 

and biologists, have taken over the field of NMR, 

and they are doing most of the "physics" nowadays. 

As a consequence, because chemical technology is 

more "up front" in the public and commercial eye, 

people know more about NMR than ever before. 

Also MRI has had an impact upon the public in the 

1 Present address: MRSC, Department of Radiology, 

UCSF, San Francisco, California 94143 

David C. Newitt 1 and Erwin L. Hahn 

Physics Department 


Berkeley, California, 94720 

127 

127 

129 

131 

132 

132 

medical and health world, and in scientific research 

the analytic techniques made possible by NMR have 

been applied in one form or another to investigations 

in many disciplines. 

In contrast to the utilitarian revelations of the 

works of Richard Ernst, the authors of this article 

present in his honor the results of an experiment 

of the opposite sort, which they hope is acceptable, 

because most likely the reader will not find our experiment 

particularly useful. As will be seen in what 

follows, the electric resonance detection experiment 

is an interesting exercise in proving that nature will 

yield the reciprocal of a given effect if one goes to 

the trouble to expose it. In the course of interpreting 

such experiments one is forced to improve his 

understanding of things he thought he understood 

but in fact did not. 

II. Nuclear Electric Resonance 

Detection 

Magnetic one-quantum signal detection of the 

evolution of multiquantum nuclear spin coherence


always requires the transfer of multiquantum superposition 

states into one-quantum superposition 

states (1). A directly observed two-quantum nuclear 

electric quadrupole radiation signal is conceivable 

theoretically but beyond observation experimentally 

(2), since it would be of the order of 10~~ 9 the size 

of an average NMR signal. In this gedanken experiment 

one would place the sample in a quadrupole 

capacitor to detect the direct two-quantum nuclear 

quadrupole radiation signal. However, for nuclear 

quadrupole moments located at noncentrosymmetric 

crystal sites, as in the case of As and Ga in 

GaAs, net local electric-dipole moments are induced 

in neighboring atoms by the electric quadrupole field 

of the nucleus. In this report we assume the "stick 

and ball model" (3). The electric field due to the 

nuclear quadrupole falls off as r~ 4 , where r is the distance 

between the point nuclear quadrupole and the 

point neighboring polarizable atom. The summation 

of quadrupole induced dipole moments over the 

set of nearest-neighbor atoms and over the spin ensemble 

yields a detectable macroscopic polarization. 

The polarizability of the local atomic environment 

effectively magnifies (3) the otherwise unobservable 

direct quadrupole radiation signal by a factor on the 

order of 10 +6 , so that a direct electric signal may be 

observed by placing the sample between the plates 

of a capacitor. 

In a previous experiment (3), nuclear electric 

resonance detection (NERD) was first demonstrated 

using the 30 MHz transition of 35 C1 in NaC103. In 

that experiment a small magnetic field was applied 

to remove the degeneracy of the m = ±1/2, ±3/2 

states. The resulting mixed m = ±1/2 states allow 

the development of a detectable electric polarization 

FID signal after a single pulse. The electric 

signal was characterized by a beating of different 

| Am | = 1,2 transition frequencies between the 

mixed m = ±1/2 states and the m = ±3/2 states, 

distinguishable from the beat frequency signature 

produced by stray pickup of a direct nuclear magnetic 

signal at the same Larmor frequency. In GaAs 

the observation of a pure |Am| = 2 transition from 

75 As at the sharply tuned frequency 2u is free of 

any nuclear magnetic signal at frequency to. However, 

there is a small reactive signal pickup transient 

from the transmitter pulses at frequency u>. 

In general the observation of a one-quantum or 

two-quantum electric signal requires that the expec- 

tation values 

I±Iz> = , Tr{p(IzI 

(1) 

be finite, which occurs only if the density matrix 

p is nonlinear in the nuclear spin operators. Thus 

in any system with equally spaced levels (including 

the degenerate NQR 35 > 37 C1 levels in NaC103), it is 

not possible to observe a NERD signal if the initial 

density matrix p is specified by a high temperature 

population distribution proportional to Iz, in which 

case the above traces of odd operators are zero. The 

requirement of a nonlinear p is met in the case of 

the zinc-blende structure, including GaAs and most 

other III—V semiconductors, by applying an external 

static electric field which produces a quadrupole 

shift due to the linear Stark effect (4). In the special 

case of NaClO3 the electric FID signal is observed 

immediately after a single pulse because initial 

signals which beat with one another, associated 

with different frequencies, have different amplitudes, 

which is not the case for GaAs where a minimum of 

two RF pulses is required. 

The NERD-induced polarization effect may be 

denned as the inverse of the linear Stark effect, 

where the former involves oscillating off-diagonal 

elements, and the latter involves on-diagonal elements 

which account for quadrupole frequency 

shifts. Both effects are expressed by the following 

Hamiltonian perturbation in dyadic form (3): with 

electric field gradients. The stick and ball description 

assumes that a nuclear quadrupole point source 

electric field induces polarization in nearest neighbor 

point atoms. This cannot account for the polarization 

spread over charge distributions and covalent 

bonds. Hence the definition of the "stick" distance 

is a vague one. Although one can only predict orders 

of magnitude of signal amplitudes by this approach, 

it is most valuable for predicting the signature and 

the sample orientation dependence of pulse transient 

signals which characterize the NERD phenomena. 

A rough estimate of the NERD signal strength is 

obtained by expressing the local quadrupole electric 

field 

HQ Q = — PQ • E — E 

Q • 

Q (2) 

The macroscopic polarization induced by the precessing 

local quadrupole electric field EQ is given

Vol. 16, No. 1/2 129 

by PQ = N/3a- EQ, where a is the atomic polarizability 

tensor. The Boltzmann factor j3 pertains to 

N participating quadrupole spins in the crystal. The 

electric field and corresponding oscillating voltage V 

on the capacitor plates are given by V = (E-n)d = 

47r(PQ-n)d, where n is normal to the capacitor plate 

and d is the plate separation. The alternative form 

of HQ, applicable to the dc linear Stark effect, defines 

E as the externally applied static electric field, 

where PE = N/3o;E for an isotropic polarizability a. 

Here one views the applied electric field as inducing 

internal atomic dipole moments which interact with 

local nuclear quadrupole electric fields EQ. 

The above model is a less rigorous equivalent of 

the usual analysis in terms of the quadrupole interaction 

as EQ = eQS/r 4 , where S = 25 is taken as the 

Sternheimer antishielding factor, the 75 As gyromagnetic 

ratio 7 = 0.73 MHz/kG, Q = 0.3 • 10" 24 cm 2 , 

a = 10 24 cm 3 (assumed isotropic), ro = 1.2 • 10~ 8 

cm (estimated as one-half the As—Ga lattice distance, 

at the center of the covalent bond), and 

N = 10 22 cm" 3 . Upon application of typical circuit 

parameters, scaled from the estimate given in 

detail in ref. (3), one obtains an approximate ratio of 

the 75 As NERD signal to the conventional magnetic 

NMR signal in the present experiment of about 1/10 

to 1/100. 

III. Experimental Results 

The arrangement for a two-quantum NERD experiment 

consists of two independent resonant circuits: 

an RF transmitter coil tuned to frequency 

w/2ir, inside of which is contained the sample, 

housed between two plates of a receiver capacitor 

tuned to frequency 2w/2vr = 13 MHz. The receiver 

is one used in a typical pulsed NMR system. For 

our measurements a single crystal of semi-insulating 

GaAs with dimensions 1.4 x 1.4 x 0.1 cm 3 is placed 

with the (111) crystal planes parallel to the capacitor 

plates and transmitter coil axis. The circuits 

are cooled to 77 K to reduce noise and ensure high 

resistivity of the GaAs sample. 

Applying the stick and ball model to the structure 

around an As atom shown in Figure 1, using 

isotropic polarizabilities for the four nearest neighbors, 

results in an induced polarization 

aeQ5 . 2 

Pind = "J^Q 8111 6 £> + (£» (3) 

for the (111) crystal orientation described above, 

where 0 is the angle between the static polarizing 

magnetic field Ho and the Stark field Eo. The polarization 

P;nci is summed over the spin ensemble to 

obtain the macroscopic polarization PQ expressed 

in eqn. 2, which is proportional to the signal voltage 

V. 

A DC electric field on the order of |E0 = 

20 kV/cm is applied to the capacitor to provide 

the linear Stark shifts. The Stark-induced electric 

field gradient for this orientation is given by eq = 

2R|Eo|/3, where R = 1.9 x 10 10 cm" 1 is the linear 

Stark coefficient (4) for 75 As. The resulting quadrupole 

frequency shift is 

3 cos 6 — 1 (4) 

The angle 8 = 90° is chosen to provide the maximum 

NERD signal and an wq of the order of 7 kHz for 

the 75 As nuclei. Figure 1 shows the energy-level 

diagram and the NMR and NERD spectra for this 

system. 

Figure 2 shows 75 As two-quantum FID and echo 

signals and the interference between them for a two 

pulse 90x — r — 90~)-x sequence. The inverses of all 

RF pulse widths exceed level broadening and electric 

Stark shifts. The second pulse alternates in phase by 

180° from one two-pulse sequence to the next. The 

alternate data runs are added and subtracted from 

the signal average so that the nuclear signals add but 

the reactive pickup signals from the constant phase 

transmitter pulse cancel out. As the pulse spacing 

time r is increased, the emergence of the electric 

quadrupole echo at t—2r may be seen, although it 

is rapidly attenuated by dephasing due to magnetic 

inhomogenaeties and dipolar interactions. 

The prediction of FID and echo signals may be 

carried out by use of the Majorana formula (5) to 

evaluate spin wave functions and expectation values, 

or a density matrix technique such as that devised 

by Bowden and Hutchison (6) may be used. 

Since the spin levels are broadened by both electric 

quadrupole and magnetic dipolar perturbations, 

we assume for simplicity that the broadenings due 

to these perturbations are independent of one another. 

The echo refocusing of electric strain inhomogeneous 

isochromats in this picture accounts for


CD 

i—l 

c 

ID 

£_ 

0 

i l-Quantum NMR 

* 

i 

i 

i 

i 

i 

i 

i 

i 

i 

1 

i 1 

i / 

2-Quantura NERD 

A 

/ ' 

\ 

/ ' \ M\ 

/ ' M 

; 

A 

-20 -10 0 10 

Frequency Offset (kHz) 

20 

2co-coa 

2co+coa 

Figure 1: Tetrahedral structure of the four nearest neighbors in the zinc-blende structure, with the resulting 

energy-level diagram and NMR and NERD spectra for a spin 1=3/2 nucleus subject to a Stark-induced 

quadrupole shift. In the bottom plot the dotted line shows the spectrum of a normal NMR experiment on 

Stark shifted 75 As in GaAs, while the solid line shows the spectrum of a two-quantum NERD experiment on 

the same sample. 

observed NERD echo signals. As we are detecting 

a two-quantum coherence, the magnetic broadening 

isochromats do not refocus at the same time as the 

quadrupole interactions for a two pulse sequence. 

Therefore the NERD echo amplitude lifetimes T2e 

remain very short, on the order of a millisecond, because 

of the defocusing caused by inhomogeneous 

and homogeneous magnetic broadening. The quadrupole 

echo is visible because the quadrupole dephasing 

time, T£Q = 50 /xs, is significantly less than 

the magnetic dephasing time, TgM = 200 us. 

The dotted lines in Figure 2 are fits to the data 

according to this simple model of independent magnetic 

and quadrupolar broadening, where only the 

pulse separation time t is varied. The inverse of 

the quadrupole broadening of the system varied between 

T20 — 40 and 50 /zs during the data runs 

because of progressive damage to the sample caused 

by the applied high voltage. We believe this damage 

is caused by the migration of charged defects 

or impurities, which over time produces changes in 

bulk strain and results in charge layers at the (111)

Vol. 16, No. 1/2 131 

en 

-i—i 

cz 

~* 

(Arb. 

r—\ 

CD 

C 

CD 

~—4 

1 

w 

X 

-100 0 100 

Time 

\y 

200 

(US) 

55 

20 

320 

240 

• ^ — 

jiS 

US 

300 400 

Figure 2: The detected two-quantum NERD signals following two 90° pulses. The time r between the two 

pulses is shown for each run and the runs have been offset so the second pulse is at t = 0 on the horizontal 

axis. The dotted lines are fits to the experimental data, as described in the text. 

surfaces. We have found that a fixed electric field 

ranging up to lkV/cm caused by these charge layers 

opposes the applied field Eo. This fixed field can be 

removed by warming the sample to room temperature 

for several hours, which then yields an increase 

of T^Q to 80-90 [is. 

A clearer measurement of the two-quantum 

NERD echo may be obtained by observing the 

echoes produced by a three pulse sequence, as this 

allows simultaneous or near-simultaneous refocusing 

of the magnetic and electric isochromats. For 

spin 1 = 3/2 nuclei the first two pulses generate 

one-, two-, and three-quantum coherences among 

the spin levels, and the third pulse in turn transfers 

these prepared coherences among the levels 

to provide observable two-quantum electric signals. 

Figure 3 shows two sets of data obtained from a 

90x — Ti — 90-tx ~ T 2 ~ 90x sequence. In the top 

trace T\ = 50 [is, which is relatively short compared 

to the inhomogeneous dephasing time T^Q = 70 fis. 

A portion of the two-quantum coherence seen as an 

FID following the second pulse is recreated after the 

third pulse as an echo at time t = 2T2 = 1 /is. In this 

case both the electric and the magnetic isochromats 

refocus at approximately the same time. The bottom 

trace shows the multiple echoes formed by refocusing 

of the electric isochromats when T\ = 200 /xs 

and T2 = 600 [is are both longer than T^Q. We 

observe the three echoes labeled El, E2, and E3 at 

times predicted by the inhomogeneous broadening 

model, but cannot achieve a reasonable fit to the 

signal amplitudes for the different echoes for these 

three pulse sequences. 

IV. Conclusions 

The direct detection of electric two-quantum coherence 

signals from an I = 3/2 spin system has 

been demonstrated without the need for an extra 

RF pulse to transfer unobservable two-quantum coherence 

to one-quantum coherence as required in


CO 

-I-J 

cz 

en 

-i—i 

CO 

RF Pulses 

RF Pulses 

500 1000 

Time (|is) 

E2 E3 

^ .. A A , 

1500 

Figure 3: Two-quantum NERD FID and echo signals 

from three 90° x-axis pulses. Pulses are applied 

at t = 0, 50 and 550 /is for the top trace and t = 0, 

200 and 800 /xs for the bottom. The stronger signals 

after the second pulse in each trace are scaled 

down by a factor of five relative to the signals after 

the third pulse, and the lower trace is scaled up by 

a factor of two relative to the upper trace. Three 

quadrupole echoes, centered at t = 1000, 1200, and 

1400 /xs, labeled El, E2, and E3, are visible in the 

bottom trace. 

NMR multiquantum methods. The time evolution 

of the two-quantum coherence is mapped out in one 

"shot," whereas for NMR an additional inspection 

pulse must be applied for successive times in repeated 

pulse sequences to map out the two-quantum 

coherence. 

Our echo analysis does not take into account the 

complicated magnetic dipolar echo-dephasing effects 

caused by the pulse reorientation of local dipolar 

fields. Many of the predicted echoes which occur 

following three pulses not only interfere with FID 

transients, but interfere among themselves if they 

are to be observed at all because the echo decay lifetimes 

are too short to always clearly resolve them. 

In some instances a predicted echo cannot be seen, 

or an echo predicted to be canceled out by the applied 

pulse sequence phase cycling is clearly visible. 

We do not understand this at present and hope to 

resolve it in a later report. 

Given a fixed number of pulse excited spins over 

the entire spin spectrum, the initial FID amplitude 

of the electric polarization depends only upon the 

local distance and polarizability of atomic bonds 

and electrons in the vicinity of precessing nuclear 

quadrupole moments. On the other hand the initial 

FID signal in a conventional pulsed NMR experiment 

would be independent of these properties. One 

may conceive of experiments in which variations of 

these properties may be studied in terms of observed 

changes in the initial electric signal. Applications of 

external pressure, acoustic vibrations, and electric 

fields which induce charge layers in semiconductor 

structures or charge density waves in special systems 

are examples for future investigations. 

Beyond the two-quantum case in NMR, an advanced 

and rigorous review of multiple quantum 

NMR spectroscopy techniques is provided in a 

highly comprehensive account (7) of modern NMR 

techniques by Ernst and co-authors. Under one 

cover, this account as a book includes descriptions 

of the important researches by Ernst and his collaborators 

at the ETH, Zurich which were recognized 

by the Nobel Prize. 


We gratefully acknowledge helpful discussions 

with John Keltner, Larry Wald, and Charles Pennington 

and the support of the National Science 

Foundation. 


1 

C P. Slichter, "Principles of Magnetic Resonance," 

3rd ed., Chapter 9, Springer-Verlag, New 

York/Berlin 1990. 

2 

M. Bloom and M. A. LeGros, Can. J. Phys. 

64, 1522 (1986). 

3 

T. Sleator, E. L. Hahn, M. B. Heaney, C. Hilbert 

and J. Clarke, Phys. Rev. B 38, 8609 (1988). 

4 

N. Bloembergen, in "Proceedings, XI Colloque 

Ampere Conference on Electric and Magnetic Resonance, 

Eindthoven, 1962" (J. Smidt, Ed.), p. 39

Vol. 16, No. 1/2 133 

North-Holland, Amsterdam, 1963; F.A. Collins and 

N. Bloembergen, J. Chem. Phys. 40, 3479 (1961). 

5 

E. Majorana, Nuovo Cimento 9, 43 (1932); F. 

Bloch and I. I. Rabi, Rev. Mod. Phys. 17, 237 

(1945). 

6 

G. J. Bowden and W. D. Hutchison, J. Magn. 

Reson. 67, 403 (1966). 

7 

R. R. Ernst, G. Bodenhausen and A. Wokaun, 


and Two Dimension," Chapter 5, Clarendon Press, 

Oxford, 1990.

134 

Calender of Forthcoming 

Conferences in Magnetic 

Resonance 

April 9-10, 1994 

Symposium on In Vivo Magnetic Resonance 

Spectroscopy VII, San Francisco, California 

The Symposium is designed to be a participatory 

workshop in which many of the attendees will 

make presentations concerning their recent experimental 

work. The Symposium will emphasize experimental 

methods and techniques directed towards in 

vivo magnetic resonance spectroscopy. 

The Symposium is being held just prior to the 

35th ENC meeting, which is also being held in the 

Monterey area at Asilomar. Thus, the Symposium 

is scheduled to facilitate attending both the Symposium 

and the ENC conference. 

The deadline for receiving abstracts is 

March 4, 1994. 

For further information, please contact: 

Radiology Postgraduate Education 

Room C-324 

University of California School of Medicine 

San Francisco, CA 94143-0628 USA 

Phone: 415-476-5731 

Fax: 415-476-9213 

For Registration, please call: 

Phone: 415-476-5808 

Fax: 415-476-0318 

April 10-15, 1994 

35th Experimental Nuclear Magnetic Resonance 

Conference, The Asilomar Conference Center, Pacific 

Grove, CA (USA) 

For information contact: 

ENC 

815 Don Gaspar Avenue 

Santa Fe, NM 87501 

Phone: 505-989-4573 

Fax: 505-989-1073 


June 5-10, 1994 

12th European Experimental NMR Conference, 

Oulu, Finland 

The scientific program will be arranged by the 

Local Organizing Committee with the support of 

national NMR specialists and the EENC International 

Committee. Following the traditions of these 

conferences a selected group of leading experts will 

be invited to give talks on the most recent topics in 

experimental NMR spectroscopy. In addition to the 

lecture program two poster sessions will take place. 

A limited number of contributions will be selected 

for oral presentation on the basis of the submitted 

abstracts. The organizers will endeavor to create 

a setting in which new ideas and critical discussion 

will provide a good basis for innovative thinking and 

practical conclusions. 

The scientific program includes the following 

topics: 

-New experimental NMR techniques 

-Multidimensional NMR techniques 

-Relaxation and molecular dynamics 

-NMR application to organic and inorganic 

chemistry 

-NMR in liquid crystals and polymers 

-NMR in solids 

-NMR in biological systems 

-In-vivo NMR spectroscopy 

-NMR microscopy and imaging in material sciences 

-Data analysis 

For scientific and general information contact: 

Prof. Jukka Jokisaari 

University of Oulu 

Department of Physics 

FIN-90570 Oulu FINLAND 

Phone: +358-81-553 1308 

Fax: +358-81-553 1287 

E-mail: FYS-JJ@Finou.Oulu.Fi 

Lab. Manager Petri Ingman 

University of Oulu 


FIN-90570 Oulu FINLAND 

Phone: +358-81-553 1622 

Fax: +358-81-553 1603 

E-mail: Pingman@Phoenix.Oulu.Fi

Vol. 16, No.1/2 135 

July 16-21, 1995 


Conference, Sydney, Australia 

The venue will be the University of Sydney, 

where there is low-cost student accomodation in addition 

to many local hotels and "serviced apartments." 

The project already has strong support 

from the University, State and Federal authorities. 

A particular effort is planned to raise money for 

student bursaries to help younger scientists participate 

in the meeting. The ISMAR conference will be 

combined with the Australian Magnetic Resonance 

meeting which is usually well attended. It is proposed 

to commemorate the 50th anniversary of the 

discovery of NMR at this meeting. 

The ISMAR-95 Committee: 

Leslie D. Field (Chairman), David Doddrell 

(Convenor), William Bubb (Secretary), Frances 

Separovic (Treasurer), Peter Barron, Michael Batley, 

Graham Bowden, Paul Callaghan, Bruce Cornell, 

John Hanna, Garry King, Glenn King, Philip 

Kuchel, Bridget Mabbutt, George Mendz, Barbara 

Messerle, Carolyn Mountford, Jim Pope, and Graham 

Town. 

For further details contact: 

Dr. Les Field, Chair ISMAR-95 

Department of Organic Chemistry 

University of Sydney 

Sydney NSW 2006 Australia 

Phone: 612-692-2060 

Fax: 612-692-3329 

E-mail: ismar-95@biochem.su.oz.au 

The editor would be pleased to receive 

notices of future meetings in the field of 

magnetic resonance so that they could be 

recorded in this column.

136 

Recent Magnetic Resonance Books 

1 Magnetic Resonance of Carbonaceous Solids 

(1993). Edited by Robert E. Botto and Yuzo 

Sanads. American Chemical Society, Washington, 

D.C., 664 p. (Advances in Chemistry Series). 

1 Chemical Society Reviews Volume 22 No. 5 

(1993). Contents: Bruker Lecture: The nuclear Zeeman 

interaction in electron resonance. The EPR 

spectra of organic radical ions. On the possibility of 

an insulator-metal transition in alkali metal-doped 

zeolites. Some aspects of the electron paramagnetic 

resonance spectroscopy of a d-transition metal compounds. 

Why can transient free radicals be observed 

in solution using ESR techniques? Progressive saturation 

and saturation transfer ESR for measuring 

exchange processes of spin-labelled lipids and 

proteins in membranes. Polarized positive muons 

probing free radicals: A variant of magnetic resonance. 

The chemistry of cyclopropylmethyl and 

related radicals. 

l 2D NMR: Density Matrix and Product Operator 

Treatment by Gheorghe D. Mateescu and Adrian 

Valeriu, Case Western Reserve University (1993). 

ISBN 0-13-013368-x, 200 pp. 

1 Basic One- and Two-Dimensional NMR Spectroscopy, 

Second, Enlarged Edition by Horst 

Friebolin, Organic Chemical Institute, Heidelberg, 

Germany (1993). VCH Publishers, Inc., New York. 

ISBN 1-56081-796-8. 

1 Structure Elucidation by NMR in Organic 

Chemistry - A Practical Guide by Eberhard Breitmaier 

(1993). John Wiley k Sons, New York, NY. 

Hardback: ISBN 0-471-93745-2, $63.95; Paperback: 

ISBN 0-471-93381-3, $35.00. 

1 Progress in Biophysics and Molecular Biology 

Volume 59 No. 3 (1993). Contents: Hydration and 

heat stability effects on protein unfolding. Derivation 

of locally accurate spatical protein structure 

from NMR data. 

1 Progress in Nuclear Magnetic Resonance Spectroscopy 

Volume 25 No. 1-3(1993). Contents: NMR 

and fractal properties of polymeric liquids and gels. 

x New additions to the list. 



Volume 25 No. 4(1993). Contents: Sulfur- 

33 NMR. Photo-CIDNP of biopolymers. 


Volume 25 No. 5 (1993). Contents: NMR 

studies of drug-DNA interactions. NMR studies of 

dynamics in nucleic acids. 


Volume 25 No. 6 (1993). Contents: 

Density dependence of rotational and translational 

molecular dynamics in liquids studied by high pressure 

NMR. 

1 Annual Reports on NMR Spectroscopy Volume 

26 (1993). Contents: Applications of NMR to food 

science. Structural studies of peptides and polypeptides 

in the solid state by nitrogen-15 NMR. Application 

of high-resolution NMR spectroscopy to polymer 

chemistry. The application of cation NMR to 

living systems: Multinuclear NMR of azo dyestuffs. 

1 Biological Magnetic Resonance: NMR of Paramagnetic 

Molecules Volume 12 (1993). Contents: 

NMR methodology for paramagnetic proteins. Nuclear 

relaxation in paramagnetic metalloproteins. 

Paramagnetic relaxation of water protons: effects 

of nonbonded interactions, electron spin relaxation, 

and rotational immobilization. Proton NMR spectroscopy 

of model hemes. Proton NMR studies of 

selected paramagnetic heme proteins. Heteronuclear 

magnetic resonance: applications to biological 

and related paramagnetic molecules. NMR of polymetallic 

systems in proteins. 

Fundamentals of Nuclear Magnetic Resonance 

by J. W. Hennel and J. Klinowski (1993). Contents: 

Elements of quantum mechanics, magnetic properties 

of the nucleus, nuclear paramagnetism, motion 

of pagnetization, continuous wave NMR, pulsed 

NMR, NMR liquids, the dipolar interaction, and nuclear 

magnetic relaxation. ISBN 0-582-06703-0. 

1 Biological Magnetic Resonance: Carbohydrates 

and Nucleic Acids (1992). Contents: Highresolution 

X H-NMR spectroscopy of oligosaccharidealditols 

released from muncin-type O-glycoproteins. 

NMR studies of nucleic acids and their complexes.

Vol. 16, No.1/2 137 


Volume 24 No. 6 (1992). Contents: Solid 

state NMR studies of vanadia based catalysts. NMR 

studies of superionic conductors. 

1 Biological Magnetic Resonance: In Vivo Spectroscopy 

Volume 11 (1992). Contents: Localization 

in clinical NMR spectroscopy. Off-resonance frame 

spin-lattice relaxation: Theory, and in vivo MRS 

and MRI applications. NMR methods in studies 

of brain ischemia. Shift-reagent-aided 23 Na NMR 

spectroscopy in cellular, tissue, and whole-organ 

systems. In vivo 19 F NMR. In vivo 2 H NMR studies 

of cellular metabolism. Some applications of ESR to 

in vivo animal studies and EPR imaging. 

1 Magnetic Resonance Microscopy: Methods and 

application in materials science, agriculture and 

biomedicine (1992). Edited by Bernhard Blumich 

and Winfried Kuhn. VCH, New York, 604 p. 

Progress in Nuclear Magnetic Resonance Spectroscopy 


Multiple-quantum NMR methods. 

Advances in Magnetic and Optical Resonance 

Volume 17 (1992). Contents: Nonlinear incoherent 

spectroscopy. NOESY. Zero-field spin dynamics 

and relaxation. 

Carbohydrate and Nucleic Acid Structure by 

Magnetic Resonance Spectroscopy, Biological Magnetic 

Resonance Volume 10 (1992). Edited by 

Lawrence J. Berliner and Jacques Reuben, Plenum 

Publishing Corp., New York. 

In-Vivo Spectroscopy, Biological Magnetic Resonance 

Volume 11 (1992). Edited by Lawrence J. 

Berliner and Jacques Reuben, Plenum Publishing 

Corp., New York. 


Volume 24 No. 5 (1992). Contents: Relaxation 

in the rotating frame in liquids. Sodium magnetic 

resonance imaging and chemical shift imaging. 

Quadrupolar effects transferred to spin-1/2 magicangle 

spinning spectra of solids. 

Magnetic Resonance Spectroscopy in Biology 

*New additions to the list. 

and Medicine (1992). Edited by J. D. De Certaines, 

W. M. M. J. Bovee and F. Podo. Contents: Presents 

the experimental and basic aspects of functional and 

pathological tissue characterization of MRS. A balance 

is drawn between the basic science, practical 

technologies and biomedical applications. Covers 

recent developments in the field: localization, 2D 

NMR, spectroscopic imaging, data quantification 

and quality assessment, as well as the basic principles 

of magnetic resonance spectroscopy. Pergamon 

Press, ISBN 0-08-0410170 (flexicover) $70.00; ISBN 

0-08-0410189 (hardcover) $170.00. 

In Vivo Magnetic Resonance Spectroscopy I. 

Probeheads and Radiofrequency Pulses, Spectrum 

Analysis (1992). Edited by M. Rudin, Springer, 345 

pp. ISBN 0-387-54547-6 (hardcover) $119.00. 

In Vivo Magnetic Resonance Spectroscopy II. 

Localization and Spectral Editing (1992). Edited by 

M. Rudin and J. Seelig, Springer, 368 pp. ISBN 

0-387-55022-4 (hardcover) $119.00. 

In Vivo Magnetic Resonance Spectroscopy III. 

In Vivo MR Spectroscopy: Potential and Limitations 

(1992). Edited by M. Rudin and J. Seelig, 

Springer, 293 pp. ISBN 0-387-55029-1 (hardcover) 

$98.00. 

Annual Reports on NMR Spectroscopy. Volume 

24 (1992). Contents: Developments in solid state 

NMR. Solid state NMR imaging. NMR studies of 

interfacial phenomena. NMR measurements of intracellular 

ions in living systems. 199 Hg NMR parameters. 

Applications of NMR methods in coal 

research. 

Progress in Nuclear Magnetic Resonance Spectroscopy. 

Volume 24 No. 3 (1992). Contents: Structural 

characterization of noncrystalline solids and 

glasses using solid state NMR. 


Volume 24 No. 2 (1992). Contents: 129 Xe 

NMR as a probe for the study of microporous solids: 

A critical review. Simulation of 2D NMR spectra for 

determination of solution conformations of nucleic 

acids. 

Progress in Biophysics & Molecular Biology. 

Volume 57 No. 1 (1992). Contents: ENDOR and

138 

EPR of metalloproteins. Free energy transduction 

in polypeptides and proteins based on inverse temperature 

transitions. 


Volume 24 No. 1 (1992). Contents: 13 C 

NMR spectroscopy of oleanane triterpenoids. 

1 Nuclear Magnetic Resonance. Volume 22 

(1991/1992). Contents: NMR books and reviews. 

Theoretical and physical aspects of nuclear shielding. 

Applications of nuclear shielding. Theoretical 

aspects of spin-spin couplings. Applications of spinspin 

couplings. Nuclear spin relaxation in liquids. 

Solid state NMR. Multiple pulse NMR. Natural 

macromolecules. Synthetic macromolecules. Confer 

mational analysis. Nuclear magnetic resonance 

spectroscopy of living systems. Nuclear magnetic 

resonance imaging. NMR of paramagnetic species. 

NMR of liquid crystals and micellar solutions. 

Êlectron Spin Resonance Volume 13A (1991). 

Contents: Organic radicals in solution. Organic radicals 

in solid matrices. Organic radicals in solids. 

Fluorescence detected magnetic resonance. Theoretical 

and physical aspects of ESR. Applications of 

ESR in polymer chemistry. Industrial applications 

of ESR spectrometry. 

l NMR Basic Principles and Progress: NMR at 

Very High Field Volume 25 (1991). Contents: A 

brief history of high resolution NMR. Molecular 

orientation in high-field high-resolution NMR. Behavior 

of the NMR relaxation parameters at high 

fields. Structural studies of biomolecules at high 

field. Solid state NMR in high and very high magnetic 

fields. 

NMR Basic Principles and Progress: High Pressure 

NMR Volume 24 (1991). Contents: Solid state 

NMR studies at high pressure. High pressure NMR 

investigations of motion and phase transitions in 

molecular systems. High pressure NMR studies on 

water and aqueous solutions. High resolution variable 

pressure NMR for chemical kinetics. Glass 

cell method for high pressure, high-resolution NMR 

measurements. Applications to the studies of pressure 

effects of molecular confirmation and structure. 

x New additions to the list. 


NMR Basic Principles and Progress: Deuterium 

and Shift Calculation Volume 23 (1991). Contents: 

Deuterium NMR in the study of site-specific 

natural isotope fractionation (SNIF-NMR) dynamic 

NMR spectroscopy in the presence of kinetic hydrogen/deuterium 

isotope effects. The IGLOO- 

Method: Ab-initio calculation and interpretation of 

NMR chemical shifts and magnetic susceptibilities. 

Principles of Nuclear Magnetic Resonance Microscopy 

(1991). Clarendon Press (Oxford University). 

New York, 492 p. 

NMR at Very High Field (1991). Guest editor: 

J. B. Robert, Springer, 168 pp. ISBN 0-387-52946-2 

(hardcover) $79.00. 

Transition Metal Nuclear Magnetic Resonance 

(1991). Edited by P. S. Pregosin. Contents: The 

book contains a collection of review articles concerned 

with measuring, understanding and using the 

nuclear magnetic resonance spectra of the metals of 

Groups 3-12. The reader is provided with a view 

on how these nuclei are currently being approached, 

and what information can be obtained. The authors 

have liberally reproduced spectra as well as correlations 

relating metal-NMR data to different physical 

characteristics of their molecules. 364 pp. ISBN 

0-444-88176-X $169.00. 

Chemical Reviews. Volume 91 No. 7 (1991). 

Contents: Low-temperature solid-state NMR of proteins. 

Structure and dynamics of solid polymers 

from 2D- and 3D-NMR. NMR under high gas pressure. 

Nuclear magnetic resonance at high temperature. 

Gas-phase NMR spectroscopy. Selective 

excitation in high-resolution NMR. Application of 

the linear prediction method to NMR spectroscopy. 

High-resolution fluorine-19 magnetic resonance of 

solids. NMR determination of enantiomeric purity. 

Solid-state NMR studies of molecular sieve 

catalysis. Pulsed electron-nuclear double resonance 

methodology. Multidimensional NMR and data processing. 

One- and two-dimensional high-resolution 

solid-state NMR studies of zeolite lattice structures. 

Solid-state NMR studies of DNA structure and dynamics. 

Spin-lattice relaxation of coupled nuclear 

spins with applications to molecular motion in liquids.

Vol. 16, No. 1/2 139 


Volume 23 No. 2 (1991). Contents: Solvent 

signal suppression in NMR. 


Volume 23 No. 3 (1991). Contents: Modern 

methods of NMR data processing and data evaluation. 

H NMR magic angle spinning (MAS) studies 

of heterogenous catalysis. 

NMR - Basic Principles and Progress. Volume 

23: Deuterium and Shift Calculation (1991). 

Eds.: P. Diehl, E. Fluck, H. Gunther, R. Kosfeld, 

J. Seelig. Contents: M.L. Martin, G.J. Martin, 

Nantes, France: Deuterium NMR in the Study of 

Site-Specific Natural Isotope Fractionation (SNIF- 

NMR); H.-H. Limbach, Freiburg, FRG: Dynamic 

NMR Spectroscopy in the Presence of Kinetic Hydrogen/Deuterium 

Isotope Effects; W. Kutzelnigg, 

U. Fleischer, M. Schindler, Bochum, FRG: The 

IGLO-Method: Ab-initio Calculation and Interpretation 

of NMR Chemical Shifts and Magnetic Susceptibilities. 

Approx. 270 pp. 92 figs. 45 tabs. 

ISBN 3-540-52949-7. 


24: High Pressure NMR (1991). Eds.: P. Diehl, 

E. Fluck, H. Gunther, R. Kosfeld, J. Seelig, J. 

Jonas, University of Illinois, Urbana, IL (Guest- 

Ed.). Contents: D. Brinkmann, Zurich, Switzerland: 

Solid-State NMR Studies at High Pressure; 

K.O. Prins, Amsterdam, The Netherlands: High 

Pressure NMR Investigations of Motion and Phase 

Transitions in Molecular Systems; J. Jonas, Urbana, 

IL: High Pressure NMR Studies of the Dynamics 

in Liquids and Complex Systems; E.W. Lang, H.- 

D. Liidemann, Regensburg, FRG: High Pressure 

NMR Studies on Water and Aqueous Solutions; 

J.W. Akitt, A.E. Merbach, Lausanne, Switzerland: 

High Resolution Variable Pressure NMR for Chemical 

Kinetics; H. Yamada, Kobe, Japan: Glass Cell 

Method for High-Pressure, High-Resolution NMR 

Measurements. Applications to the Studies of Pressure 

Effects on Molecular Conformation and Structure. 

Approx. 270 pp. 148 figs. 28 tabs. ISBN 

3-540-52938-1. 


25: NMR at Very High Field (1991). Eds.: P. Diehl, 

E. Fluck, H. Gunther, R. Kosfeld, J. Seelig, J.B. 

Robert, CNRS, Grenoble, France (Guest-Ed.). Contents: 

R. Freeman, Cambridge, UK, J.B. Robert, 

Grenoble, France: A Brief History of High Resolution 

NMR; E.W. Bastiaan, C. MacLean, Amsterdam, 

The Netherlands: Molecular Orientation 

in High-Field High-Resolution NMR; D. Canet, 

Vandoeuvre-les-Nancy, France, J.B. Robert, Grenoble, 

France: Behaviour of the NMR Relaxation Parameters 

at High Fields; D. Marion, Orl ans, France: 

Structural Studies of Biomolecules at High Field; U. 

Haeberlen, Heidelberg, FRG: Solid State NMR in 

High and Very High Magnetic Fields. Approx. 175 

pp. 44 figs. 10 tabs. ISBN 3-540-52946-2. 

Modern NMR Techniques and Their Application 

in Chemistry (Practical Spectroscopy Series Volume 

11). Edited by Alexander I. Popov and Klaas Hallenga, 

Marcel Dekker, Inc. (1991). ISBN 0-8247- 

8332-8 

Annual Reports of NMR Spectroscopy. Volume 

23 (1991). Contents: NMR studies of isolated spin 

pairs in the solid state. The oxidation-state dependence 

of transition-metal shieldings. The Cinderella 

nuclei. Permutation symmetry in NMR relaxation 

and exchange. Nuclear spin relaxation in organic 

systems and solutions of macromolecules and aggregations. 

NMR of coals and coal products. 



Nuclear magnetic resonance imaging in the solid 

state. Applications of three-and four-dimensional 

heteronuclear NMR spectroscopy to protein structure 

determination. Angiography and perfusion 

measurements by NMR. 

EPR Imaging and in vivo EPR (1991). Edited 

by Gareth R. Eaton, Sandra S. Eaton, and Keiichi 

Ohno, CRC Press, Boca Raton, FL. 320 pages, 

$89.95, ISBN: 0-8493-4923-0. 

Basic One-and Two-dimensional NMR Spectroscopy 

by Horst Friebolin (1991). VCH, New York. 

344 pages. 


Volume 16 (1991). Contents: Laser excitation and 

detection of magnetic resonance. Deuterium relaxation 

in molecular solids. On the growth of multiple

140 

spin coherences in NMR of solids. 

Progress in Biophysics & Molecular Biology Volume 

56 No. 1 (1991). Contents: An evaluation of 

computational strategies for use in the determination 

of protein structure from distance constraints 

obtained by nuclear magnetic resonance. 

Radiospectroscopy of Natural Substances by B. 

F. Alekseev, Y. V. Bogachev, V. Z. Drapkin, A. S. 

Serdjuk, N. B. Strakhov and S. G. Fedin, Engl. Tr. 

Norell Pr., New Jersey, 1991. 

Nuclear Magnetic Resonance Volume 21 (1990/ 

1991). Contents: Theoretical and physical aspects 

of nuclear shielding. Applications of nuclear shielding. 

Theoretical aspects of spin-spin couplings. Applications 

of spin-spin couplings. Nuclear spin relaxation 

in liquids. Solid state NMR. Multiple pulse 

NMR. Natural macromolecules. Synthetic macromolecules. 

Conformational analysis. Nuclear magnetic 

resonance spectroscopy of living systems. Nuclear 

magnetic resonance imaging. Oriented molecules. 

Heterogeneous systems. 

NMR Applications in Biopolymers (1990). 

Edited by J. W. Finley, S. J. Schmidt, and A. S. 

Serianni. Plenum Press, New York. 515 pages. 

Fourier Transforms in NMR, Optical, and Mass 

Spectrometry, a User's Handbook (1990). Alan G. 

Marshall and Francis R. Verdun. Elsevier, Amsterdam 

and New York. 450 pages. Paperback, $49.95. 

ISBN 0-444-87412-7. 

Nuclear Magnetic Resonance Volume 19, Specialist 

Periodical Reports (1990). G. A. Webb, Senior 

Reporter. Royal Society of Chemistry, London. 

591 pages. $252.00. ISBN: 0-85186-422-8. 

A Compilation of Chemical Shift Anisotropies 

(1990). T. Michael Duncan. The Farragut Press, 

Madison, Wisconsin. 158 pages. $24.95, paperback; 

$39.95, hardcover. ISBN: 0-917903-01-3. 

NMR, Basic Principles and Progress Volume 

22, Isotope Effects in NMR Spectroscopy (1990). 

Edited by P. Diehl, E. Fluck, H. Giinther, R. 

Kosfeld, and J. Seelig. Springer-Verlag, New 

York/Berlin. 173 pages. $75.00. ISBN: 0-387- 

51286-1. 


Electron Paramagnetic Resonance of Exchange 

Coupled Systems by A. Bencini and D. Gatteschi, 

Springer Verlag, Berlin, 1990. 

Modern Pulsed and Continuous Wave Electron 

Spin Resonance by L. Kevan and M. K. Bowman 

(1990). Wiley, New York. 

Transition Ion Electron Paramagnetic Resonance 

by J. R. Pilbrow, Clarendon Press, Oxford, 

1990. 

Electron Paramagnetic Resonance of Exchange 

Coupled Systems by A. Bencini and D. Gattechi 

(1990). Springer, 287 pp. ISBN 0-387-50944-5 

(hardcover) $83.00. 

Isotope Effects in NMR Spectroscopy by S. 

Berger, J. M. Risley, N. M. Sergeyev and 

R. L. Van Etten (1990). Springer, 173 pp. ISBN 

0-387-51286-1 (hardcover) $83.00. 

17 O NMR Spectroscopy in Organic Chemistry 

(1990). Edited by David W. Boykin. This book provides 

a comprehensive review of the application of 

17 O NMR spectroscopy to organic chemistry. Topics 

include the theoretical aspects of chemical shift, 

quadrupolar and J coupling; 17 O enrichment; the 

effect of steric interactions on I7 O chemical shifts of 

functional groups in flexible and rigid systems; the 

application of 17 O NMR spectroscopy to hydrogen 

bonding investigations; mechanistic problems in organic 

and bioorganic chemistry; and 17 O NMR spectroscopy 

of oxygen monocoordinated to carbon in 

alcohols, ethers, and derivatives. CRC Press, Inc., 

Florida. ISBN: 0-8493-4867-6. 

Advances in Magnetic and Optical Resonance. 

Volume 15 (1990). Contents: Iterative methods in 

the design of pulse sequences for NMR excitation. 

Electron-nuclear polarization transfer in the nuclear 

rotating frame. Multipole NMR. Solid state and solution 

NMR of nonclassical transition metal polyhydrides. 

Low-frequency magnetic resonance with 

a dc SQUID. 

Advances in, Biophysical Chemistry. Volume 1 

(1990). Contents: Stable-isotope-assisted protein 

NMR spectroscopy in solution. 31 P and H twodimensional 

NMR and NOESY-distance restrained 

molecular dynamics methodologies for defining

Vol. 16, No.1/2 141 

sequence-specific variations in duplex oligonucleotides: 

A comparison of NOESY two-spin approximation 

and the relaxation matrix analyses. 

NMR study of B- and Z-DNA hairpins of d[(CG)3] 

in solution. Molecular dynamics simulations of carbohydrate 

molecules. Diversity in the structure of 

hemes. 

Biological Magnetic Resonance. Volume 9 

(1990). Contents: Phosphorus NMR of membranes. 

Investigation of ribosomal 5S ribonucleic acid solution 

structure and dynamics by means of highresolution 

nuclear magnetic resonance spectroscopy. 

Structure determination via complete relaxation 

matrix analysis (CORMA) of two-dimensional nuclear 

overhauser effect spectra: DNA fragments. 

Methods of proton resonance assignment for proteins. 

Solid-state NMR spectroscopy of proteins. 

Methods for suppression of the H2O signal in proton 

FT/NMR spectroscopy: A review. 


Vol. 25 pt. 5 (1990). Contents: Solid 

state NMR techniques for the study of surface phenomena. 

A primer on isotopic labeling in NMR investigations 

of biopolymers. Vanadium-51 NMR. 

One-dimensional and Two-dimensional NMR 

Spectra by Modern Pulse Techniques. Koji Nakanishi. 

(1990). University Science Books, Mill Valley, 

CA. 234 p. 

Annual Reports on NMR Spectroscopy. Volume 

22 (1990). Contents: Metal-ion NMR studies of ion 

binding. NMR studies of ligand-macromolecule interactions. 

Applications of NMR in the analysis of 

agrochemicals and pesticides. NMR nuclear shielding 

and the electronic structures of macromolecules. 

207 Pb-NMR parameters. Nuclear spin relaxation in 

diamagnetic fluids part 1. General aspects and inorganic 

applications. 


Volume 22, pt. 1 (1990). Contents: Scaling 

in one and two dimensional NMR spectroscopy 

in liquids. Oligosaccharide conformations: Application 

of NMR and energy calculations. Relaxation 

matrix analysis of 2D NMR data. 

Progress in Magnetic Resonance Spectroscopy. 

Volume 22, Part 3 (1990). Contents: NMR parameters 

of alkynes. Improved methods for quantitative 

spectral analysis of NMR data. 

Advances in Magnetic Resonance. Volume 14 

(1990). Contents: Measurement of dipole-dipole 

cross correlation by triple-quantum filtered twodimensional 

exchange spectroscopy. Assessment 

and optimization of pulse sequences for homonuclear 

isotropic mixing. Spin-1/2 description of spins 3/2. 

Optical pumping measurements of nuclear cross relaxation 

and electrix doublets. 

Quarterly Review of Biophysics. Volume 23 

(Number 1) February 1990. Contents: Biosynthetic 

incorporation of 15 N and 13 C for assignment and interpretation 

of nuclear magnetic resonance spectra 

of proteins. Heteronuclear filters in two-dimensional 

[1H, 1H]- NMR spectroscopy: combined use with 

isotope labelling for studies of macromolecular conformation 

and intermolecular interactions. 

Quarterly Reviews of Biophysics. Volume 23 

(Number 2) May 1990. Contents: Heteronuclear 

three-dimensional NMR spectroscopy of isotopically 

labelled bioilogical macromolecules. Deuterium labelling 

in NMR structural analysis of larger proteins. 

Use of deuterium labelling in NMR studies of 

antibody combining site structure. 

Principles of Nuclear Magnetic Resonance in 

One and Two Dimensions. Richard R. Ernst and 

Geoffrey Bodenhausen. Oxford University Press. 

1990. 640 pp. paper $39.95 

A Dictionary of Concepts in NMR. S.W. 

Homans. Oxford University Press. 1990. 352 pp. 

$80.00 

Nuclear Magnetic Resonance: Principles and 

Theory. Ryozo Kitamaru. Elsevier, New York, 

1990. 

Quantum Description of High-Resolution NMR 

in Liquids. Maurice Goldman. Oxford University 

Press. 1990. 288 pp. $65.00 

Modern Pulsed and Continuous-wave Electron 

Spin Resonance. Edited by Larry Kevan and 

Michael K. Bowman. Wiley, New York, 1990. 440 

P-

142 

Principles of Magnetic Resonance, Second Ed. 

by C. P. Slichter, Springer, New York, 1990. 655 p. 

Soviet Scientific Reviews Section B: Chemistry 

Reviews. Volume 14, Part 2 (1990). Contents: 

Pulsed NMR study of molecular motion in solids. 

Progress in Nuclear Magnetic Resonance Spectroscopy, 

Volume 22 No. 6 1990. Contents: Fieldcycling 

relaxometry of protein solutions and tissue. 

Implications for MRI. Solid state NMR studies of 

local motions in polymers. 

Nuclear Magnetic Resonance, Volume 20 1989/ 

1990. Contents: NMR books and reviews. Theoretical 

and physical aspects of nuclear shielding. Applications 

of nuclear shielding. Theoretical aspects 

of spin-spin couplings. Applications of spin-spin 

couplings. Nuclear spin relaxation in liquids and 

gases. Solid state NMR Multiple pulse NMR Natural 

macromolecules. Synthetic macromolecules. 

Conformational analysis. Nuclear magnetic resonance 

spectroscopy of living systems. Nuclear magnetic 

resonance imaging of living systems. NMR of 

paramagnetic species. NMR of liquid crystals and 

micellar solutions. 

Modern NMR Spectroscopy. A Workbook of 

Chemical Problems (1989). Jeremy K. M. Sanders, 

Edwin C. Constable, and Brian K. Hunter. Oxford 

University Press, Oxford and New York. 119 pages. 

Paperback, $19.95. ISBN 0-19-855287-4. 

Instrumental Effects in Homodyne Electron 

Paramagnetic Resonance Spectrometers (1989). R. 

Czoch and A. Francik. Translation by Anna Fidzinska. 

Wiley, New York. $69.95. ISBN 0-470-20897- 

X. 

Spin Labeling: Theory and Applications. Edited 

by L. J. Berliner and J. Reuben, Academic Press, 

New York, Vol. 3, 1989. 

Advanced EPR: Applications in Biology and Biochemistry. 

Edited by A. J. Hoff, Elsevier, Amsterdam, 

1989. 

Pulsed EPR: A New Field of Applications. 

Edited by C. P. Keijzers, E. J. Reijerse and J. 

Schmidt, North Holland, Amsterdam, 1989. 


Electron Spin Resonance, Specialist Periodical 

Report, Vol. 11B, Royal Chemical Society, London, 

1989. 

Nuclear Magnetic Resonance: Structure and 

Mechanism. Edited by Norman J. Oppenheimer and 

Thomas L. James, Academic Press, New York, 1989. 

507 p. (Methods in Enzymology). 

NMR Spectroscopy and Polymer Micro structure. 

The Conformation Connection. Alan E. Tonelli. 

VCH, New York, 1989. x 252 pp., illus. $69.50. 

Methods in Stereochemical Analysis. 

Annual Reports on NMR Spectroscopy, Vol. 21. 

Edited by G. A. Webb, Academic Press, London, 

1989. ISBN: 0-12-505321-5. 

EPR of Exchange-Coupled Systems. Alessandro 

Bencini and Dante Gatteschi. Springer-Verlag, 

Berlin, 1989. 287 pages. ISBN: 0-387-50944-5. 

Nuclear Magnetic Resonance, Vol. 18, Specialist 

Periodical Reports, G. A. Webb, Senior Reporter, 

Royal Society of Chemistry, London, 1989. 511 

pages. ISBN: 0-85186-412-0. 

Advances in Magnetic Resonance Imaging. 

Edited by Ephraim Feig, IBM Research Division, 

Thomas J. Watson Research Center. Ablex Publishing 

Corporation. 1989. 272 pp. $55.00

Vol. 16, No. 1/2 143 

Instructions for Authors 

Because of the ever increasing difficulty of keeping 

up with the literature there is a growing need for 

critical, balanced reviews covering well-defined areas 

of magnetic resonance. To be useful these must 

be written at a level that can be comprehended by 

workers in related fields, although it is not the intention 

thereby to restrict the depth of the review. 

In order to reduce the amount of time authors must 

spend in writing we will encourage short, concise 

reviews, the main object of which is to inform nonexperts 

about recent developments in interesting aspects 

of magnetic resonance. 

The editor and members of the editorial board 

invite reviews from authorities on subjects of current 

interest. Unsolicited reviews may also be accepted, 

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ARRANGEMENT: Considerable thought 

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144 

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The future of EPR, S. S. Eaton and G. R. Eaton . . . . . .:. . , •/ , . . v3. . . ., . ; 149 

Review of the EPR Data on ns^Centers in Crystals, S. V. Nistor, 

D. Schoemaker and I. Ursu . .... ... . 193 

Survey of the EPR Community on the EPR Database and Related Projects, 

C. Rudowicz - 224 

Electron Paramagnetic Resonance Investigations of the Cu 2+ ion in a Variety 

of H o s t Lattices - A Review, R. M. Krishna and S. K. Gupta .......... 239 

Calendar of Forthcoming Conferences 292 

Recent Magnetic Resonance Books . . . . ... ,]\-_',. -;•'., ; -,Z..--.:-29&-[ 

Instructions for Authors . . -.-.,-.''-.... : .:.^w; :• -%\ ; .,-.,298:. 

