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can be met even for the strongest dipole-dipole couplings
(w D » 2p·35.5 kHz). This line-narrowing effect upon increasing
rotation frequency w R on the 1 H NMR spectrum can be understood
as being due to an increase in the spin-pair character of
the 1 H- 1 H dipolar coupling. 20 Since in most cases the remaining
spins are further away, corresponding remote couplings can
effectively be ‘spun out’ and only the strongest dipolar couplings
that originate from protons at close spatial proximities
are retained. This rather simple picture indeed emanates from
an extensive theoretical treatment of multi-spin systems under
fast MAS, combining Floquet theory and perturbation theory.
20,25 The higher-spin contributions are found to scale with
increasing powers of the inverse rotor frequency and therefore
become less important at highest w R .
Magic angle spinning, however, modulates the spin interactions
periodically which means that it generates so-called rotational
echoes and the NMR data acquisition can be performed
in