Addendum to D.C: Newitt and E.L. Hahn, 

V o l . 1 6 , 1 2 7 ( 1 9 9 4 ) .... ... ..... . . . . . . . . . . . . . , . . ;; v . . . 2 9 9 i

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Contents 

The Future of EPR 

Sandra S. Eaton and Gareth R. Eaton 


University of Denver 

Denver, Colorado 80208 


A. Results of the 1987 Workshop 151 

B. Research Advances 152 

C. Goals for the 1992 Workshop 153 

D. A Perspective on EPR 154 

E. Current Themes in EPR 155 

F. Software 155 

G. Applications of EPR 155 

H. The Literature of Magnetic Resonance 157 

II. State of the Art Lecture - New EPR Methodologies: James S. Hyde 159 

A. Q-Band EPR 160 

B. Pseudomodulation 161 

C. Multiquantum EPR 161 

D. Respondent - Melvin P. Klein 162 

E. Discussion 163 

III. State of the Art Lecture - In Vivo EPR: Harold M. Swartz 163 

A. The Scope of In Vivo EPR 163 

B. Respondent - Lawrence Berliner 165 

C. Discussion 165 

IV. State of The Art Lecture - FT EPR and High-Field EPR: Jack H. Freed 166 

A. Comparison with NMR 166 

B. FT EPR 166 

C. High Frequency EPR 167 

D. Respondent - Linn Belford 169 


V. State of The Art Lecture - Pulsed EPR: Arthur Schweiger 169 

A. Comparison with NMR 169 

B. New EPR Detection Schemes 170 

C. Recent Instrumental Innovations in Pulsed EPR 173 

D. Respondent - David Singel 173 


VI. Panel Discussion - High resolution EPR 174 

A. Kinetics 174 

B. Longitudinal Detection 175 

C. Signal to noise 175 

149


D. Ex Vivo EPR; Aqueous Samples in Flat Cells 175 

E. Dielectric Resonators 175 

F. Small and/or Dedicated EPR Spectrometers 176 

VII. Panel Discussion — In Vivo EPR and Imaging 176 

A. The Question of Sample Size 176 

B. Frequency Scaling 176 

C. Interpretation of In Vivo Spectra 177 

D. Magnetic Field and Magnetic Field Gradient Control 177 

E. Low Frequency and Imaging Spectrometers 177 

F. Nitric Oxide In Vivo 177 

G. Noise in FT EPR, EPR Imaging and In Vivo EPR 178 

VIII. Panel Discussion — New Perspectives on Spins 179 

A. SQUIDs in EPR 179 

B. Multiquantum EPR 179 

C. Microwave Source Phase Noise 179 

D. Pulsed ENDOR 180 

E. Dissemination of Modern Techniques 180 

F. Software for Visualization of EPR Data 180 

IX. Summary on Instrumentation and Methodology 181 

X. The Funding Agency Perspective 181 

A. Questions Regarding Funding of EPR in the USA 181 

B. Information from the Presentation by John Beisler, DRG, NIH 182 

XI. The Vendor Perspective 183 

A. Bruker (Dieter Schmalbein) 183 

B. JEOL (Jack Francis) 184 

C. Micro-Now (Clarence Arnow) 184 

D. Oxford Instruments (Mark Woolfrey) 184 

XII. Summary Perspective 184 

A. The Horizons of EPR 185 

B. Where EPR is Today 185 

C. The Future 186 

XIII. Acknowledgment 186 

XIV. References 187

Vol. 16, No. 3/4 151 


An NIH-sponsored Workshop on the Future of 

EPR was held in Denver, Colorado, August 7, 1992, 

following the 15th International EPR Symposium. 

Participants in the Workshop included about 65 researchers 

from several countries, representatives of 

six corporations, and a representative of NIH. This 

review of the state of EPR and expression of concerns, 

hopes, and predictions for the future is based 

on the contributions of the participants in the Workshop. 

Those who presented state-of-the-art lectures, 

served as respondents, or participated in panel discussions, 

are identified in appropriate places in the 

text. When a comment/question from another participant 

in the Workshop presented information that 

should be identified with that person, the person is 

identified in the text. Otherwise, the questions and 

answers are summarized rather than quoted. The 

panel members, and Colin Mailer, Keith Madden, 

Carmen Arroyo, Ralph Weber, Francisco Jent, Ron 

Mason, and Peter Hofer were particularly active in 

the discussions. 

Some references to the literature have been provided 

to lead the reader to more extensive discussions. 

In addition to the well-known review series in 

magnetic resonance, five recent books provide summaries 

of individual topics in EPR (1-5). 

A Workshop on the Future of EPR has a lot to 

cover because EPR is such an extensive field. Our 

focus for this Workshop is a vision of the future. 

Scientists should not shy away from predicting the 

future of their field. In fact, scientists have to be 

better at this than the self-styled futurists. It is 

their profession - scientists spend much of their time 

preserving the best of the past and creating a better 

future. 

A. Results of the 1987 Workshop 

Five years ago researchers gathered to say what 

the cutting edge results from research laboratories 

implied for the future needs of EPR spectroscopy 

(6,7). At the first Workshop in 1987 there was a 

lot of controversy and a lot of discussion, but there 

emerged from the Workshop a fairly clear statement 

that the EPR field as it was then certainly needed 

the very best sensitivity and signal-to-noise (S/N) 

that one could get in the standard X-band region 

of the spectrum. This was a very high priority. 

Also important, was to exploit the information that 

could come from broadband EPR. Researchers really 

wanted a frequency range of 60 MHz to greater 

than 250 GHz, but suggested that 1-18 GHz would 

be a nice goal for the commercial instruments that 

would end up in all laboratories. As a short term 

matter the goal was narrowed to 3-15 GHz. In summary, 

the designs that emerged from the 1987 Workshop 

included two types of spectrometer, with the 

features listed: First, a 9-9.6 GHz EPR optimized 

for sensitivity and S/N. Second, a broadband EPR 

spectrometer, with the features: 

• 3-15 GHz (1-18 GHz preferred; ultimately, 60 

MHz to >250 GHz) 

• not an automatic frequency control (AFC)locked 

cavity system (except for in vivo studies) 

• encode the data from the whole modulation 

cycle 

• solid state microwave source 

• resonators designed specifically for applications 

• open architecture 

• computer control (with human interface); 

• standard computer interface 

• computer(s) integrated with the hardware to 

run the spectrometer 

• attached workstation 

• two bridges: continuous wave (CW) and saturation 

recovery (SR) electron-spin-echo (ESE) 

and Fourier transform (FT) 

• 1-2 GHz and 35 GHz accessories 

• electromagnet-based 

There were a number of issues and concerns with 

these choices: 

• narrow-band components versus broadband 

components 

• loss of sensitivity with broadband components


• loss of magnetic field homogeneity away from 

the center field 

• maybe there would need to be a g=2 spectrometer 

and a metals spectrometer 

There was vigorous debate in 1987 about 

whether the limited R&D effort available for EPR 

should be applied to ultimate sensitivity X-band 

CW; broadband EPR; or pulsed EPR. 

In 1987 many other needs were expressed, from 

need for a better high-power travelling-wave-tube 

amplifier (TWT), to need for a better measure of 

what the temperature really is at the sample, to 

needs relating to educating the next generation of 

scientists who will apply EPR to solving important 

problems in materials science and biomedical problems. 

Some of the additional needs expressed in 

1987 were discussed in the report on that Workshop 

(6). 

The design criteria for an instructional EPR 

spectrometer synopsizing the desires expressed in 

1987 would be: 

• a 3 or 4-inch electromagnet, with power supply 

that could be run from a standard 110 V wall 

outlet; 

• no cooling water required for operation for up 

to 3 hours at 3400 G; 

• >600 G scan range; 

• 100-150 mG homogeneity over the sample; 

• microwave performance of the Bruker EMS 

104; 

• data output in a format that students could 

take home to work with on a PC or Mac. 

While variable-temperature, etc., are nice, as a 

practical matter one would not do much of this in 

an undergraduate lab. The principles of rigid vs. 

fluid solution can be demonstrated with two samples, 

rather than freezing one sample. Membrane 

melting can even be done with two different samples 

rather than one sample as a function of temperature. 

With regard to proposals concerning instructional 

and routine spectrometers, there was controversy: 

some people think there should not be a large 

"low tech" market for EPR (as there is in NMR) because 

of the relative spectral anisotropies, and the 

attendant spectral interpretation difficulty. 

1. Progress Since 1987 

In spite of the gap between aspirations and reality, 

there has been an incredible amount of progress 

in the past five years (Table 1). The prototype 

of the Bruker ESP380 pulsed EPR spectrometer 

was on display at the Symposium the week of the 

1987 Workshop. Now this has matured into an instrument 

that can revolutionize EPR spectroscopy 

for those who rely upon commercial instruments. 

Bruker also responded to the needs expressed at the 

first Workshop for a low-cost instrument with the 

ECS 106. Bruker has produced the EMS 104, the first 

EPR designed for quantitative analysis. JEOL has 

produced a pulsed EPR spectrometer also, and has 

developed low-noise solid state microwave sources so 

that they do not use klystrons in their spectrometers. 

A small EPR spectrometer developed in Russia 

is being marketed by Norell in the USA. Sumitomo 

Special Metals has two versions of very small EPR 

spectrometers for instructional use. A small EPR 

which nearly matches the specifications set forth in 

1987 for an instructional EPR spectrometer was on 

display by Micro-Now at the Symposium immediately 

preceding the Workshop. Note that these criteria 

were strictly for a CW spectrometer. There 

is need to introduce time-domain techniques to students 

if EPR is to prosper. Software specifically for 

EPR has been enhanced greatly by the efforts of 

Bruker and of Scientific Software Services. Oxford 

Instruments introduced new products for temperature 

control in response to needs expressed at the 

first Workshop. 

Progress since 1987 Workshop has been striking. 

EPR spectroscopists recognized the benefits of better 

communication, and an enhanced community of 

users, with the result that the International EPR 

(ESR) Society formed. It now has ca. 1000 members 

in >35 countries. 

B. Research Advances 

The advances in EPR during the past five years 

have been phenomenal. A totally new branch of 

EPR, multiquantum EPR (MQEPR), has been developed 

by James S. Hyde and his colleagues, so 

now we should categorize EPR in three modes: CW, 

pulse and multiquantum. 

There has been a rebirth of spin labeling (a technique 

which had become thought of as "the old

Vol. 16, No. 3/4 153 

Bruker 

JEOL 

Norell 

Table 1: Summary of Commercial EPR Products 

ECS-106 low-cost EPR 

ESP 300E fully computer-controlled research spectrometer 

ESP 380 pulsed ESE and FTEPR, first demonstrated in 1987 

EMS 104 first EPR designed for quantitative analysis 

Pulsed ENDOR and stochastic ENDOR 

pulsed EPR 

L-band EPR 

PC-based EPR data station 

low-noise Gunn diode source 

cavity for aqueous samples 

small EPR built by St. Petersburg Instruments, Ltd. 

Micro-Now 

Model 8400 on display at the 1992 EPR Symposium 

Sumitomo Special Metals - Spin-X and Spin-XX 

Scientific Software Services 

PC-based acquisition/manipulation software for Bruker, Varian, and Micro-Now spectrometers 

Medical Advances - resonators, and development effort on an S-band bridge 

Oxford Instruments - variable temperature accessories 

ESR900 can now use nitrogen as well as helium 

automatic transfer lines 

CF935 dewars for wide range of S- to Q-band cavities 

sensor to measure temperature at the sample position 

Wilmad Glass - quartzware accessories 

high precision EPR tubes 

a standard sample for EPR 

stuff') due to combinations of loop gap resonators 

(LGRs) and site-directed mutagenesis. 

Both academic and industrial laboratories have 

developed lower noise oscillators. 

Indeed, there have been so many major advances 

in EPR since 1987 Workshop that there is room only 

to list a few keywords (Table 2). The vendors of 

EPR equipment and software have an almost impossible 

task of predicting the needs of those who 

develop and those who use EPR. Part of the purpose 

of this Workshop was to have researchers share 

their aspirations with manufacturers. 

C. Goals for the 1992 Workshop 

With this background, the goals for the 1992 

Workshop were: 

• Participants would learn about the power of 

new spectroscopic techniques that they could 

apply in their research. 

• Critique the predictions and desires expressed 

during the first Workshop in 1987. 

• Provide a new, updated, perspective on the 

EPR instrumentation needs of research. 

• Present a new set of predictions and criteria.

154 

Table 2: Listing of Recent Research Advances 


multiquantum EPR 

multiple resonance 

(especially pulsed ENDOR and multiquantum ENDOR) 

multifrequency 

saturation recovery 

ENDOR (especially high frequency CW ENDOR) 

high-field EPR and high-frequency EPR 

low frequency EPR 

spin echo at frequencies other than X-band 

new types of resonators 

LGR and bridged LGR, dielectric resonator 

multidimensional imaging 

in vivo EPR 

detection of radical adducts in biological fluids 

rebirth of spin labeling via 

site specific mutagenesis and oximetry 

many new pulsed EPR techniques 

FT-EPR (Bruker pulsed FTEPR) 

pulsed field gradients 

pulsed electron nuclear double resonance (ENDOR) using Davies sequence 

FT-electron-electron double resonance (FT-ELDOR) 

electron spin transient nutation 

ESEEM sequences for improved modulation depths, etc. 

ENDOR signals in small, lossy protein crystals 

low phase noise oscillators 

low noise microwave preamplifiers 

digital oscilloscopes for signal processing 

useful level of computer power at each spectrometer 

much more sophisticated data acquisition and analysis software available 

pseudomodulation - modeling of the transfer characteristics of an instrument 

rebirth of solutions to biological problems by applying the above advances 

To focus discussion, the Workshop was organized 

around seeking answers to two questions: 

• What are the EPR instrumental or software 

limits to important experiments in science? 

• What are the technology limits on instrumentation 

and software for EPR? 

These goals were not as crisply addressed as was 

hoped in advance, in part because some participants 

were too focused on what they had accomplished 

with limited resources. In addition, EPR spectroscopists 

have become acculturated to cleverly working 

within boundary conditions imposed by commercial 

instruments and funding, and had difficulty 

expressing what these limits are. 

D. A Perspective on EPR 

As an overall perspective on EPR, consider that so 

far most EPR has been CW, and most studies have

Vol. 16, No. 3/4 155 

been done in the linear response region, using homogeneous 

magnetic fields, using magnetic field scans, 

and almost all of this has been done in TE102 cavities 

(Table 3). Most of what we celebrate as benchmark 

results are exceptions to this generalization. 

EPR is becoming (as was revealed at the 15th International 

EPR Symposium in the days preceding 

the Workshop) multi-frequency, multi-dimensional, 

multi-everything; it is non-linear, time-domain; 

most of the experiments now are being done with 

home-built resonators designed specifically for the 

purpose; often experiments are being done in gradient 

fields for imaging or in vivo (Table 4). These 

changes are becoming necessary because of the 

many applications for EPR. 

E. Current Themes in EPR 

Pulsed, fourier transform, non-linear CW, imaging, 

and in vivo techniques are increasingly important. 

Resonators are being designed to fit the needs 

of the experiment, rather than fitting the experimental 

design to the resonator (or deciding not 

to do the experiment). Very low (e.g., 250 MHz) 

and very high (e.g., 250 GHz) frequency EPR have 

expanded our view of spins. Multiple pulse techniques 

are bringing to EPR powerful insights analogous 

to those that are becoming commonplace in 

NMR. Imaging and in vivo techniques are letting us 

see EPR spectra at each location in space, permitting 

us to perform, for example, oximetry in living 

animals. EPR without magnetic field modulation 

opens new vistas, in saturation recovery EPR, fastresponse 

EPR, and multiple-quantum EPR. These, 

and other current themes in EPR are listed in Table 

5. 

F. Software 

In modern EPR, software is so important that it 

deserves special emphasis in this report. One must 

pay as much attention to the quality of the software 

as to the hardware. Increasingly scientists see 

that software is a central and crucial part of EPR 

spectroscopy. Color graphics displays can help visualization 

of the information content of the EPR 

data, but can also deflect attention from the computational 

artifacts. The field needs a series of wellposed 

problems against which new software can be 

tested. For example, in the field of image analy- 

sis there are standard problems such as the Shepp- 

Logan head phantom, against which each new algorithm 

is tested. 

The crucial issues with regard to quality of EPR 

software are highlighted in Table 6. 

G. Applications of EPR 

There are many fascinating aspects of spin physics 

to be explored, and impressive new tools with which 

to explore them. However, the funding needed for 

these exploratory voyages will come largely because 

the insights to be gained have such important applications. 

To emphasize the immediate relevance of EPR to 

biomedical research, some of the applications in Table 

7 are categorized by NIH Institute. Far beyond 

the simple characterization of organic free radicals 

and transition metal complexes, there are applications 

in dental research, research on aging, research 

on the eye, etc. The list is of things that people have 

already done. This Workshop was more concerned 

to look toward the future - applications that are not 

well-known yet. 

Consider for a moment the EPR spectrum in Figure 

1. The spectrum in Figure 1 has terrible S/N, 

but it is an important sample - a sample of brain 

tissue. The purpose in showing it is not to discuss 

the questions of artifacts, etc., but to point out that 

the interpretation would be enormously improved if 

one could achieve at least an order of magnitude improvement 

in S/N. Then, consider how much more 

meaningful it would be if it were in vivo instead 

of dissected tissue. Then consider potential applications 

to heart, lung, etc. As we look toward the 

future, we should envision making this measurement 

of the EPR spectrum of brain tissue not on excised 

tissue but in vivo, localized, with at least an order of 

magnitude improvement in S/N, using the panoply 

of EPR spectroscopy techniques that have been reported 

at the EPR Symposium. 

H. The Literature of Magnetic Resonance 

According to information provided by Chemical 

Abstracts, about 4 times as many NMR as EPR 

papers were cited in CA in 1991. In 1986 the ratio 

was 3.2. It is possible that the leveling off in recent 

years reflects a maturing of CW EPR techniques to


Table 3 

EPR has been 

CW 

LINEAR RESPONSE REGION 

MAGNETIC FIELD SCAN 

HOMOGENEOUS MAGNETIC FIELD 

TE102 CAVITY 

Table 4 

EPR is becoming 

MULTI-FREQUENCY 

MULTI-DIMENSIONAL 

NON-LINEAR 

TIME DOMAIN 

PURPOSE-BUILT RESONATORS 

HETEROGENEOUS SAMPLES 

GRADIENT FIELDS 

3225.0 3235.0 3245.0 3255.0 3265.0 3275.0 3285.0 3295.0 3305.0 3315.0 3325.0 

Figure 1: X-band EPR spectrum of a piece of excised brain tissue, frozen and kept at ca. -70°C until the 

EPR spectrum was recorded at — 160°C.

Vol. 16, No. 3/4 157 

Table 5: Current Themes in EPR 

Multifrequency and multi-dimensional EPR. 

Very low frequency EPR. 

Low-frequency in vivo spectroscopy. 

Very high frequency EPR. 

High-magnetic-field EPR. 

Non-linear CW EPR. 

EPR imaging. 

Oximetry combined with imaging. 

EPR without magnetic field modulation. 

Multiple-quantum EPR. 

Saturation recovery EPR. 

Fast-response EPR. 

Emphasis on the time domain as well as on the frequency domain. 

Pulsed EPR. 

Multiple pulse techniques. 

Fourier transform EPR. 

New EPR pulse sequences. 

Magnetic field dependence in ESEEM studies. 

Multiple frequency electron spin echo. 

Applications of ESEEM to metalloenzymes. 

Practical aspects of spectrometer construction. 

Resonators designed to fit the needs of the experiment. 

Slow-wave and non-resonant microwave structures. 

Design and construction of loop-gap resonators. 

In vivo EPR. 

Spin-trapping studies in vivo. 

ENDOR of metal ions. 

Software standards and portability in the EPR community. 

Calculational and experimental aspects of molecular motion. 

Mathematical methods for the interpretation of time-domain EPR. 

Interpreting electron spin echo data. 

EPR simulation problems. 

the point that EPR does not get mentioned in the 

title or abstract, even though it was central to the 

paper. 

There is a troubling concern among EPR spectroscopists 

about financial support. Many people 

feel that the applications of EPR are more important 

than has become common knowledge. One perspective 

uses number of published papers as a measure 

of the overall importance to science. Table 8 

compares numbers of papers published in that part 

of science that explores electron spins and that part 

of science that uses other analytical methodologies. 

These numbers are just for the topics covered in 

Chemical Abstracts, which covers only about 12,000 

journals (a small subset of science). Over a fiveyear 

period EPR has grown but some other topics 

are growing very rapidly. Vendor decisions about 

their allocation of effort and resources, and funding 

agencies deciding upon allocation of resources, are 

responses to perceptions of whether this quantification 

of journal articles also reflects importance. 

C. P. Poole, in Vol 4, no. 2 of the EPR Newslet-


'(Some would like to add "infallibility" to this list!) 

ter, (August 1992) reviewed the EPR (ESR) literature 

covered in Physical Abstracts, Georef, Medline, 

Chemical Abstracts, etc. His review reveals 

that there are some 55,000 papers that have EPR 

or ESR in the title or abstract. Only a hundred of 

them are about ELDOR. But ELDOR is very important. 

One can't apply these numbers directly to 

inform funding decisions. However, the numbers are 

readily available, and will be used (and misused), 

so people concerned about planning for the future 

should be aware of them and learn to use them in 

an intelligent way. 

II. State of the Art Lecture 

- New EPR Methodologies: 

James S. Hyde 

Since the 1987 Workshop there has been a major 

advance in Q-band (35 GHz) EPR technology (8, 

9). In the past Hyde has focused the community on 

going to lower frequency (S-band or L-band) (10- 

14), but at this Workshop Hyde presented an emphasis 

on going to higher frequency. The message 

is the same - there are advantages in doing EPR 

away from X-band. The vendors should lead with 

appropriate products for research. Multifrequency 

capability should be widely available. 

A. Q-Band EPR 

A recent paper in RSI (9) brought several recent 

advances together to greatly improve Q-band performance. 

The contributing advances were each first 

Table 6: Software Issues a 

Function (applicability, boundary conditions) 

Performance (accuracy, speed, throughput) 

Operational Characteristics (user friendly?!) 

Installability 

Data Security and Protection 

Compatibility (and migratability) 

Serviceability (updating, etc.) 

Documentation 

Support (especially when "locally written") 

developed for or demonstrated at a lower EPR frequency, 

but now they jointly revolutionize Q-band 

EPR. The key contributors are low-noise microwave 

sources, loop-gap resonators, low-noise GaAsFET 

microwave preamplifiers, and pseudomodulation for 

resolution enhancement. The basic ideas were expressed 

at the Workshop 5 years ago. When taking 

advantage of modern low-noise GaAsFET microwave 

amplifiers, overall system improvement requires 

also decreasing the phase noise of the oscillator 

(15, 16, 17). The improved Q-band spectrometer 

incorporates two essential components - a 

GaAsFET preamplifier and a Gunn diode source. 

There is also a physically small 125 cm long reference 

arm electrical length equalizer that was created 

in a block by making two halves with a numerically 

controlled mill and screwing them together. The 

following equation, from the book by Robbins (18), 

summarizes the phase noise problem, as the phase 

noise density to carrier ratio: 

N, op 1 FkT /fo\ 2 

P 2P4QUW 

where Nop is the phase noise at frequency fm relative 

to a reference frequency fo; F is the noise figure 

characteristic of the device, Q is the quality factor of 

the tank to which the device is coupled. The power 

P is on both sides of the equation. The key message 

from this equation is that the phase noise increases 

as the square of the microwave frequency, and decreases 

as the square of the Q of the cavity to which 

the device is coupled. 

Hyde used a high-Q TEQH cavity with the Gunn

Vol. 16, No. 3/4 159 

Table 7: Applications of EPR 

Materials Sciences 

Magnetic interactions 

polymer super-paramagnets 

ferrimagnets 

ferromagnets 

anti-ferromagnets 

Superconductivity 

Conducting polymers 

Chemistry and Physics 

Determination and characterization 

Spin distributions 

Orbital interpretations 

Kinetics 

Spin trapping 

Topics arranged in accordance with NIH Institutes: 

General Biomedical 

Study normal and abnormal physiological function and disease states 

as directly, and as non-invasively as possible. 

Characterize metalloproteins, motion of biomolecules, free radical production, etc. 

Measurement of O2 in each organ system. 

Spin labeling to study organ-specific macromolecules and reactions. 

Heart, Lung, and Blood 

Oxidative reactions - ischemia and reperfusion injury 

Study directly the free radicals in heart tissue 

Radical generation during cardiac surgery 

Oxidative damage of lipoproteins 

Radicals in phototherapy 

Detection of NO2 exposure 

Diabetes and Digestive and Kidney Diseases 

Diabetes mellitus, Type I 

Ischemia-reperfusion gastric lesions 

The liver and kidney, along with the heart, contain the highest 

concentrations of free radicals (other than pigmented tissue). 

Halocarbon metabolism 

Arthritis and Musculoskeletal and Skin Diseases 

Inflammation 

Magnetic resonance imaging of extremities 

Characterization of contrast agents for MRI 

Spin labeling study of muscle function


Table 7: Applications of EPR (continued) 

Cancer 

Free radical generation - cancer initiation and promotion 

Vascularization and tumor necrosis 

In vivo measurement of oxygen concentration, as a function 

of growth of tumors, and in relation to therapy 

Toxicity of anticancer drugs (e.g., AZQ) 

Neurological Disorders and Stroke 

Brain ischemia 

Membrane studies 

The Parkinson-like impact of MPTP has been postulated to involve free radicals. 

Role of neuromelanin in Parkinson's disease 

Aging 

Radical reactions in the aging process 

Free radical reactions implicated in Alzheimer's disease. 

Dental Research 

Radiation-induced defects in teeth 

Free radicals in diseased teeth 

Dosimetry based on radiation-induced radicals in teeth 

Eye Institute 

Structure and dynamics of rod outer segments, rhodopsin, etc. 

Free radicals in Green's melanoma 

Subject 

Table 8 a 

atomic spectroscopy 

gas chromatography 

high performance liquid chromatography 

infrared spectroscopy (organic aspects) 

infrared spectroscopy (physicochemical aspects) 

mass spectrometry 

Raman spectroscopy 

ultraviolet and visible spectroscopy 

X-ray analysis and spectroscopy 

carbon & heteroatom NMR 

proton magnetic resonance 

solid state NMR 

electron spin resonance (chemical aspects) 

Number of abstracts 

1986 

4742 

2819 

3738 

2271 

5454 

2840 

2793 

4140 

4055 

4329 

6250 

3329 

1991 

4885 

2762 

4264 

2406 

6915 

4746 

3590 

4326 

4483 

5615 

8707 

895 

3834 

a The data in this table were provided by Chemical Abstracts Service and are based on the number of abstracts 

in their CA Selects categories.

Vol. 16, No. 3/4 161 

diode oscillator. The phase noise turned out to be 

about 23 dB lower than that of the klystron used in 

the Varian Q-band EPR spectrometers. To make an 

oscillator a functional unit of a spectrometer one has 

to have it respond to the 70 kHz AFC (automatic 

frequency control) system. This was accomplished 

with piezoelectric devices, since the displacements 

needed at Q-band are very small. 

Another aspect of phase noise is that its impact 

on the overall system can be reduced by decreasing 

the demodulation of phase noise by the resonator. 

This can be done by using a low-Q resonator, such 

as a LGR. 

The LGR implementation used at Q-band is coupled 

to the waveguide via an iris. The microwaves 

are coupled into the large hole of the LGR first, and 

then into the small hole, so the coupling is effectively 

a 2-step transformer. The LGR holds ca. 30 

nL of liquid sample. The phase noise contribution 

to the noise in the detected EPR signal is 13 dB 

better with the LGR than with the standard TEon 

cavity at Q-band. 

The Varian detection system had a higher noise 

figure than had been realized, and when the lownoise 

preamplifier was used a factor of 10 to 20 improvement 

was realized over a wide range of conditions. 

At high power the noise is from the oscillator. 

At low power the signal is 25 dB higher 

(due to the GaAsFET), but the noise is only 14 dB 

higher. Note that with the low noise amplifier the 

system becomes more sensitive to phase noise, because 

other noise sources are less important. 

Table 9 (9) contains the main lessons from this 

work: the power was adjusted to get the largest signal 

from the sample. The best geometry known at 

X-band yielded S/N = 1815. The best geometry 

known at Q-band yielded S/N = 86, about 20 times 

worse. The minimum number of spins detected was 

reduced by a factor of 200 from X- to Q-band. On 

a molarity basis nothing beats a flat cell in a TM 

cavity at X-band - it is 200 times better than the optimum 

at Q-band on a molarity basis. These swings 

of 200 either way create opportunities to optimize 

an EPR measurement for a particular problem. The 

improvements in the Q-band system have made it 

about 10 times better than the old system for detecting 

nitroxyl radicals in aqueous solution. 

In a Q-band saturation transfer EPR (STEPR) 

study Johnson and Hyde noted that in the disper- 

sion mode the signal intensity increased by a factor 

of 10, and the noise increased by a factor of 10 (20). 

The resultant S/N was about 10 times worse than 

had been demonstrated at X-band. With the recent 

improvements in the Q-band S/N, it can now be predicted 

that one should be able to achieve equivalent 

S/N in STEPR experiments at X-band and Q-band. 

B. Pseudomodulation 

The use of pseudomodulation (21, 22) to provide 

more features in the spectrum that can be parameterized, 

combined with dispersion mode STEPR in 

the new Q-band system, make possible major advances 

in the use of STEPR. Pseudomodulation is 

the convolution of a sinusoidally modulated delta 

function with the digitized data. 

fn(x, t) = f(x) * 6(x — (ax/2)cosu;t) = Efn(x)ncosnu;xtfn(x) 

These terms are derivative-like terms convoluted by 

filter functions: 

This filter function is rather like a Gaussian filter 

- it is sharp in one domain and doesn't ring in the 

other domain. 

This is a formal expression of what happens when 

one has field modulation in an EPR spectrometer. 

When one uses pseudomodulation one gets 

the derivative effect of the modulation simultaneous 

with filtering, with a distortion that is about the 

same as would be caused by the field modulation 

itself. 

C. Multiquantum EPR 

Multiquantum EPR (MQEPR) (23-28) is an exciting 

new opportunity. It looks especially promising 

for Q-band because operation of Q-band EPR 

systems at liquid He temperature is very difficult 

with 100 KHz magnetic field modulation. Magnetic 

field modulation is a severe technical problem for the 

design of EPR resonators. For the future one should


P(mW) a 

S/N 

active volume 

of sample (//L) 

no. of spins in 

the active volume 

minimum detectable 

concentration (M) 

minimum detectable 

no. of spins b 

Table 9: CW EPR Sensitivity Comparisons 

X-Band 

TMno cavity 

with flat cell 

65 

1815 

162 

1.6xlO 14 

8.8xlO~ 10 

8.8xlO 10 

LGR 

1 

186 

1.42 

1.4xlO 12 

8.6xlO~ 9 

7.5xlO 9 

Q-Band 

TEon cavity 

4.1 

103 

0.31 

3xlO u 

1.5xlO~ 8 

2.9xlO 9 

LGR 

0.16 

86 

0.031 

3xlO 10 

1.9xlO" 8 

3.5xlO 8 

a Incident power yielding most intense signal 

b Extrapolated to S/N = 1. For a single line (note that this data is for the 15 N doublet) the minimum 

detectable number of spins would be 50% of the value in the table. 

consider multiquantum EPR as a practical alternative 

to magnetic field modulation. One could pseudomodulate 

to get the normal derivative display. Indeed, 

multiquantum EPR (MQEPR) is proposed for 

many types of experiments, such as high pressure, 

low temperature, etc., where it is technically difficult 

to get modulation to the sample. 

The bridge for MQEPR uses two sources locked 

a specific frequency apart. Irradiation with two microwave 

frequencies is equivalent to irradiating with 

a single frequency that has been sinusoidally modulated. 

Non-linear response of the spin system can 

result in intermodulation sidebands, which can be 

detected. The outputs are the multiquantum transitions, 

which can be combined in various ways to get 

useful displays. MQEPR may be a useful methodology 

in the future of Q-band EPR. 

Multifrequency saturation-recovery (SR) EPR 

measurements of Ti of nitroxyl radicals in fluid solution 

have been measured from ca. 2.5 GHz to 18 

GHz. Ti has been found to be linearly dependent on 

microwave frequency. If the lengthening continues 

to 35 GHz many EPR experiments (SR, STEPR, 

MQEPR) will work better at Q-band than at lower 

frequencies. Everything is handier for liquid phase 

EPR if the Tis get longer. The construction of a 

SR EPR spectrometer at Q-band is now practical 

because pin diode switches and other components 

have improved enough. 

All of these advances taken together (low phase 

noise sources, low-noise preamplifiers, MQEPR, and 

pseudomodulation) lead to the prediction that in the 

next five years Q-band EPR will increase in significance. 

Hyde designed the Varian Q-band system in 1962 

in the V-line series of spectrometers. In 1970 this 

was converted to the E-line series of spectrometers. 

About 10 of these were sold each year, making a 

commercial success within the small EPR market. 

The new Q-band design produced in Hyde's lab is 

close to a commercial design. Drawings have been 

distributed to labs that have requested them. This 

has been produced with federal grant funding associated 

with the mission of the National Biomedical 

ESR Center. 

D. Respondent - Melvin P. Klein 

In photosynthesis research EPR signals extend 

over thousands of gauss and have to be observed 

at temperatures below 10 K. G-anisotropy and exchange 

coupling cause signals to be spread over wide 

magnetic field ranges. Much of biological spectroscopy 

has to be done at very low temperature. With

Vol. 16, No. 3/4 163 

present Q-band systems it is difficult to get below 

20 K. The variable temperature technology is an important 

current effort in which there is need for a lot 

of development. There is a severe problem getting 

magnetic field modulation to the sample - with one 

dewar assembly Klein could get only a few mG of 

modulation at the sample. Since the spectra extend 

over a couple of kG, the very small magnetic field 

modulation does not provide much S/N. The idea of 

multiquantum spectroscopy to enable one to scan a 

true absorption curve is very attractive for studying 

these broad signals. 

The critical factors in the development of the 

NMR field were the use of multiple resonance (e.g., 

13 C while irradiating 1 H), then the FT techniques, 

and now the various multiple pulse technologies. We 

now see a parallel evolution going on in EPR - for 

example, in the recent work of the Freed laboratory 

and the Schweiger laboratory. An important question 

is the extent to which these techniques can be 

combined with the MQEPR Hyde is developing to 

get even better insights. Most of the work of the 

Hyde laboratory has addressed CW and SR EPR. 

Pulsed methods have a very important future, including 

at high frequency. 

It is always helpful to be able to use smaller samples, 

so new resonators that can be more efficient 

and more effective are very important. 

Higher-Q resonators have been made using superconducting 

materials. Possibly the use of high- 

Tc materials will help stabilize solid-state sources. 

E. Discussion 

For earlier types of EPR spectrometers, Harvey 

Buckmaster and coworkers (29, 30) analyzed 

the relation between noise and balance of microwave 

bridges that incorporate a magic T. They also measured 

the characteristics of crystal detectors and 

the improvements obtainable with phase-lock microwave 

frequency stabilizers. The sensitivity in 

1967 of a spectrometer in Buckmaster's lab at 35 

GHz was the same as at 9 GHz. 

Buckmaster has always used oscillator synchronizers 

to decrease the source phase noise. The spectral 

purity of the sources is better than 10 Hz at 35 

GHz. In his spectrometers, the use of a circulator 

in a bridge does not give enough bridge balance to 

achieve the needed phase noise. To achieve the 100 

dB balance needed it was necessary to use a magic 

T, adjust the impedance of the arms, and use critical 

coupling to the resonator. The bridge balance 

depends on the Q of the resonator. Most commercial 

oscillator synchronizers cannot be used with 100 

kHz magnetic field modulation; one has to use much 

lower frequencies, of the order of 1 to 10 kHz. Proof 

that this system works well is the fact that up to the 

available 1 W source power the S/N is proportional 

to power. The system does not have a microwave 

preamplifier. Description of the 35 GHz system was 

not published because it was done exactly the same 

way the 9 GHz work was done, with comparable 

results. 

Twenty years ago Roger Isaacson had results 

with oscillator synchronizers similar to those reported 

here by Buckmaster. Isaacson emphasized 

that the key goal is to decrease klystron noise. It is 

easy to stabilize klystrons with crystal-locked oscillators. 

Beginning many years ago they have performed 

EPR with 4 Hz modulation frequency of 

light in photosynthesis, where long signal decay 

times don't allow higher frequencies. They were able 

to get the noise figure quite low by using a crystal oscillator 

lock on the klystron. Jack Freed uses phase 

locked oscillators to produce low noise at 250 GHz. 

Hyde disagrees with the statement that a circulator 

cannot be used to achieve low phase noise. 

Roger Isaacson also agrees that a magic T is not 

needed. D. A. Knoll in Hyde's lab worked on improving 

isolation in circulators (38). Instinctively, 

one wants to improve the isolation of the circulator 

by the amount of the gain of the GaAsFET amplifier. 

This is not attained by most commercial 

circulators. Colin Mailer reported that he recently 

bought an X-band circulator with high isolation at 

9.0 GHz (Pacific Microwave Technology, Camarillo, 

CA XYG1044-50). 

III. State of the Art Lecture - In 

Vivo EPR: Harold M. Swartz 

A. The Scope of In Vivo EPR 

Exciting in vivo EPR is being done in many 

laboratories around the world (4, 39-49). Some 

3'ears ago it appeared that in vivo EPR imaging was 

not going to be worthwhile, but it is now providing 

important new information. Unlike NMR imaging, 

where the high proton density in the body can


be used for the image, in most cases EPR imaging 

requires adding spins to the biological system. 

This apparent disadvantage is an advantage in some 

classes of experiments, since there is no background 

interfering signal. Thus, one can know what is 

added, and sometimes direct it to the location in 

the body where one wants it. 

The scope of in vivo EPR encompasses (4): 

• low frequency, low resolution, EPR imaging in 

vivo 

• high resolution microscopic imaging in vitro 

• in vivo spectroscopy, with and without spatial 

localization 

Important information can be obtained from in 

vivo imaging even if the resolution is low. The key is 

to keep in mind the biological goals of the measurement. 

High resolution microscopic imaging of biological 

systems is difficult to do at frequencies below 

9 GHz. A useful perspective on in vivo EPR is that 

imaging and high resolution spectroscopy are different 

ends of a continuum of multidimensional spectroscopy. 

For a particular problem one optimizes a 

tradeoff between spatial resolution and spectral resolution. 

This is an important problem that needs to 

be addressed over the next few years. 

There are a variety of detector configurations for 

in vivo EPR. The best detector is the one that gives 

the best result for a particular experiment. The 

optimum might be a surface coil, a cavity, a LGR, 

a coupled loop, an implanted loop or antenna, etc. 

Increasingly, the information one can expect to 

get from in vivo EPR is the full spectrum that one 

can get from non-in vivo EPR of model systems. In 

addition, one gets information that is pertinent to 

complex tissues. This includes: 

• oximetry 

• distribution of MRI contrast agents 

• distribution of spin-labeled drugs 

• redox metabolism 

• detecting reactive intermediates via spin trapping 

• biophysical measurements such as fluidity 

In vivo EPR can be accomplished with a straightforward 

L-band bridge and resonator interfaced to a 

commercial spectrometer. The main technical problem 

is water. There is no optimum microwave frequency 

- high frequency is desired for S/N and low 

frequency is desired for penetration of the body. A 

wide range of frequencies needs to be available so 

one can select for a particular application. The 250 

MHz spectrometer in Halpern's laboratory is probably 

as low as will give useful S/N for in vivo EPR 

for small animals. 

Naturally occurring radicals are not at high 

enough concentration to be studied with current 

EPR technology. Added radicals are of two types: 

(1) soluble radicals such as nitroxides, which distribute 

more or less uniformly, albeit with some 

targeting possible though not yet well exploited; 

and (2) particulate species, which are well localized. 

Each has advantages and disadvantages. The optimum 

type of paramagnetic material will depend on 

the experiment. Nitroxides continue to be important 

because there is a lot of flexibility in design and 

a lot of information has been accumulated about nitroxides. 

As the focus on specific targeting of spin 

labels increases, there will be increasing dependence 

on organic chemists to construct the specific labels 

needed. 

By using nitroxide radicals and surface coils, one 

can monitor accumulation in organs such as liver 

and bladder, and one can monitor redox metabolism 

as well. In addition to pharmacokinetics, one can 

study, via the effect on the EPR signal, temperature 

and oxygen concentration. The future of measurement 

of temperature and oxygen concentration in 

vivo by EPR is bright. EPR is probably the best 

technique available for oximetry in vivo. The measurement 

of oxygen concentration is very important 

medically, and the existing methods do not give the 

needed information, especially at medically significant 

low levels. 

New particulate probes for oxygen concentration 

based on lithium phthalocyanine, fusinite, or carbohydrate 

chars report oxygen concentrations, via 

EPR line broadening, at very low oxygen levels (42, 

43, 46-48). They appear to be largely inert (nontoxic) 

in vivo. The EPR linewidth response to oxygen 

of a fusinite sample has been shown to be reversible 

in vivo over a period of six months. Measurements 

of oxygen concentration in heart mus-

Vol. 16, No. 3/4 165 

cle have been performed. The potential is clearly 

present for oximetry of tumors to provide clinically 

relevant parameters to tailor radiation therapy and 

chemotherapy. 

Aspirations for the future include performing simultaneous 

assays of multiple sites using magnetic 

field gradients. The possibility of this has been established. 

The use of EPR to measure oxygen concentration 

may be the first to reach routine clinical 

application. 

The main focus for in vivo EPR in the future is 

likely to be in the areas listed below. These are areas 

in which EPR is likely to provide useful information, 

and information that is not likely to be as readily 

accessible by other techniques. 

• biophysical parameters, similar to those used 

for in vitro systems 

• pharmacokinetics, using the paramagnetic 

species as the tracer 

• redox metabolism, using metabolism of nitroxides 

as the parameter 

• oximetry, emphasizing repeated non-invasive 

measurements in tissues 

• viability of cells 

• temperature and distribution of temperature 

B. Respondent - Lawrence Berliner 

In vivo spectroscopy involves engineers, chemists, 

and medical professionals. The future depends 

rather strongly on the chemists, because in solving 

specific biomedical problems a major difficulty 

is producing a specific paramagnetic probe. 

L-band is the more appropriate frequency if you 

want to put a small animal into a spectrometer. In 

vivo EPR is a wonderful technique for studying the 

health of mice or rats, and it has the potential of 

being applied to larger animals and, perhaps, patients. 

Ex vivo EPR, e.g., on biopsy samples, on 

blood, or on fluid emissions already can yield important 

results for larger animals (humans). Depending 

upon sample size, one might use X-band, Sband, 

or L-band spectroscopy. Unfortunately, these 

applications are limited so far to labs that have 

enough engineering support to build their own resonators, 

since commercial instrument vendors are 

not supporting the instrumentation needs of this 

area. JEOL is working with a few labs in Japan, 

but no such industrial collaborations are known in 

the US. 

An important problem in in vivo EPR is coupling 

the microwaves with the sample. It is helpful 

to communicate with medical personnel to use 

the word "detector" to describe the EPR resonator, 

since this is the nomenclature familiar from radiology- 

Low resolution EPR imaging is also a chemical 

problem. The more specifically targeted the spin label, 

the higher resolution EPR imaging that is possible. 

There are lots of biological problems with the 

use of nitroxides, especially with regard to their 

metabolism. However, the pharmacokinetics will 

teach us about redox metabolism. There will be 

advantages to starting with a non-radical precursor 

which could be biologically reduced to a free radical. 

The use of solid particle probes, such as fusinite 

or lithium phthalocyanine, is limited at present because 

they have to be placed physically in the tissue. 

However, once they are in place they can provide information 

without further invasive procedures. It is 

attractive to contemplate the analogy with MRI of 

the use of magnetite coupled to antibodies as the 

future of this type of probe. Oximetry by any of 

these means holds great promise - the vision for the 

future is clinical application. 

C. Discussion 

One problem with in vivo spectroscopy so far is 

that researchers have not been able to achieve S/N 

any where near as good as one can with a flat cell 

in a TM cavity. Many have tried unsuccessfully to 

detect radical adducts in vivo. The Swartz lab has 

detected EPR of melanin in frog skin. Because free 

radical based lung damage is an important human 

health problem, the use of EPR oximetry to monitor 

oxygen in the lungs is a goal worth pursuing. Digestive 

track and fecal material should be a source 

of EPR signals for the study of biological systems. 

Unfortunately, these desired target tissues and other 

materials do not have radicals in high enough concentration 

for current spectrometers. 

In vivo could mean plants as well as animals. 

Lawrence Berliner has published examples of EPR 

imaging in plants (49). There are interesting prob-


lems, but research in the US is driven by funding 

sources, and most of the funds available are not oriented 

toward study of plants. 

Using the organic chemistry developed by Leonid 

Volodarsky, it is possible to use diamagnetic molecules 

which will become paramagnetic in vivo. 

The reason Howard Halpern is using 250 MHz 

EPR is to be able to apply it to humans. Penetration 

of the microwaves into the body is necessary. 

Even at 250.MHz the skin depth is only 7 cm in 

muscle and a bit deeper in fat. Limited penetration 

depth is not a barrier to all in vivo applications of 

EPR. For example, human skin is an important organ. 

The EPR of skin of living humans, even EPR 

imaging of skin, is accessible to X-band EPR. 

Because of the limitations of current spectrometers 

much of the discussion emphasized the great 

efforts to obtain even a simple CW EPR spectrum of 

these in vivo samples. Consider the insights possible 

if one could use, for example, FT EPR on these 

samples. As noted later, there is no advantage of 

FT if one is observing a single-line resonance unless 

the data acquisition rate can be increased. 

IV. State of the Art Lecture 

- FT EPR and High-Field 

EPR: Jack H. Freed 

A. Comparison with NMR 

The developments in the last 15 years in NMR 

that have led to the revolutionary importance of 

NMR in many branches of science include: 

• NMR: high resolution via high magnetic fields 

and associated frequencies - e.g. from 100 

MHz up to 750 MHz; EPR has available an 

even larger jump in frequency, from 9 GHz to 

250 GHz. 

• FT NMR and 2D FT NMR; EPR - analogous 

developments have been realized. 

• MRI and its applications to both materials 

science and medicine; EPR imaging has not 

been applied to humans yet, but already has 

many applications in materials science and 

biomedicine. 

B. FT EPR 

Work in the Freed lab has been driven by a 

need for better techniques for improved resolution 

in dynamics and structure in the chemical physics 

of biophysical problems. Five years ago at the Workshop 

some very new results in these areas were introduced. 

There has been a great deal of progress 

since then, including 2D FT EPR (50, 51). The S/N 

achievable in FT EPR is illustrated with a 0.75 mM 

sample of perdeuterated tempone in 16 microliters 

of a smectic liquid crystal. The effective decay rate 

of the FID following a microwave pulse for this sample 

is 200 ns. This is T?J - it includes both homogeneous 

and inhomogeneous broadening. With pulse 

widths of 5.5 ns and time resolution of 5 ns, some 

40,000 FIDs can be averaged in 6 s. The FID can 

be observed for more than 10 times the T£. Figure 

2 shows the sensitivity possible with FT EPR. 

In addition to the possibilities for enhanced S/N, 

FT EPR can also be applied to the study of transient 

species (52, 53). One can measure radicals 

with submicrosecond lifetimes, generated for example 

by a laser pulse, by recording the single pulse 

FID and performing Fourier transforms. 

The modern era in FT EPR, including initial realization 

of 2D FT EPR starts in about 1986 (54). 

Applications of 2D FT EPR in the short interval 

since then include: 

• nationally narrowed - FT EPR, 2D ELDOR; 

diffusion in liquid crystals and model membranes 

(55); 

• viscous fluids and powders - experiments are 

more challenging but they yield more microscopic 

details about motion - applicable techniques 

include 2D ESE, 2D FT, SECSY, 2D 

ELDOR; these techniques are also useful for 

structural studies via nuclear modulation. 

• 2D FT EPR imaging with pulsed field gradients 

- spatially resolved 2D FT EPR (56, 57); 

Now one can with 2D FT EPR obtain nuclear 

spin flip rates, Heisenberg exchange rates, and from 

them molecular rotational and translational diffusion 

coefficients. All of these are measured simultaneously 

on the same sample, so there is no problem 

with comparisons due to sample preparation or sample 

conditions - and, they are obtained quickly.

Vol. .16, No. 3/4 167 

Ld 

Q 

q 

cs 


1GPC/P0PC ELDOR 66C T-200nj silt 16PC/POPC ELDOfl 66C T-60Onf ellt 

taPC/POPC ELOOR 66C T-1200ni «lfw 

16PC/POPC ELOOR 66C T-2000ns elfv 

Figure 3: 2D-FT-ESR spectra of nitroxide radicals in lipid dispersions. For this sample, Tj is ca. 20-30 ns. 

Cross peaks in the upper left spectrum (for short mixing times) result from electron-nuclear dipolar interactions. 

At longer mixing times (lower right-hand spectrum) Heisenberg exchange dominates. Unpublished 

results provided by Jack Freed. 

play due to cross relaxation can be observed growing 

in as a function of mixing time. 

The technical challenge with performing pulsed 

FT EPR imaging was creating pulsed magnetic field 

gradients of 100 G/cm that persist for less than 100 

ns. All of the advantages of FT NMR imaging become 

available to research on electron spins via this 

FT EPR and pulsed field gradient technology. Spatially 

resolved 2D FT EPR (thus three dimensions) 

has been demonstrated for samples containing 15 N 

and 14 N nitroxides. 

C. High Frequency EPR 

High frequency EPR yields: 

• higher g-factor resolution - one can read the 

three nitroxyl g-values directly from the spectrum 

at 250 GHz; even for the nearly free electrons 

trapped in solids the g-tensors can be 

measured. 

• greater sensitivity to dynamics - one can measure 

picosecond motions, since the sensitivity 

of line widths to motion is about a thousand

Vol. 16, No. 3/4 169 

times greater at 250 GHz than at 9 GHz; 

• transition metal spectra with large zero-field 

splittings (ZFS) (63) - e.g., a Mn(II) complex 

with a ZFS of 5800 G can be analyzed in terms 

of second order perturbation theory. 

• better absolute sensitivity will eventually 

be realized, once spectrometer upgrades described 

elsewhere are made. 

The transition to high frequency EPR brings 

a new vocabulary to EPR. The spectrometers are 

built using quasioptics, and techniques are those of 

far infrared not microwave technology. Both hardware 

and software have to be developed to perform 

and interpret these experiments (64-67). 

Although the above techniques are available to 

others (visitors are encouraged to come to Cornell to 

learn about unpublished details), they are not fully 

developed, since there has been little funding for 

this work. There are definite needs to improve the 

technology. The most important technical problem 

in FT EPR is spectrometer deadtime. With 1 KW 

pulses the current deadtime is 60 ns. The ringing 

time of the low-Q resonator used implies one should 

be able to reach a deadtime of 25 ns. It is also important 

to extend these techniques to multi-frequencies, 

because there are advantages and disadvantages for 

various experiments at different frequencies. 

D. Respondent - Linn Belford 

These 2D FT EPR techniques are beautiful. 

There are benefits to high-field high-frequency 

that come principally from having the high frequency, 

and other benefits that come from having 

the very high magnetic fields. One advantage of high 

frequency is that one can cover large ZFSs. One 

expects extensive applications to important problems 

in metalloproteins. The high sensitivity expected 

at high frequency holds out the possibility 

of studying very small samples. The benefits from 

high field EPR come from the fact that the importance 

of the Zeeman term relative to the ZFS terms 

in the Hamiltonian increases at high field. The more 

nearly first-order spectra at high field increase the 

chance of interpretation of the spectra. 

Very few high frequency EPR spectrometers are 

available in the world. There are spectrometers in 

Russia, France, Germany, Netherlands, Japan, and 

the US. The highest frequency at which conventional 

resistive magnets are useful is 60-70 GHz. At higher 

frequencies than this there are four spectrometers in 

the US, the far-infrared spectrometer at the Naval 

Research Laboratory, the 95 GHz spectrometer at 

Illinois, the 140 GHz spectrometer at the MIT Bitter 

Magnet Laboratory and the 250 GHz spectrometer 

at Cornell. 

Some questions posed regarding high-frequency 

EPR instrumentation: 

• why are there not more spectrometers 

in the 30-70 GHz region, where nonsuperconducting 

magnets can be used? 

• should frequencies >250 GHz be pursued vigorously? 

• is it reasonable to expect that high frequency 

(millimeter range) EPR spectrometers could 

become viable commercial products? 

• can the difficulty of sweeping the supercon 

magnets be overcome? 

• is there possibility of using modern FT IR instruments 

with magnets installed for Zeeman 

splitting (66-68)? 

• can the sensitivity (especially for aqueous 

samples) be enhanced by new resonator designs? 

E. Discussion 

Jack Freed at Cornell had access to a far infrared 

laser with the same lines as are being used at Grenoble, 

but the work was quickly abandoned because 

the lasers did not provide the degree of spectral purity 

and stability that EPR spectroscopy uses in the 

microwave region. The instability of Bitter magnets 

is also a problem. Consequently, the high frequency 

spectrometer at Grenoble performs low resolution 

EPR relative to what is needed for molecular dynamics 

studies. 

In the Cornell system, a second supercon magnet 

may readily be swept ±500 G about the center field. 

This is adequate for studying organic species, but it 

is clearly inadequate for studying inorganic species, 

for which the main magnet is swept.


V. State of the Art Lecture — 

Pulsed EPR: Arthur Schweiger 

A. Comparison with NMR 

Until recently, conventional CW methods of 

measurement prevailed in EPR spectroscopy. This 

contrasts with the situation in NMR spectroscopy 

where the CW techniques have been superseded almost 

entirely by an impressive variety of elegant 

pulse techniques. Although pulse methods were introduced 

in EPR at about the same time as in NMR, 

only a small number of research groups applied pulse 

techniques to EPR in the first three decades (69, 70). 

The slow growth of pulsed EPR is probably due to 

the expensive instrumentation that was needed, and 

to the lack of digital electronics sufficiently fast for 

any but a restricted range of experiments. However, 

the situation has changed radically within the 

past few years, and pulsed EPR is undergoing extraordinary 

rapid development. New instrumental 

capabilities and new pulse techniques make it possible 

to reduce the measurement times, to increase 

sensitivity, to improve resolution, and to simplify 

complicated spectra. 

Today almost all topic areas of EPR spectroscopy 

are, or will soon be, affected by various pulse 

methods. Techniques of particular importance include 

time-resolved EPR spectroscopy, methods for 

measuring relaxation times, techniques for studying 

molecular motions, methods for the indirect detection 

of nuclear transition frequencies, electronnuclear 

double resonance, and EPR imaging. 

B. New EPR Detection Schemes 

The following topics and references will focus on 

EPR of materials in the solid state. The State of the 

Art Lecture by Freed provided references to ID and 

2D EPR techniques applied to species in solution. 

The annotated list of references provides very brief 

comments on the new EPR techniques introduced 

in the last couple of years. 

1. Electron Spin Echo 

Following an initial emphasis on saturation recovery 

measurements (71), the majority of recent pulse 

EPR experiments in the solid state measure the resonance 

phenomena via the electron spin echo (1-5, 

69, 70, 72-76). 

The popularity of the electron spin echo approach 

is due to the fact that, with a very few exceptions, 

the EPR lines of solids are strongly inhomogeneously 

broadened. As a consequence, the transverse 

magnetization caused by a microwave pulse, 

called the free induction decay (FID), rapidly decays. 

The instrumental deadtime usually prevents 

observation of the FID in solids, and the dephasing 

of the transverse magnetization has to be refocused 

by performing an electron spin echo (ESE) experiment. 

2. FID detected hole burning 

In FID-detected hole-burning (77-81), a transient 

spectral hole burnt into an inhomogeneously broadened 

EPR line by means of a selective microwave 

pulse is shifted or broadened by various types of 

perturbations (radio-frequency field, Bo-field jump, 

electric field, sample rotation, etc.), and is subsequently 

recorded in a single experiment via an FID 

following a nonselective microwave pulse. The FIDdetected 

hole-burning experiment can be applied to 

any EPR spectrum with inhomogeneously broadened 

lines, provided the relaxation times are sufficiently 

long. Many of the well-known ESE pulse 

sequences have an analogous FID-detected holeburning 

sequence that is often superior to the ESE 

experiment. 

3. CW Detection 

The detection schemes described above involve 

monitoring the transient signals (echoes, FIDs) 

emitted by the sample after pulsed excitation. An 

alternative approach is to get information about the 

perturbed spin system by measuring on-resonance 

magnetization of the spin ensemble by using weak 

CW microwave irradiation (78, 82-84). 

4. Longitudinal Detection 

Longitudinal detection (85, 86) is based on the 

observation of rapid changes in the z-magnetization 

effected by microwave pulses. Pickup coils with 

their normal oriented parallel to the static magnetic 

field are used to record the time-dependent 

z-magnetization during the pulse sequence. Longitudinal 

detection is free of artifacts caused by the 

instrumental dead-time.

Vol. 16, No. 3/4 171 

5. New Methods for the Measurement of 

the Nuclear Modulation Effect 

The standard electron spin echo envelope modulation 

(ESEEM) experiments suffer from several disadvantages. 

A number of pulse schemes have been 

developed recently to improve resolution and sensitivity, 

to separate overlapping ESEEM spectra, and 

to overcome various types of instrumental distortions 

(76, 78, 87). 

6. ESEEM at Frequencies Other Than X- 

Band 

Going to lower or higher microwave frequencies 

than X-band (88-94) may increase the depth of the 

modulation and reduce or eliminate the dispersion 

of nuclear frequencies. This ESEEM cancellation 

effect has been analyzed (91-94). 

7. Phase-Shifted Excitation 

The modulation depth may be increased by 

eliminating the decay caused by dipolar interaction 

among unpaired electrons (95). 

8. 5-Pulse ESEEM 

With the 5-pulse ESEEM sequence (96), the 

modulation amplitude can be up to a factor of eight 

larger than in the corresponding 3-pulse experiment. 

The echo signal contains no unmodulated part. 

9. Extended Time Excitation 

The entire two-pulse echo modulation can be 

obtained by a single experiment using a coherent, a 

stochastic, or a pulse-burst stimulation followed by 

a strong refocusing pulse (97,98). 

10. Coherent Raman Beats 

This experiment allows one to record the entire 

three-pulse modulation in a single experiment 

by detecting nuclear coherences with a weak probe 

pulse (84). 

11. Soft ESEEM 

By using two microwave frequencies, ESEEM can 

be accomplished with low microwave power (milliwatts 

instead of watts). Because of the use of two 

microwave frequencies one does not have to excite 

allowed and forbidden transitions simultaneously to 

get echo modulation. "Soft" ESEEM (99, 100) does 

not suffer from blind spot artifacts and the modulation 

frequency is not limited by the pulse bandwidth. 

12. Remote Echo Detection 

In this pulse scheme transverse magnetization 

representing the echo is converted into longitudinal 

magnetization (101). A two-pulse echo sequence is 

then used to read this magnetization. The procedure 

is insensitive to the deadtime of the spectrometer. 

13. Echo Modulation Echoes 

With this special three-pulse sequence the shape 

of broad hyperfine lines can be restored (102). 

14. 4-Pulse ESEEM 

The ESEEM peaks that correspond to sums 

of frequencies contain important information about 

the magnetic parameters of the nuclei. The 4-pulse 

ESEEM approach allows one to measure highly resolved 

sum peak spectra of disordered systems (76, 

98, 103). 

15. HYSCORE 

DOR 

Hyperflne Selected EN- 

HYSCORE (hyperfine sublevel correlation spectroscopy) 

is a very powerful technique to study weak 

hyperfine interactions, in particular in disordered 

systems (94, 104-107). The technique is distinguished 

by a high spectral resolution in both dimensions 

and allows one to disentangle the correlation 

features over two quadrants of the 2D frequency domain. 

16. 2D FT-EPR in Solids 

For EPR spectra covering a small field range, as is 

often the case for radicals, 2D FT-EPR techniques 

have been applied successfully for the measurement 

of the nuclear modulation effect (60, 108).


17. Fourier Transform EPR-Detected NMR 

FT-EPR detected NMR is based on the burning 

of transient holes into the EPR line by exciting 

forbidden EPR transitions and detecting the entire 

hole pattern via an FID (81). The procedure allows 

the observation of all nuclear transition frequencies 

in a single experiment. The sensitivity may exceed 

that of an ESEEM experiment by up to an order of 

magnitude. 

18. Phase Cycling 

Phase cycling is of great importance in pulsed 

EPR to record undistorted echo or FID signals (105, 

109). 

19. Double Resonance Experiments 

Along with the rapid developments in pulsed EPR 

spectroscopy, there has also been a fast-growing interest 

in pulsed ENDOR and related double resonance 

techniques (87, 110-115). There have been 

several recent reviews of the field. 

20. Optimized ENDOR 

By using a new mixing scheme the polarization 

transfer between nuclear and electron spins is 

improved, and an optimum ENDOR efficiency is 

achieved (116). 

21. Triple Resonance 

In a triple resonance experiment, nuclear transitions 

are excited with two rf pulses of different frequencies 

(110). The technique is used to determine 

relative signs of hyperfine coupling constants and to 

separate overlapping ENDOR spectra. 

22. Hyperfine-Selective ENDOR 

The procedure allows the measurement of EN- 

DOR subspectra originating exclusively from nuclei 

with a predetermined hyperfine coupling constant 

(117, 118). 

23. Radio-Frequency Driven ESEEM 

The radio-frequency driven ESEEM pulse scheme 

can create echo modulations in paramagnetic sys- 

terns that do not contain nonsecular hyperfine interactions 

(e.g., liquid solutions) (119). 

24. EPR-Detected Nuclear Transient Nutations 

and Multiple Quantum ENDOR 

EPR-detected nuclear transient nutations and 

multiple quantum ENDOR are closely related techniques 

(82, 113, 120). They can be applied to determine 

the multiplicity in ENDOR spectra as well as 

the hyperfine spectral density in different sections 

of an ENDOR spectrum. 

25. Time-Domain ENDOR 

Strong rf pulses used in the technique of timedomain 

ENDOR excite a spectral width of about 1 

MHz (121, 122). The FID of the nuclear spins is 

recorded via an electron spin echo. The sensitivity 

and resolution achieved with this pulse sequence 

may exceed that obtained with standard pulse techniques. 

26. Coherence Transfer ENDOR 

Coherence transfer ENDOR is an interesting 

experiment from the point of view of spin dynamics 

(123, 124). However, the technique suffers from 

poor spectral resolution and is therefore not of very 

general practical use. 

27. SEDOR-ENDOR Spectroscopy 

SEDOR-ENDOR is basically a SEDOR experiment 

for the nuclear spins (125). The electron spins 

are used only for the polarization of the nuclei and 

for detection. The technique allows the measurement 

of nuclear-nuclear dipole couplings. 

28. Fourier-Transform Hyperfine Spectroscopy 

Fourier-transform hyperfine spectroscopy is based 

on the FID-detected hole-burning approach (80). In 

the spectrum obtained each group of equivalent nuclei 

is represented by one peak at the hyperfine frequency, 

independent of the nuclear spin quantum 

number.

Vol. 16, No. 3/4 173 

29. ENDOR-Edited-ESEEM Spectroscopy 

A combined ENDOR-ESEEM experiment allows 

the correlation of different nuclei (126). 

30. 2+1 Pulse Train ESE 

The ESE pulse sequence termed "2+1" can be 

used to determine electron dipole-electron dipole interactions 

between paramagnetic centers (127-130). 

31. ID and 2D Pulsed ELDOR 

Pulsed ELDOR uses either two microwave frequencies, 

or a jump in the magnetic field strength, 

for the measurement of relaxation times, spatial distributions 

of paramagnetic centers, and magnetization 

transfer (131-137). 

32. EPR Imaging 

Although early EPR imaging experiments were 

performed with CW techniques, pulsed EPR techniques 

recently have become important in EPR 

imaging (56, 57, 138-142). 

33. Resolution Enhancement of Field- 

Swept EPR 

A number of methods are under development 

to disentangle field swept EPR spectra using pulsed 

EPR techniques (143). 

34. Electron-Zeeman-Resolved EPR 

An EPR spectrum can be resolved in a second 

dimension based on differences in the electron Zeeman 

interaction of different paramagnetic centers or 

different orientations in a disordered system (79). 

35. Anisotropy-Resolved EPR 

Methods have been developed to make use of 

the anisotropy of the magnetic parameters to disentangle 

powder EPR spectra by rapidly changing the 

orientation between the static field and the sample 

(144, 145). 

36. Electron Spin Transient Nutations 

Transient nutation techniques are applied to separate 

overlapped EPR spectra, to determine spin 

quantum numbers and to study photoinduced electronic 

states (78, 83, 146-148). 

C. Recent Instrumental Innovations in 

Pulsed EPR 

Over the past few years instrumentation in pulsed 

EPR has made enormous progress. The following 

discussion is restricted to resonator design and 

to spectrometers working at microwave frequencies 

other than X-band. 

1. Resonator Design 

The most significant innovation in resonator design 

(124, 149-154) in recent years is the introduction 

of the EPR loop-gap resonator (LGR) by Hyde 

and coworkers (149, 150), and the development of 

related structures for different types of pulsed EPR 

experiments, including pulsed ENDOR, and magnetic 

field jumps (144). In addition to lumpedcircuit 

resonators of the LGR type, increasingly dielectric 

resonators are finding application in EPR 

(155-157). 

2. Spectrometer Frequency 

Most pulsed EPR spectrometers operate with a 

microwave frequency of ca. 9 GHz. The developments 

up to 1987 were reviewed in (160). Recently 

several pulse EPR spectrometers operating at higher 

or lower frequencies (88, 90, 158, 159) have been described, 

including ENDOR at 97 GHz (161-163). 

Other innovations in instrumentation over the last 

few years include: 

• miniaturization of spectrometers, e.g., for 

studying irradiated foods, dosimetry, etc. 

(164, 165) 

• Fabry-Perot resonator design (64) 

D. Respondent - David Singel 

There have been many illustrations of the utility 

of multifrequency ESEEM during the Workshop 

and the preceding Symposium. Ultimately, varying 

the magnetic field and using some of the new pulse 

techniques may accomplish much the same thing in 

sorting out nuclear hyperfine and quadrupole frequencies. 

The balance between nuclear Zeeman and 

hyperfine interactions determines the amplitude of


the modulation effect. Some of the new pulse techniques 

may change this balance, but the effect depends 

on a resonant phenomenon, so the experimental 

magnetic field strength is very important. The 

Hyscore and echo-modulation-echo pulse sequences 

are ways to deal with broad lines. Ways to get rid 

of broad lines include cancellation of hyperfine and 

Zeeinan interactions and cancellation of first order 

linewidths that show up in the 14 N double quantum 

frequencies. 

Assignment of frequencies to a particular nucleus 

can be made by observing the field dependence of 

the frequencies. See for example the recent study of 

pyruvate kinase by Peisach in which distinction between 

coordination by N or P was made (166). The 

sum combination peak shift is inversely proportional 

to frequency; this suggests important applications of 

S-band ESEEM. 

E. Discussion 

The 2D FT EPR spectrometer developed by 

Freed and coworkers at Cornell has been described 

in a review article (51). Recently developed high 

power microwave switches have not been published 

- the inventor at Cornell is applying for a patent, 

and they lack funds and time to do some of the 

characterizing experiments needed to write a paper 

about the switches. Freed invites people to come to 

the lab to learn about these things. 

The real question about these new 2D FT experiments 

is whether new information can be obtained. 

For example, is there any evidence for angular 

dependences of nuclear relaxation? These are 

just the type of questions to which these techniques 

were applied by Freed and coworkers in 1989, where 

they demonstrated anisotropy of the nuclear spin 

relaxation and interpreted it in terms of molecular 

dynamics. An experimental and theoretical study 

of Heisenberg exchange in oriented liquid crystals 

showed that there is no reason to expect much 

anisotropy (55, 167). Currently, ESEEM as a function 

of frequency is often necessary to make the 

spectral patterns comprehensible. Are there new 

pulse sequences that could make the frequency dependence 

measurements unnecessary? The 5-pulse 

experiment can be continued with more and more 

pulses to increase the modulation depth. However, 

with more pulses there are limits on relaxation times 

that can be studied and one loses sensitivity. FID 

detected hole burning also gives deeper modulation, 

sometimes even in cases where one would not see 

modulation in normal 2- or 3-pulse ESEEM. If the 

Ti trend observed by Hyde continues and Ti is 

longer at Q-band and higher frequency, then some 

of the pulse sequences demonstrated at X-band are 

even more useful at higher frequency. Work is in 

progress in the Schweiger lab on pulsed Q-band. 

Applications of high-field EPR would appear to 

be extensive for species whose spectral linewidths 

do not scale with field, where one is removing, for 

example, second-order fine structure broadening. It 

is not obvious that the spectrum of a Cu(II) complex 

will be improved at high frequency. 

The major application of high field EPR to 

metalloproteins will likely be for those that have 

large ZFS, including non-Kramers even-spin systems. 

Even though the lines may be broad, highfield 

EPR will be important if a transition is observed 

at all, since they cannot be seen at X-band. 

To see a signal that one could not otherwise see 

is an enormously good reason for doing high frequency 

EPR. G-strain is considerably larger at high 

frequency for something like Cu(II) in frozen solution. 

For example, in the Cu(II) species that have 

been studied at 250 GHz at Cornell, g-strain scaled 

with field, so there was no improvement in resolution. 

Hyperfine structure resolution can even get 

worse at high frequency. Despite the g-strain linebroadening 

with increasing frequency, there are examples 

(see, e.g., Nilges, et al., in previous EPR 

Symposia) of considerably enhanced spectral information 

content for powdered Cu(II) specimens at 

95 GHz. The prospects for such enhancement are 

very case-dependent, in the experience of the Illinois 

group. 

Often the incentive for going to higher field is to 

get better g-tensor information. One expects sensitivity 

to scale roughly as frequency squared, with 

maybe + or — 1/2 in the exponent. One problem is 

that as the frequency increases and the spectra get 

broader, the magnetic field modulation amplitude as 

a fraction of linewidth decreases, so sensitivity does 

not improve as much for the normal phase-sensitive 

detected CW spectrum when the lines are broad.

Vol. 16, No. 3/4 175 

VI. Panel Discussion - High resolution 

EPR 

Panel Members: Jack Freed, Ronald Mason, 

Roger Isaacson, Lowell Kispert, Arthur Heiss 

(Bruker Instruments), Clarence Arnow (Micro- 

Now), Philip Morse (Scientific Software), Mark 

Woolfrey (Oxford Instruments). 

The topic "High Resolution EPR" for the purposes 

of this review encompasses most of the applications 

of "normal" CW EPR, whether to organic 

radicals or metals, in solid phase or in solution. 

Issues include: research and instructional, 

portable and application-dedicated, multifrequency, 

S/N, data manipulation, simulation, visualization. 

The following paragraphs summarize comments 

and questions from the audience and the panel. 

A. Kinetics 

Real-time kinetics measurements of radicals is an 

important and expanding area of EPR, and one to 

which FT EPR is making important contributions. 

See for example the work of van Willigen, Turro, 

Dinse, etc. Microsecond kinetics can be studied, 

because in this time one can obtain an FID. 

Fast-response conventional (CW) EPR is also being 

developed. Bruker has a microwave transient 

bridge which, combined with a split-ring resonator 

in a matched condition (critically coupled, not overcoupled) 

with a low Q, results in a system with 

200 MHz bandwidth for these types of experiments. 

This bridge has many of the components of the pulse 

bridge, without the switches. 

B. Longitudinal Detection 

The sensitivity for longitudinal detection is about 

a factor of 10 worse than normal detection. The 

detection coil is resonant at the frequency of the 

repetition rate of the pulse experiment. 

C. Signal to noise 

Although EPR is more sensitive than NMR on a 

per spin basis, the species of interest in biomedical 

fields are not very abundant. Therefore, there is a 

very serious S/N problem, especially for samples of, 

e.g., a microliter of protein solution. In the biomed- 

ical area one of the key priorities is improved S/N. 

Spectrometer improvements are needed. 

Concerns were expressed that the treatment of 

noise in FT EPR may not yet fully reflect the nature 

of the experiment. For example, is it possible 

to define the noise in a time-domain experiment and 

apply it in an unbiased fashion to the FT spectrum? 

Based on the discussion of noise in FT NMR by 

Ernst in 1966 (168), Freed discussed some aspects 

of noise in FT EPR (51). One problem with S/N 

enhancement via FT in EPR relative to NMR is the 

need in EPR to decrease the resonator Q (to ca. 40) 

in order to get adequate bandwidth (e.g., 100 MHz 

at 9 GHz). One expects that the signal loss is proportional 

to Q. On the other hand, NMR has to have 

slow pulse repetition rates because of the long nuclear 

Ti values. In EPR, Ti is short enough in most 

cases that some S/N improvement relative to NMR 

can be regained by faster data collection. However, 

no commercial digitizer can accept repetition rates 

as fast as EPR Tis would permit. 

D. Ex Vivo EPR; Aqueous Samples in 

Flat Cells 

Ex vivo EPR got a bad reputation a long time ago 

because of artifacts created by grinding or lyophylizing 

the sample. However, these problems are now 

recognized and ex vivo EPR studies can be done reliably. 

For example, bile or urine can be studied 

in flat cells in TM cavities, via cannulae if desired. 

S/N is a problem for in vivo EPR, even with spin 

traps. 

It has been reported that the surface of normal 

flat cells is rough enough that it introduces vortexing 

and resultant noise in some spectra when used 

as a flow cell. Specially made cells with smoother 

interior construction work better, but are more expensive. 

A newly redesigned flat cell with much 

tighter tolerances on flatness gives much better performance 

than the older flat cells. Wilmad is working 

on a redesigned flat cell, which should be available 

in a few months, to solve this problem at a 

reasonable cost. 

Loop gap resonators are worth considering for 

pulsed EPR studies of aqueous samples because 

there is fairly good separation of B and E fields in 

a LGR, especially relative to a cavity resonator. In 

addition, the Q used for pulsed EPR is low enough 

that a large amount of water can be put in the res-


onator without having much further effect on the 

Q. 

E. Dielectric Resonators 

During the Symposium preceding the Workshop, 

results presented by Roger Isaacson emphasized 

the desirability of using dielectric resonators 

to get even better separation of B and E field, while 

retaining the benefit of a higher Q where it can be 

used. Bruker markets a dielectric resonator at Xband 

in the Flex-line resonator series. This Bruker 

resonator uses sapphire in the dielectric resonators 

because other materials have too many impurities 

to be useful for CW EPR. Sapphire cut in the right 

direction, and turned in the right direction in the 

EPR probe, provides a magnetic field region of ca. 

200 G in which there are no impurity signals. If 

you cool the sapphire resonator, lines from impurity 

levels of Fe, Cr, etc., will increase in intensity, but 

not so much that they will distort the spectrum. In 

pulsed EPR these impurities do not interfere with 

the signal at all because they are in such low abundance 

and their relaxation times are so short. For 

aqueous solutions in a small cylindrical capillary a 

dielectric resonator yields a factor of 6.7 improvement 

in S/N relative to a standard resonator. The 

dielectric resonator is slightly better in this regard 

than the LGRs with which it has been compared. If 

enough sample is available, better S/N will be obtained 

for aqueous samples in a large flat cell in a 

TM cavity. 

Peter Hofer reported that tests at Stuttgart 

showed that UV light did not have any effect on 

the sapphire resonator, but gamma radiation was 

not tested. 

F. Small and/or Dedicated EPR Spectrometers 

The EPR field has been looking for a long 

time for a market for dedicated EPR spectrometers. 

The largest market that ever occurred was the sale 

of about 50 FRAT (by Syva; Syntex-Varian) spectrometers 

for drug testing, but other techniques replaced 

the use of EPR for that application. Diamond 

companies have purchased a portable EPR 

to screen for synthetic diamonds. Varian produced 

two 1 GHz spectrometers, and Micro-Now produced 

three 1 GHz spectrometers, for screening crude oil 

for vanadium many years ago. 

Dosimetry is a possible market. An ASTM committee 

is working on a standard that will permit 

EPR use in dosimetry. The Bruker EMS104 was developed 

for radiation dosimetry and is being tested 

for monitoring irradiated food in Europe. 

Clinical oximetry is a likely application for an 

EPR spectrometer. This will probably have to be 

a portable, low frequency spectrometer, not just a 

version of a standard spectrometer. 

VII. Panel Discussion — In Vivo 

EPR and Imaging 

Panel Members: Lawrence Berliner, Harold 

Swartz, Howard Halpern, Sandra Eaton, Dieter 

Schmalbein (Bruker), Mark Woolfrey (Oxford Instruments). 

A. The Question of Sample Size 

The hardware and software issues for in vivo EPR 

and EPR imaging are very different from those for 

the standard high-resolution experiment. Thus, we 

discuss together "high resolution" spectra in vivo 

and multidimensional imaging. The colloquial question 

is "When can we get the elephant into the EPR 

spectrometer?" That is, how do we get to real applications 

with samples bigger than mm size, or mouse 

size? 

In counterpoint, Hal Swartz asserts that the 

question is wrong - people are too pessimistic. With 

the existing technology and relatively simple development 

one can do a large fraction of what needs 

to be done. One can look at the elephant if only 

the first cm or so of the elephant is to be examined. 

Many interesting things are within that surface 

layer. At 250 MHz 80-90% of the things one is 

interested in from a clinical point of view are already 

accessible. The problems remaining are not fundamental, 

but merely the nitty gritty things that need 

to be sorted out. No one significant break-through 

is needed. 

For information on the use of surface resonators 

(e.g., the volume sensitivity), for cases in which the 

sample is too large to put into a resonator, see (44, 

172). 

Larry Berliner suggests another point of view 

- Why don't we try to put the EPR spectrome-

Vol. 16, No. 3/4 177 

ter inside the elephant? The hardware development 

needed is miniaturization such that the probe could 

be inserted by catheterization. 

B. Frequency Scaling 

Clearly, while the in vivo and imaging experiments 

are stimulating creative approaches to solving exciting 

problems, there remain some very fundamental 

questions. For example, it is not obvious what frequency 

scaling is appropriate to these experiments 

on complex living tissue. In NMR the penetration 

seems to scale nearly linearly with frequency, and 

not according to the square law that early literature 

would lead one to expect. One should not read conflict 

into the decision to perform imaging at different 

frequencies in different labs. Since most experiments 

were started with little or no funding, each 

lab worked with what was available. The Halpern 

spectrometer at 250 MHz is widely viewed as a close 

to optimum choice. Work in other labs at higher frequency 

than 250 MHz is not a statement that higher 

frequency is better - it is what is available and is giving 

good results on an important set of problems. It 

is a mistake to assume that one cannot obtain EPR 

spectra on almost all except the trunk of a human 

being, if one works at 250 MHz. 

C. Interpretation of In Vivo Spectra 

Extracting information from in vivo spectra probably 

requires a spectral fitting approach (169, 170). 

A reasonable fit hypothesis can be used to focus the 

entire spectral information on the few parameters 

associated with the hypothesis. This approach allows 

one to determine very small variations between 

very noisy spectra. 

One of the main problems with animal imaging 

experiments is suppressing the noise caused by 

movement of the animal. Attempts to capture the 

motional information electronically to be able to use 

it for corrections gives the side benefit that there is 

now a record of, e.g., the depth of respiration of the 

animal. 

D. Magnetic Field and Magnetic Field 

Gradient Control 

One of the main challenges for imaging experiments 

is the magnetic field control. In systems that 

use Hall probes, the current practice is laborious 

positioning to put the Hall probe in a nodal plane 

of the imaging gradient field. This becomes very 

difficult for more than one imaging dimension. 

A related problem is the quality of the gradient 

field. At the very high gradients used in EPR 

imaging, great care must be taken to ensure linearity 

of the gradient over the sample volume of interest. 

At very low RF frequencies the gradient coils 

would produce a larger field than the main Zeeman 

field. In the 250 MHz imaging spectrometer, the 

Helmholtz coils used to create the Zeeman field are 

splayed to create the gradient field (40, 171). 

It is attractive to use current control of copper 

Helmholtz coils to avoid the problems of Hall probe 

positioning on iron-core electromagnets (hysteresis 

problems prevent current control of iron-core magnets). 

However, the perturbations of the field by 

ferromagnetic materials in the vicinity is a problem. 

One has to keep ferromagnetic materials far away; 

even an infusion pump used to inject the spin probe 

into the animal can cause interference with the spectrometer. 

E. Low Frequency and Imaging Spectrometers 

Dieter Schmalbein reported that Bruker is watching 

the EPR imaging field, but until a clear application 

market develops they cannot afford the development 

costs. It would require several million 

dollars to develop a professional EPR imaging system. 

They have made several experiments, and tentatively 

would expect to use a frequency below 1 

GHz, and would expect to design a resonator that 

would accommodate a whole rat. However, it is 

judged premature to build a commercial product. 

The current market for the Bruker L-band EPR 

bridge is near zero. A new 2 to 8 GHz multifrequency 

bridge has been built using the most modern 

microwave equipment available. It has much better 

sensitivity than the L-band system, which was designed 

about 10 years ago. Until a commercial instrument 

becomes available, researchers who want 

to enter this field need to obtain information from 

one of the labs that developed instrumentation and 

software for imaging. The NIH-funded Illinois ESR 

Center (which now has a branch at Dartmouth) is 

happy to assist people, or to put them in touch with 

a lab that can assist with a specific problem outside


the experience of the Illinois Center. 

F. Nitric Oxide In Vivo 

There is much current interest in measuring NO 

in vivo, but estimated concentrations of NO in the 

body are less than micromolar. As the simple diatomic 

molecule it cannot be studied by EPR in 

vivo. Possibly it could be studied via its paramagnetic 

effect, analogous to oxygen, or by trapping it. 

But are either of these approaches likely to produce 

an image? Harold Swartz has unpublished demonstrations 

that one can trap NO with lithium phthalocyanine. 

Hemoglobin is a naturally occurring 

trap for NO. It seems very unlikely that it will be 

possible to monitor NO in vivo by EPR, let alone 

image it. If it could be done, the importance of NO 

in the body makes monitoring NO by EPR a likely 

clinical application of EPR (173). 

At the Lovelace Institute human volunteers 

breathed NO2, then their lungs were washed with 

saline and the cells studied by EPR. Heme-NO was 

observed with good enough S/N to serve as a monitor 

of NO2 exposure (174). 

G. Noise in FT EPR, EPR Imaging and 

In Vivo EPR 

Multiple fast scan vs. slow scan data collection is 

one of the key decisions for in vivo EPR imaging experiments. 

This is one of the data collection parameters 

that is optimized against the rates of motion 

of the animal, and other inherent time constants of 

the system. In the current 250 MHz imaging system, 

typically 15 sec scans are used. The current 

limit is the monitoring of the frequency of the fieldfrequency 

lock system, and the fact that IEEE488 

communication is used. 

Colin Mailer emphasized that talk about improving 

S/N to do in vivo imaging should face the reality 

that the signal relates to two parameters - the 

number of spins and Bi. In current technology there 

is a tradeoff between sample volume and Bi - the 

larger the resonator the smaller the Bi at the sample. 

With LGRs the technology appears to be close 

to the fundamental limit. 

The key to solving the S/N problem is to understand 

the noise source. For in vivo EPR, the noise 

source is likely to be the animal. Beyond the limits 

just discussed, there are problems such as how to 

make the resonator less sensitive to animal motions. 

Use of a dielectric resonator to further decouple the 

animal from the resonator might help. 

If the problem of animal motion is solved, one 

still has to work to decrease other noise sources, such 

as the source and the detection system. The recent 

introduction of a balun between the transmission 

line and the resonator in the 250 MHz imaging system 

decreased the noise by a factor of 4. The system 

is not fully optimized yet. 

The fundamental limits discussed by Colin 

Mailer have yet to be approached by the 250 MHz 

EPR system in Halpern's lab. The primary reason 

is animal motion. If one operates under conditions 

optimized for the nitroxide radical, magnetic field 

modulation amplitudes of 0.5 to 1 G can be used. 

With an input power of 100 mW, it is estimated 

that the Bi in the animal is ca. 0.3 G, a value 

that approaches saturation of the spin system. (If 

the deuterated form of the nitroxide is used, different 

conditions - e.g., Bi = ca. 0.01 to 0.03 G 

- are required for optimization, because of narrower 

linewidths.) Under these conditions, surface 

currents (eddy currents) induced by the magnetic 

field modulation and by the RF are further modulated 

by the animal-motion-induced microphonics. 

These contributions increase the breathing-related 

artifact. A balanced power delivery system is one 

possible approach to electronic suppression of this 

artifact. About two orders of magnitude noise suppression 

will be required before encountering the 

limits referred to by Colin Mailer. 

The value of Bi that is useful in CW imaging is 

limited by the relaxation time of the electron spins. 

Possibly there is an application for contrast reagents 

to shorten the relaxation times in EPR so that larger 

Bi can be applied without saturating the spin system. 

Ernst's analysis for NMR was that there would 

be little advantage to performing FT spectroscopy 

for single-line spectra. The imaging experiment inherently 

is not a single line. FT EPR or rapid scan 

spectroscopy followed by mathematical deconvolution 

(which was useful in NMR just before FT NMR 

was developed) might be used to advantage in EPR. 

100 MHz spectral width at 9 GHz requires a Q of 

ca. 40. If the center frequency drops by a factor of 

ten, but the bandwidth stays the same, then the Q 

required is 8. If the focus were on a narrower line,

Vol. 16, No. 3/4 179 

so that the Q could remain at 80, then the issue 

becomes one of sensitivity. It is not clear that the 

choice of FT vs. CW in this case is a black and 

white issue. Among the tradeoffs are the relation 

of Q to the amount of aqueous sample that can be 

put in the resonator, the repetition rate that can 

be used, etc. Imaging is an additional perturbation 

on the judgment. At low frequencies the bandwidth 

needed for even narrow lines necessitates substantial 

power. 

In any non-pulsed experiment we throw away 

a lot of information because we only look at one 

Fourier coefficient of the EPR signal. More sensitivity 

could be obtained by stacking synchronous 

demodulators. Some years ago Hyde taught us (175) 

that we should digitize the entire 100 kHz modulation 

signal and try to get all of the information out 

of each modulation cycle. Bruker markets preamplifiers 

and digitizers that have adequate speed to 

perform this type of analysis. 

VIII. Panel Discussion - New 

Perspectives on Spins 

Panel Members: James Hyde, Melvin Klein, 

Arthur Schweiger, Bruce Robinson, Harvey Buckmaster, 

Edward Reijerse, Hans Thomann, Dieter 

Schmalbein (Bruker). 

Arbitrarily gathered under this umbrella are a 

wide variety of pulse, time-domain, multiple resonance, 

and multiple modulation techniques that 

share the feature of exploiting non-linear behavior 

and relaxation phenomena. 

A. SQUIDs in EPR 

SQUID devices are almost noiseless detectors, so 

they are attractive wherever they can be used. In 

NMR SQUIDs are superior detectors up to about 

30 MHz, but at higher frequencies the standard 

methods are better. This severely limits the type 

of EPR experiment for which they could be useful. 

It is attractive to consider using a SQUID for zerofield 

EPR. Zero-field measurements would eliminate 

some of the anisotropy problems often encountered 

in EPR. 

B. Multiquantum EPR 

Modern microwave technology permits the generation 

of multiple CW frequencies with a common 

timebase. In principle, the same irradiation frequencies 

could be generated by suitable time-modulation 

of a single frequency, but summing of distinct frequencies 

seems technologically preferable. Multiquantum 

EPR is readily generalized from two or 

three frequencies (as in Hyde's papers so far), to 

N frequencies. The potential is very great. There 

are two general thrusts: as a practical alternative 

to magnetic field modulation for improved system 

stability, and as a way to obtain information on relaxation 

rates. 

Among the many applications envisaged, few 

have been explored yet, since the technique is so 

new. EPR imaging is one potential application. 

Image reconstruction algorithms require absorption 

spectra (not derivative spectra). The fact that MQ 

EPR yields absorption spectra directly makes it attractive 

to consider MQ EPR imaging. The need for 

absorption spectra is another reason for the use of 

FT EPR imaging instead of CW EPR imaging. Alternatives 

to CW for EPR imaging are imperative. 

C. Microwave Source Phase Noise 

What EPR applications would there be for a 

microwave source with 20-40 dB lower phase noise? 

At low frequency the wideband tunable microwave 

sources have poor phase noise, and with a 

low noise GaAsFET amplifier in the detection system 

one finds that the source noise dominates. This 

is a case in which reducing the phase noise of the 

source would be important. Lower phase noise at 

lower modulation frequency could be important - 

e.g., Roger Isaacson used 4 Hz modulation for experiments 

where the EPR signals under study will 

not respond rapidly. Also, with the increased use 

of microwave preamplifiers the 1/f noise of the crystal 

detector is overcome, and in many experiments 

one can more advantageously use field modulation 

in the region of 100-25,000 Hz. 

Does phase noise scale with frequency? There 

seems to be little comparison data, but the usual 

assumption is that phase noise at all frequencies 

relative to the center frequency scales with the 

microwave frequency. This may not be true for 

klystrons, where there could be mechanical vibra-


tions at particular frequencies. However, at 100 

KHz away from the carrier, phase noise appears to 

scale for klystrons. During the Symposium Mark 

Nilges showed curves for a 100 GHz oscillator, and 

some of them look like they are not scaling. 

In many cases 100 kHz modulation is no longer 

necessary, and for species with long relaxation times 

100 KHz modulation is not desirable. Lower modulation 

frequencies are likely to become more commonly 

used. Thus, phase noise at 100 KHz may not 

be the best comparison to make. 

One should be aware that using phase locking 

techniques may introduce new sources of noise. The 

reference oscillator has to be a very clean source, 

or it could become the limiting noise source in the 

system. This occurred in some cases in Buckmaster's 

lab when a synthesizer was used to phase-lock 

a source. 

James Hyde encouraged reference to Robins' 

book (18), which considers ways of handling phase 

noise. With incomplete data available regarding 

phase noise characteristics of various microwave 

sources, an overall impression is that currently 

phase-locking to a quartz oscillator is preferable below 

about 4 or 5 GHz, and a fundamental oscillator 

locked to a high-Q tank circuit is preferable at 

higher frequencies. 

A comprehensive search of the literature by Hyde 

did not uncover a device at Q-band that had better 

phase noise than the one he described (9). 

One has to build the right system even to test 

the phase noise - no commercial spectrum analyzer 

is satisfactory for the measurement. 

D. Pulsed ENDOR 

In CW ENDOR the rule of thumb is that the CW 

EPR spectrum S/N should be greater than 100:1 to 

get reasonable ENDOR results. Also one usually 

assumes that ca. 1 mM solutions are needed. In 

contrast, if one can see a pulsed EPR signal (echo) 

one can obtain pulsed ENDOR for the sample. In 

ideal cases one can invert the spins and get a 100% 

ENDOR effect using pulsed EPR techniques. However, 

the pulsed EPR signal usually has poorer S/N 

than the CW EPR signal, so a 100% ENDOR effect 

may not result in better S/N than the smaller effect 

observed in CW ENDOR. 

Typically for metalloprotein solutions one observes 

about a 5-10% ENDOR effect. How much 

signal is lost during the polarization transfer period 

depends on cross relaxation and other relaxation 

times. Cu(II) proteins at liquid He temperature 

typically have cross relaxation times of 10 ms 

or less. Tis are several hundred microsec. One does 

not want a high spin concentration, since then the 

phase relaxation time becomes short. For Cu proteins 

shortening of the phase relaxation time can 

be observed starting at about 1 mM, depending on 

where the metal is in the protein - when they are 

about 20 A apart one starts to see effects. Overall, 

the sensitivity is roughly a factor of 5 lower than for 

CW EPR. 

E. Dissemination of Modern Techniques 

A colleague once commented to Hyde with regard 

to a lecture presentation of exciting new techniques, 

"another experiment I cannot do." Engineers 

are not available in all labs to implement 

new techniques. Of the techniques that Hyde has 

developed, the most generally applied, because it 

can be implemented on largely standard spectrometers, 

is STEPR. Possibly a double-quantum EPR 

experiment using double sideband/suppressed carrier 

techniques could be implemented with a simple 

accessory. Commercial suppliers cannot do everything, 

but some things can be done, even though 

not financially justified by themselves, because they 

help carry the main product line. One possibility 

for introducing new techniques would be for groups 

of investigators to submit a joint proposal to a funding 

agency to purchase x number of accessories, and 

have the vendor produce a batch of x of them at 

one time. Another approach'would be to have, as 

an outgrowth of a Workshop such as this, an international 

commission make a recommendation between 

competing alternative demands on the limited development 

resources available. 

Many of the techniques can be done with existing 

commercial boxes if one knows how to put the boxes 

together in the right way. Maybe someone should 

publish the details of how to do these experiments 

with existing boxes. 

F. Software for Visualization of EPR 

Data 

Often software is the key to success. Without a 

combined hardware/software system one won't get

Vol. 16, No. 3/4 181 

many results. It used to be that when a lab needed 

software, someone just went home and wrote it at 

night, but now software needs are too sophisticated 

for this approach. 

There are some thorny issues about software. 

For example, even if you can write it in a night, it 

will take a week to document it in such a way that 

someone can use it. There is a lesson in commercial 

spread-sheet software. Sometimes it is better 

to force an application into some documented and 

supported commercial software rather than writing 

your own special-purpose software. It is difficult 

to make excellent general-purpose software. Maybe 

the emphasis should be on subroutine libraries, and 

easily modified software. 

The new EPR spectrometers and experimental 

methodologies described at the Symposium and 

Workshop will provide enormous amounts of information 

(or at least raw data that somehow must 

become information). Relative to slow-scan CW 

EPR, the new EPR technologies produce data at 

such a prodigious rate that data storage and subsequent 

manipulation becomes a larger problem than 

EPR labs have had to deal within the past. Although 

trivial by comparison with data generation 

rates in other fields of science (e.g., MRI, particle 

physics, or the space program), the amounts of 

data require qualitatively different computational 

approaches than are available in most EPR labs. 

Some labs already approach this problem by using 

data compression techniques, which can make 

the data storage requirements modest. For example, 

Jack Freed's FT EPR can produce a few 1 MB 

spectra per hour of spectrometer operation. Huge 

amounts of data are transferred to a supercomputer 

for the most substantive analyses. Linear predictive 

methods are used to reduce the volume of data for 

storage. Specialized software is needed for visualization 

of the multidimensional information that now 

can be generated so quickly, in order that it be communicated 

to human beings. Another approach is to 

recognize that the result of an experiment may be a 

series of Fourier coefficients, and these are what one 

would store, not all of the raw data. Others might 

be uncomfortable with the irreversible interim interpretation 

imposed on the data by these approaches. 

Now that EPR has a standard (Bruker BES 3 T) 

for storage and transfer of EPR data we need to 

consider how to present the data for visualization. 

This is a major problem. The solutions in other 

areas of science, where the visualization problem is 

analogous, are very large software packages which 

are very expensive because of the development effort 

to create them. A key issue is whether the EPR 

community will be able to support the effort needed 

to develop this software. 

Reef Morse pointed out that Scientific Software 

Services from the beginning has always provided 

source code for the marketed software. Customers 

make significant modifications. Dieter Schmalbein 

pointed out that the software provided with the 

Bruker ESP380 pulse spectrometer represents 32 

man-years of effort. More sophisticated software 

could be developed, but Bruker is limited in the 

effort that can be invested in EPR software by the 

profits that can be made in the EPR business. More 

than 90% of the EPR spectrometers are delivered to 

universities or government institutes. In contrast, 

80-90% of the customers for NMR spectrometers 

are in industry. In the NMR field a professional 

software package can be sold to industry for a reasonable 

amount of money, because industry can see 

the cost savings in terms of time saved by the software. 

IX. Summary on Instrumentation 

and Methodology 

The horizons of new EPR techniques are phenomenal. 

References were given above to many ways to 

apply pulses to spins. Many of the techniques are 

very expensive to implement. The excitement is in 

applying these techniques to problems that are now 

only being approached by the use of CW EPR. A 

lot of the discussion at this or other meetings about 

applying EPR is about just getting a CW spectrum. 

The S/N problem is bad enough for some samples 

that we sometimes struggle just getting a spectrum, 

sometimes for days at a time. But problem solving, 

in systems to which ways of studying electron spins 

can be applied, requires some of these new techniques. 

How soon can we get there? What is in our 

way? The general response at the Workshop was - 

Money. So now let us consider the money aspects.


X. The Funding Agency Perspective 

Once upon a time there was to be a fourth panel, 

but the government ran out of money and funding 

agency representatives could not attend the Workshop. 

Dr. John Beisler, Executive Secretary, Biophysical 

Chemistry Study Section, Division of Research 

Grants, NIH, was the only person invited who 

could attend. 

A. Questions Regarding Funding of EPR 

in the USA 

The questions posed regarding funding are: 

1. What funding is available for the new research 

opportunities presented at this workshop, and 

for solving the instrumentation and software 

problems highlighted? 

2. How many EPR spectrometers were funded 

in recent years? What is the average dollar 

amount of such grants? Is there an historical 

trend? 

3. What characterizes a successful EPR instrumentation 

proposal? 

4. What types of referee comments characterize 

EPR instrumentation proposals that are not 

funded? 

5. How many grants (and what dollar volume) 

have been awarded in which a major focus of 

the research proposed is the development of 

EPR instrumentation and/or methodology? 

6. How many grants (and what dollar volume) 

have been awarded in which EPR is an important 

technique even if not a major focus of 

the grant? 

7. There is a tendency to compare funding of 

EPR with funding of NMR, since they are 

both magnetic resonance techniques. Does the 

structure of instrumentation grant programs 

make funding of an NMR proposal more probable 

than funding of an EPR proposal? 

8. What do the long-range planning processes 

on-going at the federal funding agencies portend 

for research in or using EPR? 

B. Information from the Presentation by 

John Beisler, DRG, NIH 

The CRISP data base at NIH is the source of the 

factual information he presented. He also provided 

his observations and perspective as Executive Secretary 

of the Biophysical Chemistry Study Section 

at NIH. 

The most recent fiscal year for which data was 

available is FY92 (ended June 30, 1992). To query 

the data base one has to use terms that are in its 

thesaurus. The terms used were electron spin resonance 

spectroscopy, electron nuclear double resonance, 

and nuclear magnetic resonance spectroscopy. 

The number of grants includes RO1, PO1, 

P41, etc., types. Grants are listed as having e.g., 

EPR as the primary, secondary, or tertiary thrust. 

In FY92 General Medical Sciences funded 179 

projects (43% of the total awarded) in EPR. The 

Heart Institute, with 50 awards, is far in second 

place. The Cancer Institute made 24 awards. The 

Aging Institute made only three awards in the two 

fiscal years examined. There is a lot of opportunity 

for applications of EPR in some of the other 

Institutes. 

In the shared instrument program in FY87 about 

2/3 of the proposals were funded, but this was unusual. 

Because of the small number of applications for 

EPR spectrometers, they get reviewed by a panel 

for "other spectroscopy." This results in relatively 

few of the reviewers being expert in EPR, which is 

viewed by some researchers as a liability, but in a 

homogeneous review panel as for NMR, there is a 

tendency to rank all of the applications. 

Most EPR-related proposals tend to be reviewed 

by three study sections, Physical Biochemistry, Biophysical 

Chemistry, and Metallobiochemistry. Of 

the roughly 80 applications per review cycle in biophysical 

chemistry, about 24 are in NMR, 24 in crystallography, 

and a few in EPR. There is usually one 

person with specialization in EPR and a few others 

knowledgeable about EPR on the study section. 

Dr. Beisler asked various other people at NIH 

and members of study sections (past and present) 

about some of the questions asked for this Workshop. 

Some of the impressions and opinions offered 

were:

Vol. 16, No. 3/4 183 

FY87 

FY92 

EPR 

EPR 

NMR 

Table 

327 awards 

$45 8M total 

415 grants 

$57.3M total 

1763 grants 

1U 

16% primary, 80% tertiary 



Table 11: NIH Shared Instrument Program 

FY87 

NMR 51 applications reviewed, 31 funded, $7.9M total 

EPR 3 applications reviewed, 2 funded, $356K total 

FY92 

In FY92 the shared instrumentation program was cut from $32M/year to ca. $8M/year. 

3 awards for EPR, $600K total 

1. NMR and EPR proposals fare about equally 

well. 

2. The perception is that the real richness of EPR 

applications to lipid or membrane research has 

been mined. There is a low opinion of EPR in 

lipid research. 

3. EPR proposals need to emphasize what information 

on a particular problem EPR can give 

that other techniques such as NMR, fluorescence, 

X-ray, etc., cannot. 

4. For greater success, put EPR in the broader 

context of other spectroscopies. How does 

it complement the information available from 

other spectroscopies? For structural biochemistry, 

for example, what does EPR reveal 

about distances, angles, etc. 

5. Remember to speak to the reviewers rather 

than making assumptions that they have a 

background in EPR. 

6. The advantages EPR has relative to NMR are 

small sample size and high sensitivity relative 

to NMR. 

7. In the context of discussion about new hardware 

development, it is well to keep in mind 

that one can often get very reasonable data 

from a 15-year-old Varian spectrometer. Elegant 

solutions to problems can often be done 

with very simple instruments. 

Many scientists, hearing this opinion attributed 

to peer reviewers, wish to communicate the larger 

message of this workshop, that elegant new EPR 

tools are now available for more powerful problemsolving 

than was possible with the older EPR techniques. 

XI. The Vendor Perspective 

At the close of the Workshop the community 

sought the response of instrument and software vendors 

to the challenges and opportunities presented. 

A. Bruker (Dieter Schmalbein) 

As a manufacturer, Bruker finds Q-band unprofitable 

but has decided not to discontinue it! The 

Bruker Q-band system has switched from klystrons, 

which are no longer available, to Gunn oscillators,


and the sensitivity is about the same. With the 

new helium FlexLine cryostat, which is also used 

by the L-, S- and pulsed X-band systems, the Qband 

system can operate to 1.8 K, with magnetic 

field modulation from 1.5 KHz to 100 KHz without 

problem. 

Bruker continues to offer a diverse range of microwave 

bridges for many specific applications. The 

phase noise of X-band sources (klystron and Gunn 

oscillator) is suppressed 130-140 dB at 10 KHz 

from the carrier. The high output 2-8 GHz Multi- 

Frequency Bridge should meet the needs of many 

researchers. 

Over the seven-year period, 1985-1992, 37% of 

the EPR spectrometers produced by Bruker were 

delivered in the US, 19.4% in Germany, 6.5% Japan, 

4.4% England, in terms of dollars, not number of 

spectrometers. In the past 12 months the situation 

has changed, and 59% of EPR sales (in dollars) have 

been to Europe, 20% to Japan, and only 10% to the 

US. This may change in the near future. 

Since EPR is a very low volume market, Bruker 

has to be very careful in selecting the areas in which 

to invest development effort and capital. In the 

recent past they have put this effort into developing 

the most advanced spectrometers that are possible 

in a commercial market, culminating in the 

ESP380E. About 40 of these have been sold so far 

(only five in the US). Bruker has the impression that 

the ESP380E is ahead of the users - people cannot 

exploit the capabilities of the ESP380E. There is a 

need for more institutes around the world to teach 

people how to use non-stationary EPR techniques 

and to provide service to people to help them start 

using these techniques. No EPR service center in 

the US (e.g., NIH Research Resource Centers) has a 

modern commercial pulsed EPR spectrometer. Before 

Bruker can invest in making these spectrometers 

even more complicated, with capabilities such 

as pulsed ENDOR, multifrequency pulsed EPR, and 

pulsed EPR imaging, there has to be more use of 

the existing capabilities of the spectrometer. Then, 

Bruker can consider the commercial implementation 

of these new techniques. 

Up to now Bruker has not charged for EPR software 

- it was delivered as part of the spectrometer. 

Now there is evident need for much more professional, 

sophisticated, and diversified software, and 

Bruker anticipates having to hire more programmers 

and hence to have to charge for the software. 

Bruker has tried very hard to listen to what the 

researchers and other customers say they want in an 

EPR instrument. In the past everyone wanted the 

best spectrometer possible, and the specifications 

of the spectrometer were very important. Recently, 

this has changed in a few markets, especially in the 

US. In the US people seem to want the lowest price 

spectrometer, and the specifications usually are a 

minor consideration. In Europe price/performance 

is the most important consideration. In Japan, however, 

performance is most important. Bruker has to 

decide whether to develop two types of spectrometers, 

one with the highest possible performance and 

sophistication for part of the market, and another 

spectrometer at the lowest possible price. During 

the Workshop scientists have expressed desire to 

have spectrometers with higher performance and 

to have hardware and software from the manufacturer. 

But the part of the market not represented at 

the Workshop may require Bruker to put its development 

effort not into spectrometers for advanced 

techniques but into spectrometers at lower prices. 

Bruker will continue to improve the FT spectrometers. 

Pulsed ENDOR will come on the market 

next year. They will experiment with imaging techniques. 

At the moment there are no plans to go 

into high-field EPR, because they cannot foresee a 

market in this area. 

B. JEOL (Jack Francis) 

JEOL will be involved in the development and 

marketing of EPR spectrometers for a long time, 

and hopes to be more involved in conferences like 

this by next year, and possibly add a bit to what is 

being discussed. 

C. Micro-Now (Clarence Arnow) 

Micro-Now has been involved in EPR instrumentation 

for over 25 years, mostly with accessories. 

They built an L-band spectrometer and a Q-band 

spectrometer about 20-25 years ago. In the last 5 

years they have put more effort into building EPR 

spectrometers. They have built four types of spectrometers 

- for teaching, for dosimetry, a more complete 

system in modular form, and a new spectrometer, 

demonstrated at the Symposium this year. This 

new spectrometer incorporates a magnet built in

Vol. 16, No. 3/4 185 

Russia, and is very portable. The spectrometer uses 

a Gunn source. 

Their effort will generally be in the direction of 

spectrometers such as this new one, which essentially 

address the part of the market that once was 

served by the Varian E-4. 

D. Oxford Instruments (Mark Woolfrey) 

There has been no comment at the Workshop 

of limits to research due to the performance 

of cryostats, in contrast to the discussion in 1987. 

Special versions of cryostats can be made whenever 

modification of the standard cryostats would 

be helpful. 

XII. Summary Perspective 

A. The Horizons of EPR 

Much of the discussion of commercial instrumentation, 

and of NIH funding, even at this Workshop 

has been about relatively standard CW, linear, 

single-frequency (X-band), field swept EPR. The 

horizons of EPR are much different. The funding 

situation is as if you were looking East from Denver, 

and the reality of research needs is as if you 

were looking west from Denver. There is a lot of 

difficult terrain to get through to do such things 

as pulsed magnetic field jump, pulsed ENDOR, or 

multiquantum EPR. 

It is surprising, maybe even distressing, that 

changes in EPR as practiced in most laboratories 

and as described in most spectroscopy texts are so 

much slower than some of the other changes going 

on in society, especially internationally. If one looks 

back at the design criteria set forth by the 1987 

Workshop, one would make relatively few changes 

today. The priorities remain about the same. 

One can hope that some time not too far in 

the future at another Workshop the focus will have 

changed to the now largely unexplored regions of 

EPR spectroscopy: 4D, multiquantum, multifrequency, 

etc. What will be possible when we can 

see EPR spectra of brain tissue, in vivo, localized 

in a living animal, using all of the advanced EPR 

techniques we learned about at the Symposium and 

Workshop? This is where EPR is really going to be 

able to solve problems. The future has some exciting 

possibilities. Some day we will look back on the 

current S/N and wonder why people say, as they 

have for at least 20 years, that EPR is near the theoretical 

limits. Almost nothing that was reported 

today could have been done even a few years ago. 

Harold Swartz from time to time reminds us (and 

himself) that some years ago he declared that "the 

problem with EPR imaging is that there is nothing 

to image and no way to image it." At the Symposium 

and the Workshop he was a strong advocate of 

the current research and imminent clinical application 

of EPR imaging. His earlier comments, along 

with such famous quotations as "I think there is a 

world market for about five computers" (Thomas 

Watson, 1943) should be engraved on the portals of 

NIH to serve as a reminder to those who serve on 

study sections. 

B. Where EPR is Today 

The EPR perspective on a problem is very broad 

indeed (Table 12). Even though, as stated at the 

outset, much of what has been done has been CW, 

linear response, field swept, in homogeneous magnetic 

fields, and in one dimension, a few labs have 

shown the way with pulsed time domain EPR, extending 

into 2 and 3 dimensions. Hyde has recently 

opened our eyes to the possibilities of multiquantum 

EPR. 

The goals set in 1987 were ambitiously forwardlooking. 

With all of the exciting new developments 

in EPR, instrumentation and software are still way 

behind the needs of researchers. In fact we haven't 

come very far in five years toward the goals set in 

1987. This statement, which is true with respect 

to the full scope of the demonstrated possibilities of 

EPR, is not meant to in any way detract from the 

almost revolutionary advances made by instrument 

vendors in the past five years. The Bruker ESP380E 

has capabilities for pulsed X-band EPR that users 

have not yet learned to exploit. The Micro-Now 

8400 bench-top EPR makes it possible to expand 

the applications (and importantly the instruction) 

of CW X-band EPR into labs that previously could 

not afford a spectrometer. The Bruker EMS 104 is 

the first spectrometer built for quantitative EPR, 

a severely under-exploited area. The software becoming 

available is of a sophistication well beyond 

anything even dreamed of a few years ago. The 

hopes for extracting information from spectra in the 

near future are very bright. At the time of the 1987


Table 12: The EPR Perspective 

CW ID 2D 3D 4D 

multifrequency (MHz to THz) 

multiresonance (ELDOR, ENDOR, TRIPLE) 

field-swept, frequency-swept 

linear 

non-linear (ST-EPR, saturated) 

ODMR, etc. 

pulsed 

multifrequency 

ESE (Ti, T2) 

saturation recovery 

FT-EPR 

pulsed ENDOR 

pulsed magnetic field 

multiquantum 

mult ifrequency 

Workshop it was a valid point of view to declare that 

the "new" spectrometers of the day were not enough 

of an improvement over existing spectrometers to 

justify replacement of a functioning old spectrometer. 

Now, these new instrumentation and software 

capabilities change the situation entirely. 

The extreme importance of multifrequency, multidimensional 

(and, we project, multiquantum) 

EPR leaves many regions of the matrix of EPR observables 

not served by commercial instrumentation. 

The crucial issues expressed in 1987 remain - for 

example, should the limited R&D effort that is available 

in EPR be applied to creating the ultimate Xband 

CW EPR, should it be applied to broadband 

EPR, should it be applied to pulsed EPR? In this regard 

it should be recognized that the total R&D effort 

by commercial EPR instrument manufacturers 

is about the same as (maybe less than) the instrumentation 

research effort in the handful of leadingresearch 

labs around the world. In the USA in particular, 

Bruker and MicroNow are investing in EPR 

as strongly as they can prudently do so considering 

the magnitude of the EPR instrumentation market 

as it exists today. Given the severe limitations on 

research funding, it is not surprising that there is 

a "lowest bidder" attitude among purchasers, but 

this very attitude causes the capability limitations 

about which people complain. 

These companies cannot invest enough to lead in 

all areas of EPR. The task for the EPR community 

is to set some priorities on how the EPR perspective 

should advance to fill out the matrix of possible 

experiments to enhance problem solving in science. 

Guiding the selection of research progress for commercialization 

requires a collective wisdom for the 

good of science - and for the good of the fields in 

which the results of EPR will be applied. These 

Workshops are a small step toward channeling the 

best ideas of workers in EPR to guide priorities for 

our future. 

C. The Future 

It is clear that some applications need techniques 

for identifying many electron spin sites in complex 

physical or biological structures. A specific example 

is photosynthetic reaction centers. It is also clear 

that simulation and visualization of experimental results 

lag behind the ability to acquire data. 

A fundamental quandary for researchers is that

Vol. 16, No. 3/4 187 

marketing of spectrometers is demand-driven, but 

research is resource-driven. We hope that the aggregate 

market will permit manufacturers of EPR 

spectrometers to provide some leadership via marketing 

of spectrometers with capabilities that many 

researchers don't yet know that they need. The 

Bruker ESP380E is such an example - it has more 

functionality for pulsed X-band EPR than most purchasers 

have been able to exploit. 

XIII. Acknowledgment 

In this paper GRE and SSE serve as reporters/reviewers 

of the information (some of it unpublished) 

and opinions presented at the Workshop. 

Where researchers' names are associated with particular 

sections, they reviewed the section before 

the draft was submitted for publication. Numerous 

comments, corrections, and additions by Melvin 

Klein, Roger Isaacson, Arthur Heiss, Ralph Weber, 

Philip Morse, Linn Belford, Ron Mason, Harvey 

Buckmaster, and Howard Halpern helped transform 

tape recordings and notes from a meeting into this 

written report. Especially helpful comments and 

additional references were provided by Jack Freed, 

Arthur Schweiger, James Hyde, and Harold Swartz. 

In some places the wording is nearly verbatim as 

stated by a presenter or a discussant in the audience, 

or as provided by a participant after the 

Workshop. In other parts, the report is a synopsis 

and even a rearrangement of order from the oral 

presentation. The comments and references in the 

section on pulsed EPR are largely as provided by 

Arthur Schweiger. Without the extensive contributions 

of many people this report would be less complete. 

However, SSE and GRE are responsible for 

the final version and the overall focus and emphasis 

of this prospective on the future of EPR. 

Partial support of the Workshop was provided 

by NIH grant GM46669. Support of the preceding 

15th International EPR Symposium by Bruker Instruments 

Inc., Medical Advances Inc., Norell Inc., 

Wilmad Glass Inc., Scientific Software Services, and 

Micro-Now Instruments Inc. also contributed to the 

success of the Workshop. 

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152 J. Forrer, S. Pfenninger, B. Wagner, and Th. 

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Vol. 16, No. 3/4 193 

Contents 


Review of the EPR Data on ns^Centers in Crystals 

S. V. Nistor 1 and D. Schoemaker 

Physics Department 

University of Antwerp (U.I. A.) 

B-2610 Wilrijk-Antwerpen, Belgium 

I. Ursu 1 

International Center for Theoretical Physics 

34100 Trieste, Italy 

II. Production and Structure of the ns^Centers 

III. Theory of the EPR Spectra 196 

A. The spin Hamiltonian of the ns 1 -centers 196 

B. The superhyperfine interaction 200 

IV. EPR Results 201 

A. Trapped electron ns^centers 201 

1. The IB-group (Cu°, Ag°, Au°) 201 

2. The IIB-group (Zn+, Cd+, Hg+) 205 

B. Trapped hole ns 1 -centers 209 

1. The IIIA-group (Ga 2+ , In 2+ , Tl 2+ ) 209 

2. The IVA-group (Ge 3+ , Sn 3+ , Pb 3+ ) 211 

V. Concluding Remarks 216 

VI. References 219 


Several reviews concerning the EPR of the paramagnetic 

transition-metal ions in crystals are now 

available, either as periodic reports published in the 

Magnetic Resonance Review, or in books [1,2,3] and 

review papers [4, 5]. Such paramagnetic centers are 

usually observed in the as grown crystals, the paramagnetic 

state being the normal valency state of the 

impurity in the crystal-host lattice. 

The present review focuses on a different type 

of paramagnetic centers, the so-called ns^centers. 

1 On leave from the Institute of Atomic Physics, Bucuresti, 

Roumania. 

193 

194 

Such centers, consisting mainly of a paramagnetic 

ion with the ns 1 (n > 2) outer electron configuration 

(Table 1), are seldom observed in the as grown 

crystals. They are produced in crystals containing 

cationic impurities by the trapping of electrons or 

holes induced by irradiation, as well as by additive 

or electrolytic coloring. In many cases several paramagnetic 

centers with different spin Hamiltonian 

parameters were reported for the same impuritycrystal 

host system. The differences are due to 

the various locations of the paramagnetic ion in the 

crystal lattice, as well as to the presence of neighboring 

defects such as vacancies, interstitials or impurity 

anions.


Table 1: Paramagnetic ions with the ns 1 — 1 S1/2 electron configuration observed in crystals by EPR. The usual 

valency state of the impurity ion in the as grown ionic crystals is shown between brackets. 

Electron 

configuration 

(Ar)3d lo 4s 1 

(Kr^d^s 1 • 

(Xe)5d lo 6s 1 

Centers produced by 

electron trapping 

IB IIB 

Cu°(+l,+2) Zn+(+2) 

Ag°(+1) Cd+(+2) 

Au°(+1) Hg+(+2) 

The objective of the present article is to present 

a comprehensive picture of the EPR studies of such 

centers in inorganic crystals. The review is based on 

a literature survey of various reference sources carried 

out during several years when the authors were 

involved in the study of such centers. Although efforts 

have been made to include all relevant references 

until the end of 1992, it is still possible that 

omissions due to inadvertent oversight may occur. 

The paper is divided into four main parts. The 

first is a short survey of the production and structure 

of the ns 1 -centers, which is far from trivial, 

and is essential in understanding their structure and 

EPR spectral properties. 

The second part contains a short review of the 

theory of EPR spectra for systems with 5 = 1/2 and 

I > 1/2, including the case of a dominant hyperfine 

interaction, which is the appropriate one in many 

cases. Although the case has been discussed in a 

unified form [6], several approaches are to be found 

in the literature devoted to the ns 1 -centers. The 

present survey is mainly an attempt to put together 

the various approaches. 

The third and main part is a presentation of the 

EPR studies on ns^centers reported so far, the accent 

being not on chronology and priority aspects 

but on the general features connected with the formation 

and structure of the resulting centers under 

various conditions (temperature, optical treatments, 

etc.). The understanding of the structure 

and formation mechanism of the ns 1 -centers has 

markedly improved in the last decade as a result 

of the studies performed on the similar np 1 -centers, 

which are much more sensitive to the surrounding 

crystal fields. 

Centers produced by 

hole trapping 

IIIA IVA 

Ga 2+ (+l) Ge 3 +(+2) 

In 2+ (+l) Sn 3+ (+2) 

Tl 2+ (+l) Pb 3 +(+2) 

The paper also contains a set of tables in which 

the spin Hamiltonian parameters of the various ns 1 - 

centers in inorganic crystals reported until the end 

of 1992 are presented. 

II. Production and Structure of 

the ns^Centers 

The ns 1 -centers have been extensively studied 

in alkali halides (mainly chlorides), where a large 

body of data are available. The real understanding 

of their production started with the observation 

[7] that doping KC1 with certain impurities, such as 

Tl + , Ag + or Pb 2+ , strongly enhances both the rate 

of formation and the final concentration of the selftrapped 

hole centers (Vk centers) produced by irradiation 

with ionizing radiation at low (T < 100K) 

temperatures. It has been suggested that such impurity 

ions act as efficient electron-trapping centers 

(resulting in the trapped electron centers Tl°, Ag° 

or Pb + ), strongly reducing the recombination of the 

electrons and holes produced by irradiation. Many 

of the impurity ions act as efficient hole traps too. 

Consequently, by warming such a low temperature 

irradiated crystal to temperatures where the holes 

become mobile (T > 170K in KC1) it is possible to 

obtain high concentrations of the trapped-hole centers 

Tl 2+ , Ag 2+ or Pb 3+ . The various hole and electron 

trapping reactions have been extensively studied 

in KC1:T1+ and KCl:Ag + crystals [8, 9]. Further 

evidence concerning the structure of these centers 

has been obtained from the EPR studies of the 

isostructural np 1 -centers [8, 10, 11]. 

The formation and structure of the ns 1 -centers 

is determined to a large extent by the vacancies,

Vol. 16, No. 3/4 195 

present in the host lattice before irradiation as 

charge compensating cation vacancies of the divalent 

IIB or IVA impurity cations, or produced by irradiation 

in the form of anion vacancies. Their presence 

in the neighborhood of the ns 1 paramagnetic 

ions results in the lowering of the symmetry of the 

local crystal field, which is, however, little reflected 

in the EPR spectra of the ns^centers, due to the 

s-like character of their wave function. The usual 

absence of a resolved superhyperfine (shf) structure 

for the vacancy-associated ns 1 -centers makes it an 

extremely difficult task to determine their structure. 

For this reason the structural models of the various 

ns 1 -centers are based, in many cases, on indirect 

evidence. 

The main bulk of data concerning the production 

and structure of the ns^centers refers to the 

alkali halides. As suggested from earlier EPR studies 

on transition metal ions in alkali halides [4, 5], 

the monovalent cation impurities are located substitutionally 

at cation sites of the cubic lattice. In 

the case of substitutional divalent cation impurities 

an equal number of charge compensating vacancies 

are present in the lattice host, usually located in 

the nearest- neighbor (NN) or next-nearest-neighbor 

(NNN) positions. 

The irradiation of alkali halides at low temperatures 

(T < 100K) with ionizing radiation, or even 

with UV-light close to the band gap value (5-10 eV), 

produces electrons, holes and excitons, the last being 

subsequently involved in the production of anion 

vacancies and interstitials [12, 13]. The electrons 

(e~), which are mobile, are trapped either by the 

anion vacancies (va) resulting in F centers, or by 

the monovalent or divalent cation impurities (M + 

or Me 2+ ). The holes (h + ) are self-trapped forming 

\4 centers. The reactions of interest here are: 

M+ + e~ -» M° (M = Cu, Ag, Au) (1) 

(X = C1, Br, (2) 

Me 2 c + vc + e' -f Me+vc (Me = Zn, Cd, Hg) (3) 

where the subscript indicates the occupation site 

of the ion/atom (c-cation site, a-anion site, iinterstitial), 

and vc represents the neighboring 

cation vacancy. 

Upon warming the irradiated crystal several processes 

take place. The Vk centers become mobile 

(above 170K in KC1), a large fraction of them being 

trapped at the impurity ions, resulting in trapped 

hole ns 1 -centers, according to the reactions: 

(M = Ga, In, Tl) (4) 

Mei + vc+Vk Me 3 c + vc+2X~ (Me = Ge, Sn, Pb) 

(5) 

At even higher temperatures, where vacancies become 

mobile, they can be either trapped at or released 

from the ns 1 -centers. In the case of the cation 

vacancies the following reactions can take place: 

Mr + v. T>Ta M 2 c + vc 

Me 

(M = Ga, In, Tl) (6) 

(Me = Zn, Cd, Hg) (7) 

(Me = Ge, Sn, Pb) 

(8) 

where Ta is the activation temperature for the movement 

of vacancies (Ta = 220K for both vc and va in 

KC1 or RbCl [10, 11, 14]). 

As initially suggested [15, 16] in the case of the 

atomic Ag°(5s 1 ) center in KC1, the atomic ns 1 - 

centers can trap anion vacancies forming the socalled 

A% centers: 

M°c 

M°cva{A°F) (M = Cu, Ag, Au) (9) 

Such centers are produced in even larger concentrations 

by optically bleaching at T > Ta, in the 

-F-band, the crystals previously irradiated at lower 

temperatures. The analogy with a similar process 

previously observed in alkali halide crystals doped 

with alkali impurities [17], by which FA centers, (i.e. 

F centers next to alkali impurities) were obtained, 

has been initially the main argument supporting the 

reaction (9). The direct demonstration of the validity 

of reaction (9) came later from the studies 

[10, 18] of the isostructural M°(l)-np 1 centers (M = 

Ga, In, Tl), which have shown that such centers can 

be also produced by the reactions: 

M+ 

T>Ta 

M°cva = A% = 

(10) 

(11) 

Reaction (10) is also valid for M = Cd, resulting in 

the co-called A~p centers. By irradiation with ionizing 

radiation at temperatures where vacancies are 

mobile, besides the Ap centers, various other centers 

are produced. Of special interest are the negative 

ions. The existence of such ions, supposed to be


located at anionic sites of the lattice, has been earlier 

proposed [19, 20] from optical studies on additively 

or electrolytically colored alkali halides doped 

with copper, silver or thallium. Their production 

by X-ray irradiation at RT is now supported by 

the EPR observation of the Sn" [11], Pb~ [21] and 

Bi° [22, 23] centers in KC1 crystals. The mechanism 

through which they are produced has been under 

debate since then [24]. By optical bleaching at 

300K in the negative ions optical absorption band 

(B-band), a new ns 1 -center called Ag^ has been observed 

[15, 16] in KCl:Ag + crystals. The proposed 

production mechanism of this center, suggested to 

be a Ag° atom at an anion site, consists of a simple 

ionization step: 

Ag" (12) 

Based on the positive identification by EPR spectroscopy 

of the Ag°, Ag^ and Ag° centers, the 

following sequence of reactions has been proposed 

[15, 16] to explain the production of negative ions: 

(A) Ag+ H 

(B) Ag°H 

(C) Agâ 

(D) Ag- 

hv{Ag°F) 

—Âga 

(13) 

where (A) and (B) correspond to reactions (1) and 

(9), respectively. Reactions (B) and (C) take place 

by optical excitation in the F and Kg°F absorption 

bands, respectively. Reactions (B) and (D) 

are thermally activated. Reaction (C) has been 

found to take place even at low temperatures, suggesting 

a tunneling process. The above set of reactions 

exclude the interstitialization of the silver 

atom [25, 26, 27]. Its general character remains to 

be confirmed from the study of other ions and lattice 

hosts. Although no Cu^ centers have been observed 

yet, the reactions (13) are considered to determine 

the formation of the Cu~ negative ions too 

[28]. Supporting evidence for the general character 

of reactions (13) comes from the identification of the 

M°, M°F and M° centers (M = Ga, In, Tl) in KC1 

and NaCl crystals after X-ray irradiation at room 

temperature [18, 29]. 

us -centers have been also observed in mixed alkali 

halides. Such centers exhibit a characteristic 

shf pattern due to the presence in the first neighborhood 

of the second type of anion. 

The production properties and structure of the 

ns 1 -centers in other lattice hosts are less known. 

Such centers were observed after irradiation with 

ionizing radiation, but very little effort has been 

devoted towards the study of their production and 

structural properties. It is, however, expected that 

in other ionic crystals the accompanying lattice defects 

would behave in a similar way as in alkali chlorides. 

In certain oxides and semiconductors, the 

ns 1 -type of paramagnetic centers have been already 

observed in the as grown crystals. In the latter case 

the concentration of the ns 1 -centers could be drastically 

changed by illumination in the band gap as a 

result of trapping the resulting free electrons/holes. 

III. Theory of the EPR Spectra 

A. The spin Hamiltonian of the ns 1 - 

centers 

The EPR spectra of the ns 1 ( 1 5) paramagnetic 

centers can be described by the general spin Hamiltonian 

H = g-S + S-A-I- gNfiNH • I 

(14) 

with the usual notations [1, 2], Here 5 = 1/2 and / 

may have one or more values, corresponding to the 

nuclear isotopes of the ns 2 -impurity involved (Table 

2). I n is the nuclear spin of the neighboring ligands. 

The spin Hamiltonian (14) contains terms describing 

the electronic Zeeman, hyperfine (hf), nuclear 

Zeeman, nuclear quadrupole (7 >l/2) and superhyperfine 

(shf) interactions, respectively. 

Due to the strong s—character of the electron 

wave function it is considered that the main contribution 

to the hf parameter A comes from the 

isotropic Fermi contact term 

— 

(15) 

where | 4>ns{ty | 2 represents the ns-wave function 

density at the central nucleus. A contribution to the 

isotropic hf parameter through the exchange polarization 

mechanism of the ns-electron with the inner 

electronic shells is expected to occur [2]. However,

Vol. 16, No. 3/4 197 

Table 2: Characteristic parameters of the naturally abundant nuclear isotopes with spin / ^ 0 occuring in 

the ns^centers. 

Nucleus 

63 Cu 

65 Cu 

67 Zn 

69 Ga 

71 Ga 

73 Ge 

107 Ag 

109 A g 

m Cd 

U3 Cd 

113In 

115In 

115 Sn 

117 Sn 

119 Sn 

197 Au 

199 Hg 

201 Hg 

205^ 

207pb 

Abund.(%) a 

69.09 

30.91 

4.11 

60.40 

39.60 

7.76 

51.82 

48.18 

12.75 

12.26 

4.28 

95.72 

0.35 

7.61 

8.58 

100 

16.84 

13.22 

29.50 

70.50 

22.6 

I(h) 

3/2 

3/2 

5/2 

3/2 

3/2 

9/2 

1/2 

1/2 

1/2 

1/2 

9/2 

9/2 

1/2 

1/2 

1/2 

3/2 

1/2 

3/2 

1/2 

1/2 

1/2 

9Nl*N 1 MHz\a 

h \ kG > 

1.1285 

1.2090 

0.2664 

1.0219 

1.2984 

-0.1485 

-0.1723 

-0.1981 

-0.9028 

-0.9444 

0.9310 

0.9329 

-1.392 

-1.517 

-1.587 

0.0731 

0.760 

-0.280 

2.433 

2.457 

0.8899 

* 2 (0)(au- 3 ) 6 

4.617 

4.617 

6.739 

10.18 

10.18 

13.40 

7.170 

7.170 

10.03 

10.03 

14.06 

14.06 

17.64 

17.64 

17.64 

12.86 

17.37 

17.37 

22.97 

22.97 

27.96 

^(MHz) 6 

5,995 

6,423 d 

2,087 e 

12,210 

15,514 d 

-2,363 

-1,593 d 

-1,831 

-13,650 

-14,279 d 

20,139 d 

20,180 

-38,523 d 

-41,938 d 

-43,920 

2,876 

41,880 

-15,429 d 

182,005 d 

183,800 

81,510 

A) xp (ymz) 

5,866.91 C 

-1,976.94/ 

-14,3853 

-15,385 9 

3,053.5^ 

40,507^ 

-14,995* 

175,90(P 

77,900 fc 

a 

Based on data published in Handb. of Chem. and Phys., 55th ed., CRC Press, Cleveland, 1974 and by 

Varian Assoc, Palo Alto, 1972. 

6 

Reference [30]. 

c 

Reference [31]. 

d 

Calculated by multiplying the value for the other isotope with the ratio of the corresponding nuclear mo- 

ments. 

e Reference [32]. 

/ Reference [33]. 

9 Reference [34]. 

h Reference [35]. 

{ Reference [36]. 

j Reference [37]. 

k Reference [38]. 

in the analysis of the hf parameter of the ns 1 centers 

this contribution is not explicitely considered, being 

either neglected or formally included in the contact 

term. 

Theoretical evaluations, as well as experimental 

data obtained from magnetic resonance measurements 

on ion beams or ions (atoms) trapped in inert 

gas matrices show (Table 2) that several I ^ 0 

isotopes exhibit large hf splittings (A 3> g/j,BH), at 

least in the microwave X-band (9 GHz) in which the


EPR measurements are usually performed. For this 

reason, in many cases, the spin Hamiltonian parameters 

are now determined by fitting the experimental 

magnetic field values of the EPR transitions with 

the corresponding values obtained from a numerical 

diagonalization of the spin Hamiltonian (14). 

In several particular cases accurate values of the 

spin Hamiltonian parameters have been obtained 

by fitting the transition fields with analytical solutions 

corresponding to the diagonalization of the 

spin Hamiltonian (14) in various approximations. In 

all cases the energy levels are mainly determined by 

the first two terms, which are the largest. 

The nuclear quadrupole interaction term has 

been considered only in a very few cases. It vanishes 

for / < 1/2. In other cases it is either too 

small, or it is difficult to determine, being a second 

order phenomena. 

The superhyperfine (shf) interaction with the 

nuclei of the neighboring ligands has been taken 

into consideration only in those cases when the corresponding 

structure in the EPR spectrum is resolved. 

Its theoretical treatment will be discussed 

separately. 

In the high symmetry crystal-lattice hosts, such 

as alkali halides, the EPR spectra, of the n5 1 -centers 

are isotropic, or there is a small anisotropy (~ 1%) 

in g and A, which is neglected. The EPR spectra 

are then described by the simple spin Hamiltonian 

H = -S + AS-I- I (16) 

The eigenvalues of (16) are given by the Breit-Rabi 

formula 

E(F,mF) = —— - 

±- AW 1 + 

Am p 

21 + 1 

1/2 

(17) 

where F — S + I,mF = m ± ^,x = 

gfiB)H/AW = gTfiBH/AW, AW = (A/2)(2I + 1). 

In the zero magnetic field there are only two levels 

with energies (A/2)I and -(A/2)(I + 1), separated 

by AW. Two types of transitions are observed, 

corresponding to the selection rules in the 

extreme cases: 

> A: AF = ±1, AmF = ±1 

(AM = ±l,Am = 0) 

< A: AF = 0, AmF = ±1 

(18) 

(19) 

In the strong magnetic field approximation [formula 

(18)] the intensity of the transitions are ~ 

jg 2 HBH 2 , where Hi is the microwave magnetic field 

component. For such transitions the spin Hamiltonian 

parameters can be determined with the aid of 

the following general formulae: 

21+1 

-A(2mgTfiBH) - (hu + 

-(gTiiBH) 2 = 0 

9T \ A ) 

V A 

hv + 

V 

(20) 

where v is the microwave frequency of the ESR transitions. 

In the g^BH S> A case, a perturbation solution 

of the spin Hamiltonian (16) in the third order 

of approximation gives the following formula for the 

magnetic field at resonance [40]: 

hv A I 1 A A 

gfj,B 

I A A 2 

Ag/j,B(hv) 

-m 2 gp,B hv 

\ 

H 7 

A 

A A 

g\xB 

(21) 

In the case of a weak magnetic field the spin 

Hamiltonian parameters can be determined from the 

following formula: 

A 2 

1 / r, ,, U \ 2 

— | I 

+(hv ± gNiiNH) 2 + = 0 (22) 

For some of the ns 1 -centers, such as Pb 3+ or Tl 2+ , 

two transitions corresponding to the selection rules 

(19) are observed at the magnetic fields H\ and H2. 

The spin Hamiltonian parameters are then obtained 

in a good approximation with the simple formulae: 

2hv(hv + A) 2hv(hv - A) 

9 = (2hu (2hv - 

(23)

Vol. 16, No. 3/4 199 

A = 

(24) 

Additional transitions, corresponding to the selection 

rules AM +_ 2, Am = 0, ±1, normally forbidden 

in the high field limit, can be observed in intermediate 

cases with intensities lower by a factor of 

(A/g^sH) 2 compared to the normally allowed ones. 

In many crystal lattices with lower symmetry the 

EPR spectrum of the ns x -centers exhibits a clear 

anisotropy, which was attributed [41] to the presence 

of an odd crystal field component which mixes the 

excited 2 P state into the ground 2 S state. 

The exact solutions of the anisotropic spin 

Hamiltonian (14), from which the last two terms 

were neglected, have been reported earlier [42, 43, 

44] for the case of the magnetic field along one of 

the principal axes, when 5 = 7 = 1/2. In the case 

of H || z they are: 

= ^ ± \ 

\{AX - 

(25) 

\(AX + Ay)2 

(26) 

The solutions for H \\ x and H \\ y are obtained 

by cyclic permutations of gi and Ax. Similar expressions 

have been reported for the 5 = 1/2, I = 5/2 

system [45, 32]. 

Approximate solutions to the secular equation, 

for moderately anisotropic spectra were obtained 

[46] by considering the anisotropy as a perturbation 

added to (16). The starting point is the expression 

of the magnetic field transition for the isotropic case 

written as, 

where 

/ _ 

/\2 

and 

Hm = H'm (for gNfiN = 0) 

Formula (27) is valid for all positive solutions and, 

in particular, for all values of 

/u/» (A/2) (21+1). 

The corrections to the EPR transitions, at fixed 

m, in the first order of perturbation associated with 

the anisotropy in the spin Hamiltonian are given by 

where 

coszm+i] 

m+-J coszm+± (28) 

1/2 

1/2 

sin 2. 

(29) 

and 

m 

Pm = 

(30) 

1 + 1/2 

In a different approach [47] the spin Hamiltonian 

(14) has been expressed in a reference frame associated 

to the magnetic field. Afterwards, only the 

following part of the rotated Hamiltonian has been 

diagonalized: 

ASZIZ 

1 (AzAxy + AxAy 

Axy 

(S+I- + S-I+) + [{QX COS 2 ip + Qy sin 2 

sin 2 6 + Qz cos 2 6] II - gNpNHIz 

(31) 

Here g and A have the usual [1] angular dependence 

of the polar angles 0 and ip of the magnetic field, in 

the frame associated to the principal axes of the g, A 

and Q tensors, considered coaxial. Assuming small 

anisotropies, the rest of the terms were neglected. 

Analytical expressions for the energy levels, wave 

functions and transition probabilities were obtained 

for I > 1/2, S = 1/2. 

Solutions for the first two terms of the spin 

Hamiltonian (14) with rhombic symmetry, for S =


I = 1/2, have been obtained [48] by rewriting it in 

a coordinate system associated with the magnetic 

field (H || C): 

Ho 

Hi 

H2 

H3 

— Ho + Hi + H2 + H3 

= gPHSt + KStl? 

= KiS+I?+KtS-I? 

— A20+J4- + A2O-i- 

— 1\3J + 1— + JX-iO — l^- 

(32) 

(33) 

(34) 

(35) 

(36) 

where K{ are polynomial expressions of g,, A, and 

orientation angles of H. The relative contribution 

of Hj's to 7is differs from center to center, but Hi 

is considered to be the smallest, at least for centers 

with large hf coupling. 

B. The superhyperflne interaction 

The interaction of the s-electron with the magnetic 

momenta of the neighboring ligands is considered 

as a perturbation, producing the shf splitting 

of the EPR lines. However, for the majority of the 

ns -centers its contribution consists only in an inhomogeneous 

broadening of the EPR lines. Neglecting 

the shf interaction in determining the spin Hamiltonian 

parameters might result in significant errors if 

a low field transition with energy comparable to the 

shf splitting is considered. 

Due to the usually isotropic character of the ns 1 - 

type EPR spectra the shf structure represents the 

main source of information concerning the structure 

of the involved center. 

The number and the intensity of the various components 

of the shf structure are obtained by the binomial 

rules [2, 40]. The shift of each component 

from the center of the EPR line is given by 

[{A\f cos 2 6 + {A\) 2 sin 2 d\^ (37) 

where 9 is the angle between the direction of the 

magnetic field and the bond direction, and mn represents 

the nuclear magnetic moment of the n-th ligand. 

Formula (37) can be rewritten by introducing 

the isotropic (AJ) and anisotropic (A") components 

of the shf tensor A n ; 

= A n s 

(38) 

The isotropic part (As) is considered to be mainly 

due to a Fermi-type interaction of the s-electron 

with the ligand nucleus. The anisotropic part (Aa) 

is a sum of two contributions: the anisotropic interaction 

of the p-orbitals (Ap) and the dipole-dipole 

magnetic interaction {Ap) between the paramagnetic 

electron and the ligand nucleus: 

A — A AD (39) 

The quantitative analysis of the shf parameters 

is usually performed [2, 49] by admixing the n's and 

n'p orbitals from the neighboring ligands into the 

central ns orbital. By considering covalency effects 

it is possible to explain the large positive Ag shift 

and the decrease of the hf constant A, compared to 

the free ion value Af. The same molecular orbital 

(MO) model in a covalency calculation offers a consistent 

interpretation of the optical absorption spectra 

of the ns 2 - and ns ^centers in crystals [50, 51]. 

According to the MO model, initially applied 

to octahedral [52] coordination (MX6 clusters) and 

tetrahedral [53] coordination (MX4 clusters) of ligands, 

the wave function of the paramagnetic electron 

is written as: 

where 

(40) 

(41) 

^s is the ns orbital of the central ion. Xs and X 

the linear combinations of atomic orbitals (LCAO) 

of the neighboring ligands with the same symmetry 

properties i.e., the a\g and a\ representations of the 

Oh and Td symmetry groups, respectively [49, 54]. 

Neglecting the overlap of the atomic orbitals, the 

hf constant is given in both cases by: 

A = N 2 Af 

where Aj is the free nsMon (atom) hf constant. 

The shf constants are given by: 

A, = HNX.fA", 

AD = 

(42) 

(43) 

where / is 1/6 and 1/4 for the MX6 and MX4 clusters, 

respectively. A® and A® represent the free ligand 

ion hyperfme parameters, 

2 

~-3\ 

5* /n'p 

(44)

Vol. 16, No. 3/4 201 

The Ag shift is given by the following formula, 

valid for both coordinations [53]: 

= ~N 2 [\l + XaXsmR{3px \x\3s) 

xAE(p- s)Ti~ lAE 

(45) 

where m is the electronic mass, R is the distance 

to the ligand, AE(p — s) is the energy separation 

between the n'p and n's orbitals, ((r) is the spinorbit 

interaction constant of the n'p electron and 

AE is the energy separation between the ground 

antibonding a\g orbital and the nonbonding t\g orbital, 

which can be determined from optical spectra. 

Formula (45) explains the large Ag shift observed 

for the ns 1 -centers in crystals with strong covalent 

bonding and offers the possibility of connecting the 

EPR and optical spectra. 

The relevant free-atom values in the above formulae 

were calculated [30] for elements from thallium 

to bismuth, using Hartree-Fock-Slater atomic 

orbitals [55]. Formula (42) shows a decrease of the 

hf-constant with an increase of the covalency. The 

consistency of the MO model has been checked for 

various ns 1 -centers by fitting the covalency parameters 

As and \a to the measured shf constants and 

afterwards calculating the hf constant A, according 

to formulae (44). The calculation usually results in 

a smaller hf-constant. Better results were obtained 

by considering [56] the overlap of the orbitals. The 

theory of Watanabe has been further refined [57], 

by choosing the wave functions which diagonalize 

the spin-orbit interaction as the basis wave functions. 

Such an approach takes a better account of 

the larger spin-orbit interaction in the progression 

of ligands from S, Se to Te. 

IV. EPR Results 

A. Trapped electron ns^centers 

Trapped electron ns -centers are easily produced 

by irradiating with ionizing radiation crystals doped 

with IB or IIB cation impurities, as well as by subsequent 

optical bleaching and/or pulse anneal at various 

temperatures. The corresponding trapped electron 

ns 1 -centers have been mainly observed in alkali 

halide crystals. 

1. The IB-group (Cu°, Ag°, Au°) 

With very few exceptions, the ns^centers associated 

with the IB-group impurity cations have been 

reported in copper and silver doped alkali halides. 

Gold centers were less studied, mostly due to the 

difficulties in doping (Tables 3-5). It is worthwhile 

mentioning that the IB-group cations, with 

d 10 outer electron configuration, can also trap holes 

resulting in paramagnetic d? transition ions. 

The alkali halide crystals employed in these studies 

were grown from melt, with about 0.1 to 0.2 

mol% of the impurity halide added. Both copper 

and silver halides being stable at high temperatures, 

large amounts of the corresponding Cu + or Ag + impurity 

ions are found in the crystals grown from melt 

(about 10% of the initial concentration). Due to 

the thermal instability of the gold halides, the doping 

with gold was done by adding the metal to the 

melt, under a chlorine atmosphere. 

The trapping of electrons by the Ag + and Cu + 

ions in alkali halides has been earlier suggested 

[25, 58] to explain the new optical absorption bands 

observed after X-ray irradiation. 

The first EPR spectrum of a ns 1 —center(Ag°) 

has been observed [9] in a KCl:Ag crystal after 

electron-irradiation at 77K. It consisted of two transitions 

attributed to the superposition of the hf components 

from the two silver isotopes with 7=1/2 

(Table 2). The interpretation of the well resolved 

shf structure confirmed the substitutional localization 

in a regular six-fold octahedral coordination, 

which suggests that the center is produced according 

to the reaction (1). The substitutional model of 

the Ag° centers in KC1 and NaCl, has been latter 

confirmed by ENDOR measurements [71, 72]. 

Cu° centers in alkali chlorides [31, 61] and Au° 

centers [59] in NaCl and KC1, have been also observed 

after X-ray irradiation at 77K. Their EPR 

spectra exhibit a more or less resolved shf structure 

and were interpreted with the spin Hamiltonian (16) 

to which the shf interaction was added. 

Due to the presence of two isotopes with I = 

3/2 (Table 2), the X-band EPR spectra of the Cu° 

centers consist of a pair of lines for each isotope, 

attributed to the (F = l,mF = -1) (F = 

2,mF = -2) and {F = 2,mF = -2) (F = 

2, mp = — 1) transitions (A > g(5H approximation). 

Gold has only one natural isotope with nuclear 

spin / = 3/2 and hf splitting A ~ g(5H (Table 2).


Table 3: The EPR parameters of the Cu°—type centers at 77K. The hf parameter A and the shf parameters 

As and Ap for the NN anion ligands are given in MHz. 

Center 

Cu^ in LiCl 

Cu° in NaCl 

Cu° in KCl 

Cu° in KCl 

Cu° in RbCl 

Cu£ in NaCl 

Cu°, in KCl 

Cu°(I") in KCl 

Cu°(I) in quartz a 

Cu°(II) in quartz" 

Cu°(III) in quartz a 

g 

1.999 

1.997 

2.000 

1.9992 

2.004 

1.995 

1.998 

5x=2.004 

5y=1.998 

5z=2.004 

p2=2.004 

52=2.006 

5,876 

5,566 

4,844 

4,858.1 

4,405 

2,380 

2,578 

4,800 

Ax=3,191 

^=3,186 

Az=3,130 

A2=3,029 

A2=3,464 

a Measured at 120K. Shf interaction with one 29 Si ligand. 

Three EPR transitions were observed [59] in the Xband. 

It has been mentioned [59] that before X-ray irradiation 

the alkali chlorides doped with copper or 

gold had to be annealed at high temperatures and 

quenched to 77K. This observation suggests that a 

certain amount of the two impurities enters the lattice 

in a higher valency state (+2, +3), resulting in 

impurity-cation vacancy aggregates which have to 

be thermally dispersed. 

From the analysis of the isotropic shf constant As 

of the Cu° and Ag° centers in alkali chlorides and 

in KBr, it has been found [66] a significant outward 

relaxation (between 14% and 27%) of the nearest ligands. 

This effect has been explained as an accommodation 

effect of the larger Cu° and Ag° atoms, 

compared to the host lattice cations. 

A strong temperature dependence of both hf constant 

A and isotropic shf constant As, has been observed 

at low temperatures, for the Ag° and Cu° 

centers in LiCl, NaCl and KCl [67], and for the Cu° 

centers in RbCl [61]. With the exception of the Cu° 

in KCl and RbCl, for all other centers both parameters 

decrease by increasing the temperature. No 

As 

75 

67 

31 

36 

28 

28 

503 

Ap 

5.6 

5.6 

2.8 

A,(r)=560 

28.3 

References 

[31] 

[31] 

[31] 

[60] 

[61] 

[62] 

[63] 

[64] 

[65] 

[65] 

[65] 

quantitative interpretation of the above results has 

been given yet. 

The quantitative evaluation [70] of the isotropic 

shf constant As for the Cu° and Ag° centers and 

of the hf constant A for the Ag° center in alkali 

chlorides, in the frame of the Adrian theory [68], 

resulted in a good fitting with the experimental data 

only for the Ag° centers in KCl and RbCl. 

An unusual behavior of the shf structure of the 

Cu° center in KCl at very low temperatures (T < 

20K) has been reported [60]. By lowering the temperature, 

the observed shf structure, characteristic 

for an interaction with six equivalent chlorine nuclei, 

becomes unresolved at T < 40K. Below 20K 

the shf structure is again resolved, but its interpretation 

shows that the Cu° atom is now displaced to 

an off-center position, along a (111) direction. A 

theoretical analysis of the shf parameters temperature 

dependence shows [69] that in the 30-40K range 

the interaction constant of the Cu° atom increases 

2.8 times for the nearest ligand lying in the direction 

of the off-center displacement and decreases for the 

other NN ligands. 

It has been suggested [61] that the similar tem-

Vol. 16, No. 3/4 203 

Table 4: The EPR parameters of the Ag°—type of centers at 77K. The hf parameter A and the shf parameters 


Center 

Ag" in LiCl 

Ag° in NaCl 

Ag° in NaCl a 

Ag° in KCl 

Ag° in KCl a 

Ag° in RbCl 

Ag° in KBr 

Ag° in KI 

Ag£, in LiCl 

Ag^ in NaCl 

Ag£ in KCl 

Ag£ in RbCl 

Ag°(I") in KCl 

Ag^(Br-) in KCl 

Ag° in SrCl2 

Ag° in KCl 

Ag° in L1KSO4 

Ag° in (NH4)2SO4 b 

Ag° in K2SO4 c 

Ag° in K2SO4 d 

Ag°(I) in quartz e 

Ag°(II) in quartz 6 

Ag°(III) in quartz 6 

g 

2.001 

1.999 

1.9951 

2.000 

1.9963 

2.001 

1.987 

1.966 

1.996 

1.996 

1.998 

1.994 

1.989 

1.996 

1.9934 

1.997 

2.0012 

2.002 

2.001 

#x=2.0002 

3y=1.9935 

fir2=2.0000 

52=1.9955 

02=1.9957 

\ im A\ 

1,927 

1,870- 

1,883 

1,890 

1,889 

1,878 

1,870 

1,855 

1,395 

1,835 

1,305 

1,285 

1,838 

1,323 

1,444 

2,025 

1,966 

2,133 

2,136 

^=1,300 

Ay=1,304 

A2=l,251 

^2=1,316 

4*=1,386 

ENDOR measurements. 

Measured at 290K. 

X-ray irradiated at 77K. 

X-ray irradiated at 300K. 

Measured at 120K. Shf interaction with one 29 Si ligand. 

perature dependence of the hf constant A observed 

for the Cu° center in KCl and RbCl must be due to 

the same off-center displacement of the Cu° atom. 

Another type of ns 1 -centers, called PSp centers, 

have been observed [75, 15] in silver doped alkali 

chlorides after X-ray irradiation at RT followed by 

optical bleaching in the F-band. Such centers have 

been latter obtained [63, 62] in copper doped NaCl 

and KCl, directly by X-ray irradiation at RT. Their 

As 

79.2 

68.3 

68.99 

37.2 

37.8 

29.4 

219 

269 

29.8 

35.7 

53.9 

351.7 

Ap 

2.8 

5.6 

4.0 

2.8 

3.89 

20 

>ls(I-)=404 

As(Br")=267 

6.1 

17.7 

References 

[70] 

[70] 

[71, 72] 

[70, 9] 

[71] 

[70] 

[73] 

[73] 

[74] 

[74] 

[74, 75, 15] 

[74] 

[76] 

[77] 

[78] 

[79, 75, 15] 

[78] 

[80] 

[81] 

[81] 

[65] 

[65] 

[65] 

concentration could be further increased by bleaching 

in the F-band. k°F centers have been directly 

observed [74] in silver doped thin films of alkali chlorides. 

A°F centers have not yet been reported in gold 

doped crystals. The corresponding spin Hamiltonian 

parameters are given in Tables 3 and 4. No shf 

structure has been observed in the EPR spectra of 

the A 1 ^ centers. 

It has been suggested [75] that the A°p center


Table 5: The EPR parameters of the Au°—type centers at 77K. The hf parameter A and the shf parameters 


Center 

Au^ in NaCl 

Au° in KC1 

Au£ in NaCl 

AuS in KC1 

Au£ in RbCl 

Au°, in NaCl 

Au°, in KC1 

Au°, in RbCl 

g 

2.001 

2.004 

2.00 

2.020 

2.024 

2.012 

2.010 

2.020 

consists of a ns 1 -atom (A = Cu°, Ag°) next to an 

anion vacancy. Because the unpaired electron is expected 

to be partly localized at the anion vacancy, 

it is possible to consider the A°F center as being an 

F-center next to the cation impurity. 

In the absence of a clear anisotropy of the EPR 

spectra, or of a resolved shf structure, the structural 

model of the AF centers had to be supported by 

indirect arguments. The proposed structural model 

has been initially based on the similar production of 

the A^ centers with the F^ centers [17]. 

Additional arguments favoring the A°F center 

model, were based on the analysis of the hf constant 

shift 8A and of the linewidth of the various 

ns x -centers [75]. 

According to formulae (15) and (42) the quantity 

A -Aj 

A~ = 8A •f (46) 

which is the relative shift of the hf constant A to the 

free atom/ion hf constant Af, represents the degree 

of the delocalization of the paramagnetic electron 

at the neighboring ligands. Due to the F-character 

of the unpaired electron wave function at the anion 

vacancy site, the A°F structural model with a 

neighboring anion vacancy involves a large 8A shift. 

By examining the hf constant of the corresponding 

M° and A°F center (Tables 3,4), it was found 

that in each particular case 8A(A°F) > 6A(M®). 

For example, in the case of the Ag° centers in KC1 

8A{A%) = 34% > 6A(Ag°) = 4.4%. This type of 

| i97 A| 

2,840 

2,530 

2,350 

2,170 

1,980 

2,780 

2,410 

2,160 

As 

46.2 

36 

Ap 

56 

References 

[59] 

[59] 

[59] 

[59] 

[59] 

[59] 

[59] 

[59] 

argument has been latter employed to identify new 

A°F centers. 

Considering the linewidth of the ns 1 -centers as 

being mainly determined by the isotropic shf constant 

As, in the case of the AF centers one has to 

consider the shf interaction with five anions next 

to the ns 1 atom and the shf interaction with five 

cations next to the anion vacancy. It is then expected 

that crystals grown with various isotopic 

pure cations will exhibit different linewidths of the 

A°F centers. Using single crystals of alkali chlorides 

grown from the isotopic pure cations 39 K, 41 K, 

85 Rb and 87 Rb, a variation in the linewidth of the 

Ag^ centers from 4.5 mT in 39 KC1 to 16 mT in 

87 RbCl was determined [82], which could be accounted 

for by the anion vacancy model. New 

ns^centers, called Cu°(X~~) and Ag°(X~), where 

X~ =I~ and Br~, have been observed [64, 77, 83] 

in mixed crystals of KCl(KI) and KCl(KBr). The 

structural model, inferred from the analysis of the 

shf structure is based on a M° model (M = Cu, Ag) 

with one of the six neighboring ligands replaced by 

an impurity anion. The larger isotropic shf constant 

As (X~) due to the shf interaction with the NN impurity 

anion, compared to the shf constant with the 

NN host anions, suggests a local deformation of the 

crystal lattice. 

The trapping of an anion vacancy next to a 

cationic substitutional neutral impurity atom is now 

supported by the direct observation [10, 18] of such 

a process in the EPR spectra of the anisotropic

Vol. 16, No. 3/4 205 

np 1 -M°(l) centers (M=Ga,In,Tl). An analysis of 

the production properties of the A°F centers [15, 75] 

shows that reactions (9) and (11) are involved in the 

formation of both M°(l) and A^ centers. 

Alkali chloride crystals doped with gold exhibit 

after X-ray irradiation at 77K, besides the cubic Au° 

centers, a second type of ns^centers, called Au° centers 

[59]. The Au° centers are converted to new Au° 

centers by annealing above 140K. The Au° centers 

exhibit the largest 6A shift and an isotropic splitting 

of the EPR lines in 7 equidistant components, with a 

maximum along a (100) direction. They are considered 

[59] to consist of an Au° atom at a cationic site, 

with a Vfc center in the NN anion site, along a (100) 

direction. The Au°, centers, with a 6A shift slightly 

larger compared to the Au° centers and with similar 

linewidths, are considered [59] to be Au° centers 

with a perturbing defect in a NNN position. 

The X-ray irradiation at RT of the silver doped 

alkali chlorides results in the formation of Ag°, Ag 2+ 

and F-centers, with their characteristic EPR spectra, 

as well as of negative Ag~ ions, supposed to 

be localized at anion sites and identified by their 

optical absorption B-band [19, 20]. 

The Ag° center, observed [15, 75] after optical 

bleaching at 300K, in the B-band of the KCl-Ag 

crystals, is considered to be a silver atom at an unperturbed 

anion site, produced according to reaction 

(12). In the absence of a resolved shf structure 

the anion localization of the silver atom is suggested 

by the smaller linewidth; 2.1 mT for the Ag° centers 

in KC1, compared to 4.1 mT for the Ag^ centers, 

both at 300K. Because they are produced at temperatures 

where the vacancies are mobile, the presence 

of vacancies in the neighborhood of the Ag~ or Ag° 

centers cannot be however completely excluded. 

The observed linewidth and hf constant increase 

with temperature of the Ag^ centers, for T < 100K, 

has been explained [79] by an off-center displacement 

in a (111) direction, by analogy with the Cu° 

centers in RbCL 

The production of a dimer-type of trapped electron 

center has been reported [84] in KCl:Ag crystals, 

after long X-ray irradiation at RT. The resulting 

Agj" center exhibits an isotropic EPR spectrum 

with ^=1.986, suggesting the unpaired electron to 

be localized in a s-type orbital. A well resolved shf 

structure could be observed in samples doped with 

silver enriched in the 109 Ag isotope. It has been sug- 

gested that the Ag j" center consists of two Ag + ions 

in a cation site, which have trapped an electron. 

Ag° centers have been reported in X-ray irradiated 

SrCl2 and LiKSC-4 crystals doped with silver 

[78]. A partly resolved shf structure has been observed 

for the SrCl2 crystals, suggesting a cationic 

localization of the Ag° atom, but no detailed analysis 

has been reported. Atomic Ag° centers have 

been also observed [85, 81] after X-ray irradiation 

at RT of silver doped (NH4)2SO4 and K2SO4 crystals, 

both exhibiting low symmetry crystal lattice 

and structural phase (SP) transitions. 

2. The IIB-group (Zn+, Cd+, Hg+) 

The elements of the IIB-group are expected to 

enter the crystal lattice in their +2 valency state. In 

the case of the alkali halides, in which the resulting 

ns 1 -centers were mainly reported, several effects are 

to be expected: 

• The segregation coefficient during the growth of 

such doped crystals is larger than in the case of the 

doping with monovalent impurities. Consequently 

a smaller concentrations of IIB-group impurities is 

found in the resulting crystals. For example, the 

concentration of cadmium in the KBr crystals was 

found to be 200 times smaller than in the melt [86]. 

• The IIB-group impurities enter the lattice accompanied 

by an equal number of charge compensating 

cation vacancies, usually at NN lattice sites. 

• The impurity-charge compensating vacancy 

pairs have the tendency to aggregate, even at RT. 

Consequently, before producing ns^centers by irradiation 

the samples have to be annealed at temperatures 

close to the melting point and quenched at RT 

or even at lower temperatures, in order to achieve 

their dispersion. 

The presence of trapped electron ns 1 -centers in 

crystals doped with IIB impurities has been initially 

suggested [87] from optical studies on additively colored 

KChCd crystals. 

Cubic Cd,f centers have been observed by EPR in 

alkali chlorides [88, 89] after X-ray irradiation at RT, 

or after X-ray irradiation at 77K followed by warming 

up to temperatures close to RT, where the initially 

bound cation vacancy could move away. Cubic


Zn+ centers in NaCl and cubic rlg^ centers in LiCl, 

NaCl and KC1 were obtained by similar production 

procedures [90]. They all exhibit well resolved shf 

structures, characteristic for a substitutional Me + 

(Me = Zn, Cd, Hg) ion in a regular octahedral coordination 

of chlorine ligands. 

The EPR spectra of the Zn+ centers in NaCl 

exhibit only one transition at g ~ 2, due to the even 

isotopes. The hf transitions from the 67 Zn isotope, 

with 7 = 5/2 and natural abundance of 4.16%, could 

be observed [90] only in crystals doped with 88% 

enriched 67 Zn isotope. 

Natural cadmium contains six isotopes, of which 

four are even isotopes (7 = 0) and only two exhibit 

nuclear moments ^jv > 0 (Table 2). The X-band 

spectrum of the Cd + centers consists of a line at 

g ~ 2, from the even isotopes and two pairs of lines 

due to the hf transitions of the odd isotopes, 

and 

(F = l,mF = 1) (F = 0,mF = 0) 

(F=l,mF = = l,mF = 

Natural mercury contains, besides the even isotopes 

with 7 = 0, two isotopes with 7 = 1/2 and 

3/2 and nuclear momenta of opposite sign (Table 

2). Consequently, the X-band EPR spectra exhibit, 

besides the g ~ 2 line, two lines from the hf transitions, 

and 

(F = l,mF = -1) (F = l,mF = 0) 

(F = 1, mF = 0) *—> (F = 1, mF = 1) 

of the 199 Hg isotope and one line from the hf transition, 

(F = 2, mF = 1)

Vol. 16, No. 3/4 207 

Table 6: The EPR parameters of the Zn + -type centers at 77K. The hf parameter A and the shf parameters 


Center 

Zn+ in NaCl 

Zn+ in CaCO-3 

Zn+ in K2SO4 

site I 

Zn + in K2SO4 

site II 

g 

1.999 

311=2.0008 

5x=1.9965 

^=1.9975 

3y=1.9965 

p2=2.0010 

3x=l-999 

^=2.004 

gz=2.005 

RT irradiation. The resolved shf structure has been 

interpreted with a substitutional model in which the 

Cd + ion is surrounded by a regular cube of eight F~ 

ligands. 

EPR spectra attributed to Cd + centers have 

been reported in Cd 2+ doped f3—K2SO4 crystals 

[94] and Cd 2+ doped (NH4)2SO4 crystals [95, 96] after 

X-ray irradiation at RT. The two rhombic EPR 

spectra (Table 7) have been attributed to Cd + ions 

at the two inequivalent cation sites with Cs symmetry, 

which are distinguished by their different coordination. 

It has been reported [94] that the Cd + 

centers are not produced in the /3—K2SO4 crystals 

by X-ray irradiation at 77K. No shf structure has 

been reported for these centers. 

Anisotropic EPR spectra attributed to Zn + type 

centers have been reported in irradiated CaCO3 

(calcite) [32] and K2SO4 crystals [45]. The EPR 

spectrum, observed after 7-ray irradiation at RT of 

natural calcite crystals containing 0.05% zinc, exhibits 

axial symmetry, characteristic for a Zn + ion at 

a Ca 2+ site. The strong intensity of the EPR spectrum 

made possible the observation of the hf structure 

of the 67 Zn isotope. The observed six hf components 

were attributed to the AF — 1, Amp = 0 

transitions. The spectral parameters (Table 6) were 

determined by using the following analytical expressions 

of the resonance fields for the axial case [32]: 

hv 

\ 67 A 

2,030 

A||=l,444 

A_L=1,412 

As=l,569 

Ay=l,568 

Az=l,595 

i4x=l,730 

Aj,=l,750 

^=1,750 

Aa 

56 

5/?3,4 = T^ 

where 

Ap 

5.6 

for H || (111), and 

References | 

[90] 

[32] 

[45] 

[45] 

= 9\\, 

A=z:A \\ 

a = 2 142] 

9 = 9±, 

a = 4 [{hvf - Iî] 

a + â 2 \ ' hv (49) 

a I hv 

16 

for HI (111). 

The number of the Zn + centers observed in 

K2SO4 crystals after irradiation at RT depends on 

the nature of radiation [45]. Eight centers have been 

observed after X-ray irradiation and four centers after 

7-ray irradiation. No EPR spectra attributed to 

Zn + centers could be observed after irradiation at 

77K. Two of the Zn + centers, called I and II, and 

considered to be situated substitutionally at the two 

K + sites, were found to be the most stable, their 

concentration increasing by subsequent warm-up to 

400K, an effect also reported in alkali chloride crystals 

[91]. EPR spectra were recorded in both X and


Table 7: The EPR parameters of the Cd + —type centers at 77K. The hf parameter A and the shf parameters 


Center 

Cd+ in LiCl 

Cd+ in NaCl 

Cd+ in KCl 

Cd+ in LiCl 

Cd+(I) in NaCl 

CdJ(II) in NaCl 

Cd+(III) in NaCl 

Cd+(I) in KCl 

Cd+(II) in KCl 

Cd£ in LiCl 

Cd+ in NaCl 

Cd+ in KCl 

Cd+ in CaF2 

Cd+ in SrF2 

Cd+ in BaF2 

Cd+(I) in /3-K2SO4 

Cd + (II) in /3-K2SO4 

Cd+ in (NH4)2SO4 a 

site I 

Cd+ in (NH4)2SO4 a 

site II 

Measuring temperature 290K. 

g 1 r AI 

1.998 

1.996 

1.996 

1.998 

1.995 

1.998 

2.000 

1.998 

1.998 

1.993 

1.990 

2.00 

1.9984 

1.9965 

1.9896 

1.999 

0X=1.996 

5y=1.998 

c/2=2.000 

gx=l.9975 

gy=1.9972 

5z=2.0002 

Vol. 16, No. 3/4 209 

Table 8: The EPR parameters of the Hg + —type of centers. The hf parameter A and the shf parameters As 

and Ap for the NN ligand are given in MHz. 

Center 

Hg+ in LiCl 

Hg+ in NaCl 

Hg+ in KCl 

Hg+ in (NH4)2SO4 

site I 

Hg+ in (NH4)2SO4 

site II 

Hg+ in KH2PO4 

Hg+ in NH4H2PO4 

T(K) 

77 

77 

77 

290 

290 

300 

300 

g 

1.997 

1.999 

1.998 

0X=1.9959 

gy=1.9948 

gz=1.9927 

5X=1.9941 

5y=1.9941 

&=1.9967 

5||=1.9965 

pj.=1.9972 

511=1.9959 

5±=1.9950 

148K, the phase transition temperature to the ferroelectric 

phase of NH4H2PO4. The shf structure 

has been attributed to the interaction with protons 

(7=1/2). 

B. Trapped hole ns^centers 

The trapped hole n^-centers are easily produced 

by irradiating with ionizing radiation crystals 

doped with IIIA or IVA cation impurities. However, 

in studying their production properties one should 

take into consideration that such cations can also 

act as electron traps, resulting in paramagnetic np 1 - 

type centers [98]. The trapped hole ns 1 -centers have 

been observed not only in alkali halides but also in 

many other ionic and semiconducting crystals. 

1. The IIIA-group (Ga 2+ , In 2+ , Tl 2+ ) 

The IIIA-group cations enter the alkali halides lattice 

mainly as monovalent ions. Consequently, it is 

possible to grow doped crystals containing relatively 

large concentrations of such impurities, especially 

thallium. It seems that in gallium or indium doped 

alkali halide crystals a certain amount of impurities 

are in a higher valency state (+3). This could explain 

the increased concentration of the ns 1 -centers 

32,690 

32,100 

32,790 

Ax=34,046 

Ay=M,08Q 

A2=34,060 

Ax=34,043 

Ay=33,962 

Az=34,009 

A||=34,174 

A±=33,994 

A||=33,944 

^x=33,973 

54.2 

47.2 

38.0 

13.4 

13.0 

Av 

13.4 

11.4 

8.94 

References 

[90] 

[90] 

[90] 

[95] 

[95] 

[36] 

[36] 

obtained in samples annealed at high temperatures 

before irradiation, as well as the presence of new 

ns 1 -centers with cation vacancies in their structure 

after low temperature irradiation [99, 100]. 

Cubic ns^M 24 " (M = Ga, In, Tl) centers have 

been obtained in alkali chloride crystals after X-ray 

irradiation at various temperatures. The highest 

concentration was obtained [52, 56, 99, 100] by irradiating 

at 77K and pulse-annealing at temperatures 

where the holes are mobile (> 170K in KCl). 

The resulting Ga 2 +, In 2+ and Tl 2 ," 1 " centers exhibit 

a well resolved shf structure for the magnetic field 

along the main crystal axes. The analysis of the shf 

structure confirms [52, 56] the regular octahedral 

symmetry of the surrounding ligands. 

Additional isotropic EPR spectra, without shf 

structure, attributed to noncubic n^-centers have 

been observed [99, 100] in gallium and indium doped 

KCl crystals after X-ray irradiation at 77K. The one 

(Ga 2+ )' and the two (In 2+ )' and (In 2+ )" centers observed 

in KCl have been considered to consist of a 

Ga 2+ and In 2+ substitutional ion, respectively, next 

to a cation vacancy. The presence of two noncubic 

In 2+ centers has been attributed [100] to the existence 

of two ns 1 ion-cation vacancy configurations. 

It is considered [100] that in the (In;? + )" centers,


which are produced at higher temperatures than 

the (In 2+ )' centers and exhibit a partly resolved shf 

structure, the vacancy is farther away from the In 2+ 

ion, resulting in a smaller perturbing effect. 

High concentrations of cubic Tl 2+ centers were 

produced by X-ray irradiation at 77K of double 

doped KCl:Tl:Pb and NaCl:Tl:Pb crystals [100]. 

This effect has been explained by the strong electron 

trapping properties of the Pb 2+ ions [101, 102]. By 

warming up such crystals, at temperatures corresponding 

to the onset of motion of cation vacancies 

released by the Pb + centers, it has been than possible 

to obtain Tl 2+ vc centers according to reaction 

(6). The presence of such centers was reflected in 

the splitting of the Tl 2+ hf structure in two components 

with less resolved shf structure. 

The EPR spectra of the M 2+ (M = Ga, In, Tl) 

centers were described by the spin Hamiltonian (16), 

with or without the shf interaction term. 

The EPR lines of the Ga 2+ centers, observed in 

the X-band, were attributed to the transitions (F = 

2,mF = -2) (F = 2,mF = -1) and (F = 

\,mF — —1) *—* (F = 2, mF = —2) from the two 

natural isotopes 69 Ga and 71 Ga, both with nuclear 

spin / = 3/2 (Table 2). 

Indium has two natural isotopes, 113 In and 115 In, 

both with / = 9/2 (Table 2). The X-band EPR spectrum 

consists of one line, due to the transition (F = 

5,mF = —5) (F = 5,mF = —4), which can be 

seen at high magnetic fields (~ 1.5T). Another transition 

(F = -5,mF = -5) (F = 4,mF = -4) 

has been observed in the Q-band. 

The large zero-field splitting and the close nuclear 

momenta of the two thallium isotopes 203 Tl 

and 203 Tl, both with / = 1/2 (Table 2), yields an 

EPR spectrum consisting of two lines. They represent 

the superposition of the transitions (F = 

l,mF = 0) (F = l,mF = -1) and (F = 

l,mF = 1) (F = l,mF = 0) from the two 

isotopes. The spin Hamiltonian parameters can be 

determined with the formulae (23,24). 

The isotropic EPR spectrum, without shf structure, 

observed [103] in SrCl2:Tl crystals after X-ray 

irradiation at 77K, has been attributed to Tl 2+ ions 

with a neighboring charge compensating vacancy. 

By pulse annealing above 130K the vacancy moves 

away resulting in a partly resolved shf structure. 

Isotropic Ga 2+ centers [104, 105, 106], In 2+ centers 

[107, 105] and T1 2 + centers [105] have been ob- 

served in ZnS crystals by photostimulation. All centers 

exhibit large 5A shifts, compared to the corresponding 

cubic centers in alkali chlorides (see Tables 

8-10). Such large 6A values can be explained by the 

stronger covalent character of the bondings in ZnS 

(formula 42). 

Slightly anisotropic ns 1 -type EPR spectra, attributed 

to Ga 2+ in silicon [109], In 2+ in ZnO 

[110], Tl 2+ in hexagonal ZnS [105] and in K2SO4 

[111, 112], have been also reported. The anisotropy 

of the EPR spectra of the Tl 2+ centers in the orthorhombic 

/3-K2SO4 has been quantitatively explained 

[111] by the effect of the odd crystal field 

component at the cation sites (C5-local symmetry). 

By using a cluster model in deriving the effective 

crystal field operator, a good agreement between the 

calculated and the experimental spin Hamiltonian 

parameters has been obtained [111]. 

The spin-lattice relaxation time T\ of the Tl 2+ 

centers in K2SO4 has been measured in the 1.5 to 

25K temperature range by observing the spin-echo 

signal [113]. It exhibits a temperature dependence 

of the form: 

Tf 1 = LOT x 3.3 x l(T 5 T/(0/T) (50) 

where T is the temperature, #=120K is the Debye 

temperature and f(0/T) is a factor describing the 

deviation from a pure Raman process, attributed 

[113] to the large hf splitting. 

Tl 2+ centers produced by X-ray irradiation 

have been used as paramagnetic probes in studies 

concerning structural phase transitions, such as 

the paraelectric/ferroelectric transition in KD2PO4, 

Rb2H2PO4 and (NH4)2SO4 crystals [41, 114, 115, 

116, 117] and the paraelectric/antiferroelectric transition 

in NH4H2PO4 crystals [118]. The measured 

spin Hamiltonian parameters (Table 11) are slightly 

but clearly anisotropic, reflecting the local symmetry 

of the paramagnetic center and the changes in 

the local symmetry, such as the lowering of the symmetry 

by going from the paraelectric phase to a ferroelectric 

or antiferroelectric one. 

The spontaneous symmetry breaking and the local 

freeze-out during the transition from the paraelectric 

to the ferroelectric phase has been studied 

[117] in the KH2ASO4 crystals using both Tl 2+ and 

AsO4~ paramagnetic centers, simultaneously produced 

by X-ray irradiation at 77K. The spectra of 

both centers exhibit axial symmetry in the high

Vol. 16, No. 3/4 211 

Table 9: The EPR parameters of the Ga 2+ —type centers. The hf parameter A and the shf parameters As 

and Ap with the NN ligands are given in MHz. 

Center 

Ga^+ in NaCl 

Ga 2+ in KCl 

Ga 2 , + in KCl 

Ga 2+ in ZnS(cub) 

Ga 2+ in ZnS(hex) 

Ga 2+ in ZnS a 

Ga 2+ in Si 

a ODMR measurements. 

T(K). 

77 

77 

77 

20 

20 

2 

g 

2.062 

2.012 

.2.01 

1.9974 

2.0006 

2.001 

2.001 

5||=2.0014 

51=1.9973 

9,350 

8,860 

6,320 

6,076 

6,200 

Acub=6,080 

Ahex=Q,150 

A||=3,292 

A±=3,253 

As 

52.2 

47.9 

Ap 

12.1 

11.5 

References 

[99] 

[99] 

[99] 

[105, 106, 108] 

[105, 106, 108] 

[104] 

Table 10: The EPR parameters of the In 2+ —type centers. The hf parameter A and the shf parameters As 

and Ap for the NN ligands are given in MHz. 

Center 

In 2+ in KCl 

(In 2+ )' in KCl 

(In 2+ )" in KCl 

In 2+ in ZnS(cub) 

In 2+ in ZnS(hex) a 

In 2+ in ZnO a 

T(K) 

77 

77 

77 

77 

2 

2 

2 

2 

g 

1.98 

2.00 

1.98 

1.993 

0H=1.9574 

51=1.9562 

14,700 

12,000 

14,000 

9,362 

9,720 

9,630 

9,510 

A,|=100.24 

A_L=100.14 

As 

52.4 

49.2 

a ODMR measurements. The hf constants correspond to three different sites. 

temperature, paraelectric phase, and orthorhombic 

symmetry with additional splittings due to the presence 

of four inequivalent lattice sites, in the low temperature, 

ferroelectric phase. It has been observed 

that the temperature dependence around the transition 

temperature Tc of the additional line splitting 

due to the presence of domains of opposite polarization 

is different for the two paramagnetic centers. 

The corresponding spontaneous dynamic sym- 

Ap 

13 

12 

[109] 

References 

[100] 

[100] 

[100] 

[105] 

[107] 

[110] 

metry breaking, seen above Tc in the EPR spectra 

of AsO^", but not of Tl 2+ , has been explained by 

the different coupling of the two defects to the surrounding 

pseudospins. 

2. The IVA-group (Ge 3+ , Sn 3 +, Pb 3+ ) 

The impurities of the IVA group of elements enter 

the ionic crystals mainly as divalent ions: Ge 2+ , 

Sn 2+ and Pb 2+ . Consequently, monovalent lattice


Table 11: The EPR parameters of the Tl 2+ —type centers. The hf parameter A and the shf parameters As 


Center 

Tl^+ in NaCl 

Tl 2+ in KCl 

Tl 2+ in RbCl 

Tl 2+ in KBr 

Tl 2+ in SrCl2 

T1 2 + in ZnS(cub) 

Tl 2+ in ZnS(hex) 

Tl 2+ in CdTe 

T1 2 + in K2SO4 

site I 

Tl 2+ in K2SO4 

site II 

Tl 2+ in NH4H2PO4 a 

(antiferro. phase) 

Tl 2+ in KH2PO4 

and KH2As04 b 

(ferro. phase) 

Tl 2+ in Rb2H2PO4 


Tl 2+ in KD2PO4 


Tl 2+ in (NH4)2SO4 


T(K) 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

85 

77 

110 

77 

85 

g 

2.009 

2.010 

2.010 

2.067 

2.0120 

2.0095 

511=2.0093 

5_L=2.0103 

2.035 

^=1.997 

5y=1.995 

^=1.998 

^=1-993 

gy=1.994 

gz=1.997 

5^=1.988 

Sy=1.994 

gz=l.998 

ly=109,145 

A=108,103 

Aa 

45.9 

42.6 

42.6 

173.3 

697.7 

a Slightly different values of the hf constant are reported in Reference [121]. 

6 As reported in Reference [16]. 

hosts, such as alkali halides, can be doped only with 

relatively low concentrations (~ 10 2 ppm) of such 

impurities. The doping with germanium is even 

more difficult due to the low boiling point and thermal 

instability of germanium halides. The presence 

of the charge compensating cation vacancies is expected 

to have the same consequences as in the case 

Ap 

17.1 

15.9 

15.9 

70.2 

185 

of doping with IIB impurities. 

References 

[56] 

[56, 52] 

[56] 

[56] 

[103] 

[105] 

[105] 

[119] 

[111] 

[111, 112] 

[118] 

[115, 41] 

[114] 

[41] 

[116] 

Ge 3+ centers have not yet been reported in alkali 

halides. However, germanium doped NaCl and 

KCl crystals have been obtained and the electron 

trapped Ge + centers could be observed after X-ray 

irradiation [122]. 

A Ge 3+ center, exhibiting the largest reported hf

Vol. 16, No. 3/4 213 

Table 12: The EPR parameters of the Ge 3+ —type centers. The hf parameter A and the shf parameters As 


Center 

Ge d+ in BaGeF6 

Ge 3+ in ZnS(cub) 

Ge 3+ in ZnSe 

Ge 3+ in ZnTe 

Ge 3+ in CdS 

Ge 3+ in CdTe 

Ge 3+ in quartz; 

A(GeLi) center 


C(GeLi) center 


(Ge(I)e~)~ center 


(Ge(II)e~)~ center 


(Ge(A)e-/Li+)°, 

or A, or AM+ center 


(Ge(A)e-/Na + )° 

center 


(Ge(C)e-/Li+), 

or C, or Cji/+ center 


(Ge(C)e-/Na+) 

center 

T(K) 

30 

77 

77 

77 

77 

20 

300 

300 

77 

77 

77 

300 

77 

300 

g 

2.0038 

2.0086 

2.4026 

2.1375 

5H=2.0021 

5_L=2.0059 

2.1451 

Sx=1.9913 

5y=1.9965 

5z=2.0014 

5X=2.0000 

5y=1.9973 

5Z=1.9962 

51=1.9941 

52=2.0012 

53=2.0023 

51=1.9936 

52=2.0010 

53=2.0015 

51=1.9907 

52=2.003 

53=2.0019 

51=1.9918 

52=2.0002 

53=2.0015 

51=1.9947 

52=1.9983 

53=2.0014 

51=1.9959 

52=1.9970 

53=2.0005 

| 73 A| 

1,779 

914 a 

782 

657 

635.6 

a A value of 864MHz is reported in Reference [130]. 

A±=990 

615 

Ax=278.69 

Ay =295.63 

Az=282.06 

Ax=864.5 

Ay=823.15 

A2=825.3 

Ac=776 

constant, has been observed [123] in 7-ray irradiated 

powders of BaGeFg. The center, which seems to be 

a self-trapped hole, exhibits a shf structure from a 

regular octahedron of six NN F" ligands. 

The EPR spectra of the Ge 3+ centers consist of 

Ac=782 

Ac=785 

Ac=758 

Ac=845 

386 

508 

476 

573 

As 

Ac/( 29 Si)=3.6 

Ac,,( 29 Si)=6.7 

Ac»/( 29 Si)=ll 

Ai( 7 Li)=1.15 

A2( 7 Li)=2.94 

A3( 7 Li)=1.29 

yli( 23 Na)=1.71 

A2( 23 Na)=2.74 

yl3( 23 Na)=1.71 

Ai( 7 Li)=2.3 

A2( 7 Li)=-0.2 

A3( 7 Li)=-0.9 

Ai( 23 Na)=1.9 

^2(23Na)=2.5 

A3( 23 Na)=2.97 

Ap 

98.1 

204 

192 

170 

References 

[123] 

[124] 

[125] 

[126, 124] 

[108] 

[127] 

[126] 

[128, 129, 121, 46] 

[128, 129, 121, 46] 

[121] 

[121] 

[128, 121] 

[129, 121] 

[128, 121] 

[121] 

an intense line at 5 ~ 2 from the even isotopes and 

a weak hf structure of 10 lines from the 73 Ge isotope 

with / = 9/2 (Table 2). Due to the small 

zero-field splitting, the hf structure is due to the 

AM = ±l,Am = 0 transitions, described by for-


Table 13: The EPR parameters of the Sn 3+ —type centers. The hf parameter A and the shf parameters As 


Center 

Sn 3+ in NaCl 

(Sn 3+ )' in NaCl 

(Sn 3+ )" in NaCl 

Sn 3+ in KCl 

(Sn 3+ )' in KCl 

(Sn 3+ )" in KCl 

(Sn 3+ )/ in KCl 

(Sn 3+ )// in KCl 

Sn 3+ in SnCl2 

Sn 3+ in Snl2 

Sn 3+ in SnSO4 

Sn 3+ in K2SnF6 

Sn 3+ in CdS 

Sn 3+ in CdSe 

Sn 3+ in CdTe 

Sn 3+ in ZnS(cub) 

Sn 3+ in ZnS(hex) 

Sn 3+ in ZnSe 

Sn 3+ in ZnTe 

Sn 3+ in ZnO 

T(K) 

77 

77 

77 

77 

77 

77 

35 

35 

77 

77 

77 

30 

77 

77 

20 

77 

20 

g 

2.011 

2.00 

2.00 

2.013 

2.00 

2.00 

2.011 

1.997 

2.00 

2.00 

1.993 

2.0011 

5,1=2.0024 

5J_=2.0031 

5,1=2.0059 

2.1012 

2.0057 

2.0075 

2.0176 

2.0251 

2.1001 

1.9877 

mulae (20). The spin Hamiltonian parameters of 

the various Ge 3+ centers are presented in Table 12. 

Although the 73 Ge isotope has a small abundance, 

the corresponding hf structure has been reported 

in irradiated SiO2 (quartz) [43, 46, 128, 129]. 

Ge 3+ centers have been also observed in as grown 

II-VI semiconductors doped with germanium by diffusion. 

The concentration of the Ge 3+ centers could 

be drastically altered by photoexcitation with light 

of energy close to the band gap. The shf structure 

observed in ZnSe [125], ZnTe [126, 124] and CdTe 

[126], has been attributed to the interaction of the 

4s electron with the nuclei of the tetrahedrally coordinated 

ligands 77 Se (/ = 1/2, 7.58% abundant), 

123 Te (/ = 1/2, 0.9% abundant) and 125 Te (/ = 1/2, 

7% abundant), respectively. 

| 119 ^| 

24,600 

20,500 

25,200 

24,400 

20,100 

25,200 

19,220 

22,610 

4is=17,495 

As=28,676 

i4is=29,330 

29,745 

.4,1=15,825 

Ax=15,212 

X|,=13,663 

11,794 

15,644 

16,353 

14,780 

14,291 

12,265 

9,974 

46.1 

49.5 

51.2 

48.9 

320.6 

597 

541 

Ap 

15.2 

14.1 

20.5 

12.6 

94.5 

204.7 

224 

References 

[26] 

[131] 

[131] 

[26] 

[131] 

[131] 

[132] 

[132] 

[133] 

[133] 

[133] 

[123] 

[127] 

[127] 

[126] 

[130] 

[134] 

[57] 

[108] 

[126] 

[135] 

The natural tin contains, besides the even isotopes, 

three isotopes with nuclear spin / = 1/2, but 

different nuclear momenta and abundances (Table 

2). For this reason it is difficult to study the hf interaction 

of the Sn 3+ centers in crystals doped with 

natural tin. Various Sn 3+ centers were reported in 

NaCl and KCl doped with SnCl2 containing 87.8% 

117 Sn [26, 131], as well as in KCl doped with tin 

enriched in the 119 Sn isotope [132]. 

Besides the g ~ 2 line from the even isotopes 

the X-band EPR spectra of the Sn 3+ exhibit at 

high magnetic fields two hf lines due to the AF = 

0, Amp = ±1 transitions. The hf constant A can 

be determined with the aid of formulae (23,24). The 

spin Hamiltonian parameters of the Sn 3+ centers reported 

in the literature are presented in Table 13.

Vol. 16, No. 3/4 215 

Sn 3+ centers with isotropic lines and well resolved 

shf structure were obtained [26] in KC1 and 

NaCl in a maximum concentration, by X-ray irradiation 

at 77K and pulse-annealing around 160K. 

Two Sn 3+ centers, called (Sn 3+ )' and (Sn 3+ )", 

exhibiting anisotropic high field hf transitions were 

observed [131] in both NaCl and KC1 after X-ray 

irradiation at 77K. The (Sn 3+ )" center exhibits a 

C2 symmetry axis, attributed to the presence of a 

NN cation vacancy, along a (111) direction. 

Other two Sn 3+ centers, called (Sn 3+ )/ and 

(Sn 3+ )//, with resolved shf structure at 35K, have 

been also reported in KC1, after X-ray irradiation 

at 77K and warming up at various temperatures 

[132]. The (Sn 3+ )/ center reaches its maximum concentration 

after pulse annealing at 230K. The shf 

structure, due to the interaction with six neighboring 

ligands, exhibits a (111) symmetry attributed to 

the presence of an interstitial Cl~ ion. The (Sn 3+ )// 

center reaches its maximum concentration by pulseannealing 

at 280K. The suggested structural model 

consists of a Sn 3+ ion with two neighboring cation 

vacancies. 

Sn 3+ centers, which seems to represent selftrapped 

holes at cationic sites, were reported in 

SnCl2, Snl2 and SnSO4 crystals [133] after X-ray 

irradiation at 77K and in K2SnFg powder after 

7-irradiation [123]. The Sn 3+ center observed in 

K2SnFg exhibits the largest reported hf constant in 

a crystal lattice, characteristic for a strongly ionic 

compound. 

Sn 3+ centers have been also observed in various 

II-VI semiconductors. With the exception of CdS 

and CdSe, where they exhibit axial symmetry, in all 

other crystals the Sn 3+ centers are isotropic. 

Pb 3+ centers have been reported in alkali chlorides, 

in alkali earth fluorides, in various oxides and 

in II-VI semiconductors (Table 14). 

Natural lead contains only one odd isotope 

( 207 Pb) with / = 1/2 (Table 2). Due to the large 

zero-field splitting, the EPR spectra of the Pb 3+ 

centers consist of a line at g — 2 due to the even 

isotopes and two lines at higher magnetic fields due 

to the two AF — 0,Amj? = ±1 transitions. The 

spin Hamiltonian parameters for the isotropic case 

are determined by formulae (23,24). 

Two types of Pb 3+ centers have been observed 

in KCl:Pb crystals [138] after X-ray irradiation at 

77K and subsequent warm-up. The first one, al- 

ready produced after irradiation, reaches its maximum 

concentration by pulse-annealing at 220K. Its 

well resolved shf structure has been described in a 

good approximation by the interaction with a regular 

octahedron of six chlorine ligands. It has been assumed 

that an accompanying charge compensating 

cation vacancy may be present in a (2,0,0) site, or 

further away. The second Pb 3+ center was produced 

by pulse-annealing above 220K. It had the same g 

and A values, but a less resolved shf structure, attributed 

to the presence of a second cation vacancy. 

The source of the cation vacancies seems to be the 

Pb + centers, also produced by X-ray irradiation 

[29, 101]. Similar Pb 3+ centers have been observed 

in other alkali chlorides [26, 131, 136]. Two types of 

Pb 3+ centers have been reported [131] in KC1 and 

NaCl, after X-ray irradiation at 77K, and attributed 

to different configurations of Pb 3+ -vc pairs. 

Pb 3+ centers have been reported [85, 139] in lead 

doped CaF2 and BaF2 crystals, after X-ray irradiation 

at 77K or RT and in SrF2 after X-ray irradiation 

at 77K. The well resolved shf structure corresponds 

to a substitutional Pb 3+ ion surrounded by 

a cube of eight F~ ligands. Due to the large shf 

interaction the forbidden (Am/ = ±1) transitions 

are partly allowed. A second type of Pb 3+ centers 

exhibiting different shf structure has been observed 

[139] at T


symmetry around the < 111 > axes and shf structure 

due to the interaction with one 19 F ligand 

nucleus, has been observed only in TI1O2 crystals 

grown from a PbF2 based flux. The center is considered 

to consist of a substitutional Pb 3+ ion, with 

one of the eight nearest O 2 ~ ligands substituted by 

an F~ ion. The presence of both Pb 3+ and Pb 3+ 

centers was also reported [142] in as grown ThO2 

crystals prepared from a PbF2 based flux. In this 

case it has been found that their concentration is 

greatly enhanced by illumination with 400 nm light. 

Pb 3+ centers with isotropic EPR spectra, attributed 

to substitutional Pb 3+ ions at cubic sites 

have been reported in the as grown crystals of 

ZnO and CaO [144], Lu3Ga50i2, Y3A15O12 and 

Lu3Al5012 [42]. 

Axial Pb 3+ centers, at substitutional cationic 

sites, in CaW04 crystals [146, 147] and CaCO3 (calcite) 

crystals [44, 143, 145], have been observed after 

X or 7-ray irradiation. The EPR spectra of the 

Pb 3+ centers in CaW04 exhibit a partly resolved 

shf structure, attributed to the interaction with the 

183 W nuclei (I = 1/2, 14.4% abundance). The hf 

constant of the Pb 3+ centers in CaCO3 exhibits [44] 

the same temperature dependence as the one previously 

observed for the Cd+ centers in KC1 (formula 

47). The temperature dependence of the hf constant 

and the large Lorentzian linewidth of the various 

transitions have been quantitatively explained [152] 

in terms of a Raman spin-lattice relaxation corresponding 

to a Kramers spin system with large hf 

interaction. 

Pb 3+ centers with axial symmetry were reported 

in as grown YPO4 and LUPO4 orthophosphates prepared 

from lead based fluxes [148]. In an unexpected 

way, the shf interaction parameters with the 31 P nuclei 

of the second shell of ligands has been found to 

be larger than for the first shell. 

Photosensitive Pb 3+ centers have been also observed 

in the II-VI semiconductors, ZnSe [150], 

ZnTe [27, 125, 126, 124] and CdS [133, 127] as well 

as in CaSe [151]. 

The spin Hamiltonian parameters of the IVAgroup 

of ns 1 —centers in cubic II-VI semiconductors 

(Tables 12-14) exhibit specific features: large 

and positive Ag = g - ge shifts and large hf shifts 

6A. The above characteristics have been explained 

[53, 57] in a satisfactory manner with the holetrapped 

MO model. The model, briefly presented 

in paragraph 1.3.2., describes the wave function of 

the paramagnetic electron as a linear combination 

of the central ns wave function and the s-p orbitals 

of the ligands (formulae 40,41). Quantitative analysis 

of the experimental spin Hamiltonian parameters 

have been initially performed for the n5 1 -centers 

in zinc chalcogenides [150, 153] using Watanabe's 

model [53]. Further analysis, have been performed 

for the ns^centers in zinc chalcogenides [57], for the 

Ge 3+ and Pb 3+ centers in zinc chalcogenides and 

CdTe [149], and for the Ge 3+ , Sn 3 + and Pb 3+ centers 

in CdTe and ZnTe [126]. The analysis show 

that the increased spin-orbit coupling in the S, Se, 

Te sequence of ligands is responsible for the positive, 

increasing Ag shift, observed along the zinc or 

cadmium chalcogenides sequence. In the same manner 

the hf shift 6A decreases with the ionicity of the 

ligand bonds. 

V. Concluding Remarks 

The present survey shows that among the various 

inorganic crystal-hosts of the n5 1 -centers the 

interest was mainly concentrated on the cubic alkali 

halides. However, even inside this group of compounds 

there is a strong discrepancy between alkali 

chlorides and bromides, in which many ns^centers 

have been observed, the alkali iodides in which a few 

such centers have been observed and the alkali fluorides 

and cesium halides in which ns 1 -centers have 

not been reported yet. In this connection the study 

of the ns^centers in the latter crystal-hosts would 

be of interest regarding the validity of their production 

and recombination mechanisms under irradiation. 

Although a relatively large number of ns 1 -centers 

have been reported in other cubic and non-cubic 

crystal-lattices, only a few reports are concerned 

with the identification of their structural model 

i.e., their position in the lattice and the presence/absence 

of neighboring lattice defects. This is 

not at all surprising considering that in the absence 

of a resolved shf structure the structure determination 

is extremely difficult. 

Several papers have been devoted, especially in 

the last years, to the study of the ns 1 -centers produced 

in crystals with low symmetry lattice exhibit-

Vol. 16, No. 3/4 217 

Table 14: The EPR parameters of the Pb 3+ —type of centers. The hf parameter A and the shf parameters As 


Center 

Pb^ + in LiCl 

Pb 3+ in NaCl 

(Pb 3+ )' in NaCl 

(Pb 3+ )" in NaCl 

Pb 3+ vc in KCl 

Pb 3+ 2vc in KCl 

(Pb 3+ )' in KCl 

(Pb 3+ )" in KCl 

Pb 3+ in RbCl 

Pb 3+ in CaF2 

Pb 3+ in SrF2 

Pb 3+ in BaF2 

Pb 3+ in PbCO3 

Pb 3+ in BaPbF6 

Pb 3+ in PbF2 

Pb 3+ in ThO2 

Pb 3+ in ThO2 

Pb 3+ in CeO2 

Pb 3+ in CaO 

Pb 3+ in ZnO 

Pb 3+ in CaCO3 

(calcite) 

Pb 3+ in CaWC-4 

Pb 3+ in YPO4 

Pb 3+ in LuPO4 

Pb 3+ in Y3Ga5Oi5 

Pb 3+ in Lu3Ga5Oi2 

Pb 3 + in Y3A15O12 

Pb 3+ in Lu3Al50i2 

Pb 3+ in CdS 

T(K) 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

30 

77 

77 

77 

77 

1.6 

1.6 

77 

100 

300 

300 

300 

300 

300 

77 

g 

2.033 

2.034 

2.040 

2.040 

2.034 

2.034 

2.030 

2.030 

2.0033 

2.0020 

2.007 

2.0018 

1.9963 

2.00 

2.0023 

2.007 

1.9666 

5,1=1.9704 

5_L=1.9637 

1.9649 

1.999 

2.013 

5||=l-9704 

31=1.9637 

5H=1.9919 

51=1.9887 

5||=2.0001 

51=2.0002 

5||=2.0001 

31=2.0011 

2.002 

2.001 

2.002 

2.000 

5H=2.0020 

5_L=2.0049 

|207A| 

33,600 

33,600 

35,500 

35,500 

33,000 

33,000 

33,000 

33,000 

32,700 

52,800 

51,350 

49,580 

34,700 

47,868 

47,100 

36,875 

Ay=35,796 

^1=35,404 

36096 

32,070 

24,220 

Ay =35,796 

AJ_=35,404 

A||=38,410 

Aj_=38,437 

A{\ =48,691 

A±=48,810 

A,, =49,530 

Ai=49,800 

Ax=37,860 

^=37,980 

A2=37,790 

38,130 

40,138 

41,427 

Ay =36,800 

As 

36.4 

40.2 

87.7 

43.6 

36.3 

313.7 

381 

288 

259 

231 

39.4 a 

A 1 = 7.65 6 

A n = 37.2 fc 

A 1 = 6.72 6 

A 11 = 40.0 6 

Ap 

27.9 

18.3 

15.6 

20.8 

14.2 

121 

46.8 

122 

123 

126 

8.24 a 

References 

[136, 137] 

[26, 136] 

[131] 

[131] 

[138] 

[138] 

[131] 

[131] 

[136] 

[85, 133, 139] 

[78] 

[85, 139] 

[85, 139] 

[133] 

[123] 

[140] 

[141, 142] 

[141, 143, 142] 

[141] 

[144] 

[144] 

[44, 143, 145] 

[146, 147] 

[148] 

[148] 

[42] 

[42] 

[42] 

[42] 

[133, 127]

218 

Center 

Pb 3+ in CdTe 

Pb 3+ in ZnSe 

Pb 3+ in ZnTe 

Pb 3+ in CaSe 

T(K) 

20 

77 

77 

Table 14: continued. 

g 

2.2054 

2.0721 

2.167 

2.173 

a The shf parameters are referring to the 19 F ligand 

b The shf parameters are referring to the 31 P ligand. 

\' M7 A\ 

14,642 

20,654 

15,680 

20,480 

As 

416.5 

215 

130 

Ap 

186 

110 

70.3 


References 

[126, 149] 

[150] 

[27, 125, 126, 124] 

[151] 

Table 15: The EPR parameters attributed to the VA group of ns 1 centers. The hf parameter A for the 75 As, 

121 Sb and 209 Bi isotopes and the shf parameters As and Ap are given in MHz. 

Center j T(K) 

As 4+ in CsAsF6 

Sb 4+ in CsSbF6 

Bi 4+ in CsAsF6 

a A/( 75 As)=14,660 MHz. 

6 A/( 121 Sb)=35,100 MHz. 

c A/( 209 Bi)=77,530 MHz. 

30 

30 

g 

2.0030 

2.0015 

2.0134 

ing structural phase transitions (SPT). Besides producing 

and describing their EPR properties, the resulting 

ns 1 -centers have been employed in certain 

cases as paramagnetic probes in investigating the 

mechanism of the SPT. Considering the wide temperature 

range in which some of the n^-centers can 

be observed by EPR, it is expected that their use as 

microscopic probes in the study of the SPT will be 

extended. 

It should be also mentioned that other impurity 

ions, besides those presented in Table 1. are able in 

principle to produce new ns^centers. It is the case 

of the VA-group of elements (As 4+ , Sb 4+ , Bi 4+ ), as 

well as Al 2+ and Si 3+ . 

In this respect one should mention the reported 

observation of new EPR spectra in 7-irradiated 

polycrystalline samples of CsAsF6, CsSbF6 [154] 

and CsAsF6 doped with BiF^r [155]. Although the 

resulting paramagnetic species were assigned to free 

radicals of the type MeF|~ (Me = As. Sb, Bi), re- 

\A\ 

9,403 a 

21,390 6 

36,020 c 

As 

693 

697 

414 

Av 

160 

153 

163 

6A 

0.36 

0.39 

0.55 

References 

[154] 

[154] 

[155] 

spectively, the parameters (Table 15) corresponding 

to the spin Hamiltonian (16) describing the observed 

spectra, strongly suggest the presence of Me 4+ (ns 1 ) 

centers. The large hf shift 8 A and shf coupling parameters 

As and Ap of the observed centers result 

from a strong delocalization of the central ns 1 electron 

to the neighboring ligands, which may explain 

their assignment to free radicals. 

Acknowledgments 

One of the authors (I.U.) would like to express 

his gratitude to Professor Abdus Salam for the kind 

invitation to work at the ICTP-Trieste, as well as 

for continuous support, encouragement, advice and 

criticism. Financial support from the Belgian Ministry 

of Science Policy (DPWB) and from the University 

of Antwerp (U.I.A.), for one of the authors 

(SVN) and from the International Center for The-

Vol. 16, No. 3/4 219 

oretical Physics (ICTP), Trieste for another author 

(IU) is gratefully acknowledged. 


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B. Vitt, Phys. Stat. Sol. 37, 255 (1970). 

[147] G. Born, A. Hofstaetter and W. Tolksdorf, 

Phys. Stat. Sol. b66, 305 (1974). 

[148] M. M. Abraham, L. A. Boatner and M. Rappaz, 

Phys. Rev. Lett. 45, 839 (1980). 

[149] R. M. Bilbe, J. E. Nicholls and J. J. Davies, 

Phys. Stat. Sol. bl21, 339 (1984). 


287 (1969). 

[151] N. Yamashita and S. Asano, J. Phys. C9, 165 

(1976). 

[152] F. F. Popescu and V. V. Grecu, J. Phys. C15, 

1547 (1982). 

[153] T. Iida and H. Watanabe, Phys. Lett. A26, 

541 (1968). 

[154] A. R. Boate, J. R. Morton and K. F. Preston, 

Chem. Phys. Lett. 50, 65 (1977). 

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J. Chem. Phys. 67, 4302 (1977).


Contents 

Survey of the EPR Community on the EPR Database 

and Related Projects 

Czeslaw Rudowicz 

Department of Physics- and Materials Science 

City Polytechnic (University from 1994/95) of Hong Kong 

Kowloon Hong Kong 


II. Questionnaires and analysis of responses 224 

A. EPR-Q: The Future of EPR Spectroscopy of Transition Ions 225 

B. P-EPR: Planning EPR-database structure 231 

C. ML: Membership aspects 234 

III. Concluding remarks 236 

IV. References 238 


EPR studies provide a wealth of information, 

which can be best utilized if available in a computersearchable 

form. Establishment of a computerized 

EPR-related database would require, among 

other things, standardization of notations and units. 

These proposals have been put forward to the International 

EPR (ESR) Society [IES] in the two 

submissions in August 1990 (1): On Unification of 

Notations Used in EPR and On Establishment of a 

Computerized EPR-related Database and the EPR 

community (2). A feasibility study of the EPRrelated 

database project followed starting in early 

1991. The objectives of the pilot study were: (i) to 

find out the opinions of the EPR community concerning 

the above two proposals, (ii) to investigate 

the users' requirements and identify the data needs, 

and (iii) to work out a Feasibility Study Report for 

consideration by the IES. 

The present survey and the proposed EPR 

database project are perceived as a service to the 

EPR community under the auspices of IES. The 

idea of an EPR database has also been discussed 

at the EPR meetings held in Denver [EPR Newsletter 

[EN] 4/3, 7 (1992); 5/2, 5 (1993)]. A poster 

summarizing the preliminary results of this study 

has been presented at the EPR Symposium in Denver 

(3). In this paper the results of the analysis 

of the 70 plus valid responses received to date are 

presented. 

II. Questionnaires 

of responses 

and analysis 

For a meaningful analysis of responses the pertinent 

background on the stages of the project and 

working out of the questionnaires is important. The 

project started with the setting up of a namelist 

of EPR researchers working mainly in the area of 

transition-metal and rare-earth ion - EPR studies in 

early 1991. The namelist, complied using dBASE- 

IV, was based on an extensive survey of literature 

published since 1980 onwards and supplemented 

with addresses received from private contacts with 

EPR researchers. The questionnaire, The Future 

of EPR Spectroscopy of Transition Ions [EPR-Q] 

(1,2), has served as an initial test for working out the 

main questionnaire, Planning EPR-database Structure 

[P-EPR], in mid-1991. Included in the main 

set [EPR-DB], apart from P-EPR, were the addi-

Vol. 16, No. 3/4 225 

tional questionnaires: Mailing List for Future Issues 

[ML] and EPR-related Conferences [EPR-Con]. 

The full set of questionnaires, i.e. EPR-Q and 

EPR-DB, and the two submissions, accompanied 

by an Open letter to EPR community members, have 

been dispatched to about 800 researchers in late 

1991 and successively to over 100 more researchers 

thereafter. The paper (2), where the rationale for 

standardization of symbols in EPR was detailed and 

pertinent references were given, had also been enclosed. 

The analysis of responses began in mid-1992. 

In order to increase the number of responses a note 

on the project has been placed in EN [3/4, 6 (1991)] 

distributed in early 1992. However, it has generated 

but a few additional responses. 

The geographical distribution of responses is presented 

in Table 1. There are two types of responses: 

(i) Full, i.e. responses to the full set of questionnaires 

(EPR-Q and EPR-DB), and (ii) EPR-Q, 

i.e. responses to EPR-Q only. The rate of response 

(%) is calculated including both (i) and (ii) with respect 

to the total number of EPR-DB sets sent. 

Some special cases are also indicated in Table 1. 

In several cases the envelopes with EPR-DB have 

been returned as 'undelivered' mail or the person 

has indicated only that he/she has 'left the field' of 

EPR in the meantime. In a few instances 'Mailing 

list only'has been returned. The mailing of the 

EPR-DB questionnaires coincided with the major 

changes on the political map of Europe. Since it 

was difficult to accomodate these changes explicitly 

in our geographical listing, the new countries are 

considered jointly under the former name indicated 

by an asterisk, whereas the responses from the West 

and East Germany were merged. Several responses 

have been received after the analysis of data was 

completed. Including these responses would slightly 

increase the total response ratio in Table 1. The 

overall response ratio of about 8-9% is disappointingly 

low. We don't think, however, that this lack of 

attention is malicious; rather it is due to the natural 

tendency of (very busy) people to focus on their 

own immediate problems. 

The results of the analysis of responses are organized 

into three parts concerned with (A) EPR-Q 

- in Figures 1 to 5, (B) P-EPR - in Figures 6 to 12 

and Table 2 and 3, and (C) ML - only the aspects 

pertinent to the membership of the EPR community 

are included here. 

A. EPR-Q: The Future of EPR Spectroscopy 

of Transition Ions 

For the questions in Figure 1 the lack of answer 

(no answer) and the no opinion answer are 

merged, while the firm no answer is indicated explicitly. 

For the question A7.1 in Figure 2 the of 

minor use and negligible use answers are merged, 

yielding 6%, whereas the combined percentage of 

the very useful and useful answers is 91%. This indicates 

a very strong support for the idea of a comprehensive 

computerized EPR database. Financial 

viability of the EPR database looks promising gauging 

from the percentage of the potential subscribers: 

14% very likely and 65% probably. Hence the end 

product of the EPR database project is likely to become 

a saleable commodity. 

The overwhelming support by respondents for 

all other proposals dealt with in Figures 1 and 2 

is evident, except for the financial commitments regarding 

development of an all-purpose user-friendly 

EPR computer package [Figure 2, A6.2(ii)]. The responses 

indicate that a strong need exists within the 

EPR community for (i) the internationally accepted 

standards on EPR nomenclature and conventions 

and (ii) a glossary of terms used in EPR (Figure 

1) as well as (iii) an EPR computer package (Figures 

1 and 2). The first two proposals can only be 

successfully dealt with if cooperation between IS- 

MAR, IES and IUPAC, at a proper level, can be 

ensured. The author's attempts to bring about such 

cooperation have not been successful so far. Possibility 

of cooperation on these and related projects 

with AMPERE Society and regional EPR/ESR societies 

should also be investigated. The extension 

to the spin S>l/2 systems of the Recommendations 

for EPR/ESR Nomenclature and Conventions for 

presenting experimental data in publications [(4); cf 

also EN 3/1, 9 (1991)], dealing only with the S = 1/2 

systems, is crucial for the EPR database project 

(2). To the best of our knowledge, the work on 

this extension, planned under the auspicies of IU- 

PAC Commission 1.5 (5), has not continued. The 

lack of financial resources and manpower seems to 

be the major obstacle in pursuing these proposals. 

The situation is better with regard to the EPR 

computer programs, due to efforts of Prof. R. Cammack, 

Chairman of the IES Computer Software 

Committee, who has complied a database of available 

EPR programs [EN 4/3, 6 (1992)]. The names

226 


GA 

AF 

AP 

EU 

LA 

NA 

Table 

Country 

South Africa 

Zimbabwe 

subtotal 

Australia 

China 

Hong Kong 

India 

Israel 

Japan 

New Zealand 

South Korea 

Taiwan 

Vietnam 

subtotal 

Belgium 

Bulgaria 

CIS (f. USSR)* 

Czechoslovakia* 

Denmark 

France 

Germany* 

Greece 

Hungary 

Italy 

Netherlands 

Poland 

Portugal 

Romania 

Spain 

Sweden 

Switzerland 

Turkey 

UK 

Yugoslavia* 

subtotal 

Argentina 

Brazil 

Mexico 

Venezuela 

subtotal 

Canada 

USA 

subtotal 

total 

': Geographical Distribution o: 

No. 

Sent 

1 

1 

2 

27 

16 

1 

34 

2 

78 

8 

5 

5 

1 

177 

11 

3 

128 

14 

1 

69 

65 

3 

10 

26 

38 

28 

1 

5 

28 

2 

18 

3 

36 

5 

366 

6 

21 

4 

6 

37 

23 

156 

179 

889 

Response 

Full 

0 

0 

0 

3 

3 

1 

3 

0 

2 

0 

1 

0 

0 

13 

1 

0 

12 

2 

0 

1 

1 

2 

2 

1 

2 

4 

0 

1 

3 

0 

1 

1 

2 

0 

24 

0 

1 

0 

0 

1 

1 

6 

7 

57 

EPR-Q 

0 

0 

0 

1 

1 

0 

2 

0 

1 

0 

0 

0 

0 

5 

0 

0 

1 

0 

0 

0 

4 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

6 

0 

0 

0 

0 

0 

0 

4 

4 

16 

% 

0.0 

0.0 

0.0 

14.8 

25.0 

100.0 

14.7 

0.0 

3.8 

0.0 

20.0 

0.0 

0.0 

10.2 

9.1 

0.0 

10.2 

14.3 

0.0 

1.4 

7.7 

66.7 

20.0 

3.8 

7.9 

17.9 

0.0 

20.0 

10.7 

0.0 

5.6 

33.3 

5.6 

0.0 

8.2 

0.0 

4.8 

0.0 

0.0 

2.7 

4.3 

6.4 

6.1 

8.2 

Responses 

Unde- 

livered 

0 

0 

0 

1 

1 

0 

0 

0 

7 

0 

0 

0 

0 

8 

0 

0 

7 

0 

0 

1 

0 

0 

1 

0 

7 

0 

0 

0 

0 

0 

1 

0 

2 

0 

12 

0 

0 

0 

0 

0 

1 

9 

10 

37 

Left the 

field 

0 

0 

0 

0 

1 

0 

0 

0 

0 

1 

0 

0 

0 

2 

0 

0 

0 

0 

0 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

1 

0 

4 

0 

0 

0 

0 

0 

0 

0 

0 

6 

Mailing 

list only 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0. 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

1 

2 

3 

6

Vol. 16, No. 3/4 227 

Compound 

AMX3 

A2MX2 

Table 2: Compounds by Molecular Formula or Specific Ion 

A2MX4 

[A=alkaline; M=divalent; X=O,F] 

ABF6-6H2O 

[A=Mn 2+ , Ni 2+ , Cu 2+ , Co 2+ , 

Fe 2 +, Zn 2+ , Cd 2+ , Mg 2+ , Ca 2+ ; 

B=Si 4+ , Ge 4+ , Ti 4 +, Zr 4 +, Mg 4+ ] 

BGO 

Bi2Sr2Ca2Cr3O4 

BiVO4 

BSO 

CaF2, Cai_xSrxF2 

Ca2Fe205 

Ca3Ga2Ge3Oi3 

Ca3Ga2Ge4Oi4 

CaO - systems 

Ga2C>3 - systems 

GeO2 - systems 

CdTe 

Co 2+ compounds 

Material 

Apatites 

Biomolecular 

Catalysts ceramics 

Complex with chelate ligands 

Diamond like crystals 

Disordered solid 

Ferroelectric materials 

Fluorites 

Garnets 

Germanium 

Glasses 

Graphite intercalation compounds 

Halides 

Freq. 

5 

1 

2 

2 

1 

1 

3 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

Compound 

Co2Si04 

Cr 3+ compounds 

Fe 2+ compounds 

Fe 3+ compounds 

Gd 3+ compounds 

LaGaC-3 

Li(RE)F4 [RE=Y, Yb, Dy, Er] 

LiH 

LiNbO3 

LiOH 

Mn 2+ compounds 

MX2 

NdGaO3 

PbTe 

PrGaO3 

Rb2MnxCr1_xCl4 

REnXmOt [RE=Rare earth ions] 

Sn_xBaxF2 

XmOi [X=P, V, As, Al, Ti, Nb, Si, Bi] 

Y2Ba2Cu307_8 

Table 3: Materials by Name of Specific Group 

Fxeq. 

1 

6 

1 

1 

1 

2 

3 

2 

1 

2 

2 

5 

Material 

Inorganic compounds 

Ionic crystals 

Magnetic materials 

Minerals 

Optoelectronic materials 

Organic compound 

Oxides 

Paraelectric crystals 

Piezoelectric crystals 

Free radicals 

Spin traps 

Superconducting materials 

Transition-metal ion compounds 

Freq. 

5 

2 

1 

2 

1 

T-H 4 

2 

.1 

4 

1 

5 

3 

Freq. 

1 

1 

1 

2 

1 

1 

1 

1 

3 

1 

2 

1 

1 

1 

1 

1 

1 

1 

1 

1

228 

Al 

A2 

A6.1 

A8.1 

94%" 6% 

90% 7% 

89% , 10% 

76% 24% 

10 20 30 40 50 

Frequency 


60 70 80 

I yes no D no opinion and no answer 

Figure 1: Answers to Al, A2, A6.1 and A8.1. 

Al-Would you find it useful if there were internationally accepted standards on EPR nomenclature and 

conventions? 

A2-Do you feel the need for a glosary of terms used in EPR, containing precise definitions of basic notions? 

A6.1-Would you find it useful if an all-purpose user-friendly EPR computer programme package for analysis, 

simulation and fitting EPR spectra was available? 

A8.1-Would you welcome establishment of an EPR Documentation Center? 

of respondents who indicated some EPR/ESR programs 

developed in their groups (as revealed by 

the question Cl in ML), and which have not been 

listed in the 1991 edition of the ESR/EPR Software 

Database, have been passed on to Prof. Cammack. 

An EPR Documentation Center, whose establishment 

(Figure 1, A8.1) has received strong support 

(76%),.could take up a leading role in achieving the 

above goals, including development and on-going 

running of the EPR database. 

The results of the inquiry on the preferred (i) 

notation for the zero-field splitting [ZFS] terms, 

(ii) axis system, and (iii) unit for the ZFS parameters 

are presented in Figures 3, 4 and 5, respectively. 

The extended Stevens (ES) operators (6,7) 

have received majority of 'votes' (49%). There was 

quite a large proportion of 'undecided votes' (27%), 

whereas the NS, BST, and KS/BCS operator notations 

(for definitions and references, see ref. 7) rated 

at or below 8%. Among other notations suggested, 

apart from a few ephemeral notations, several respondents 

indicated as a complementary one the 

conventional S.D.S (and a, F) notation. Question 

A4 (Figure 4) appears, in retrospect, to be poorlyconstructed, 

since fully meaningful answers would 

require drawings of the crystal structures and axis 

systems. In Remarks several people mentioned the 

crystallographic, principal, and magnetic axis systems. 

Strong views that precise definitions should 

be always provided for the axis systems used in EPR 

studies were also expressed. This again reconfirms 

the need for a glossary of terms used in EPR. 

Assuming that our sample of respondents is representative, 

these results are encouraging since they 

reveal that a much more coherent consensus on the 

ZFS notations (Figure 3) as well as on the unit for 

the ZFS parameters (Figure 5) exists within the 

EPR community, contrary to what could be expected 

judging by the messy situation prevailing in 

the literature in this regard (for a detailed review, 

see ref. 7). Nevertheless, the question of unification 

and standardization of notations used for the various 

spin Hamiltonian terms remains a thorny issue 

[EN 2/3, 6 (1990); 5/2, 6 (1993)], whose solution 

has been seriously attempted neither by the EPR 

community nor EPR organizations so far. Since

A6.2(i) 

Vol. 16, No. 3/4 229 

A7.2 

A7.1 

31% 36% 

25% 53% 

14% 65% 

10 20 30 40 50 

very likely 11 probably CD not likely ^ no answer 

42% 49% 

10 20 30 40 

Frequency 

[D very useful H useful D of minor use M no answer 

50 

17% 

60 70 80 

6% 

60 70 80 

Figure 2: Answers to A6.2(i), A6.2(ii), A7.2 and A7.1. 

A6.2-Would you be prepared to contribute to the development of such a package, (i) by working on the 

project? (ii) by obtaining financial assistance through your institution? 

A7.2-If you would find a comprehensive EPR database useful or very useful, do you think your institution 

would subscribe to release of the EPR database information? 

A7.1-How do you preceive the usefulness of a comprehensive computerized EPR database? 

no answer 

27% 

KS/BCS 

4% 

ES - the extended Stevens 

NS - the normalized 

Stevens 

BST - the Buckmaster, 

Smith-Thornley 

KS/BCS - the Koster-Statz, 

Buckmaster- 

Chatterjee-Shing 

others - other notations 

Figure 3: Answers to A3 - preferred notation for the ZFS Hamiltonian.

230 Bulletin of Magnetic Resonance 1 

30 

25 -- 

20 -- 

10 -- 

Vol. 16, No. 3/4 231 

1990, when the question of setting up a nomenclature 

committee has first been put forward to IES, 

"this is a continuing problem" [EN 2/3, 6 (1990)]. 

It should be realized that the internationally accepted 

standards on EPR nomenclature and 

conventions are essential for the future of the EPR 

field and thus a nomenclature committee should be 

established as soon as it is practically possible. However, 

only 9% of respondents declared willingness to 

become members of a pertinent committee (see Figure 

10, BlOc). 

B. P-EPR: Planning EPR-database 

structure 

Since most of the results are self-explanatory, we 

comment briefly on the findings presented in Figures 

6 to 12 and Tables 2 and 3. Out of the 57 

full responses, the majority of respondents indicated 

the chemical formula, paramagnetic ion/species and 

the values of the ZFS and Ze parameters, including 

the experimental errors, as the most useful 

data types (Figure 6). Other data types mentioned 

were: stress dependence of the ZFS parameters, 

isotopic composition, drawings of the structural 

formula of the species or the immediate environment 

of the magnetic site, hyperfine interactions 

for organic radicals, environment information 

like solvent of liquid radical solutions, EPR spectra 

(which could be electronically mailed to the 

database in a specific format if adopted internationally), 

protein concentration, values of the ZFS 

parameters in original notations, microwave power, 

modulation amplitude, sweep rate (powder spectra), 

preparation conditions, EPR linewidth, halfwidth 

and its isotropic properties, and magnetic exchange 

interactions. This reveals a wide range of options 

which should be taken into account during the 

planning phase of the development of a full-scale 

EPR database. However, including the drawings of 

structures and the actual EPR spectra in the EPR 

database would require graphical capabilities and 

a large-scale storage media, which would increase 

the costs significantly. Interestingly, out of the two 

options: (i) the actual EPR spectra database and 

(ii) the database of spin Hamiltonian parameters (as 

proposed here), the latter option was most favoured 

by the participants at the EPR 1992 meeting in Denver 

[EN 4/3, 7 (1992)]. Most recently a discussion 

on these two options has been initiated by Dr P. 

Morse on the EPR LIST electronic network [EN 5/3, 

5 (1993)] starting in February 1994. Several useful 

ideas have been generated initially, however, quickly 

the interest in this topic has faded. 

There is no uniformity on the most important 

compounds/materials or ions/species. The answers 

are grouped into compounds by molecular formula or 

specific ion in Table 2 and into materials by name 

of specific group in Table 3, whereas the frequency 

distribution of ions/species, transition-metal ions, 

and main group ions is presented in Figures 7, 8a, 

and 8b, respectively. Direct listing of ions may be 

more meaningful. The 52 responses indicating explicitly 

ion/species yield the following count: 3d ions 

(6), transition-metal ions (8), rare-earth ions (12); 

V2+/4+ (2/2), Cr 2+ / 3+ / 5+ (4/15/2), Mn 2 +/ 3+ / 4 +' 

(25/4/3), Fe 2+ / 3+ / 4+ (7/25/1), Co 2+ (5), Ni 2+ (6), 

Cu 2+ (17), Eu 2+ (2), Gd 3+ (13), Mo 5+ (2), VO 2 + 

(3). Paramagnetic species mentioned only once are 

not listed here. The results reflect the various widely 

spread research interests of the researchers, however, 

a definite focus on the transition-metal ions 

in technologically important materials may be noticed. 

The latter aspect may be helpful in searching 

for funds for the future development of a full-scale 

EPR database. Support from industrial companies, 

which use EPR techniques and/or utilize EPR data 

for materials characterization, could be sought. Out 

of the few commercial producers of EPR equipment, 

strong support for the EPR database has been declared 

by the Bruker, who could also help with marketing 

the product. Question B9 (Figure 10) is 

strongly related to the 'chemical content' and hence 

is considered here. Although within the question 

Bl the researchers listed particular chemical structures 

(Table 2 and 3), the majority (70%) would 

like to have all chemical structures studied by EPR 

techniques listed in the EPR database (Figure 10, 

B9). Other suggestions were, e.g. 'initially crystalline 

systems, later all other chemical structures' 

and 'inorganic compounds'. 

It is worthwhile to mentioned here that at the 

EPR 1992 meeting in Denver P'rof. J. Weil volunteered 

to collect "inorganic" data, whereas Prof. H. 

Buckmaster agreed to assemble data from reprints 

in the way that he did in his reviews published in 

Mag. Reson. Rev. series [EN 4/3, 8 (1992)]. According 

to our informal information as of August 

1993, no progress has been made in this regard be-

232 

a - chemical formula 

b - doping level 

c - paramagnetic ion/species 

d- spin 

e - site symmetry 

f - spin Hamiltonian symmetry used 

g - definition of the axes with respect to the 

crystallographic ones 

h - frequency 

i - temperature range studied 

j - magnetic field range applied 

k - values of the zero-field splitting (ZFS) 

parameters 

kl - with the experimental errors included 

k2 - without the experimental errors included 

1 - values of the electronic Zeeman (Ze) 

parameters 

11 - with the experimental errors included 

12 - without the experimental errors included 

m - type of the original notation used for ZFS 

parameters 

n - bibliographical data, i.e. source reference 

cause of various other commitments. A more coordinated 

effort is needed to bring about substantial 

progress in the EPR database project. 

From the suggested list of queries (Figure 9) the 

most useful seem to be (i) References to EPR studies 

of the ion X in the compound Y, (ii) Papers on 

the ion X with spin Y in the site of symmetry Z, 

and (iii) Values of the ZFS parameter X for the ion 

Y at symmetry Z. Other comments on the possible 

queries made include requests for information on the 

type of phase transition, type of ligand, crystallographic 

classes, values of the hyperfine interaction 

a 

- 

b 

- 

c 

- 

d 

- 

e 

- 

f 

- 

g 

h 

i 

j 

k 

kl 

k2 

Figure 6: Answers to Bl - most useful data types. 

1 

11 

12 

m 

n 


_ I 

_ ^ 

] 

0 

1 

1 

J 1 

"1 

1 | 

| 

_ l 

1 

20 40 

Frequency 

constants, name of starting material as well as desire 

for a large scientific state-of-the-art database system 

capable of flexible information searches. 

Responses to questions concerning technical aspects 

of the database structure and organization 

are summarized in Figures 10 and 11. Most people 

(57%) want all authors and full title to be included 

in the bibliographical data (Figure 10, B3), 

whereas the minimal option is still satisfactory for 

some (25%). The 'votes' on a topical (30%) versus 

numerical (35%) database are nearly equally split, 

with similar number of 'undecided votes' (Figure 10, 

60

Vol. 16, No. 3/4 233 

carbon oxide ions 

2% 

rare-earth ions 

13% 

B4). The former option is less costly and easier to 

implement, whereas the latter one is much more 'labor 

intensive'. Other comments on the database 

structure were, e.g. "a simple topical database will 

be cheaper to establish and maintain, and more institutions 

will be able to afford the subscriptions", 

"small-scale, probably available on work stations or 

PC, high speed searches", "in order to keep the 

database size reasonable, the format of data storage 

should depend on the type of the paramagnetic 

species-for marketing purposes one would call this 

'object oriented'", "EPR spectrum + spin Hamiltonian 

-f Bibliographical details". 

There is no special preference for the type of 

software to be used (Figure 10, B5), which indicates 

most probably a lack of sufficient knowledge on 

the technicalities of database systems among the respondents. 

This is confirmed by the answers to the 

question B6 regarding the database systems with 

which people have experience. The names specified 

by a handful of people (numbers in brackets) 

included either general purpose databases, e.g., 

dBASE (2), Fox-pro (2), Paradox (2), and Oracle 

(1) or large scientific databases, e.g., Chemical Abstracts 

(2), Cambridge Crystallography (3), Inspec 

(2), SCI (1) and CCOD (1). Similarity the listing of 

the database systems available at the respondents' 

institution (question B7) included the same names 

as given in the answers to the question B6 and, additionally, 

Dialog, SQL, and Pascal (CNRS). The 

opinions on the scale of the EPR database are pre- 

Figure 7: Frequency distribution of ions/species. 

mam group ions 

10% phosphate 

3% 

transition metal ions 

64% 

sented in Figure 11. A majority (54%) opted for a 

large full-scale database, comprehensive with regard 

to data types and literature sources. 

Feasibility of the development of a full-scale EPR 

database hinges on several factors, among others, 

the existence of other EPR-related databases and 

the level of support from EPR community, which 

were probed in the question BIO (Figure 10) and 

Bll (Figure 12), respectively. The knowledge of 

other EPR-related databases (Bll, Figure 12) is 

very low (7%). The items listed by this 7% of 

respondents include one EPR book (published in 

1965), two review article series (Mag. Reson. Rev. 

and Landolt-Bornstein), STDB II, 'ESR/EPR in 

CAS-online', and 'Bruker' (?). The only EPRrelated 

computer database in this listing is STDB 

II, which is a database for spin trapping. This confirms 

that no EPR-related computer database exists 

at present. Concerning the level of support from the 

EPR community, the question of the low response 

rate in the EPR database survey aside, a tangible 

support for the EPR database project has been directly 

shown by about a quarter of respondents who 

declared their willingness to share the work and to 

take on some aspects of the development of the EPR 

database (Figure 10, BlOa, b). Hence the numbers 

involved are enough for efficient multinational work 

on the project.


A IB 

17% .— 

^ ^ 

B 

VIIIB 

33% 

Group VI 

70% 

Group VII 

im IVB 

2% 2% 

VB 

3% 

VIB 

•^^^ 18% 

Group II 

Group III 

10% 

Figure 8: A) Frequency distribution of transition metal ions. B) Frequency distribution of main group ions. 

C. ML: Membership aspects 

The survey reveals the following pattern of membership 

of the EPR-related societies among the 25 

respondents who provided answers to this question 

(numbers in brackets): (a) International EPR Society 

[20], (b) ISMAR [6], (c) Ampere Group [4], (d) 

ESR Group of the Royal Society of Chemistry [2], 

(e) Others [6]. Note that one person may be a member 

of more than one organization, while 48 respondents 

did not provide any indication on their membership 

or returned only the EPR-Q. The organizations 

specified under others are: the 'country re- 

lated' ones, which includes three national EPR/ESR 

groups (Poland, Hungary, Czechoslovakia) and two 

probably internal Russian ones (SMRM, ISDE - ?), 

as well as ESR Applied Metrology, ESR Dating and 

Dosimetry and American Institute of Ultrasound in 

Medicine. 

The analysis of the brief description of the research 

interests given by the respondents provides 

suggestions for future amendments to the fieldsof-interest 

codes for members of IES [cf EN 5/2 

(1993)]. We have tried to categorize the research 

interests revealed in our survey according to the 28 

fields used by IES. The results are as follows (num-

Vol. 16, No. 3/4 

What queries would be useful to you? 

a - References to EPR studies of the 

ionX 

al - in the compound Y 

a2 - in the compound Y and the 

symmetry Z 

a3 - the symmetry Z 

b - Papers on the ion X with spin Y in 

the site of symmetry Z 

c - Values of the ZFS parameter X for 

the ion Y at symmetry Z 

Other useful qualifiers to be used to 

narrow the search, 

d - time period 

e - frequency 

f - temperature range 

bers in brackets indicate no of occurences of research 

interests which fall within a given IES category): 

1. BIOMED [8], 2. POLAR [0], 3. COAL [0], 4. 

COMP [14], 5. CRYST [15], 6. DMR [4], 7. FERR 

[2], 8. FREE [0], 9. GEOL [0], 10. EPRI [3], 11. IN- 

STR [2], 12. LABEL [3], 13. LIQ [2], 14. MEMBR 

[2], 15. ION [5], 16. METALP [2], 17. OXY [0], 

18. PEPR [1], 19. PHOTO [1], 20. POL [2], 21. 

RAD [4], 22. SOLID [20], 23. SUPERC [11], 24. 

SURFACE [1], 25. KINETICS [2], 26. TRAP [2], 

27. VIVO [0], 28. CA [0]. 

The research interests, which do not fall within 

any IES code can be classified into five groups, 

namely, (a) EPR-related experimental techniques, 

(b) EPR-related theoretical aspects, (c) physical 

properties, (d) specific materials, and (e) other areas. 

The list compiled from the responses com- 

al 

a3 

0 10 

Figure 9: Answers to B2. 

20 

Frequency 

30 40 

235 

prises: (a) APR [1], EPR dating [1], EPR dosimetry 

[3], ESE (ESEEM) [2]; (b) group theory [1], 

Jahn-Teller effect [2], ligand field theory [3], superposition 

model [2]; (c) defects and impurites [13], 

electron spin relaxation [1], exchange interactions 

[1], paramagnetic centers [2], phase transitions [12], 

spin-lattice coupling [2]; (d) high sensitivity scintilators 

[1], low dimensional conductors [1], metal 

films [1], semiconductors [3]; (e) catalysis [1], crystallography 

[1], FIR [1], magnetism [1], mesoscopic 

systems [1], Mossbauer spectroscopy [1], NMR [3], 

optical spectroscopy [2], susceptibility [2]. The distribution 

of fields within the IES list and the above 

list indicate the neccessity for a more adequate coding 

for the fields of interest as well as for a more 

precise specification of the content of each code. 

It would be worthwile to introduce, instead of the

BIO 


Figure 10: Answers to B3, B4, B5, B9 and BIO. 

B3-Should the bibliographical data include: [a] all authors and full title, [b] only the minimum information 

necessary to identify the reference, [c] no opinion. 

B4-Would you be satisfied with [a] a topical database which would contain references on specific paramagnetic 

systems (i.e. compound/ion or species) and a searchable list of topics dealt with in a given source 

paper, OR [b] it is essential to retrieve from the database the numerical data on the parameters describing 

EPR spectra (i.e. ZFS and Ze parameters)? [c] no opinion. 

B5-Preferred type of software to be used: [a] commercial, [b] specially developed, [c] adopted from a related 

database system, [d] no opinion. 

B9-In your opinion should the EPR-database comprise data on [a] particular chemical structures only (at 

least at the initial stages of development)-then please name these structures OR [b] all chemical structures 

studied by the EPR technique? 

BlO-Would you like to become a member of [a] a panel of potential EPR-database users which will work 

out the User Requirements Report, [b] a group which will develop and test a prototype of EPR-database, [c] 

a committee which will work out "Recommendations for EPR Nomenclature and Conventions pertaining to 

spectra of spin S>l/2 systems". 

present coding, a more comprehensive one based on 

the five groups (a-e) used above, provided it is technically 

feasible within the existing IES membership 

database. 

III. Concluding remarks 

It had been planned to produce and test a smallscale 

prototype at the second stage of the EPR 

database project. To this end a detailed study of 

alternative EPR database structures has been carried 

out using the results of the survey concerning 

the demands on the data structure and possi- 

ble query systems. Since the present feedback has 

been insufficient, the project could not go beyond 

working out the framework of a small-scale prototype 

database, whereas its actual implementation 

has been postponed. The aspects arising from this 

survey and pertaining to the feasibility of a fullscale 

EPR database as well as the database structure 

and organization could be discussed in detail in 

the Feasibility Study Report. The alternative EPR 

database structures as well as several scientific and 

technical questions pertinent to the EPR database 

and related projects could also be dealt with therein. 

The experience gained during this project can be 

utilized in future provided there is sufficient support

Vol. 16, No. 3/4 

medium 

22% 

Figure 11: Answers to B8 - the scale of the EPR-database. 

Figure 12: Answers to Bll - Do you know of any other EPR-related databases? 

from the EPR community and EPR-related organizations 

for the continuation of the EPR database 

project to its full completion. The present situation 

in this regard has been succinctly evaluated by Prof. 

G. Eaton, who has suggested [EN 5/2, 6 (1993)]: 

"Greater support from the membership is needed to 

justify the effort involved, and there should be a committee 

to oversee the implementation". The author's 

personal and open interaction with EPR researchers 

was helpful and supportive for the project, while the 

questionnaires probably tended to generate a variety 

of negative feelings and annoyance at yet an- 

other time-consuming intrusion. Thus even though 

the response rate was low we believe that the views 

expressed represent those of the EPR community 

members as a whole. This survey has enabled us to 

learn about some qualitative trends. We ended up 

with the strong conviction that increases in support 

of the EPR database and the related projects from 

EPR organizations are vital for the continued health 

of the area. The grants must be made available, the 

tangible support by EPR organizations must be offered, 

if we expect more than the present efforts. 

Finally, the author would welcome further re- 

237


sponses as well as any comments on the EPRdatabase 

project and the related ones, their feasibility, 

resources available and/or required, and 

strategy for future development. Full set of the 

questionnaires and attachements is available from 

the author (FAX: 852 788-7830, Email: APCES- 

LAW@CITYU.HK). It is hoped that this paper will 

encourage wide consultations within the EPR community. 

Acknowledgments 

We thank City Polytechnic of Hong Kong for 

financial support for this project. We would like 

also to thank those researchers who took their time 

to complete the questionnaires. Helpful correspondence 

with Dr. H. Kon and Prof. J.R. Durig is 

gratefully acknowledged. 


ûdowicz, C. 1990, 13th International EPR 

Symposium, Denver [abstract]. 

2 Rudowicz, C. 1991, Bull. Magn. Reson. 12, 

174. 

3Rudowicz, 

C. 1993, 16th International EPR 

Symposium, Denver [abstract]. 

4 

Kon, H. 1989, Pure & Appl. Chem. 61, 2195. 

5 

Durig, J.R. 1990, private communication. 

6 

Rudowicz, C. 1985, J. Phys. C18, 1415; ibidem 

C18, 3837. 

7 

Rudowicz, C. 1987, Magn. Res. Rev. 13, 1; 

1988, ibidem 13, 335.

Vol. 16, No. 3/4 239 

Contents 

Electron Paramagnetic Resonance Investigations of the 

Cu 2+ ion in a Variety of Host Lattices - A Review 

R. M. Krishna and S. K. Gupta 

EPR Group, Materials Characterization Division, 

National Physical Laboratory, New Delhi - 110 012, INDIA 


II. Ground State of Cu 2+ Molecular Ion 240 

III. Spin-Hamiltonian Analysis 240 

IV. Spin-Hamiltonian and Bonding Parameters 241 

V. Applications 242 

A. Determination of Spin-Lattice Relaxation (Ti) of Host Ions 242 

B. Bonding Parameters 242 

C. Phase Transition Studies 243 

VI. Appendix: Data Tabulation 

VII. Abbreviations Used 

VIII. Acknowledgments 

IX. References 


The Cu 2+ ion with the 3d 9 configuration has been 

of particular interest because it represents a relatively 

simple one magnetic hole system, which can 

provide information regarding the electron wavefunction 

in ligand fields of various symmetries. The 

electron paramagnetic reasonance (EPR) spectrum 

of this ion is the least complex among all other divalent 

ions, because of the simple hyperfine structure. 

The Cu 2+ ion has also been used as an impurity 

probe in a variety of host lattices, since the 

fine structure study of Cu 2+ ion in undiluted copper 

Tutton salts by Bleaney et al. [46] and the observation 

of hyperfine (hf) structure in magnetically 

dilute salts by Penrose [347]. The main emphasis 

of the EPR studies of Cu 2+ in different hostlattices 

has been in the determination of site symmetries 

and orientations, the study of phase transi- 

243 

243 

243 

243 

tions,bonding parameters and magnetic properties 

of the systems. Experimental results of EPR investigations 

of Cu 2+ in single and polycrystals prior to 

1988 have been reviewed earlier by Misra and Wong 

[293]. The extensive experimental work which has 

been published since then now needs compilation. 

The scope of this review article is concerned with 

the EPR experimental investigations of the cupric 

ion in single crystals, polycrystals as well as liquids 

that have appeared between 1985 and 1992. The 

literature survey itself is provided in the form of a 

table in the appendix. Every care has been taken 

to include all the references, and any omissions are 

either due to the non-availability of the article or an 

inadvertent oversight.


II. Ground State of Cu 2+ Molecular 

Ion 

The electronic configuration of divalent copper 

(electron spin S = 1/2, nuclear spin I = 3/2 for each 

of the 69.09% abundant 63 Cu and the 30.91% abundant 

65 Cu isotope) is [Ar] 3d 9 . The ground state of 

this ion is the same as those of a d 1 system having 

a single unpaired electron. This 2 D5/2 ground state 

configuration can split further in different crystal 

field environments. As shown in Figure 1, in an octahedral 

crystal field the 2 D state of this ion splits 

into two states, a doublet 2 Eg and a triplet 2 T2g, 

with 2 Eg being the ground state . The separation 

between these two levels called 10Dq. When the 

symmetry is tetragonal, the triplet splits into singlet 

( 2 B2g) and doublet ( 2 Eg) levels for which the 

corresponding atomic orbitals are dixy> and diyz>, 

while the 2 Eg state splits into two non-degenerate 

2 Big and 2 Ajg levels with the respective atomic orbitals 

dix2-y2> and di3Z2-r2> • The ordering of these 

levels will depend upon whether the symmetry corresponds 

to that of a tetragonal compression or an 

elongation. A further lowering of symmetry from 

tetragonal to orthorhombic will lift the remaining 

degeneracy and perhaps mix the wave-functions corresponding 

to the states. A detailed discussion of 

the ground state wave-function has been presented 

by Misra and Wong [293] in their earlier review article, 

and we will not repeat this material here. 

III. Spin-Hamiltonian Analysis 

EPR spectra for a paramagnetic ion are traditionally 

interpreted using the conventional spin- 

Hamiltonian (SH), first introduced by Abragam and 

pryce [2]. The general description of each Hamiltonian 

term is given by Bowers and Owens [54], and by 

Bleaney and Abragam [47]. The SH which describes 

the EPR of Cu 2+ ion [47] is 

H = /3eH-gS + S-A-I + I-Q-I 

-gNj3N-H-I —• (1) 

where f3e is the Bohr magneton, S = 1/2 and I = 3/2 

for Cu 2+ . The first term represents the electronic 

Zeeman interaction, the second term is the interaction 

of the unpaired spin with the nuclear spin, the 

third term is the energy of interaction of the nuclearquadruple 

moment with the electric field gradient, 

and the last term represents the nuclear - Zeeman 

interaction between the external magnetic field and 

the nuclear spin. Usually the last two terms due to 

nuclear Zeeman and quadruple interactions are neglected 

as their contribution is small for the Cu 2+ 

ion. For orthorhombic symmetry the SH of Cu 2+ in 

the principal axis system becomes [47] 

H = /3e(gzzHzSz + gxxHxSx + gyyHySy) 

+ A1ZS2 + BIXSX + ClySy —•+ (2) 

where A = Azz; B = A C = Ayy and other 

terms have their usual meaning. For axial symmetry 

(gx = gy = g±; Aj. = Ax = Ay; gz = g||; and 

Az = AM) the SH then becomes 

H = 

(3) 

Both the g- and A-tensors are assumed to be coaxial, 

thus permitting the use of the perturbation results 

to get the magnetic field resonance values as given 

by [241,473], 

2 ][A|gf/K 2 g 2 

= Ho - Km - [Aigi/4Hog 2 ][A|gf/K 

l)-m 2 )-m 2 / 2 Ho[A 2 g 2 

where m = 3/2,1/2, -1/2 and -3/2 

Ho = hi//gA, 

g gf 2 - gfcos 2 0 

(4) 

and '#' is the angle between the magnetic field and 

z- axis of the g and A tensors. Here all coupling 

constants are expressed in Gauss and 'i/ is the microwave 

resonance frequency in Hertz. 

EPR spectra of Cu 2+ which do not depend on 

the orientation of the magnetic field have been observed 

in solutions, powders, glasses and sometimes 

in single crystals also [352,43,3]. The lack of field 

dependence arises in these cases because of the random 

orientations of the molecules or complexes.

Vol. 16, No. 3/4 241 

Free 

ion 

-T2g V •lyz> 

10 Dq 

4Dq 

-6Dq 

Octahedral 

coordination 

"B29 

Tetragonal 

elongation 

Ixy- 

2 2 

I3z-r 

Rhombic 

distortion 

Figure 1: Schematic energy level diagram of Cu 2+ in octahedral, tetragonal and rhombic crystal fields. 

There exists two limiting cases of field independent 

spectra for randomly oriented spin systems. Powders, 

glasses with stationary random orientations 

and viscous solutions having slowly tumbling molecules 

are at the one extreme and produce lineshapes 

which are powder patterns characteristic of the randomly 

orinted spins. Systems with rapidly tumbling 

molecules such as those in non-viscous solutions or 

in the gaseous phase are at the other limit, with 

anisotropic SH terms that are averaged out to zero 

by the rapid tumbling motion. The SH for such a 

spectrum reduces to [118,277] 

H = /3egoH • S + AOI • S (5) 

Here g0 and Ao are the isotropic g factor and 

hyperfine coupling constants. The isotropic and 

anisotropic g and A parameters are related by 

[277,220] 

go = (g|| + 2gJJ/3 or g0 = (gx + gy + gz)/3 — (6) 

Ao = 

or 

Ao = (Ax Az)/3 (7) 

If the tumbling motion of the complex molecules is 

slow, then EPR spectrum for a bulk sample results 

from the superposition of spectra of molecules randomly 

oriented in all possible directions, and the 

result is a broad powder like spectrum. 

IV. Spin-Hamiltonian and Bonding 

Parameters 

The spin-Hamiltonian parameters (SHP) are used 

to extract information concerning the molecular ion 

and its surrounding environment in the host. SHP 

are usually evaluated from resonant field measurements 

at different orientations of a single crystal. 

The EPR spectra in lower symmetry systems show 

extrema along three mutually perpendicular principal 

directions,the z, x and y-axes. The z- axis is defined 

as the direction of maximum spread, while the 

x-axis is the direction of minimum spread. From the 

resonant field measurements of allowed transitions 

(AMs = ±1, Ami = 0) along z, x and y-axes, one 

can evaluate SHP using perturbation expressions


(for details see section (III)). If the SH has dominant 

fine structure terms, a perturbation treatment leads 

to systematic deviation from the true eigenvalues 

and hence from the observed spectra. The evaluation 

of the parameters in this case can be performed 

by diagonalizing the entire spin-Hamiltonian Matrix 

(SHM). Generally the least square fitting (LSF) procedure 

employing diagonalization of a SHM is used 

to evaluate the SHP. Misra [294-299] has reviewed 

a number of techniques dealing with the LSF evaluation 

of SHP, which can be readily applied to the 

Cu 2+ ion. On the other hand, from the values of 

the SHP and the optical absorption data one can 

get information about the interaction of the central 

molecular ion Cu 2+ with its chemical environment. 

The Molecular Orbital (MO) approach [268,332, 

254], which is more sophisticated treatment, has 

been applied to the bonding of the divalent copper 

ion. A large number of bonding parameters were 

reported in earlier papers [383,233,255]. Since different 

authors make use of different expressions, the 

direct comparison of MO parameters becomes very 

difficult. Hence, no attempt has been made here to 

include these parameters in the experimental data 

tabulations found in the appendix. Some expressions 

involving MO and SH parameters are given in 

the next section. 

V. Applications 

A. Determination of Spin-Lattice Relaxation 

(Ti) of Host Ions 

Spin-lattice relaxation (SLR) results from energy 

transfer from the spin system to the lattice. 

The EPR technique has been used widely to study 

SLR. The spin-echo technique which can be used to 

measure SLR directly is limited to very low temperature 

determinations because of the relatively short 

Cu 2+ spin-lattice relaxation times (SLRT) at high 

temperatures. The SLRT of host ions is also very 

short (particularly above 77K), making it difficult to 

measure directly, but it can be estimated from the 

observed linewidth (LW). The observation of EPR 

is often not possible in paramagnetic hosts because 

of the broadening of the EPR lines by impurity interactions. 

If the host SLR narrowing is effective, 

sharp line EPR spectra of impurity ions can become 

observable [330,78,389,300]. In such cases the impu- 

rity ion linewidth (AH) can be related to the host 

SLRT (Ti) as follows [301,458] 

Tx = (3/20) * (h/gh/?e * (8) 

Here H 2 d = 5.1 (gh/?en) 2 Sh(Sh + 1), gh is the g-factor 

of the host ion, Sh is the spin of the host ion, n 

is the number of host spins per cm 3 which can be 

calculated from crystallographic data, and AH is 

the EPR linewidth of the impurity ion. From the 

observed AH of the impurity ion, one can use this 

expression to estimate the host SLRT. These studies 

can make it possible to estimate the extremely fast 

SLRT at relatively higher temperatures. 

B. Bonding Parameters 

The MO parameters and electronic energy levels 

can be related to the g and A tensors as follows 

[268,332,254] (where small overlap terms are 

neglected). 

g2 = 2.0023 - [8Ao/AE( 2 Blg - 2 B2g)] 

{a 2 /? 2 - £09)} — (9) 

gz = 2.0023 - 

1 

f 

2 fif 

(g,|-2.0023) 

+3/7(gx - 2.0023) ± 0.04 

(10) 

(11) 

where p = Aoa/?i/AE( 2 Blg -> 2 B2g), a' = (1 - a 2 )^ 

-I- aS, a 2 cu> P 2 , 0\ are the MO bonding coefficients, 

P (tcu/?e/?N < r~ 3 >) is the dipolar coupling term, 

Ao(= —828cm" 1 ) is the spin-orbit coupling constant, 

AE( 2 B\g —> 2 i?2g) is the energy separation 

between the Big ground state and the B2g excited 

doublet. The parameter a 2 cu denotes the in-plane 

cr-bonding coefficient, /3, 2 is the in-plane 7r-bonding 

coefficient and 0 1 is the out-of-plane 7r-bonding coefficient. 

The value of a 2 cu indicates the covalency 

of the (T-bond between copper ion and its ligands, 

and it has a value of 1 if the bond is totally ionic; 0.5 

if it is totally covalent. The value of f3\ 2 is affected 

by the delocalization of the electron on the ligands, 

and is expected to decrease as the a 2 cu value increases. 

The values of a 2 cu of copper complexes 

typically vary from 0.80 to 0.95 [268].

Vol. 16, No. 3/4 243 

C. Phase Transition Studies 

The Cu 2+ probe has been widely used to study 

phase transitions (PT) in a large number of host 

lattices [280,452,302,378,515]. The use of impurity 

ions in studying PT has been discussed by Muller 

[318] and by Owens [338]. The effects of PT on the 

EPR spectra are (1) a change in" the angular dependence 

of the spectra, (2) anomalous variations of LW 

and line shape near the PT temperature because 

LW's are sensitive to the fluctuations of the nearest 

neighbors, (3) observation of forbidden hf transitions: 

the appearance of forbidden hf transitions 

along a principal axis suggests either a lowering of 

the symmetry or a tilt of its principal axes both of 

which may be due to the structural phase transition, 

and (4) changes in the SLRT of the impurity ion 

[300]. PT can be identified very easily from discontinuities 

in the LW parameters. The LW temperature 

dependence has been successfully used to identify 

incommensurate co-operative Jahn-Teller (JT) 

PT's in R2PbCu(NO2)6, (R = K,Rb,Tl) compounds 

(149,493,335,373). Copper ions have also been used 

to study the PT's and molecular ordering in liquid 

crystals [98]. 

VI. Appendix: Data Tabulation 

The survey of the literature between 1985 and 

1992 is given in tabular form in the Appendix. The 

table contains the SHP of Cu 2+ ions in liquids and 

single and polycrystals. Whenever g and A- parameters 

are isotropic, only one numerical value has been 

listed for each. The g- values are dimensionless. 

Hyperfine splitting parameters are given in units of 

10~ 4 cm" 1 unless otherwise indicated. The following 

abbreviations have been used in the appendix as 

well as in the text. The comments column summarizes 

the highlights of the investigation presented in 

the table. 

VII. Abbreviations Used 

absor., absorption; CaL, calculated; coeff., coefficients; 

Const., constant; constd., constructed; 

depend., depending; diff., different; dir., direction; 

EPR, electron paramagnetic resonance; ESR, electron 

spin resonance; estm., estimated; exptl., experimental; 

GS, ground state; GSWF, ground state 

wave-function; hf., hyper fine; hfs., hyperfine structure; 

interact., interaction; JT, Jahn-Teller; JTE, 

Jahn-Teller effect; LNT, liquid nitrogen temperature; 

LS, line shape; LSF, least square fitting; LT, 

low temperature; LW, linewidth; magn., magnetic; 

MO, molecular orbital; NMR, nuclear magnetic resonance; 

obsd., observed; optl., optical; PT, phase 

transition; reptd., reported; RT, room temperature; 

SH, spin-Hamiltonian; shf., superhyperfine; 

SHM,spin-Hamiltonian matrix; SHP, spin- Hamiltonian 

parameters; SLR, spin lattice relaxation; 

SLRT, spin lattice relaxation time; spec, spectra; 

sub., substitution; supercond., superconductor; 

temp., temperature; WF, wave-function; ZFR, zerofield 

resonance. 

VIII. Acknowledgments 

The authors are extremely grateful to Dr. Krishan 

Lai, Head, Materials Characterization Division, 

National Physical Laboratory; Prof. S.V.J. Lakshman, 

Formerly Vice-Chancellor, S.V.University, 

Tirupati; Prof. J. Lakshmana Rao, Department of 

Physics, S.V. University, Tirupati; Prof. V.P. Seth, 

Department of Physics, M.D. University, Rohtak 

and Dr. Prem Chand, Department of Physics, Indian 

Institute of Technology, Kanpur for their constant 

encouragement and suggestions in preparing 

the manuscript. 

One of the authors (RMK) is thankful to the 

Council of Scientific and Industrial Research (CSIR) 

for Scientist fellowship (No. B8552). Also RMK 

wish to thank his wife, Madhavi, for the various 

ways in which she assisted in the preparation of the 

manuscript. 

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A. Abragam and M.H.L. Pryce, Proc. Roy. Soc. 

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3 

I.S. Ahuja and S. Tripathi, Spectrochim Ada A 

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4 

I.S. Ahuja and S. Tripathi, Spectrochim. Chim. 

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5 

I.S Ahuja and S.Tripathi, Indian J. Chem. A 

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6 

N. Akihiko and H. Kazumi, Jpn. J. Appl. Phys. 

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I. Aksenov and S. Katsuaki, Jpn. J. Appl. 

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N.E. Alekseevskii, 

LA. Garifullin, N.N. GarifYanov, B.I. Kochelaev, 

A.V. Mitin, V.I. Nizhanovskii, L.R. Tagirov and 

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9 

N.E. Alekseevskii, LA. Garifullin, 

N.N. GarifYanov B.I. Kochelaev, A.V. Mitin, V.I. 

Nizhanovskii, L.R. Tagirov and E.P. Khlybov, Sov. 

Phys. JETP (USA) 67, 805 (1988). 

10 

N.E. Alekseevskii, LA. Garifullin, N.N. 

GarifYanov. B.I. Kochelaev, V.I. Nizhanovskii, 

L.R. Tagirov and E.P. Khlybov, Sov. Phys. Solid 

State (USA) 30, 909 (1988). 

U 

N.E. Alekseevskii, A.V. Mitin, 

V.I. Nizhankvskii.I.A. Garifullin, N.N. GarifYanov, 

G.G. Khaliullin, E.P. Khylbov, B.I. Kochelaev and 

L.R. Tagirov, /. Low Temp. Phys. 77, 87 (1989). 

12 

G.A. Aliev, A.V. Ivanov and M.L. Rachkovskii, 

Dokl. Akad. Nauk. SSSR (Phys. Chem.) 318, 606 

(1991). 

13 

A.A. Alybakov, V.A. Gubanova, K. Kudabaev 

and K. Sharsheev, Phys. Stat. Solidi (B) 146, K135 

(1988). 

14 

G. Amoretti,E. Buluggiu, A. Vera, G. 

Calestani and F.C. Matacotta, Z. Phys. B: Condensed 

Matter (Wg) 72, 17 (1988). 

15 

D. Andrea, G. Dante, P. Luca, B.A. Laure and 

B. L. Claude, Phys. Lett. 175, 589 (1990). 

16 

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Bulletin of Magnetic Resonano

Vol. 16, No. 3/4 257 

Table 1: Appendix: Data Tabulation 

S.No Host Lattice Site Spin-Hamiltonian Parameters 

1. AgCl 

2. AgCl 

3. AgCl 

4. AGeO3 

(A=Fe,Mn,Cu) 

5. (2-aminomethylquinoline), 

s-aminomethylquinoline:Cu(II) 

6. Antipyrine and its derivatives 

7. Ampholyte ANKB-50:Cu 2+ -Ni 2+ 

8. AsCdCl3 

9. (04As)CuCl3 

10. BaCuC-2 

Y2Cu2Os 

11. BaCuO2 

12. BaCuC-2 

Y2Cu2Os 

Y2BaCuO5 

Al2CuO4 

13. Ba2Cu2O5 

14. [Ba(HCOO)2] 

15. [Ba(NH2SO3)2] 

16. B15C5- 65 Cu(II) 

I 

II 

I 

II 

§Z gx gy Az Ax 

2.302 2.067 2.067 115 41.5 41.5 

1.930 2.170 2.170 

2.09 

2.20 2.12 2.08 

2.11 

2.22 2.09 2.09 

2.22 

2.362 2.076 2.071 -151 7 

2.385 2.083 2.047 -90 37 

11 

82 

2.269 2.048 2.058 170G 20G 24G 

2.030 2.408 2.296 10.39 5.00 3.00 

2.036 2.389 2.287 10.54 5.64 2.92 

Comments Ref, 

site thermally un- [460] 

stable at 135K, induced the 

decay of Cu 2+ site. 

Cu 2+ centres produced by UV [461] 

illumination at 50K. 

Cu 2+ superhyperfine struc. [345] 

EPR spectra were observed 

with four Cl ligands. 

Below 22K, ESR signal obsd. [387] 

and above 22K disappeared. 

The Cu ions forms square - [503] 

planar complexes with 2-amine 

ligands. 

SHP and MO coeff. of solu- [485] 

tions reported. Bonding 

lengths depends more on type 

of complex than on solvent. 

Formation of chelating ex- [467] 

changer characterized by ESR. 

At T < 235K the Cu 2+ ions [28] 

tetrahedrally coordinated. 

ZFR, SHP. [136] 

Due to exceptional spin-spin [55] 

dipolar brodening absence of 

EPR signal observed. 

EPR study for diff. cupric [496] 

compounds presented. 

LW increases and intensity [497] 

decreases at LT. 

YBCO showed no detectable [446] 

ESR signal either above or 

below Tc. 

Sub. for Ba 2+ sites and [66] 

Cu 2+ enter Inst. sites. 

Cu 2+ ions enter the lattice [316] 

interstitially. 

GS wavefunction is of the [495] 

form 3dz2.


S.No Host Lattice Site Spin-Hamiltonian Parameters Comments Ref. 

17. /?" - alumina 

18. BiCaSrCu2Ox 

19. 

20. BiCaSrCuO 

21. Bi-Ca-Sr-CuO 

Bi(Pb)-Ca-Sr-Cu-O 

Tl-Ca-Ba-Cu-O 

Tlo.sPbo.5(Cao.8Ao.2)Sr2Cu20y 

22. BiCaSrCuO 

23. Bi2CuO4 

24. Biguanide derivatives:Cu(II) 

25. Binuclear Copper complexes 

26. Bi(Pb)-Sr-Ca-CuO 

27. Bi(Pb)-Sr-Ca-Cu-O 

Ca2CuO3 

28. Bis [cinchoninium 

tetrachloro-Cu(II)]-3H2O 

29. Bis(Glycine) CaCl2-4H2O 

30. Bis(metronidazole)CuCl2H2O 

31. Bis(2-hydroxylphenyl- 

Ketoxime) Cu(II) 

32. Bis(N-Methyl Salicylaldiminato)- 

Cuo.49Nio.s1 

33. Bis(N-CH3-2-amino-l-clycIopentenedithiocarboxylato)Cu(II) 

I 

II 

gx gy 

2.385 2.097 2.072 91 

Vol. 16, No. 3/4 259 


I BiPbSrCaCuO 

gx gy As, Ax 

35. Bis(2-hydroxyphenylketoxime) 

Cu(II) 

36. Bis(2,4-dimethylpyridine)Cu(II) 

37. BiSrCaCu2Ov 

38. Bi2Sr2CaCu2Oy 

Bi2-xPbxSr2Ca2CuOy 

39. Bi2(Sr,Ca)3Cu2Oy 

40. Bi2Sr2CaCu2O8 

41. Bi2Sr2CaCu2O8+x 

42. Bi-Sr-Ca-Cu-O films 

43. Blue Copper Protein azurin 

44. BSA-Cu(II)(l:l) 

BSA-Cu(II)(2:l) 

45. Butyl titanate polymers: 

Copper carboxylate 

46. CAeruloplasmin 

2.268 2.050 2.050 191 10 

I [2.24 -2.78] 

II 2.003 

2.227 

2.1 

2.1 

2.26 2.07 2.07 160G 

2.17 2.02 2.07 212G 

2.17 2.02 2.02 211G 

2.203 2.050 2.050 -76 -10" 3 

10 

Comments Ref. 

EPR spectra behaves diff. [500] 

below and above 104K due to diff. 

supercond. phases. 

Hf and shf spectra observed. 

SHP and bonding parameters 

estimated. 

[87] 

The measured g-factor values [170] 

indicate a pure Ix2-y2> groundstate. 

Two types of EPR signals [423] 

exist, one is temperature dependence 

and other one is temp, independent. 

EPR signal near 3300G ori- [424] 

ginate from the 85 K phase. 

The anisotropy of resonance [217] 

field observed. 

Single EPR signal observed [451] 

in both samples, g-factor 

indicating the dominance of 

Cu 2+ spins. 

No ESR signal detected due [273] 

to absence of cuprate impurities. 

ESR LW increases with thick- [438] 

ness of films. 

S-band EPR spectrum of blue [175] 

copper protein azurin explained 

by pseudomodulation. 

Two distinct EPR features [343] 

observed. SHP reported for diff. 

pH values of diff. complexes. 

ESR study indicates rate of 

electron transfer from Cu(II) 

titanate to substrate molecule is 

faster. 

10~ 3 SHP analysed interms of 

sample MO theory and Cu(II) 

present in plasma of human 

blood is discussed. 

47. CaBaAlF 2.320 2.055 2.055 130G 25-30G Glasses. [199] 

[155] 

[240]



Comments Ref. 

48. Ca(C4H3O4)2 5H2O 2.033 

gx 

2.289 

gy 

2.289 

Az 

109 

Ax 

26 26 Cu 2+ -in a compressed octahedral 

position. GS wavefunction 

is of the form 

[317] 

49. CaCd(CH3COO)4-6H20 

50. CaCd(CH3COO)4-6H2O 



53. CaCd(CD3COO)4-6D2O 

54. Cadmium tartrate-5H2O 

55. CaF2 

56. Cao.sTi2(P04)3 

57. CdK2(SO4)2-6H2O 

58. Cd(NH4)2(SO4)2-6H2O 

59. Cd(NH4)2(SO4)2-6H2O 

60. Cesium trichlorocuprate 

61. C2Hs(CH3)2NMnCl4 

62. Chalcanthite 

63. CH2C12 

CH2C12 + acetone 

CH2C12 + Br2 

CH2C12 + h + acetone 

2.3547 2.0646 

2.365 2.054 2.054 

2.441 2.283 2.02 

2.0646 420 

MHz 

2.802 2.103 2.147 76 

2.370 2.060 2.060 

2.374 2.197 2.128 282.4 

GHz 

29 

MHz 

0.410 0.030 

GHz GHz 

97 

79.9 

GHz 

29 

MHz 

0.030 

GHz 

97 

137 

GHz 

Structural PT at 130 + IK [302] 

obsd.; SHP reported over the 

range 300-5.4K. 

New 2nd order PT observed [69] 

at 128K due to molecular re- 

arrangements between Ca 2+ [70] 

and Cd 2 " 1 " sites in acetate groups. 

Calculated EPR results indi- [511] 

cates Cu 2+ ions sub. for 

Cd 2+ sites. 

PT observed at 132 ± 0.5K. [310] 

Impurity ions play important 

role in occurrence of PT. 

SHP evaluated by LSF; weak 

forbidden-hf lines obsd., Cu 2+ 

lattice sites identified as 

two magnetically inequivalent. 

EPR signal arises due to 

impurity phases. 

Ground state WF is of the 

form dix2-y2>. Below 823K JT 

distortion obsd. 

Cu 2+ sub. for Cd 2+ sites 

MO Coeff. 

2.355 2.172 2.054 101G 25.6G 54.77G Sub. for Cd 2+ sites. Ground 

state wavefunction constr. 

2.3613 2.0522 2.1721 0.333 

GHz 

2.172 2.05 

2.170 2.045 

2.160 2.045 

2.160 2.045 

2.05 208 

2.045 103 

2.045 110 

2.045 110 

0.151 

GHz 

15 

14 

0.074 

GHz 

90 

14 

Pseudo JTE observed. 

SHP reported. 

EPR LW study with temp, and 

cone, impurity ion reported. 

SHP and vibrational parameters 

discussed. 

SHP reported for other solvents 

and data attributed to 

the ground state dix2-y2>. 

[228] 

[505] 

[197] 

[402] 

[401] 

[308] 

[150] 

[454] 

[370] 

[404]

Vol. 16, No. 3/4 261 


64. [(-C6H4NH-)(C104)o.4H20] 

[(-C6H4NH-C6H4NH-)1-x - 

2.0027 

gx gy A2 Ax 

(-C6H4NC6H4=N-)xO.4H2Ojn 

[(-C6H4NH-)(C104)o.40.6H20]n 

65. (C59H61O8N6FeCu3)n(PP6)2n 

66. Cis-Cu(NH2CH2COO)2- 

H2O 

67. (Co(l-3-diaminopropane)3] 

CuCls-3H2O 

68. Cobalt Fluorosilicate 

hexahydrate 

69. Cs2C2O4H2O 

70. CsCuCl3 

71. CsH2PO4 

72. CsH2PO4 

73. Cu+, Ag+, and Au+ 

74. [Cu(acpc)2] 

[Cu(L-alao)2] 

[Cu(DL-alao)2(H2O)] 

[Cu(DL-ProO)2(H2O)2] 

[Cu(glyo)2 H2O] 

75. CuAl6(PO4)4(OH)8-4H2O 

2.0036 

2.0027 

2.24 

2.216 2.103 2.073 

2.225 

2.130 

Comments Ref. 

i) EPR signal intensity [275] 

thermally activated temp. 

depend. 

ii) EPR signal is temp. 

independent for other 

perchlorates. If it 

adsorbed oxygen then 

signal temp, dependent. 

The structure of the com- [179] 

pound confirmed by EPR 

and Mossbauer studies. 

Single crystal EPR results [168] 

assigned to orthorhombic 

symmetry. Temp, 

dependence exchange 

coupling estimated. 

ESR LW changes from [346] 

axial to orthorhombic 

symmetry. 

The LW continuously in- [81] 

crease with decreasing 

temp. 

Cu 2+ enter at interstitial [193] 

sites. SHP reported at RT. 

PT at 420K; temp, 

dependence EPR spec, 

over the range 

120 - 560K. 

[453] 

Temp, dependence EPR [477] 

spectra exhibited. 

2.2575 2.1866 2.1866 30G 27G 27G SHP, ZFR [476] 

2.0023 

2.210 

2.253 

2.255 

2.263 

2.277 

2.0068 

2.071 

2.037 

2.041 

2.046 

2.068 

2.0068 

2.038 

2.057 

2.068 

2.081 

2.061 

2.305 2.112 2.034 

3363 

MHz 

3363.5 

MHz 

3363.5 The SHP interpreted in [463] 

MHz terms of orbital 

characteristics. 

Bond lengths, bonding [159] 

parameters reported, 

electronic data 

also presented. 

GS wavefunction con- [409] 

structed for Cu 2+ ions as 

dlx2-y2> • 

76. Copper-amino acid CORRIGENDUM [110]



gx gy Az Ax 

77. Copper-amino acid 

complexes 

78. 

79. 

80. 

81. 

Cu(5A4-2AA)2(NO3)2+7xT 

Cu(AA)2(NO3)2+2xT 

Cu(A)5(NO3)2+5xT 

Cu(AA)2 

Cu(OX)2 

Cu(AA)(OX) 

Cu(AA)(5,7Cl-OX) 

Cu(AA)(5,7Br-OX) 

Cu(AA)(5,7I-OX) 

Cu(AA)(5,7NO2-OX) 

Cu(AA)2 

Cu(SA)2 

Cu(Cl-SA)2 

Cu(2Br-SA)2 

Cu(2I-SA)2 

Cu(2NO2-SA)2 

Cu(Acetyl-SA)2 

Cu(AA)(SA) 

Cu(AA)(Cl-SA) 

Cu(AA)(2I-SA) 

Cu(AA)(NO2-SA) 

Cu(AA)(Thio-SA) 

Cu(AA)(Acetyl-SA) 

Cu(AA)(2NO2-SA) 

CuAc2Im2 

Cu2Ac4(CH3-lIm)4-6H2O 

Cu2AC4(CH3-lIm)4-6H2O 

(Powder) 

82. Some Aliphatic Polyamine 

Cu(II) compounds 

2.203 

2.280 

2.126 

2.291 

2.244 

2.242 

2.234 

2.242 

2.242 

2.238 

2.291 

2.284 

2.280 

2.292 

2.292 

2.300 

2.280 

2.289 

2.299 

2.295 

2.296 

2.295 

2.276 

2.300 

2.263 

2.310 

2.304 

83. CuAlS2 2.32 

84. CuAlS2 [2.05-2.31] 

85. Cu(3-AMI)4(C1O4)2 2.278 

Cu(3-AMI)4(NO3)2 

2.274 

2.023 

2.061 

2.075 

2.042 

2.054 

2.060 

2.054 

2.059 

2.061 

2.054 

2.051 

2.057 

2.055 

2.061 

2.060 

2.064 

2.060 

2.051 

2.052 

2.051 

2.056 

2.069 

2.06 

2.072 

2.078 

2.023 

2.061 

2.075 

2.042 

2.054 

2.060 

2.054 

2.059 

2.061 

2.054 

2.051 

2.057 

2.055 

2.061 

2.060 

2.064 

2.060 

2.051 

2.052 

2.051 

2.059 

2.069 

2.06 

2.072 

2.078 

2.064 2.181 

2.051 2.166 

202 

178 

207 

159 

167 

144 

162 

159 

162 

177 

159 

142 

150 

147 

147 

141 

153 

149 

149 

149 

146 

140 

149 

144 

190 

172 

20 

16.5 

mT 

15.03 

mT 

15 

25 

32 

25 

30 

27 

14 

15 

19 

22 

19 

20 

18 

25 

11 

14 

18 

19 

11 

19 

17 

31 

13 

4.98 

mT 

5.23 

mT 

15 

25 

32 

25 

30 

27 

14 

15 

19 

22 

19 

20 

18 

25 

11 

14 

18 

19 

11 

19 

17 

31 

13 

11.04 

mT 

11.23 

mT 

Comments Ref. 

Two angular variation [356] 

of gyromagnetic factor 

measured by ESR in 

single crystals of several 

complexes. ESR show a single, 

exchange collapsed line. 

Structural changes of [221] 

Gel samples indicated by 

Cu(II) EPR spectra. 

SHP of solutions and powder [18] 

samples reported. MO coeff. 

evaluated. 

SHP and MO coeff. estimated [19] 

and assinged to an axial 

symmetry. 

The EPR pattern does not [125] 

show any feature characteristic 

for the triplet paramagnetic 

state. 

ESR LW varies with solvents. [236] 

The exptl. & cal. LW for diff. 

solutions were reported. 

A symmetrical line shape has [176] 

been observed. 

ESR spectra appears depen- [7] 

ding on annealing atmosphere. 

Ground state WF observed [391] 

with admixture of dix2-y2> and 

and dz2- Rhombic symmetry 

observed in both complexes.

Vol 16, No. 3/4 263 


-867[Cu(AMH)2] (QH)2 

[Cu(AMH)2] Cl2 

2.171 

2.177 

gx 

2.056 

2.062 

gy 

2.056 

2.062 

Az 

210 

205 

Ax 

21 

25 

[Cu(AP'UH)2] (OH)2 

2.175 2.058 2.058 202 24 

[Cu(AP'UH)2] Cl2 

2.179 2.054 2.054 202 17 

(Cu(AMEUH)] Cl2 

2.173 2.058 2.058 203 24 

[Cu(AEEUH)2] Cl2 

2.181 2.065 2.065 205 25 

87. [Cu(bPt)(CF3SO3)(H2O)]2 

88. Cu(benzac)2- pyridine 

89. Cu(II) biguanide complexes 

90. Cu(II)-bis (amino-acid) 

complexes 

91. Cu(BP3CA)Cl2H2O 

92. Cu5(BTA)6(RNC)4 

93. Cu(C11H12ON2)6(C104)2 

94. Copper Complex in the 

slow motion regime 

95. Cu 2+ complexes 

96. Some binary and ternary 

Cu(II) compounds. 

97. Bi- and tricyclic 

Cu(II) chelates 

98. Binary and ternary 

Cu(II) compounds 

99. Some Cu(II) complexes 

100. Some Cu(II) complexes 

101. Cu compounds 

2.232 

2.302 

2.055 

2.067 

2.256 2.046 

2.06 2.19 

2.051 

2.062 

2.066 

-492 

MHz 

-25 

MHz 

21 

25 

24 

17 

24 

25 

-25 

MHz 

2.19 0G 77G 77G 

Comments Ref. 

SHF reported for dm. solvents. 

MO coeff. also reported. 

ZFR dominant. 

Results of ESEEM and CWEPR 

reported. 

[36! 

[37] 

[75] 

SHP and MO coeff. reported. [368] 

Solutions SHP reported. [120] 

GS wavefunction is of the 

form of admixture of Ix2-y2> 

and 3z2-r2. 

g and A values are found to 

be nearly independent of temp. 

2.3416 2.0376 2.0360 0.3656 0.870 0.0473 SHP were made up to liquid 

GHz GHz GHz helium temp. 

A fast compututional method 

for stimulating EPR lineshapes 

presented. 

EPR of Cu 2+ in frozen solutions 

is presented by a 

theoretical method. 

SHP data presented both at 

RT and LNT. 

Structural studies of chelates 

conformed by ESR. 

SHP of solution spectra and 

LW studies presented. 

SHP of diff. complexes reptd 

[231] 

[32] 

[303] 

[114] 

[117] 

[17] 

[358] 

[348] 

[45] 

SHP of polycrystalline ESR [237] 

exhibit axial symmetry as well 

as rhombic symmetry depending 

on the ligand environment. 

Covalency parameter evaluated. 

Relationship between the [250] 

correlation and structure of 

Cu containing compounds 

examined.



102. Cu(II) complexes in 

solutions 

103. Cu(II)-Collagen complex 

104. Octacoordinated copper 

complexes 

105. Cu(II) complexes with 

organic liquids 

106. 

107. 

108. 

109. 

110. 

Cu(II) in square 

planar lattices 

Copper Calcium Acetate- 

6H20 

Cu(2-CA)o.5S04 

Cu(3-CA)2SO4 

Cu(4-CA)3SO4 

Cu(2-CP)2SO4 

Cu(3-CP)2SO4 

Cu(4-CP)2SO4 

(CA = Cyanoaniline) 

(CP = Cyanopyridine) 

Cu(2-CA)0.5SO4 

Cu(2-CA)2SO4 

Cu(4-CA)3SO4 

Cu(3-CP)2SO4 

Cu(2-CP)2SO4 

Cu(4-CP)2SO4 

(CA = Cyanoaniline) 

(CP = Cyanopyridine) 

CuCe oxide 

111. Copper Cerium oxide 

112. 

113. 

114. 

CuCe Oxide 

Cu(CioH2oN8)Cl2 

Ni(CioH2oN8)Cl2 

Cu(C8H8O2N)8 

Cu(C8H8O3N)2 

Cu(C9H10O3N)2 

Cu(C1iH8O2N)2 

Al 

A2 

K 

gx gy Az Ax 

2.19 2.04 2.04 

2.370 

2.404 

2.407 

2.398 

2.393 

2.336 

2.402 

2.268 

2.267 

2.284 

2.260 

2.219 

2.267 

2.2079 

2.1233 

2.2079 

2.248 

2.249 

2.254 

2.146 

2.070 

2.057 

2.048 

2.051 

2.036 

2.081 

2.052 

2.079 

2.060 

2.063 

2.045 

2.060 

2.079 

2.0403 

2.0403 

2.0403 

2.061 

2.061 

2.060 

2.073 

2.070 

2.057 

2.048 

2.051 

2.036 

2.081 

2.052 

2.079 

2.060 

2.063 

2.045 

2.060 

2.079 

2.0403 

2.0403 

2.043 

2.061 

2.061 

2.060 

2.073 

13mT 

133G 

113G 

113G 

126G 

146G 

120G 

170G 

82G 

85G 

150.91 

148.74 

141.62 

135.23 

1.6mT 

18.3G 

20.8G 

18.3G 

26.6G 

6.95G 

19.9G 

27G 

40G 

13.5G 

8.80 

7.90 

7.17 

8.06 

1.6ml 

18.3G 

20.8G 

18.3G 

26.6G 

6.95G 

19.9G 

27G 

40G 

13.5G 

8.80 

7.90 

7.17 

8.06 

Comments Ref. 

ESR LW against temp, plotted; [353] 

Dynamics of solvent-solution 

interaction. 

JT energy reported using 

EPR measurements. 

EPR and structural parameters 

presented. 

Structure of complexes 

discussed with the help of 

ESR data. 

ZFR 

J values presented at diff. 

temp, using ID, 3D models. 

ESR data indicate the 

presence of unpaired electron 

in the dix2-y2> orbital 

of the Cu(II) ion. SHP of 

powder samples and bonding 

parameters also reported. 

SHP reported for both solution 

powder complexes. 

SHP measurements were 

made both at X- and 

Q-band frequencies. 

Well resolved EPR spectrum 

of Cu 2+ observed in 

perpendicular components. 

Two nearly equivalent Cu 2+ 

ions separated by an oxygen 

ion appears. 

SHP reported. 

Interaction of solvent with 

EPR spectra presented. 

MO coeff. 

[415] 

[129] 

[104] 

[435] 

[416] 

[432] 

[5] 

[21] 

[22] 

[20] 

[64] 

[357]

Vol. 16, No. 3/4 265 


gx gy Az Ax 

115. CuCi8Hi6N4Cl2 

116. 

117. 

118. 

119. 

120. 

Cu(CH3CO2)2 

(2,6Me2Py)2 

[Cu(cit)] 

(Cu(l-mal)] 

Cu/[Zn(l-mal) 

(H2O)2]H2O 

[CuMg(cit)2H_2] 4 - 

[CuZn(cit)2H_2] 4 - 

[CuPd(cit)2H_2] 4 ~ 

Cu(2-BOP)Cl2 

Cu(3-BOP)Cl2 

Cu(4-BOP)Cl2 

Cu(2-BOP)2Br2 

Cu(3-BOP)2Br2 

Cu(4-BOP)2Br2 

[Cu(Li)2) 

[Cu(LiH)2]Cl2 

[Cu(L2)a] 

[Cu(L3)2] 

[Cu(L4)2] 

[Cu(L5)2] 

[Cu(L5H)2]Cl2 

Cu(ClO4)2-5ANT 

Cu(ClO4)2-6ANT 

Cu(ClO4 2-2AMFH2O 

121. CuCl2 - Graphite 

122. I/CuCl2 

II/Cu(NO3)2 

123. (CuCl2Ll)2 

(CuCl2-L2)2 

124. CuCl2-2Py 

CuBr2-2Py 

125. Cu(CN)|- 

Cu(CO)3 

Ag(CN)^ 

Ag(CO)3 

126. Cu(CO)3 

2.248 

2.368 

2.374 

2.425 

2.297 

2.297 

2.325 

2.262 

2.247 

2.245 

2.208 

2.115 

2.108 

2.170 

2.176 

2.173 

2.174 

2.173 

2.173 

2.168 

2.4311 

2.4311 

2.3241 

2.061 

2.080 

2.080 

2.089 

2.062 

2.062 

2.068 

2.066 

2.051 

2.050 

2.041 

- 

- 

2.059 

2.061 

2.057 

2.061 

2.063 

2.061 

2.058 

2.0686 

2.0686 

2.0671 

2.061 

2.080 

2.080 

2.089 

2.062 

2.062 

2.068 

2.135 

2.080 

2.080 

2.041 

- 

- 

2.059 

2.061 

2.057 

2.061 

2.063 

2.061 

2.058 

2.0957 

2.0957 

2.0893 

23.6 

mT 

142 

140 - 

120 

173 

173 

161 

208 

207 

209 

204 

203 

203 

210 

13 

13 

17 

2.183 2.075 2.075 163G 

2.200 2.049 2.049 200G 

2.14 

2.18 

2.0004 

2.0010 

1.9987 

2.0009 

2.0010 

2.04 

2.04 

2.0049 

2.0029 

2.0035 

2.0009 

2.0036 

2.04 

2.04 

2.0049 

2.0029 

2.0035 

2.0009 

2.0021 

262 

MHz 

225 

MHz 

168 

MHz 

1586 

MHz 

225 

MHz 

3.5 

mT 

10 

10 

10 

12 

12 

07 

23 

22 

24 

20 

19 

19 

25 

20G 

53G 

74 

MHz 

0 

MHz 

89.5 

MHz 

1586 

MHz 

0 

3.5 

mT 

10 

10 

10 

12 

12 

07 

23 

22 

24 

20 

19 

19 

25 

20G 

53G 

74 

MHz 

0 

MHz 

89.5 

MHz 

1586 

MHz 

0 

Comments 

Ref. 

Non equivalent Cu(II) sites [130] 

obsd.; Exchange integral 

explained LW of EPR. 

Anisotropy of LW obsd. due [171] 

to isotropic exchange interaction. 

The Cu(II) ion coordination [52] 

environment in hetrodinuclear 

species is different from the 

Cu(II) monocitrate species. 

EPR data indicate the pres- [3] 

ence of unpaired electron in 

dix2-y2> orbital of Cu(II) ion 

in an axial symmetry. 

SHP of powder as well as [383] 

solution spectra presented. 

MO coeff. reported. 

Information concerning the [119] 

structure of title compound 

presented. 

EPR study reported on Cu(II) [224] 

Mn(II) ions. 

Liquid crystalline phases [90] 

and solid polycrystals characterized 

by its EPR pattern. 

EPR and magnetic suscepti- [377] 

bility data presened. 

EPR spectrum always reduced [336] 

to Lorentzian singlet. 

Ag(CO)3 is unique.being 

pyramidal where the other 

three are planar. 

Isotropic interaction increases 

with increasing temp. 

[173] 

[172]



gx gy Az Ax 

127. [Cu3(C2S 

CH2OH)2]2C1O4 

2.073 2.121 2.117 

2.056 2.150 2.104 

128. 

129. Cu(2,5-Dimethyl 

Benzoxazole) (0104)2 

130. Cu(2,5-dimethylbenzoxazole) 

2 Br2 

131. Cu(tn)2(SCN)2 

[Cu(tn)2NCS]B0 

[Cu(tn)2NCS]C104 

132. [Cu(dach)2] C1O4)2 

[Cu(dach)Br] C1O4 

[Cu(dach)Br2] 

133. (Cu2(dien)2Cl2](C104)2 

134. [Cu(den)NCS)]NO3 

[Cu(den)NCS]B04 

Cu(den)2(NO3)2 

Cu(den)2(C104)2 

Cu(Pn)2(NCS)2 

Cu(Pn)2Br2 

135. Cu(II) dimers 

136. [Cu(dap)2]BF4 

137. [Cu(dpt)en](B04)2 

138. Cu(dtc)2 

Cu(Hy)2 

Cu(Sal)2 

Cu(dtc)(Hy) 

Cu(dtc)(Sal) 

I 

II 

2.26 

2.380 

2.212 

2.222 

2.274 

2.076 

2.097 

2.102 

2.232 

2.243 

2.246 

2.231 

2.203 

2.2145 

2.2506 

2.1985 

2.2020 

2.0480 

2.1074 

2.1201 

2.0758 

2.0767 

2.084 

2.072 

2.069 

2.050 

2.032 

2.070 

2.054 

2.058 

2.072 

2.053 

2.0450 

2.0911 

2.0911 

2.074 

2.072 

2.069 

2.050 

2.032 

2.070 

2.054 

2.058 

2.072 

2.053 

2.0768 

2.0111 

2.0111 

115G 

167.4 

172.0 

155.3 

91.4 

72.5 

74.2 

-185G 

-167G 

-175G 

-170G 

-190G 

-192G 

467 

MHz 

127.8 

133.1 

78G 

87.5G 

59.5G 

82.5G 

71.4G 

7.5G 

10.5 

8.2 

25 

-29G 

-23G 

-25G 

-10G 

-29G 

-26G 

94 

MHz 

29.2 

29.2 

5.5G 

10.5 

8.2 

25 

-29G 

-23G 

-25G 

-10G 

-29G 

-26G 

138 

MHz 

9.4 

9.4 

Comments 

Nearly rhombic distortion [502] 

spectra observed. 

EPR LW narrowing observed [97] 

with increasing temp, and g-factor 

decreases with anion S-Se 

substitution. 

Isotropic spin rotational 

mechanism is responsible for 

the residual LW. 

EPR study showed complexes 

possesses distorted octahedral 

units. 

Molecular motion is responsible 

for anisotropic and 

non-diffusional in the comlexes. 

SHP reported for the titled 

compound with various solvents. 

[390] 

[392] 

[71] 

[174] 

Exchange coupling parameter [151] 

estimated. 

SHP reported for solutions [264] 

as well as powder samples. 

Covalency parameter discussed. 

Temp, dependence ESR study [177] 

indicates the crystal has 

trigonal bipyramidal coordination. 

The pseudotetrahedral sturc- [288] 

ture of solution changes with 

crystalline nature. 

Two inequivalent molecules [262] 

observed. The geometry around 

Cu(II) ions changes due to JT 

distortion. 

LW are temp, dependent and [457] 

isotropic go estimated from 

the EPR spectra in solutions.

Vol. 16, No. 3/4 267 

S.No Host Lattice 

139. [Cu(dap)2] V!+ BF4 

[Cu(cat.30)] 2+ BF4 

Powder 

140. Cu(II)-diglycine complexes 

141. (Cu2(dien)2Cl2](C104)2 

142. [Cu(2,5-DMC)2]2 

[Cu(2,5-DMC)2](4,7-DMP) 

[Cu(2,5-DMC)2](2,9-DMP) 

143. [Cu(dmc)2(2,9-dmphen)]H2O 

[Cu(dmc)2(phen)]H2O 

[Cu(dmc)2(4,7-dmphen)] 

144. [Cu2(3-Et-pyr)4(dmf)2] 

145. [Cu(ethylenedibiguanide)] 

[Cu(ethylenedibiguanide)] 

[Cu(trimethylenedibiguanide)] 

[Cu(piperazinedibiguanide)] 

[Cu (m-phenylenedibiguanide) ] 

[Cu(phenylbiguanide)2]Cl2 

146. Cu(EDtc)2- L 

Cu(EDtc)2- L' 

147. Cu(Edtc)2-L 

Cu(Edtc)2-L' 

148. Cu2 [F2(dmpz)2(mpz)4](BF4)2 

Cu2 [F2(mpz)2(dmpz)4](BF4)2 

149. Cu(4F3NA)2Cl2-2H20 

Cu(4F3NA)2Br2 

Cu(4F3NA)2 (SCN)2 -3H2O 

150. [Cu-F-hect] 

[Cu-OH-hect] 

151. Cu(II)-Fe(III) complexes 

Site Spin-Hamiltonian Parameters 

gx gy Az Ax 

1 2.277 2.074 2.074 

II 2.277 2.070 2.070 

I 2.282 2.076 2.076 

II 2.281 2.078 2.078 

2.283 2.088 2.088 

I 

II 

I 

I 

II 

A 

B 

2.214 2.046 2.057 

2.40 

2.28 

2.02 

2.02 

2.276 

2.276 

2.09 

2.06 

2.31 

2.31 

2.06 

2.06 

2.09 

2.06 

2.17 

2.17 

2.06 

2.06 

2.30 2.05 2.05 

2.08 

2.19 

2.17 

2.18 

2.16 

2.16 

2.102 

2.104 

2.102 

2.104 

2.05 

2.05 

2.05 

2.05 

2.05 

2.028 

2.030 

2.028 

2.030 

2.05 

2.05 

2.05 

2.05 

2.05 

2.028 

2.030 

2.028 

2.030 

2.038 2.288 2.098 

1.978 2.320 2.055 

2.394 

2.346 

2.347 

2.388 

2.355 

2.40 

2.26 

2.26 

2.087 

2.087 

2.078 

2.06 

2.07 

2.07 

2.077 

2.077 

2.078 

2.06 

2.07 

2.07 

71.4G 

208 

220 

182 

169 

188 

155/ 

166G 

150/ 

161G 

155/ 

166G 

150 

161G 

120G 

125G 

120G 

120G 

140G 

118 

50 

50 

32 

33 

36 

35 

35 

38G 

37G 

38G 

37G 

7G 

5.5G 

13G 

32 

33 

36 

35 

35 

38G 

37G 

38G 

37G 

5G 

4.5G 

13G 

Comments Ref. 

EPR shows the solution exist 

pseudotetrahedral structure 

because of rapid electron 

transfer kinetics. 

SHP. 

LW of the EPR lines strong 

dependent and increase linearly 

with temp. 

Resolved EPR spectra obsd. 

at 125K. SHP presented at 

RT also. 

Environment effect of three 

compounds were discussed. 

SHP discussed in terms of 

known binuclear structure. 

The observations of nine 

nitrogen Shf lines on the 

high field indicate the 

presence of four equivalent 

nitrogen atoms around Cu(II) 

ion. 

Structure of paramagnetic 

centres discussed. SHP 

reported for various dithiocarbomate 

complexes. 

The structural ordering 

described by ESR. SHP repor 

for various complexes. 

[287] 

[279] 

[164] 

[514] 

[201] 

[121] 

[448] 

[183] 

[187] 

Good agreement found between [148] 

exptl. and cal. values. GS is 

of the form dix2_y2>. 

The solvent effect on LW. [396] 

The GS wave function and 

MO coeff. evaluated. 

Three types of Gu(II) sites [469] 

observed. 

EPR study reported for [453] 

Cu(II)-Fe(III) complexes.


S.No 

152. 

153. 

154. 

155. 

Host Lattice Site 

CuPu2-2 MeOH 

Powder 

Solution I 

II 

[Cu(Gly)A]+ 

[Cu(Pro)A]+ 

[Cu(Phe)A]+ 

[Cu(Try)A]+ 

[Cu(His)A] + 

[Cu(Hm)A] + 

[Cu(GlyGly)A] 

[Cu(GlyPro)A]+ 

[Cu(GlyLeu)A] 

[Cu(GlyTry)A] 

Cu(Gly Ala) (bipy) -4H2O 

Cu(GlyAla)(Phen)-3H2O 

Cu(Gly Phe)(bipy)-4H2O 

Cu(GlyPhe)(phen)-3H2O 

Cu(GlyTyr)(bipy)-4H2O 

Cu(GlyTyr)(phen)-3H2O 

Cu(GlyTyr)(dmph)-4H2O 

Cu(GlyGly)(bipy)-3H2O 

Cu(GlyGly)(phen)-3H2O 

Cu(GlyGly)(dmph)-4H2O 

Copper Glutamate 

156. Cu(HCOO)2-4H2O 

157. (Cu-heme-SL2) 

158. CuH-[Al]-ZSM-5 

CuH-[Al]-ZSM-5 

CuH-[Ga]-ZSM-5 

159. CuH-Chab. 

CuH-SAPO-34 

160. Cu [H2NCH(CH3)2 

CHCO2]2H2O 

I 

II 

I 

II 

I 

II 

_ 

2.342 

2.388 

2.355 

2.246 

2.282 

2.264 

2.265 

2.286 

2.286 

2.257 

2.292 

2.206 

2.204 

2.226 

2.225 

2.236 

2.231 

2.232 

2.232 

2.220 

2.243 

2.243 

2.230 

2.339 

Spin-Hamiltonian Parameters 

gx 

2.083 

2.082 

2.082 

2.073 

2.073 

2.061 

2.048 

2.062 

2.070 

2.044 

2.073 

2.045 

2.043 

2.078 

2.086 

2.058 

2.078 

2.064 

2.061 

2.085 

2.058 

2.057 

2.084 

2.043 

gy 

2.083 

2.082 

2.112 

2.073 

2.073 

2.061 

2.048 

2.062 

2.070 

2.044 

2.073 

2.045 

2.043 

2.078 

2.086 

2.058 

2.078 

2.064 

2.061 

2.085 

2.058 

2.057 

2.084 

2.083 

Az 

133 

147 

191 

168 

180 

176 

169 

170 

178 

153 

167 

169 

164 

169 

172 

177 

175 

172 

171 

157 

162 

170 

410 

MHz 

Ax 

Vol. 16, No. 3/4 269 


162. CuInSe2 

A 2.0030 

gx gy Az Ax Ay 

B 2.1642 

163. [CuL2(SQ)] 

[CuLSQ] 

164. CuL2L'2 (BPh4)2 

Powder 

Solution 

165. Cu(II)-L-Phenylalamine 

166. Cu(L-Leu)2 

167. Cu(II)-L-Serine 

168. CuL4:MeOH:CHCl3 

CuL2:Me0H:CHCl3 

169. Cu2L 

Cu2L(OH) 

Cu2L(OH)2 

170. CunL2 

171. Cu(L-Leucine) 

172. Cu(L-Met)2 

173. Cu(L-PHE)2 

174. Cu(L-Phe)2 

175. [Cu(MHBQ)2] 

I 

II 

2.0050 

2.0046 

2.2683 2.0800 2.0500 165G 10G 

2.2730 - - 173G 12G 

2.2720 2.0040 2.0940 170G 9G 

2.265 2.072 2.072 

2.281 2.053 2.053 174 13 

2.273 2.053 2.053 174 

2.00 

2.00 

2.00 

2.263 2.058 2.058 172 

2.266 2.058 2.058 168 

2.262 2.058 2.058 

2.263 2.073 2.073 

2.266 2.075 2.075 

2.24 2.05 2.07 195G 

18.7 

Comments Ref. 

Isotropic EPR signals obsd. [342] 

The spin densities on the [379] 

Cu and P were found to vary 

oppositely, which could be 

expected from the electron 

affinity. 

10G Square planar geometry with [261] 

12G N-coodinated ligands obsd. 

9G 

LW variation and isotropic [291] 

SHP, go and A values reported. 

Exchange interaction were [433] 

discussed between Cu(II) pairs. 

Spin rotational relaxation [292] 

mechanisms discussed; isotropic 

g and A values reported. 

13 ESR data computed to cal. 

complex stability constants. 

SHP reported for various 

solvents. 

[455] 

Structure of binuclear [400] 

Cu(II) complexes confirmed 

by EPR. 

18.7 Both complexes EPR study [12] 

assigned to distorted square 

planar coordination. 

Anisotropy g-factor depends [100] 

on temp, and external field. 

Two magn. non-equivalent [248] 

Cu(II) ions in the lattice 

caused by exchange interaction. 

Two magn. non-equivalent [108] 

Cu(II) sites due to the 

exchange interaction obsd. 

Spin dynamics explained by [109] 

exchange interaction of 

Cu 2+ pairs. 

Based on Magnetic, IR, elec- [351] 

tronic, PMR and ESR data the 

complex structure assigned.



gx gy A2 Ax 

176. Cu88-xMni2T: 

177. Cu(MCMQ)2 

Cu(PCMQ)2 

Cu(MHBQ)2 

Cu(PHBQ)2 

Cu(MFQ)2(CH3COO)2 

Cu(PFQ)2(CH3COO)2 

Cu(MAQ)2(CH3COO)2 

Cu(PAQ)2(CH3COO)2 

Cu(MUQ)2(CH3COO)2 

Cu(PUQ)2(CH3COO)2 

Cu(MTUQ)2(CH3COO)2 

Cu(PTUQ)2(CH3COO)2 

178. Cu(MDtc)2Am 

Cu(MDtc)2MAm 

Cu(MDtc)2DeAm 

Cu(MDtc)2Py 

179. Cu(MDtc)2Am 

Cu(EDtc)2Am 

Cu(MDtc)2-Py 

Cu(EDtc)2-2Py 

180. Cu-methoxonitrophenolates 

181. [Cui_xMgx(HCO2)2]-4H2O 

[CUl_xZnx(HCO2)2].4H2O 

182. (Cuo.89Mn0.n)/copper 

spin glasses 

183. [Cu(MPQ)2(CH3COO)2] 

[Cu(PPQ)2(CH3COO)2] 

[Cu(HMP)2] 

[Cu(HPQ)2] 

184. [Cu(II)(N-CH3TPP)CF3SO3], 

[Cu(N-CH2C6H4NO2HTPP)] 

2.14 

2.13 

2.24 

2.23 

2.20 

2.18 

2.23 

2.22 

2.20 

2.21 

2.20 

2.21 

2.00 

2.00 

2.00 

2.00 

2.00 

2.004 

2.00 

2.003 

[2.36 - 2.12] 

[2.36 - 2.12] 

2.25 

2.28 

2.23 

2.20 

2.213 

2.220 

2.03 

2.03 

2.06 

2.05 

2.05 

2.04 

2.05 

2.04 

2.05 

2.05 

2.05 

2.05 

2.111 

2.109 

2.117 

2.118 

2.111 

2.131 

2.181 

2.114 

2.06 

2.07 

2.06 

2.05 

2.055 

2.065 

2.03 

2.03 

2.06 

2.05 

2.05 

2.04 

2.05 

2.04 

2.05 

2.05 

2.05 

2.05 

2.102 

2.091 

2.091 

2.060 

2.102 

2.094 

2.060 

2.064 

2.06 

2.07 

2.06 

2.05 

2.055 

2.065 

173 

142 

167 

173 

143 

173 

~26/ 

28G 

~24G 

~24/ 

26G 

~22G 

26/ 

28G 

28G 

~22G 

23.4/ 

25G 

3200 

MHz 

3300 

MHz 

3900 

MHz 

3700 

MHz 

149G 

142G 

74 

68 

87 

56 

99 

80 

95/ 

102G 

102G 

98/ 

105G 

122/ 

131G 

95/ 

102G 

108G 

122/ 

131G 

122/ 

130G 

600 

MHz 

200 

MHz 

300 

MHz 

700 

MHz 

_ 

_ 

74 

68 

87 

56 

99 

80 

84.6/ 

90.3G 

85G 

81/ 

87G 

54G 

84.6/ 

90.3G 

86G 

54G 

58/ 

63.8G 

600 

MHz 

200 

MHz 

300 

MHz 

700 

MHz 

_ 

_ 

Comments Ref. 

EPR LW explained by inverse [96] 

susceptibility. 

Based on the data,the Cu 2+ [354] 

complexes assigned to 

tetragonal or square 

planar geometry. 

SHP were detected. [186] 

SHP of solution reported. [188] 

Exchange interaction para- [471] 

meter estm. 

ESR LW at particular temp. [74] 

decrease with increasing 

dopant concentration. 

Increasing anisotropy as [247] 

spin-glass layer thickness is 

decreased is briefly discussed. 

Ground state is of the form [371] 

ofdix2-y2>. MO coeff. estd. 

Solutions. Nitrogen effect [447] 

on superhyperfine structure.

Vol. 16, No. 3/4 271 


185. Cu(II)N-acetyl glycinate-H2O 

Cu(II)N-acetyl methioninate 

2.149 

2.158 

gx 

2.080 

2.050 

gy 

2.080 

2.050 

Az Ax 

Cu(II)N-acetyl alaninate 

2.428 2.090 2.090 

Cu(II)N-acetyl valinate 

Cu(II)N-acetyl glutamate 

Cu(II)Cyanoacetate 

Cu(II)Thiodipropionate 

2.441 

2.265 

2.385 

2.289 

2.086 

2.104 

2.120 

2.106 

2.086 

2.104 

2.120 

2.106 

186. Cu(II)-N-aryl glycinate 

187. Cu(NO3)2- 2.5H2O 

Powder 

188. 63 Cu3 in N2 matrix 

189. Cu2(2-NO2C6H4COO)4(DMSO)2 

190. 63 Cu/Ni(Et2-dtph)2 

63 Cu/Ni(PrS-dtph)2 

191. Cu(II)-n-amine complexes 

192. Cu/Nafion/CDsCN 

193. CuNaY Zeolite 

(Faujasite) 

194. Cu(4%)Nafion/CH3CN 

(soaked once) 

Cu(100%)Nafion/CH3CN 

(soaked once) 


(soaked twice) 


(soaked once) 

Cu(4%)Nafion/CD3CN 

(soaked twice) 

195. Cu(NA)2Cl2 

Cu(NICA)2Cl2 

Cu(INA)2Cl2 

Cu(NA)2Br2 

Cu(NICA)2Br2 

Cu(INA)2Br2 

Cu(NA)3(SCN)2 

I 

II 

2.365 

2.400 

2.102 

2.07 

2.068 

2.07 

1.9769 2.0042 1.9905 

2.412 2.089 2.089 

2.1082 

2.1080 

2.1066 

2.0230 

0.0223 

2.0226 

2.0259 

0.0255 

2.0246 

145 

145.6 

150 

I 2.3931 2.074 2.074 129.7G 

II 2.4201 2.074 2.074 119.2G 

27.7 

28.5 

26.6 

29.9 

30.5 

28.4 

Comments Ref. 

SHP of powder as well as 

solutions were measured. 

Ground state wave function 

is of the form dix2-y2>- 

[146] 

LNT EPR study reported. [252] 

Automatic fitting procedure [113] 

were used for calculating the 

g-factors and LW. 

The hf interaction is nearly [251] 

isotropic. GS is of the form 

2AI- 

Optical, IR and Magnetic [272] 

properties reported. 

X-ray data reported and [178] 

confirmed by EPR. 

Bonding nature of the [508] 

amino groups presented. 

After cycle of soaked and [196] 

drying all four equivalent 

ligands replaced by four 

N2 ligands. 

The differences in EPR [126] 

results observed are attributed 

to migration of Cu(II) 

ions in aluminosilicate. 

2.3335 2.0720 2.0720 159 11 11 ESR parameters studied at [195] 

different band frequencies. 

2.3480 2.0794 2.0794 158 11 11 

2.3472 2.0749 2.0749 160 12 12 

2.3720 2.0830 2.0830 146 5 5 

2.4100 2.0770 2.0770 137 7 7 

2.233 

2.227 

2.252 

2.142 

2.152 

2.142 

2.159 

2.063 

2.080 

2.051 

- 

- 

- 

_ 

2.063 

2.080 

2.051 

- 

- 


complexes at room and 

lower temp, and GS is of 

the form diX2-y2> 

or dxv.



Cu(NICA)2(SCN)2 

Cu(INA)2(SCN)2 

Cu(NICA)2SO4 

Cu(INA)2SO4 

g* 

2.152 

2.149 

2.159 

2.155 

gx 

- 

- 

- 

- 

gy 

- 

- 

- 

- 

As Ax 

196. [Cu(NCN)] 2+c 

[Cu(NSN)] 2+d 

[Cu(NSN-Me)] 2+d 

[Cu(NCN)2] 2+c 

] 

[Cu(NSN): 

12+d 

[Cu(NSN-Me)] 2+d 

197. Cu(II) - Ni(II) pairs 

198. [Cu(NH3)4]SeO4 

[Cu(H2O)3(CH3NH2)]SeO4 

[Cu(H2O)3(C3HsNH2)]SeO4 

[Cu(H2O)3(C3H7NH2)]SeO4 

[Cu(H2O)3(C5HiiNH2)]SeO4 

[Cu(H2O)3(C5H5NH2)]SeO4 

[Cu(H2O)3(C9H7N)]SeO4 

[Cu(C2H8N2)2]SeO4 

[Cu(C3H10N2)2]SeO4 

[Cu(H20)2(CioH8N2)]Se04 

[Cu(NH3)4]WO4 

[Cu(C2H8N2)]WO4 

[Cu(C3Hi0N2)]WO4 

199. Cu(NH3)3Cl4 

200. Cu(NN)2X2 

201. Cu(II) with N,N-dialkyl 

amino acids 

202. (CuO)x(V205)o.55-x(Te02)0.45 

203. x(CuO-V2O5)(l-x)(Na2OP2O5) 

204. xCuO(l-x) [2P2O5-Na2O] 

205. Copper Oxide 

206. C11O4 

CuO2S2 

CuO2Se2 

207. Cu4OCl6(TPPO4) 

208. [(L')Cu(u-OH)2Cu(L')] 

(C1O4)2 

2.323 

2.333 

2.335 

2.306 

2.264 

2.262 

2.32 

2.32 

2.30 

2.31 

2.33 

2.32 

2.33 

2.30 

2.32 

2.32 

2.32 

2.29 

2.31 

2.074 

2.078 

2.075 

2.063 

2.053 

2.052 

2.08 

2.11 

2.06 

2.10 

2.09 

2.09 

2.11 

2.09 

2.16 

2.14 

2.12 

2.05 

2.12 

2.074 

2.078 

2.075 

2.063 

2.053 

2.052 

2.206 2.070 2.066 

161 

132 

136 

165 

183 

183 

2.426 2.089 2.089 119 

2.359 2.079 2.079 122G 

2.264 2.076 2.076 108G 

2.259 2.076 2.076 109G 

Comments Ref. 

12 12 12 SHP reported for diff.ligand [53] 

15 15 environments. Optical data 

17 17 17 also reported. 

18 18 

22 22 

22 22 

Method to calculate the g [38] 

and A tensors discussed. 

The g-signals are very sharp [122] 

and the values are temp, 

independent. NMR data and 

magnetic data also reported. 

SHP parameters estimated by [135] 

CNDO/2 technique. 

GS is of the form dix2-y2> • [232] 

ESR spectra influenced by [131] 

solvent and substituent diff. 

Glasses. 

Glasses. 

[444] 

[489] 

21 21 GS is of the form 3dxy. [76] 

ZFR observed at and under [408] 

the critical temp.(Tc). 

Covalency bonding increases [350] 

in order CuO4 < CuO2S2 

< CuO2Se2. 

Magn. dipole-dipole coupling [385] 

const, calculated. 

2.250 2.06 2.06 ZFR. [337]

Vol. 16, No. 3/4 273 


209. Cu4OX6L4 

2.10 

g* gy Az Ax 

210. 

Cu(OX)2 

Cu(OX)(SA) 

Cu(OX)(Ace-SA) 

Cu(OX)(Cl-SA) 

Cu(OX)(2Br-SA) 

Cu(OX)(2I-SA) 

Cu(OX)(2NO2-SA) 

Cu(OX)(Thio-SA) 

211. Cu(II)Polyamine and 

Imidazole complexes 

212. Cu(PPO)4(ClO4)2-H2O 

Zn(Cu) (PPO)! (C1O4) 2 -4H2O 

(Zn:Cu = 100:1) 

213. [Cu2(Phen)2(C2O4)(NO3)2] 

214. Cu(PhP)2Cl2 

Powder 

215. Cu(l-Phenylpyrazole)2Cl2 

216. Cu[P(OMe)3]3 

Cu(Pme3)3 

Cu(CO)3 

217. Cu(PBTT)2Cl2 

Cu(PTT)2Cl2 

Cu(PFTC)2Cl2 

Cu(DPBTB)4Cl2 

Cu(PBTB)2Cl2 

Cu(PBTT-H)2 

Cu(PFTC-H)2 

Cu(DPBTB-H)2 

Cu(PBTB-H)2 

218. 63 CuPF3 

63 Cu 13 CO 

I 

II 

2.196 

2.167 

2.160 

2.268 

2.186 

2.168 

2.204 

2.168 

2.047 

2.050 

2.052 

2.059 

2.045 

2.063 

2.088 

2.065 

2.047 

2.050 

2.052 

2.059 

2.045 

2.063 

2.055 

2.065 

162.8 

2.371 2.101 2.080 146 

2.335 2.0897 2.0795 127.5 9.69 7.73 

2.285 

2.068 

2.320 

2.206 

2.060 

2.206 

2.068 

2.206 

2.068 2.206 2.206 

2.0025 

2.0023 

2.0010 

2.3992 

2.4056 

2.2991 

2.2205 

2.3600 

2.4037 

2.3426 

2.2317 

2.2572 

1.999 

1.9966 

2.0030 

2.0016 

2.0029 

2.0633 

2.0649 

2.0382 

2.0191 

2.0342 

2.0578 

2.0417 

2.0128 

2.0246 

2.0030 

2.0016 

2.0029 

2.0633 

2.0633 

2.0382 

2.0191 

2.0342 

2.0578 

2.0417 

2.0128 

2.0246 

280 

MHz 

293 

MHz 

225 

MHz 

62.2G 

60.0G 

80.0G 

72.5G 

74.0G 

60G 

79.17G 

79.2G 

70G 

40 

MHz 

34 

MHz 

10G 

20G 

15G 

12.5G 

19.6G 

15G 

11.25G 

15G 

19.1G 

40 

MHz 

34 

MHz 

10G 

20G 

15G 

12.5G 

19.6G 

15G 

11.25G 

15G 

19.1G 

Comments Ref. 

Symmetric and skew-symmet- [57] 

ric parts discussed with the 

help of ZFR. 

Powder data presented. [16] 

Resolved at LNT. 

Resolved at LNT and RT. 

Resolved at LNT. 

MO coeff. For all complexes 

LNT data also presented. 

SHP were presented diff. [411] 

solution spectra. Axial EPR 

spectra exist in all the 

complexes. 

The metal-ligand length in [395] 

the z, x - directions in 

Zn(II) complexes are more 

longer and the bond length 

in Y-dir. is more shorter 

than the corresponding 

bond-lengths in Cu(II). 

ZFR; X-ray data presented. [35] 

EPR signals became single [127] 

line at LT. 

At 77K EPR signal due to 

magnetically ineuivalent 

Cu 2+ complexes collapsed 

into single line. 

Cu ions undergoes sp 2 

hybridization with p-ligands 

donating their lone-pair 

electrons. 

[128] 

[156] 

ESR signals caused by some [491] 

defect in the crystal. 

Magnetic properties and 

SHP reported. GS is of 

the form 2Ai. 

[157]



gx gy A2 Ax 

219. CU2PMO11VO4O2IH2O 

220. Cu(PTT)2Cl2 

221. Cu(PU)5(ClO4)2 

222. 

223. 

224. 

225. 

226. 

227. 

228. 

229 

Cu(pyb)Cl2 

Cu(pyi)Cl2 

Cu(pyim)Cl2 

Cu(PZ)2Cl2 

Cu(PZ)4Br2 

Cu(PZ)4(ClO4)2 

Cu(RCO)2L2 

Cu2REP(u-OH)(C104)2 

Cu2REP(u-Cl)Cl2 

Cu(I) sulphide 

[Cu2(Sal-/3-al)2H2O]H2O 

Cu(2+) on silicon surface 

[Cu(S2CNHCHRCO2H)2] 

(R = Me.Et) 

230. Cu(SHA)2-2H2O 

231. Cu(Sal)2-4H2O 

Cu(Sal)2(2-pycar)2 


232. Cu(II)-semiquinonato 

complexes 

233. Cu(salgly) L(H2O)X 

234. Cu(Sal)2-4H2O 



Si 

s2 

2.05 

2.349 

2.295 

2.307 

2.300 

2.268 

2.15 

2.61 

2.30 

2.294 

2.23 

2.20 

2.12 

2.077 

2.069 

2.090 

2.063 

2.050 

2.04 

2.053 

2.07 

2.10 

2.077 

2.069 

2.090 

2.063 

2.050 

2.05 

2.053 

120G 

150G 

158G 

170 

191 

166 

40G 

33G 

25G 

Mn(II) > Fe. 

2.310 2.065 2.065 

2.304 2.075 2.075 

2.310 2.060 2.060 

154. 1 12.9 

170 10.2 

12.9 

10.2 

[85] 

[394] 

[165] 

[355] 

[472] 

[487] 

[265] 

[62] 

[213] 

Formation of different [459] 

symmetries of the complexes were 

discussed. 

ZFR. [15] 

The complexes show moderate [349] 

antimicrobial activity against 

Fungi. 

SHP used for estimate MO 

coefficient 

[270]

Vol. 16, No. 3/4 275 


235. Cu(Sal-enNH2)ClO4 

Cu(Sal-enNH2)NO3 

Cu(Sal-pnNH2)ClO4 

Cu(Sal-pnNH2)NO3 

Cu(5-NO2Sal-enNH2)NO3-H2O 

Cu(5-NO2Sal-PnNH2)NO3-H2O 

236. Cu(Saox)2 

Cu(apox)2 

Cu(mpox)2 

Cu(ppox)2 

Cu(bpox)2 

Cu(opox)2 

237. CuSO4-5H2O 

238. CuSO4-5H2O 

239. [Cu2(tembma)2(bat)] 

(NO3)3 

240. [Cu2(t-Buty.py)4(N3)2] 

(C1O4)2 

241. Cu(Tl)(EDTC)2 

Cu(Tl)(MDTC)2 

Cu(Tl)(BDTC)2 

Cu(Ni)(EDTC)2 

242. Cu-(Thalocyanine)0.2 

243. Cu(II)with triedentate 

salicylaldimines 

244. Cu(II) trimers 

245. CuThO2 

246. Copper Thorium 

Oxides 

247. CuTl2(EDtc)4 

0 

t 

2.251 

2.251 

2.273 

2.273 

2.250 

2.276 

2.179 

2.185 

2.189 

2.190 

gx gy Az Ax 

2.060 

2.045 

2.042 

2.058 

2.045 

2.052 

2.060 

2.045 

2.042 

2.058 

2.045 

2.052 

2.130 2.063 2.190 

2.240 2.070 2.030 

2.086 

2.087 

2.087 

2.087 

2.025 

2.026 

2.025 

2.023 

2.025 

2.026 

2.025 

2.023 

2.088 2.023 2.023 

2.090 2.024 2.024 

2.089 2.027 2.027 

186 

188 

172 

172 

189 

174 

157 

157 

157 

157 

155/ 

165G 

150/ 

160G 

148/ 

158 

41 

41 

41 

44 

39.4/ 

42.2G 

40.9/ 

43.8G 

41/ 

44G 

41 

41 

41 

44 

39.4 

42.2G 

40.9/ 

43.8G 

41/ 

44G 

Comments Ref. 

ESR spectra show the depolimerization 

of the dimers 

by the polar solvents. SHP 

for diff. solvents reported. 

SHP, IR and optical data 

reported for several solutions. 

Investigation of dehydration 

processes. 

The Cu 2+ ions are magnetically 

equivalent. Angular 

dependence EPR LW discussed. 

ZFR. 

Two magnetically distinct 

sites observed. ZFR. 

GS is of the form of 

diX2-y2> or d/xy>. 

[246] 

[243] 

[484] 

[420] 

[36] 

[244] 

[182] 

Indirect exchange inter- [132] 

ation between Cu 2+ ions showed 

by EPR. 

The role of OH groups on [202] 

the structure of adducts 

analysed. 

EPR LW changes with temp. [506] 

The result of symmetric 

anisotropic exchange. 

SHP reported. [33] 

ESR parameters change with [21] 

temp, due to two non-equivalent 

Cu 2+ ions. 

Depending on temp, and [184] 

preparation conditions Cu-Tl 

complex formed.



gx gy Az Ax 

248. [Cu(trien)en]BO4 

2.222 2.058 2.058 504 

MHz 

[Cu(trien)en](ClO4)2 

2.180 2.058 2.058 

249. [Cu(trien)(enMe4)](Bh4)2 

[Cu(trien)(enEt2)](BPh4)2 

250. Cu-tylacetonate; 

Cu-phthalocyanine 

251. CuX2(4-picdine)2 

252. 

253. 

254. 

CuX2(H20)2 

CuX2(Py) 

Cuo.5Zr2(P04)3 

63 Cu/Zn(AP)2(NO3)2 

255. Diaqua (15-Crown-5-Ether) 

Zn(II) Nitrate 

256. Dicyanoquinonedimino-Cu 2+ 

257. Diopfase 

258. ErBaCu3O7-s 

HoBa2Cu3O7_s 

259. EuBa2Cu3O7_s 

260. Eu2CuO4 

261. [Fe(III)Cu(II)(BPMP)Cl2] 

(BPhy)2 

262. FeSi6-6H2O 

263. Iron Silicate Zeolite 

264. Garnet 

2.1937 

2.1898 

2.301 

2.318 

2.3919 

2.24 

2.24 

2.48 

2.0916 

2.0565 

2.005 

2.042 

2.1009 

2.05 

2.05 

2.01 

2.0516 

2.0465 

2.005 

2.042 

2.081 

2.05 

2.05 

2.01 

2.28 2.03 2.03 

2.380 

188.7 

188.4 

2.27 2.07 2.07 176G 

33.4 

28.7 

19.1 

9.5 

Comments Ref. 

For both the complexes GS is [393] 

of the form diX2-y2> • SHP of 

solutions and powders reptd. 

Bonding parameters estimated [263] 

SHP reported for diff. solvents 

and systems attributed 

to distorted compressed tetrahedral 

symmetry. 

By correlating EPR and optl. [320] 

data covalency parameters cal. 

At lower temp. diff. symme- [225] 

tries appeared. 

ZFR. [271] 

JT distortion below 793K. [198] 

-21.4 -10 d- orbital coeff. and GS-WF [427] 

constd.; Cu 2+ sub. for Zn 2+ . 

SHP reported. [86] 

Localized Cu 2+ spin present [313] 

independently of conduction 

electrons. 

SHP and crystal field para- [372] 

meters reported. 

A non-resonant absorption [215] 

peak observed below Tc of 93K. 

Significant diff. observed [143] 

between EPR signal of Cu 2+ in 

tetragonal and orthorhombic 

phase. 

Unusual ESR signal in single [466] 

crystal observed and disappears 

above ~215K. 

Unusual line broadening [200] 

observed by ESR and Moessbauer. 

The exchange parameter (J) [384] 

=(0.30 ± 0.003)cm- 1 at 4.2K. 

Introduction of Cu 2+ ions [214] 

leads to reduction of ESR 

signal. 

Cu 2+ ions orbital study in [42] 

octahedral surroundings.

Vol. 16, No. 3/4 


265. GdBa2Cu3Oy 

gz gx gy Az Ax Ay 

266. GdBa2Cu30y 

267. GdBa2Cu3O7_s 

268. GdBa2Cu3O7_s 

269. Gd2CuO4 

270. [(Gd0.sEuo.5)2Cu04] 

271. Gdo.sReo.sBa2Cu307_, 

272. GdT2Ge2 

(T=Co,Ni,Cu) 

273. GdT2Sn2 

274. GdyYi_yBa2Cu3O6+x 

275. (Gly)2CaCl2-4H2O 

276. (Gly)2CaCl2-4H2O 

277. (gly)3Ca(NO3)2 

278. HxLa18Sr0.2CuO4 

279. hnap-bac. ea 

hnap-bac. py 

hnap-bac 

hnap-acac. dea 

hnap-bac 

280. hnap.acac 

hnap.bac 

hnap.Ind. 

hb.benH 

2.021 

2.07 

2.01 

1.989 

Comments Ref. 

277 

Exchange interactions dis- [328] 

cussed between metal ions. 

Intensity and LW of EPR [329] 

varies with temperature. 

EPR spectrum intensity [141] 

increases with decreasing temp. 

Lowering the g-anisotropy [430] 

by the orientation provides 

at LT. 

The mechanism of supercond. 

discussed. Low field EPR 

signal observed at 260K. 

[399] 

ESR show anomalous aniso- [99] 

tropy for temp, below T ~ 280K 

of the Cu 2+ ions. 

Cu 2+ LW and LS were almost [142] 

independent. 

EPR LW and g-shift depend on [203] 

number of d-electrons. 

Thermal broadening of LW 

increases with decreasing 

d-electrons. 

LW vartion with temp, and 

ZFR observed. 

SHP reported. 

2.308 2.115 2.034 -73 40.1 113.4 GS-WF is of the form 

ala dx2—y2— b dz2 >. 

2.274 2.049 2.081 127 50 20 MO coeff. evaluated. 

2.219 

2.176 

2.245 

2.289 

2.252 

2.243 

2.252 

2.325 

2.297 

2.054 

2.061 

2.056 

2.053 

2.055 

2.055 

2.055 

2.072 

2.071 

2.054 

2.061 

2.056 

2.053 

2.055 

2.055 

2.055 

2.072 

2.071 

192 

149 

182 

179 

186 

186 

186 

148 

158 

16 

10 

21 

18 

21 

19 

21 

16 

10 

21 

18 

21 

19 

21 

Two types of Cu 2+ centres 

formed like single ion and 

cluster ions. 

The study of adducts and 

their influence on the struct 

of the Cu complexes in the 

solutions reported. 


solvent solutions and reported 

data evidence of 

Cu(II) complexes. 

[204] 

[407] 

[163] 

[166] 

[169] 

[443] 

[124] 

[162]



gx gy Az Ax 

281. Hydrated Monopyrazine- 

Zinc sulphate - Ammonium 

sulphate, Magnesium acetate 

282. K-(BEDT-TTF)2Cu[N(CN)2]Br 

K-(BEDT-TTF)2Cu(N(CN)2]I 

283. K2Cd(SO4)2-6H2O 

284. K2C2O4H2O 

285. K3Cu(CN)4 

286. KCuF3 

287. KHCO3 

288. Ko.73Lio.27Tao.3 

289. KMgClSO4- 3H2O 

290. KNH4SO4 

Powder 

291. K2PdCl4; K2PdBr4; CdCl2 

292. K2ptCu(NO2)4 

293. K2SeO4 

I 

II 

I 

II 

III 

2.0058 2.0020 2.0020 

2.0058 2.0020 2.0020 

2.3330 2.0721 2.0663 

2.2403 2.0647 2.0525 

2.0004 2.0049 2.0049 

2.295 

2.292 

0.4832 

GHz 

0.260 

MHz 

0.262 

MHz 

0.0486 

GHz 

0 

0.074 

MHz 

0.0504 

GHz 

0 

0.074 

MHz 

2.2342 2.0452 2.0452 576.6 85.9 85.9 

MHz MHz MHz 

2.330 2.030 2.242 63.05 47.41 47.24 

2.095 

2.119 

2.100 

2.073 

2.073 

2. 121 

2. 103 

2. 107 

2.098 

2.101 

2.121 

2.103 

2.107 

122G 34G 65G 

58.6 

91 

66.6 

71.3 

75.6 

54.1 

71.3 

75.6 

54.1 

2.034 2.389 2.148 23.2 118.7 45.9 

Comments Ref. 

EPR and optical data [ 474 1 

reported. 

The temperature and [209] 

angular dependence of 

the parameters of the 

resonance line analysed. 

Ground state of Cu 2+ ion [512] 

is of the form admixture 

of d-orbital. 

EPR showed four magnetically 

inequivalent Cu 2+ 

sites, consisting two pairs 

of physically equivalent 

sites. Pseudostatic and 

dynamic JTE appears 

below above 172K. 

Two paramagnetic Cu 2+ 

centers observed in t - 

irradiated samples EPR 

spectra. 

Temp, behaviour of the 

field discussed. 

[309] 

[314] 

[180] 

Resolved hfs observed and [410] 

LW relatively narrow. EPR 

data assigned to axial 

symmetry. 

Cu 2+ EPR and x-ray data [107] 

reported. 

Dynamic JTE observed. [88] 

Cu 2+ sub. Mg 2+ sites. 

Cu 2+ ions enter at K + sites. [327] 

GS is of the form dix2-y2> • 

MO coeff. estimated. 

Theoretical expressions [25] 

were presented for g, hf, 

shf parameters of d 9 square 

planar complex. 

Structure and orientation [92] 

of Cu(II) complex discussed 

and g and A terms are 

interpreted in terms of GS 

wave-function parameters. 

The splitting of resonance [515] 

lines depends on ml; paramagnetic 

centre obsd.

Vol. 16, No. 3/4 279 


294. K2SO4 - ZnSO4 

gz gx gy Az Ax 

295. K2SO4-Na2SO4-ZnSO4 

296. 

297. 

298. 

KTaO3 

KTaO3 

K2ZnF4 

299. K2ZnF4 

300. K2ZnF4 

301. 

302. La4Ba2Cu2Oio 

303. 

304. 

305. La2CuO4 

Lai.8Sro.2Cu04-y 

Yo.2Ba0.8Cu04-y 

306. La2CuO4 

Y2BaCuO5 

YBa2Cu3O7-s 

Bi2Sr2CaCu2O8+s 

307. La2CuO4 

308. LaCuO3-s 

309. La2CuO4 

I 

II 

I 

II 

2.238 

2.194 

2.045 

2.045 

2.014 2.381 

1.987 2.395 

2.531 2.123 

Comments Ref. 

Glasses. SHP reported. 

Glasses. 

2.045 172 172 172 Angular dependence EPR 

2.045 193 . 

GS dix2-y2> and ferromagnetic 

exchange interaction appears 

with decreasing temp. 

The compound shows a ferromagnetic 

transition at around 5K. 

[488] 

[192] 

[58] 

[59] 

[319] 

[158] 

[375] 

[152] 

[153] 

[154] 

EPR spectra of Cu 2+ observed [144] 

attributed to axial symmetry 

with dix2-y2> GS. 

Results indicate main part [259] 

of Cu ions in spinless Cu + state. 

The energy levels and g- [333] 

factors of Cu 2+ ion calculated 

with 'O' ligand field. 

Theory compared with 

exptl. data. 

The hydrogen effect on EPR [442] 

and Magn. susceptibility 

studied. 

GS wavefunction of the form [285] 

dlx2-y2>- 

EPR signal not obsd. upto [245] 

570K, because the presence of 

small number of holes in CuO2 

plane due to the oxygen nonstoichiometry.



gx gy Az Ax 

2.12 

310. La2CuO4+s 

311. [L2Cu2Cu(dmg)2Br]ClO4- 

CH3OH 

312. Laponite Clay:Cupric Ion 

313. Lai.82Sro.i8(Cui-.xZnx)04 

314. Lai_xSrxCui_yZnyO4 

315. Lithium hydrazinium 

sulphate 

316. LiKSO4 

Li(NH4)SO4 

LiNaSO4 

317. LiKSO4 

318. LiTaO3 

319. Ln2Cu2O5 

(Ln = Rare-earth ions) 

320. Macrocyclic complexes 

321. MCuCl3 

(M=K, Cs, Rb, NH4) 

322. (2-Methylimidazole) 

(N-Salicylideneslycinato)Cu(II) 

323. Mg(CH3COO)2-4H2O 

324. Magnesium Potassium 

Phosphate hexahydrate 

325. MgNa2(SO4)2-4H20 I 

CoNa2(SO4)2-4H2O 

I 

II 

II 

2.247 2.068 2.068 

2.36 2.060 2.060 145 

2.1 

2.4307 2.083 2.083 116 14 14 

2.400 

2.396 

2.197 

2.320 

2.3738 

2.181 

2.050 

2.167 

2.075 

2.0960 

2.044 

2.099 

2.167 

2.018 

2.0960 

9.4 

mT 

70 

108 

2.4 

mT 

56 

27 

8.2 

mT 

50 

27 

Comments Ref. 

Strong Cu 2+ EPR signal obsd. [486] 

if the quenching of the sample 

fast at LT. 

The study indicate square- [72] 

pyramidal geometry around Cu 2+ 

ions with GS dix2-y2>- 

The system consists poten- [367] 

tial catalytic significance. 

Significance this result [102] 

verifying diverse microscopic 

mechanism of high-Tc supercond. 

Common feature of all spec. [103] 

was a signal with an isotropic g 

andLW. 

Cu 2+ ions entered lattice [315] 

interstitially. Charge compen. 

achieved by release of protons. 

Room temp, dynamic isotropic [324] 

JT spectra, there JT systems 

similar to each other. 

The ground state is predominantly 

dix2-y2>. 

Static and dynamic JTE 

observed. 

No ESR signal observed bet. 

77K and 550K except Lu2Cu2O5. 

Superhyperfine interaction 

spectra observed. 

Temp, dependence LW, EPR 

spectra, g values. 

Cu(II) environment approx. 

square planar coordination. 

Optical and MO coeff. data, 

presented. 

[13] 

[212] 

[115] 

[94] 

[147] 

[419] 

[305] 

SHP and MO coeff.evaluated. [366] 

Cu 2+ ions assigned to tetragonal 

symmetry. 

2.3991 2.1979 2.0299 0.4430 0.2513 0.2060 Two physically equivalent [300] 

GHz GHz GHz magnetically inequivalent sites 

2.3991 2.1979 2.0299 0.4202 0.2427 0.1986 obsd. in each sample. SLRT of 

GHz GHz GHz Co 2+ estimated. 

2.4023 2.1926 2.0256 0.3678 0.2363 0.1679 

GHz GHz GHZ

Vol. 16, No. 3/4 281 


gx gy Az Ax 

326. MgNH4PO4-6H2O 

2.074 2.427 2.142 27 76 

327. MgO 

328. MgTl2(SO4)2-6H2O 

329. M'2M"(SO4)2-6H2O 

(M' = Rb, M" = Mg) 

Powder 

330. Mononuclear Cu(II) 

compounds 

331. N-(4-alkoxysalicylideme)-4'alkylanilines 

complexes 

332. NaCl 

333. NaF 

334. NaF 

335. NaF : Cu 

336. NaioFe4Cu4Wi807oH6-29H20 

337. NaNH4SO4-2H2O 

Powder 

338. NaY-Zeolite 

339. Na2Zn(SO4)2-4H2O 

340. Na2Zn(SO4)2-4H2O 

341. (n-Bu4N)2[Cu(dsit)2] 

342. [N(CH3)4]2CuCl4 

I 

II 

2.076 59.8 

2.395 2.094 2.094 106 34 

2.3739 2.0270 2.1182 100 57 

2.458 2.105 2.105 

[2.0-2.5] 

2.5665 2.093 2.093 

34 

0 

Comments Ref. 

GS is of the form dix2-y2> • 

electronic absorption data 

reported. 

Well resolved EPR spectra 

of Cu 2+ and Cu 3+ ions obsd. 

Powder. Cu ions sub. Mg 

MO coeff., EPR spectrum 

attributed to D2h symmetry. 

Structural investigations 

reported. 

SHP reported. 

Charge carrier trapped 

centres detected by EPR. 

JT effect observed at LT. 

g and A values varies with 

temperature. 

226 240 240 Cu + ion conversions into Cu° 

MHz MHz MHz and Cu 2+ has been investigated 

2.327 2.116 2.099 81 18 27 The observed EPR spectrum 

consisted of broad line 

centered and weak second line. 

2.345 

2.359 

2.408 

2.144 

2.144 

2.088 

2.70 

2.208 

2.088 

2.0195 2.145 2.392 

2.2740 - 2.088 

2.019 2.100 2.075 

2.080 

123G 38G 50G Cu 2+ ions sub. Na + sites. 

Mo coeff. evaluated. 

14.6 1.5 1.5 EPR study used for identifying 

Cu 2+ complexes in 

single crystal. 

Cu 2+ ions enter sub. into 

Zn 2+ ions. SHP reported. 

70.4 24.9 55.6 The amount of Ix2-y2> pre- 

37.5 - 82.5 sent in the GS decreases as 

one goes to LT. 

.2+ 

[417] 

[405] 

[364] 

{421] 

[181] 

[276] 

[450] 

[267] 

1462] 

[290] 

[478] 

[365] 

[123] 

[24] 

[397] 

42 152 53 Two magnetically non-equiv- [219] 

alent anions esr spectra obsd. 

EPR LW decrease with temp.; [112] 

LW of Cu 2+ ions anomalously 

large.



gx gy Az_ Ax 

343. [N(CH3)4]2CuCl4 

2.267 2.085 2.124 

344. NdBa2Cu3O7_s 

345. Nd1.8sCeo.x5CuO4.-v 

346. [NEt4]2Cu(mnt)2 

[NEt4]2Ni(mnt)2 

347. NH4CI 

348. [NH3)5CoImCu(dien) 

ImCo(NH3)s](ClO4)6-4H2O 

349. (NH4)3H(SO4)2 

350. (NH4)3H(SO4)2 

351. NH4I 

352. (NH4)3UF8 

353. (NH4)2(Zn(NH3)2(CrO4)2] 

(NH4)2[Cd(NH3)2(CrO4)2] 

354. N,N'-hexamethylene-bis- 

(2,5-dihy droxyacetophenoneiminato)Cu(II) 

N,N'-tetramethylene-bis- 

(2,5-dihydroxyacetophenoneiminato) 

Cu (II) 

N,N'-ethylene-bis- 

(2,5-dihydroxyacetophenoneiminato)Cu(II) 

355. Oxyfluoroborate 

356. Paramagnetic centres 

in crystals 

I 

II 

III 

2.52 

2.086 

2.085 

2.045 

2.0095 

2.021 

2.320 

2.424 

2.002 

2.018 

2.017 

2.019 

2.022 

2.256 

2.209 

2.223 

2.080 

2.090 

2.272 

2.234 

2.234 

2.021 

2.026 

2.256 

2.209 

2.223 

2.080 

2.079 

2.272 

2.214 

2.219 

162 

15 

177.9 

71 

96 

10.93 

mT 

0.0117 

GHz 

14.78 

mT 

15.77 

mT 

2.162 2.058 2.058 127 

2.223 2.050 2.050 127 

2.236 2.040 2.050 120 

39 

79 

25 

57 

20 

5.74 

mT 

0.0057 

GHz 

13 

13 

12 

39 

79 

25 

57 

20 

1.79 

mT 

0.0057 

GHz 

13 

13 

12 

Comments Ref. 

PT observed at 298K aniso- [440] 

tropy LW at LT explained by 

dipole-dipole interaction 

between Cu 2+ pairs. 

ESR spectra of samples were [139] 

explained in terms of crystal 

field splitting. 

CESR signal obsd. intensity [269] 

and g-factor of signal varies 

with temp. 

Axial EPR spectra observed [239] 

in both cases. 

Temp, dependence EPR spectra [376] 

observed and interpreted with 

dynamic vibronic coupling. 

The bonding between Cu(II) [91] 

and ligands is covalent. SHP 

reported. 

PT, dynamic JTE. EPR study. [29] 

Cu 2+ ion sub. NH4 ion and [481] 

coordinates six oxygen atoms 

from six nearest sulphate ions. 

PT discussed. 

PT. Ground state wave- [67] 

function is of the form 

di3z2_r2> at LNT. 

Cu 2+ EPR spectrum exhibits [43] 

isotropic quartet. 

EPR spectra showed unusual [475] 

temp, dependence between room 

to liquid helium temp. 

SHP. MO coeff. of diff. 

solvents reported. 

Glasses. Anisotropic hfs 

observed. 

[465] 

[362] 

Intensity properties of EPR [513] 

line shape discussed.

Vol. 16, No. 3/4 283 


g* gy Az Ax Ay 

357. t'-Pb3V2O8 

2.333 2.076 2.076 

358. Ph4AsCuCl4 

359. Ph3As(OH)2[CuBr4] 

360. Pillared Clay 

361. [(PipdH)2CuBr4] 

362. Polyacrylamide 

363. Polyacrylamide gels 

GdBa2Cu30y 

365. {U-(PU)2[CU2(PU)8]}(C1O4)4 

366. 

367. 

368. 

369. 

R2BaCuO5 

(R=rare earth metals) 

R2BaCu05 

(R=Rare Earth) 

RBa2Cu3O7-s 

(R=Rare earth) 

Rb2CdCl4 

370. Rb2CdCl4 

371. Rb2Cd(SO4)2-6H2O 

I 

II 

2.269 2.037 2.192 

2.2749 2.0788 2.0446 

2.045 2.290 2.063 

2.145 

2.270 

2.240 

2.216 

2.030 

2.030 

2.070 

2.355 

2.133 

2. 110 

2. 133 

2. 355 

1.980 1.985 1.985 

50.2 74.8 

50.2


S.No Host Lattice Site Spin-Hamiltonian Parameters Comments 

Ref. 

gz gx gy As Ax Av 

372. [(R'R2P)2Cu(adcoR") 

Two equivalent Cu centres [482] 

CuPR2R')2] within one molecule give rise 

to diff. isotope combinations. 

+ 

373. R2SO4B2O3ZnSO4 

(R=Li,Na,K and Cs) 

374. R2SO4-B2O3-CdSO4 

(R=Li, Na, K or Cs) 

375. Rb2Zn(SO4)2-6H2O 

376. Silica Sol.Gels I 

II 

377. Silicotungstic heteropoly acid 

378. Sr0.6oCao.4oCu02 

379. Sr(CH3COO)2l/2H2O 

380. SrC4H2O4-4H2O 

Mg(C4H3O4)2- 6H2O 

381. Sr(HCOO)2- 2H2O 

Powder 

382. Sr2CuO3 

Cao.5Sri.5Cu03 

Cai.5Sro.5Cu03 

Ca2CuO3 

Ba2CuO3+x 

383. SrCuO2 

Sr2CuO3 

384. SrCuO2 

385. 65TeO2-(35-x)CuO-xCuCl2 

386. Tetramethylammonium 

Manganese Chloride 

2.3654 2.0270 2.1114 99 

2.53 

2.47 

137 

158 

2.18 71G 

2.3721 2.0643 2.0643 386 0 

MHz 

2.294 2.072 2.072 107 

2.357 2.148 2.039 143 63 

2.399 2.100 2.077 119 25 

2.410 2.106 2.079 120 

2.078 

2.072 

2.077 

2.035 2.114 2.114 

2.0 

2.0 

Glasses. [426] 

MO coeff. & SHP reported. 

Glasses. The SHP of Cu 2+ ions [363] 

indicate strong tetragonaldistortion 

MO coeff. evaluated. 

52 0 EPR spectrum interpreted to [422] 

rhombic symmetry. MO coeff. 

presented. 

SHP reported at diff. temp. [80] 

and chemical and structual changes 

discussed. 

Paramagnetic Cu 2+ used as [456] 

probe for investigating hydrate 

conversions in samples. 

EPR spectrum consists of [501] 

seven hf lines associated with 

a pair of identical Cu ions. 

0 The EPR data indicate Cu 2+ [304] 

ions incorporated at a site, 

characterized by a three fold 

symmetry. 

MO coeff. reported by corre- [30] 

38 lating optical and EPR data. 

15 Eight coordination host 

cation sites provided for 

Cu 2+ impurity. 

[68] 

Compounds containing Cu-O [26] 

chains found ESR silent at 

room and at LNT. 

The effect of the water on [160] 

the samples discussed. 

EPR study explained by the [63] 

formation of defects of two 

neighbouring Cu 2+ ions. 

No hfs observed due to Cu 2+ [441] 

A symmetry appears in the [331] 

ESR LS at RT but at LT the 

line is more symmetry.

Vol. 16, No. 3/4 285 


387. Thiosemicarbazone 

complexes 

gx gy Az Ax 

388. 

389. Tl2Mg(SO4)2-6H2O 

390. Tl2Ni(SO4)2-6H2O 

391. Tl2Zn(SO4)2-6H2O 

392. [(TMpyP)H2] 4+ 

[(TMpyP)M] 4 + 

(M=VO 2+ ,Cu 2+ ,Zn 2+ ) 

393. trans-bis(a - picoline)bis 

(4,4,4 - trifluoro-1- 

(2-thenoyl) 

butanedione - l,3)Cu(II) 

394. Trans-bis(L-2-aminobutyrato)Cu(II)Trans-bis(DL-2-aminobutyrato)Cu(II) 

395. Triammonium hydrogen 

disulphate 

2.25 

2.350 

2.219 

2.348 

2.162 

2.065 

2.20 

2.125 

2.065 

2.20 

2.125 

116 

22G 

2.185 2.087 70 

2.346 2.079 2.075 -154 

2.257 

2.257 

396. Tridentate Hydroxy- [2.194-2.325] 

napthoyl hydrazone 

397. WO3 

398. 60 XF4-5LaF3-20BaF2-15 

NaF (X=Zr,Hf) 

399. Yo.2Bao.8CuOx 

2.415 

2.193 

400. YBa2Cu3O7 2.161 

401. YBa2Cu3O7-x 2.176 

2.056 

2.054 

2.056 

2.054 

2.053 2.050 99 

2.033 2.033 

2.160 2.160 700 

2.055 2.055 65G 

[212-148] 

50 

18G 

40 

50 

Comments Ref. 

Based on ESR and Magn. 

data all complexes assigned 

to square-planar structure. 

EPR signal obsd. below Tc. 

SHP and MO coeff. reported. 

18G Cu 2+ ions sub. Ni 2+ sites. 

covalency parameters indicate 

the Cu(II) ions more covalent 

character in host lattice. 

25 GS wavefunction constructed 

and Cu 2+ sub. Zn 2+ sites. 

The study indicate the 

tetracationic porphyrins interinteract 

with and exist as 

monomeric entities. SHP 

reported for diff. ligand 

environments. 

-26 -26 MO coeff. calculated. 

[242] 

[40] 

[233] 

[234] 

[235] 

[205] 

[412] 

GS is of the form dix2_y2> [249] 

observed. The role of lattice 

symmetry in Cu-amino acid 

complexes estimated. 

Temperature dependence EPR [289] 

studies reported. 

SHP reported for diff. sol- [167] 

vents and Magn. properties 

reported. 

24.5 18.9 Ground state wave function [274] 

of the form dix2-y2> • Two 

models of copper centres 

discussed. 

760 

Diff. composition of glass [50] 

SHP reported and GS is of 

the form of dix2-y2> • 

GS is of the form dix2_y2>. [281] 

760 Cu 2+ in anisotropic environ- [61] 

ment due to the presence of 

rapid oscillating distortions. 

0 Depending on both temp. [398] 

and microwave freq. 

Resonant field 

determined.



gx gy Az Ax 

402. YBa2Cu3O7_x 2.2167 2.0475 2.0475 166.5G 25G 15G 

403. YBa2Cu3O7-* 

404. Y2Ba2CuOs 

405. Y2BaCuO5 

406. Y-Ba-Cu-O 

407. YBa2Cu3O7_s 

408. YBa2Cu3O6+x 

409. YBa2Cu307_s 

410. YBa2Cu3O8 

411. YBa2Cu3O7-x 


414. YBa2Cu3Ox 


2.24 2.06 2.06 

2.200 2.060 2.060 

2.047 2.05 2.05 

2.215 2.065 2.065 

413. YBa2Cu3O7_x 2.194 2.069 2.069 72G 

2.315 

[2.03-2.06] 

2.16 2.019 

2.2 

416. YBa2Cu3O7-x 2.224 2.051 2.051 

417. YBa2Cu3O7_x 

Comments Ref. 

g// value varied with temp, 

g ~ 2 assigned to additional 

weak broad EPR line. 

EPR directly detected small [428] 

superconducting domains 

and Cu 2+ inclusions. 

At RT uniaxiai EPR spectrum [226] 

observed for Cu 2+ ions. 

Cu 2+ EPR signal observed. At [206] 

LT the EPR line broadened 

and disappeared at around 20K. 

Non-superconducting in dis- [93] 

torted octahedral surroundings. 

Cu 2+ EPR signal existed 

only in fraction of samples. 

Electronic charge compensation [34] 

of copper discussed. 

EPR LW temp, independent. 

EPR signal from superconductivity 

phase due to 

small quantity of Cu 2+ ions. 

Localized Cu 2+ position 

centres established. 

Cu 2+ signals used for calculating 

the oxygen deficiency. 

EPR results assigned to 

orthorhombic symmetry. 

[210] 

[14] 

[9] 

[39] 

[10] 

Density of magnetic moments [31] 

decreases with temp.; increasing 

from LNT to superconductive 

transition. 

EPR spectrum attributed to [138] 

compressed rhombic symmetry. 

EPR signal absence from [48] 

Cu 2+ ions. 

EPR LW independent on temp. [84] 

EPR signal disappeared at [256] 

T>Tc.

Vol. 16, No. 3/4 287 




419. 

420. 

Y2BaCuO5 

Y2BaCuO5 

YBa3Cu2Oy 

421. Y2BaCuOs 

422. Y2BaCuO5 

423. YBa2Cu3Ox 

Bi2Sr2CaCu2Ox 


Y2BaCuO5 


426. Yi+xBa2_xCu3Oy 

427. YBa2Cu3O7_y 



430. Yttrium Barium Copper Oxide 

431. Y2BaCuO5 


I 

II 

2.075 2.086 2.086 90G 75G 75G 

2.23 2.09 2.09 

2.40 

2.23 

2.222 

2.208 

2.109 

2.120 

2.100 

2.05 

2.20 

2.20 

2.107 

2.09 

2.050 

2.047 

2.055 

2.050 

2.10 

2.05 

2.061 

2.09 

2.094 

2.047 

2.120 

2.050 

2.23 

2.10 

2.215 2.065 2.065 

2.20 2.10 2.10 

2.23 2.03 2.03 

Comments Ref. 

Resonance signal of DPPH [222] 

deposited on specimen shifted. 

Intensity of EPR signal of 

Cu 2+ ions measured at room 

temperature. 

Isotropic and strong EPR [282] 

signal observed in unannealed 

crystals; EPR signal absence 

for Cu 2+ ions in annealed 

crystals. 

Causes for EPR signal [278] 

absence of black phase discussed. 

Due to Brown and 

green phase impurity weak Cu 2+ 

EPR signal observed. 

Temp, depedence of ratio of [223] 

EPR intensity to that of DPPH 

at room temp, reported. 

SHP and Magn. suceptibility [283] 

reported. 

EPR signal silence at temp. [284] 

of upto 570K of Cu 2+ ions. 

EPR LW and intensity changes [323] 

with temp.; JTE suggested for 

possible correction. 

EPR signal observed due to [510] 

impurity phases. 

Superconducting material. [133] 

EPR signal observed due to [111] 

dark phase: LW temp, dependence. 

Diminishing microwave loss [464] 

with increasing impurity 

phases. 

LW temp, dependence from [11] 

normal state to superconducting 

state. 

EPR line intensity varies [340] 

with temperature. 

Temp, dependence of the EPR [105] 

signal and susceptibilities 

discussed. 

The structure, electrical [498] 

conductivities and Magn. 

susceptibilities reported.



gz gx gy A2 Ax Ay 

433. Yttrium Barium Copper 

Oxide (YBCO) 


435. YBa2Cu3O7-s 

YBa2(Cui_xFex)3O7-s 


437. YBa2Cu3O7-s 



Bi4/3Pb2/3Sr2CaCu2O8+x 


441. YBa2(Cu1_xFex)3O7_s 

442. YBa2Cu306.8±o.i 


444. Y-Ba-Cu-O 


Ca2Sr2Bi2Cu30io-x 



Bi2Sr2CaCu2O8 


Green phase 2.264 2.056 2.137 

Brown phase 2.262 2.038 2.038 

Black phase EPR signal silent 

2.055 

2.050 2.222 2.094 

2.223 2.091 2.091 

2.218 2.06 2.06 

Comments Ref. 

Low-field EPR signal is [207] 

non-resonant in nature. 

EPR spectra changes with [73] 

time of exposure of H2O. 

ESR study explained with [382] 

oxygen-deficiency and Fedopant. 

Below Tc, EPR line shifts [359] 

due to local fields. 

Comments provided on ZFR [499] 

and non-resonant of powders 

as well as single crystals. 

Single EPR line obsd. above [101] 

Tc, below it resolved into two. 

ESR signal is const, with [208] 

temp, below Tc. 

g-values increases with [218] 

temp, becomes maximum at 230K 

and g-values decreases, but 

weak signal appeared with 

original signal below 130K. 

Size and shape of signal [65] 

near zero-field microwave 

absor. analysed. 

SHP. [229] 

SHP and NMR data estimated. [360] 

Local Magn. flux density of 

sample measured by EPR probes. 

Cu 2+ state stabilized by 

five oxygen ligands. 

EPR signal depends on 02 

pressure and annealing temp. 

[326] 

[321] 

gav related to superposition [429] 

of vibronically coupled orbital 

states Ix2-y2> and 3z2-r2. 

Both compounds exhibit EPR [41] 

broadening at LT. 

gav-factor related to super- [430] 

position of vibronically 

coupled orbital states Ix2-y2> 

and 3z2-r2.

Vol. 16, No. 3/4 289 


449. YBa2Cu3O6+y 

Sz gx gy Az Ax Ay 





454. YBa2Cu3Oy 


Ca2Sr2Bi2Cu3Oi0_x 

456. YBa2Cu3O6+y 

457. YBa2(Cuo.98Coo.o2)0T 

458. Y2Cu2Os 

459. Y2Cu2Os 

460. Yo.gEro.iBai. 

461. Y1_xGdxBa2Cu3O7 

462. Yx-xGdxBaa 

463. Zeolites 

464. Zeolites NaX 

Zeolites KX 

Zeolites KA 

A 

B 

A' 

A 

A' 

C 

D 

2.39 2.07 2.07 

2.270 2.020 2.020 

2.23 

2.23 

2.39 

2.03 

2.08 2.08 

2.08 2.08 

2.285 2.06 2.06 

[2-2.3] 

2.108 

2.04 2.04 

2.049 2.083 2.083 

2.062 

2.081 

2.060 

2.062 

2.060 

2.067 

2.074 

2.356 

2.406 

2.373 

2.343 

2.374 

2.385 

2.327 

2.356 

2.406 

2.373 

2.343 

2.374 

2.385 

2.327 

138G 

90G 

125G 

130G 

125G 

HOG 

145G 

Comments Ref. 

EPR signal observation on [380] 

local oxygen order. 

EPR study presented by diff. [431] 

scientists explained. 

Due to heat treatment pro- [106] 

cess amplitude of EPR signal 

decreases, but g-factor LW. 

lineshape unchanged at measured 

temp. 

LW variation studies with 

temp. 

SHP. 

Below Tc, shifting and 

broadening observed of EPR line. 

Low field ESR intensities 

of Cu 2+ studied. 

The ZFR depends on the 

crystal field. 

The efficiency of the method 

demonstrated by LT. 

Temp, dependence of single 

broad EPR line observed. 

For superconductivity phases 

associated with lattice 

defects weak EPR signal obsd. 

No EPR signal observed at 

any temp, because of green phase. 

EPR spectrum observed for 

Cu 2+ ions. 

Gd ions decoupled from Cu-O 

network of material. 

Two kinds of dipole-coupled 

Cu 2+ pairs existed and explained 

by EPR. 

Cu 2+ located at diff. sites 

in zeolites shows unique spectra. 

[439] 

[211] 

[286] 

[322] 

[381] 

[194] 

[361] 

[341] 

[306] 

[8] 

[494] 

[507] 

[79]



gx gy Az Ax 

465. Zeolites and Oxides 

466. Zn(BDtc)2 

Cd(PmDtc)2 

Cd(MfDtc)2 

Zn(PmDtc)2 

467. Zn(II)-bis-(L-histidine) 

468. Zn-bis(N,N'-di-isopropyldi- 

Thiocarbamate) 

469. 

470. 

471. 

472. 

Zn(C4H4N2)SO4-3H2O 

Zn(Cu)(trien)I2 

[Cu(trien)NCS)B04 

Cd(Cu)(trien)I2 

Zinc Maleate-4H2O 

Powder 

Zn(I)-Malate Trihydrate 

Powder 

473. Zni_xMxCr2O4 

474. ZnO - B2O3; 

PbO - B2O3 

475. ZnSiF6-6H2O 

Powder 

476. ZnTiF6-6H2O 

477. ZnTiF6-6H2O 

I 

II 

2.087 

2.093 

2.095 

2.103 

2.085 

2.102 

2.108 

2.085 

2.103 

2.005 

2.086 

2.108 

2.278 

2.026 

2.030 

- 

2.025 

2.036 

2.026 

2.030 

2.032 

2.026 

2.028 

2.034 

- 

2.031 

2.070 

2.026 

2.030 

- 

2.025 

2.036 

2.026 

2.030 

2.032 

2.026 

2.028 

2.034 

- 

2.031 

2.070 

156/167G 

153G 

149G 

139/49G 

- 

157/168G 

142/152G 

127/136G 

157/168G 

153/164G 

136/146G 

157/168G 

123/132G 

13.9 

tnT 

2.080 2.020 2.015 32.9 

2.3875 

2.207 

2.201 

2.206 

2.043 

2.060 

2.4249 

2.423 

2.467 

2.460 

2.1924 

2.067 

2.374 

2.330 

2.0879 

2.088 

2.10 

2.114 

2.430 2.12 

2.0205 

2.047 

2.207 

2.210 

2.0879 

2.088 

2.10 

2.116 

2.12 

0.324 

GHz 

166.5G 

166G 

167G 

150G 

29.5 

-120 

120 

44G 

39G 

- 

9G 

35G 

45G 

32G 

22G 

45G 

35G 

25G 

- 

23G 

2.5 

mT 

44G 

39G 

- 

9G 

35G 

45G 

32G 

22G 

45G 

35G 

25G 

- 

23G 

2.5 

mT 

67.9 28.3 

0.181 

GHz 

25G 

46.8 

-11 

23 

0.104 

GHz 

15G 

39.7 

9.5 

23 

Comments Ref. 

g-factors and coordination 

sites discussed. 

Two types of Cu 2+ exists 

namely square-planar 

monomer and 

tetrahedral dimer. 

Solid-like and liquid-like 

spectra obsd. at LT. 

SHP reptd. 

[483] 

[185] 

[378] 

ZFR and exchange coupling [425] 

constant determined. 

Dynamic JTE observed at [307] 

334 ± IK. 

GS wavefunction constructed [260] 

and MO coeff. calculated. 

Ground state wave function [468] 

is of the form d2!2. Sub. for 

Zn 2+ sites. 

EPR spectrum shows [251] 

forbidden transitions 

with a normal intensity. 

JT distortions in tetra- [374] 

hedral coordination. 

Decrease in the interaction [490] 

between electron and nuclear 

spin moments with increasing 

CuO concentration. 

JT energy detected and pot- [258] 

ential barrier is 110 cm" 1 . 

EPR and SLR study of Cu 2+ [82] 

ions at different temp. 

EPR showed PT. PT temp. [83] 

decreased with increase in 

impurity concentration.

Vol. 16, No. 3/4 291 

S.No Host Lattice Site Spin-Hamiltonian Parameters Comments Ref. 


478. ZnTiF6-6H2O 2.472 2.097 2.097 107 SHP presented over the temp. [386] 

range 4-160K. 

479. ZnZ6F-6H2O Results reported in terms [257] 

of JT effect. 

480. 60ZrF4 - 5LaF3 - 2.500 2.065 2.065 80 25 25 Glasses. [49] 

20BaF2 - 15NaF


Calendar of Forthcoming 

Conferences in Magnetic 

Resonance 

March 26-30, 1995 

36th Experimental Nuclear Magnetic Resonance 

Conference, Boston Marriott Copley Place, Boston, 

Massachusetts (USA) 


ENC 

815 Don Gaspar Avenue 

Santa Fe, NM 87501 

Phone: 505-989-4573 

Fax: 505-989-1073 

May 16-19, 1995 

Nordic NMR Symposium "Experimental NMR 

in Liquids and Solids", Stockholm, Sweden 

Organized by the Swedish NMR Center, Mariaskolgatan 

83, S-104 62 Stockholm, Sweden. First 

circular will be sent in January. Abstract and registration 

deadline is March 15th. 

The information contact is either: 

Charlotta Damberg 

Email: csd@nmr.se 

Fax: +46-8-6697369 

Phone: +46-8-6167484 

or 

Lotta Johansson 

Email: lotta@nmr.se 

Fax: +46-8-6697369 

Phone: +46-8-6167483 

May 19-30, 1995 

International School of Biological Magnetic Resonance, 

2nd Course: "Dynamics and the Problem 

of Recognition in Biological Macromolecules" - Ettore 

Majorana Centre for Scientific Culture, Erice, 

Sicily, Italy 

An advanced graduate course devoted to the 

analysis of the dynamic behavior of biological 

macromolecules by nuclear magnetic resonance. 

10 days of lectures, workshops and tutorials with 

approximately 20 lecturers, attendance is limited to 

75 students. Sponsored by FEBS, NATO and the 

sponsors of the Ettore Majorana Centre. Registration 

including full room and board during the course 

is $1,000 US. Some partial scholarships are available. 

Preliminary Program and Lecturers: R. Boelens 

(Utrecht), C. M. Dobson (Oxford), S. W. Englander 

(U. Penn.), S. Forsen (Lund), C. W. Hilbers 

(Nijmegen), T. Holak (Munich), T. S. Jardetzky 

(Northwestern), O. Jardetzky (Stanford), 

M. Karplus (Harvard), R. Ladenstein (Stockholm), 

J.-F. Lefevre (Strasbourg), M. Levitt (Stanford), 

J. L. Markley (Wisconsin), S. J. Opella (U. Penn.), 

H. Oschkinat (Heidelberg), R. Rigler (Stockholm), 

G. C. K. Roberts (Leicester), R. G. Shulman (Yale), 

B. D. Sykes (Alberta) and G. Wagner (Harvard) 

will lecture on: Basic NMR Methods for Structure 

and Dynamics Studies, Simulated and Observed 

Molecular Dynamics, Dynamics of Polysaccharides, 

Protein-Small Molecule Interactions, Protein Motion 

and Folding, Nucleic Acids and Protein-Nucleic 

Acid Interactions , Protein-Protein Recognition and 

Protein-Lipid Interactions. 


Ms. Robin Holbrook, Course Administrative 

Assistant 

Email: holbrook@camis.stanford.edu 

or the Directors 

Dr. Oleg Jardetzky 

Email: jardetzky@camis.stanford.edu 

Fax: 415-723-2253 

Dr. Jean-Francois Lefevre 

Email: lefevre@bali.u-strasbg.fr 

Fax: +33 88 65 53 43 

May 27-June 2, 1995 

6th Chianti Workshop on Magnetic Resonance 

"Nuclear and Electron Relaxation", San Miniato 

(Pisa), Italy

Vol. 16, No.3/4 293 

The present Workshop, in the spirit of the series 

of the Chianti Workshops, aims at bringing together 

scientists involved in theoretical and experimental 

aspects of nuclear and electron spin relaxation to 

study the structure and dynamics of molecules. 

The main topics to be discussed by NMR and 

EPR scientists will deal with: structure determination 

of biomolecules, spin polarization phenomena 

and processes, relaxation in paramagnetic systems, 

quasi-ordered phases, spin imaging, new methodologies. 

The program will consists of invited lectures 

and poster presentations. 

Participants intending to present posters (1 m. 

wide x 1.5 m. high) on work related to the topics 

of the Workshop are asked to submit an abstract 

(max. 1 page A4 format typed single-spaced) of the 

proposed communication not later than April 15, 

1995. Since the total number of participants is limited, 

acceptance will be on a "first come first served" 

basis. There is a registration fee of 250,000 Italian 

Lira for active participants and 120,000 Italian Lira 

for accompanying persons. The cost of the accomodation, 

based on sharing a twin-bedded room, plus 

all meals (including Chianti wine!) will be 700,000 

Italian Lira per person. 


Prof. Riccardo Basosi 

Dept. of Chemistry 

University of Siena 

Pian dei Mantellini, 44 

53100 Siena, Italy 

Tel: 39/577-298040 

Fax: 39/577-280405 

or 

Prof. Claudio Luchinat 


University of Florence 

Via G. Capponi, 7 

50121 Florence, Italy 

Tel: 39/55-2757563 

Fax: 39/55-2757555 

or 

Prof. Carlo A. Veracini 


University of Pisa 

Via Risorgimento, 35 

56100 Pisa, Italy 

Tel: 39/50-918266 

or the Program Chairman 

Prof. Klaus Mobius 

Dept. of Physics 

Free University of Berlin 

Arnimalle 14 

D-14195 Berlin, Germany 

Tel: 49/30-8382770 

Fax: 49/30-8386046 

June 18-24, 1995 

Ampere Advanced Institute "High Resolution 

and Spatially Resolved NMR in Solids", Villa 

Monastero, Varenna sul Lago di Como, Italy 

Program: Nuclear spin interactions in solids; 

Multiple pulse NMR experiments; Multiple quatum 

spectroscopy; Spin dynamics; NMR imaging 

of solids and materials; Xenon NMR spectroscopy; 

New recent developments. Director of the Course: 

Prof. Bruno Maraviglia, La Sapienza University, 

Rome, Italy. 

Participation Fee: 1,300,000 Italian Lira for attendance, 

full board and lodging. Closing date for 

application: March 10, 1995. 


Mrs. Donatella Pifferetti 

Centro di Cultura 

Villa Monastero Varenna 

Piazza Venini 1 

22050 Varenna, Italy Phone: +39-341-831261 

Fax: +39-341-831281 

June 25-28, 1995 

Workshop on "Structure Determination Using 

NMR," Pittsburgh, PA, USA 

Pittsburgh Supercomputing Center (PSC) is offering 

biomedical researchers a workshop on " Structure 

Determination Using NMR." The objective is 

to introduce participants to the different techniques

294 

for the elucidation of solution structures of biological 

macromolecules from nuclear magnetic resonance 

data. 

The workshop will consist of lectures and handson 

sessions. The programs AMBER, Mardigras and 

MidasPlus will be discussed. Hands-on sessions will 

be emphasized. Participants will be able to work on 

the examples provided or on their own experimental 

data. No prior supercomputing experience is necessary. 

Workshop Leaders are: Dr, David Case, The 

Scripps Research Institute; Dr. Thomas James, 

University of California, San Francisco; Dr. Julie 

Newdoll, Computer Graphics Laboratory, University 

of California, San Francisco; and Dr. Uli 

Schmitz, University of California, San Francisco. 

This workship is funded by a grant from the 

Biomedical Research Technology Program, National 

Center for Research Resources, National Institutes 

of Health. Travel, meals and hotel accommodations 

for researchers affiliated with U.S. academic institutions 

are supported by this grant. Enrollment is 

limited to 20. 

Deadline for applications is April 28, 1995. 


Nancy Blankenstein 

Pittsburgh Supercomputing Center 

230C Mellon Institute 

4400 Fifth Avenue 

Pittsburgh, PA 15213 

Email: blankens@psc.edu 

Fax: 412-268-8200 

July 16-21, 1995 


Conference, Sydney, Australia 

The venue will be the University of Sydney, situated 

within 5 kilometers of the center of the city of 

Sydney. Accommodations will be available in colleges 

at the University of Sydney or delegates may 


choose from the extensive range of budget-priced to 

luxury hotels which Sydney offers. Presentations 

will be via plenary lectures, invited lectures, colloquia 

and poster sessions. There will be specially 

invited lectures from some of the pioneers of NMR 

to commemorate the 50th anniversary of its discovery. 

A comprehensive trade display will exhibit the 

latest advances in magnetic resonance hardware and 

software. 

The preliminary program includes sessions on: 

-Advances in imaging and microscopy 

-Inorganic and multinuclear NMR 

-Chemical applications of NMR 

-EPR and applications 

-Proteins and nucleic acids: structure and 

dynamics 

-Developments in multidimensional spectroscopy 

-In vivo spectroscopy and clinical applications 

-Solid state NMR 

-Membranes and liquid crystals 

-New technology and experimental methods 

-Advances in theory and computational methods 

The ISMAR-95 Committee: 

Leslie D. Field (Chairman), David Doddrell 

(Convenor), William Bubb (Secretary), Frances 

Separovic (Treasurer), Peter Barron, Michael Batley, 

Graham Bowden, Paul Callaghan, Bruce Cornell, 

John Hanna, Garry King, Glenn King, Philip 

Kuchel, Bridget Mabbutt, George Mendz, Barbara 

Messerle, Carolyn Mountford, Jim Pope, and Graham 

Town. 


Dr. Les D. Field 

Chairman ISMAR-95 

Department of Organic Chemistry 

University of Sydney 

Sydney NSW 2006 Australia 

Phone: +61-2-692-2060 

Fax: +61-2-692-3329 

email: ISMAR-95@biochem.su.oz.au 

July 23-28, 1995 

/// International Symposium on Nuclear Quadrupole 

Interactions, Brown University, Providence, 

Rhode Island, USA

Vol. 16, No. 3/4 

The Symposium, which is sponsored by the International 

Committee on Nuclear Quadrupole Interactions, 

will be devoted to all aspects of nuclear 

quadrupole interactions in solids, liquids, and 

gases covering both experiments and theory. Contributions 

are welcome in all areas involving nuclear 

quadrupole interactions, including (but not limited 

to) the following: nuclear quadrupole resonance 

spectroscopy, all forms of NMR and ESR spectroscopy, 

Mossbauer studies, NQR imaging, perturbed 

gamma ray angular correlation studies, microwave 

spectroscopy, calculations of electric field 

gradients, nuclear studies yielding NQI parameters, 

etc. Studies involving NQI in superconductors, metals, 

insulators, organic and inorganic compounds, 

polymers, biological materials, etc. are welcome. 

Reports on new developments in instrumentation 

for techniques that measure NQI will also be appreciated. 

The program will consist of Plenary Lectures 

and contributed papers for oral or poster presentations. 

The Proceedings of the Symposium will be 

published in an international journal. 


Professor Philip J. Bray 


Box 1843 

Brown University 

Providence, Rhode Island 02912 USA 

September 17-20, 1995 

International Conference on Molecular Structural 

Biology, Organized by the Austrian Chemical 

Society, Vienna, Austria 

Posters are invited on any of the conference topics. 

Outstanding posters will be selected for 20 minutes 

oral presentations. Abstract deadline: May 31, 

1995. 

Topics: The impact of molecular biology on 

structural biology 

Biomolecular structure determination 

X-ray diffraction 

NMR spectroscopy 

Dynamics and function of biomolecules 

Computation methods 

Protein engineering and desing 


A. Kungl 

Gesellschaft Oesterreichischer Chemiker 

AG Biophysikalische Chemie 

Nibelungengasse 11 

A-1010 Wien, Austria 

Tel: 43/1-587249 

Fax: 43/1-587966 

e-mail: msb95@helix.mdy.univie.ac.at 

or 

Prof. Claudio Luchinat 


University of Florence 

Via G. Capponi, 7 

50121 Florence, Italy 

Tel: 39/55-2757563 

Fax: 39/55-2757555 

or 

Prof. Carlo A. Veracini 


University of Pisa 

Via Risorgimento, 35 

56100 Pisa, Italy 

Tel: 39/50-918266 

or the Program Chairman 

Prof. Klaus Mobius 

Dept. of Physics 

Free University of Berlin 

Arnimalle 14 

D-14195 Berlin, Germany 

Tel: 49/30-8382770 

Fax: 49/30-8386046 

295 

The editor would be pleased to receive 

notices of future meetings in the field of 

magnetic resonance so that they could be 

recorded in this column.

296 


Recent Magnetic Resonance Books D.C., 664 p. (Advances in Chemistry Series). 



Copper-zinc superoxide dismutase: a paramagnetic 

protein that provides a unique frame for the NMR 

investigation. Variable angle sample spinning NMR 

in liquid crystals. 


Volume 26 No. 3 (1994). Contents: Multinuclear 

and multidimensional NMR methodology 

for studying individual water molecules bound to 

peptides and proteins in solution: principles and applications. 

17 O NMR studies of hemoproteins and 

synthetic model compounds in the solution and solid 

states. 

1 Progress in Nuclear Magnetic, Resonance Spectroscopy 

Volume 26 No. 4 (1994). Contents: Fluorine 

NMR of proteins. Isotope labeling in solution 

protein assignment and structural analysis. 

1 Annual Reports on NMR Spectroscopy Volume 

28(1994). Contents: Application of NMR spectroscopy 

to the science and technology of glasses and 

ceramics. High-resolution solid-state NMR studies 

on ceramics. NMR studies of zeolites. NMR studies 

of higher-order structures of solid polymers. NMR 

studies of organic thin films. 

1 Handbook of Electron Spin Resonance (1994). 

Edited by Charles P. Poole, Jr. and Horacio A. 

Farach. 550 pages, including 205 tables and figures, 

ISBN 1-56396-044-3, cloth, List Price: $115.00. 


Volume 18 (1994). Contents: Polarization transfer 

and spin diffusion in solid-state NMR. Fermions on 

a Frenkel chain: Nonlinear optical response of linear 

aggregates. 

X NMR Techniques in Catalysis (1994). Edited 

by Alexis T. Bell and Alexander Pines. Marcel 

Dekker, New York, 432 p. 

Magnetic Resonance of Carbonaceous Solids 

(1993). Edited by Robert E. Botto and Yuzo 

Sanads. American Chemical Society, Washington, 

J New additions to the list. 

Chemical Society Reviews Volume 22 No. 5 

(1993). Contents: Bruker Lecture: The nuclear Zeeman 

interaction in electron resonance. The EPR 

spectra of organic radical ions. On the possibility of 

an insulator-metal transition in alkali metal-doped 

zeolites. Some aspects of the electron paramagnetic 

resonance spectroscopy of a d-transition metal compounds. 

Why can transient free radicals be observed 

in solution using ESR techniques? Progressive saturation 

and saturation transfer ESR for measuring 

exchange processes of spin-labelled lipids and 

proteins in membranes. Polarized positive muons 

probing free radicals: A variant of magnetic resonance. 

The chemistry of cyclopropylmethyl and 

related radicals. 

2D NMR: Density Matrix and Product Operator 

Treatment by Gheorghe D. Mateescu and Adrian 

Valeriu, Case Western Reserve University (1993). 

ISBN 0-13-013368-x, 200 pp. 

Basic One- and Two-Dimensional NMR Spectroscopy, 

Second, Enlarged Edition by Horst 

Friebolin, Organic Chemical Institute, Heidelberg, 

Germany (1993). VCH Publishers, Inc., New York. 

ISBN 1-56081-796-8. 

Structure Elucidation by NMR in Organic 

Chemistry - A Practical Guide by Eberhard Breitmaier 

(1993). John Wiley & Sons, New York, NY. 

Hardback: ISBN 0-471-93745-2, $63.95; Paperback: 

ISBN 0-471-93381-3, $35.00. 

Progress in Biophysics and Molecular Biology 

Volume 59 No. 3 (1993). Contents: Hydration and 

heat stability effects on protein unfolding. Derivation 

of locally accurate spatical protein structure 

from NMR data. 


Volume 25 No. 1-3(1993). Contents: NMR 

and fractal properties of polymeric liquids and gels. 


Volume 25 No. 4(1993). Contents: Sulfur- 

33 NMR. Photo-CIDNP of biopolymers. 


Volume 25 No. 5 (1993). Contents: NMR

Vol. 16, No.3/4 297 

studies of drug-DNA interactions. NMR studies of 

dynamics in nucleic acids. 



Density dependence of rotational and translational 

molecular dynamics in liquids studied by high pressure 

NMR. 

Annual Reports on NMR Spectroscopy Volume 

26 (1993). Contents: Applications of NMR to food 

science. Structural studies of peptides and polypeptides 

in the solid state by nitrogen-15 NMR. Application 

of high-resolution NMR spectroscopy to polymer 

chemistry. The application of cation NMR to 

living systems: Multinuclear NMR of azo dyestuffs. 

Biological Magnetic Resonance: NMR of Paramagnetic 

Molecules Volume 12 (1993). Contents: 

NMR methodology for paramagnetic proteins. Nuclear 

relaxation in paramagnetic metalloproteins. 

Paramagnetic relaxation of water protons: effects 

of nonbonded interactions, electron spin relaxation, 

and rotational immobilization. Proton NMR spectroscopy 

of model hemes. Proton NMR studies of 

selected paramagnetic heme proteins. Heteronuclear 

magnetic resonance: applications to biological 

and related paramagnetic molecules. NMR of polymetallic 

systems in proteins. 

Fundamentals of Nuclear Magnetic Resonance 

by J. W. Hennel and J. Klinowski (1993). Contents: 

Elements of quantum mechanics, magnetic properties 

of the nucleus, nuclear paramagnetism, motion 

of pagnetization, continuous wave NMR, pulsed 

NMR, NMR liquids, the dipolar interaction, and nuclear 

magnetic relaxation. ISBN 0-582-06703-0. 

Biological Magnetic Resonance: Carbohydrates 

and Nucleic Acids (1992). Contents: Highresolution 

X H-NMR spectroscopy of oligosaccharidealditols 

released from muncin-type O-glycoproteins. 

NMR studies of nucleic acids and their complexes. 


Volume 24 No. 6 (1992). Contents: Solid 

state NMR studies of vanadia based catalysts. NMR 

studies of superionic conductors. 

Biological Magnetic Resonance: In Vivo Spec- 

troscopy Volume 11 (1992). Contents: Localization 

in clinical NMR spectroscopy. Off-resonance frame 

spin-lattice relaxation: Theory, and in vivo MRS 

and MRI applications. NMR methods in studies 

of brain ischemia. Shift-reagent-aided 23 Na NMR 

spectroscopy in cellular, tissue, and whole-organ 

systems. In vivo 19 F NMR. In vivo 2 H NMR studies 

of cellular metabolism. Some applications of ESR to 

in vivo animal studies and EPR imaging. 

Magnetic Resonance Microscopy: Methods and 

application in materials science, agriculture and 

biomedicine (1992). Edited by Bernhard Blumich 

and Winfried Kuhn. VCH, New York, 604 p. 



Multiple-quantum NMR methods. 


Volume 17 (1992). Contents: Nonlinear incoherent 

spectroscopy. NOESY. Zero-field spin dynamics 

and relaxation. 

Carbohydrate and Nucleic Acid Structure by 

Magnetic Resonance Spectroscopy, Biological Magnetic 

Resonance Volume 10 (1992). Edited by 

Lawrence J. Berliner and Jacques Reuben, Plenum 

Publishing Corp., New York. 

In-Vivo Spectroscopy, Biological Magnetic Resonance 

Volume 11 (1992). Edited by Lawrence J. 

Berliner and Jacques Reuben, Plenum Publishing 

Corp., New York. 


Volume 24 No. 5 (1992). Contents: Relaxation 

in the rotating frame in liquids. Sodium magnetic 

resonance imaging and chemical shift imaging. 

Quadrupolar effects transferred to spin-1/2 magicangle 

spinning spectra of solids.


Instructions for Authors 

Because of the ever increasing difficulty of keeping 

up with the literature there is a growing need for 

critical, balanced reviews covering well-defined areas 

of magnetic resonance. To be useful these must 

be written at a level that can be comprehended by 

workers in related fields, although it is not the intention 

thereby to restrict the depth of the review. 

In order to reduce the amount of time authors must 

spend in writing we will encourage short, concise 

reviews, the main object of which is to inform nonexperts 

about recent developments in interesting aspects 

of magnetic resonance. 

The editor and members of the editorial board 

invite reviews from authorities on subjects of current 

interest. Unsolicited reviews may also be accepted, 

but prospective authors are requested to 

contact the editor prior to writing in order to avoid 

duplication of effort. Reviews will be subject to critical 

scrutiny by experts in the field and must be 

submitted in English. Manuscripts should be sent 

to the editor, Dr. David G. Gorenstein, Department 

of Human Biological Chemistry & Genetics, 

The University of Texas Medical Branch, Galveston, 

Texas 77555 USA. (409) 747 6800. Fax No. (409) 

747 6850. 

MANUSCRIPTS must be submitted in triplicate 

(one copy should be the original), on approximately 

22x28 cm paper, type-written on one side 

of the paper, and double spaced throughout. If the 

manuscript cannot be submitted on computer tapes, 

floppy disks, or electronically (see below), please 

type with a carbon ribbon using either courier 10 

or 12, gothic 12, or prestige elite type face with 10 

or 12 pitch. All pages are to be numbered consecutively, 

including references, tables, and captions to 

figures, which are to be placed at the end of the 

review. 

ARRANGEMENT: Considerable thought 

should be given to a logical ordering of the subject 

matter and the review should be divided into 

appropriate major sections, and subsections, using 

Roman numerals, capital letters, and Arabic numerals 

respectively. A table of contents should be included. 

TABLES: These are to be numbered consecutively 

in the text with Arabic numerals. Their place 

of insertion should be mentioned in the text, but 

they are to be placed in order at the end of the 

paper, each typed on a separate sheet. Each table 

should be supplied with a title. Footnotes to tables 

should be placed consecutively, using lower case letters 

as superscripts. 

FIGURES are also to be numbered consecutively 

using Arabic numerals and the place of insertion 

mentioned in the manuscript. The figures are 

to be grouped in order at the end of the text and 

should be clearly marked along the edge or on the • 

back with figure number and authors' names. Each 

figure should bear a caption, and these should be 

arranged in order and placed at the end of the text. 

Figures should be carefully prepared in black ink 

to draftsman's standards with proper care to lettering 

(typewritten or freehand lettering is not acceptable). 

Graphs should include numerical scales 

and units on both axes, and all figures and lettering 

should be large enough to be legible after reduction 

by 50-60%. Figures should be generally placed on 

sheets of the same size as the typescript and larger 

originals may be handled by supplying high-contrast 

photographic reductions. One set of original figures 

must be supplied; reproduction cannot be made 

from photocopies. Two additional copies of each figure 

are required. Complex molecular formula should 

be supplied as ink drawings. 

REFERENCES to the literature should be 

cited in order of appearance in the text by numbers 

on the line, in parentheses. The reference list is to be 

placed on separate sheets in numerical order at the 

end of the paper. References to journals should follow 

the order: author's (or authors') initials, name, 

name of journal, volume number, page, and year of 

publication. The abbreviation of the journal follows 

that used in the Chemical Abstracts Service Source 

Index. References to books should include in order: 

author's (or authors') initials, name, title of book, 

volume, edition if other than the first, publisher, 

address, date of publication, and pages. 

FOOTNOTES should be used sparingly and 

only in those cases in which the insertion of the 

information in the text would break the train of 

thought. Their position in the text should be 

marked with a superscript Arabic numeral and the 

footnotes should be typed at the bottom of the relevant 

page in the text, separated from the latter by 

a line. 

SYMBOLS AND ABBREVIATIONS:

Vol. 16, No. 3/4 299 

Mathematical symbols should be typewritten wherever 

possible. Greek letters should be identified in 

pencil in the margin. In reviews containing a number 

of mathematical equations and symbols, the author 

is urged to supply a list of these on a separate 

sheet for the assistance of the printer; this will not 

appear in print. Standard abbreviations will follow 

the American Chemical Society's HANDBOOK 

FOR AUTHORS names and symbols for units. 

PERMISSIONS: It is the responsibility of the 

author to obtain all permissions concerned with the 

reproduction of figures, tables, etc, from copyrighted 

publications. Written permission must be obtained 

from the publisher (not the author or editor) of the 

journal or book. The publication from which the 

figure or table is taken must be referred to in the 

reference list and due acknowledgement made, e.g. 

reprinted by permission from ref. (00). 

REPRINTS: Thirty reprints of a review will 

be supplied free to its senior author and additional 

reprints may be purchased in lots of 100. 

INSTRUCTIONS FOR SUBMITTING 

MANUSCRIPTS ON FLOPPY DISKS 

OR ELECTRONICALLY: If you have used a 

word processor to type your manuscript, please forward 

your manuscript after review and revision, in 

a computer readable form. Floppy disks or tapes 

readable on IBM, DEC, SUN, Silicon Graphics, or 

Macintosh computers are acceptable. For direct 

submission over the phone lines use 300 - 9600 baud 

ASCII transmission. Submission via e-mail (address 

david@nmr.utmb.edu) is also recommended. Additional 

details will be provided for the appropriate 

hand-shake requirements. Please supply us with the 

code for interpreting superscripts, greeks, etc. on 

your word processor. 

ADDENDUM to Detection of Two-Quantum 

Nuclear Coherence by Nuclear-Quadrupole-Induced 

Electric Polarization by David C. Newitt and Erwin 

L. Hahn. The Editors of J. Magn. Reson. 

have given permission to largely republish this article 

which appeared in J. Magn. Reson., A 106, 

140-143 (1994).

INTERNATIONAL SOCIETY OF MAGNETIC RESONANCE 

(ISMAR) 

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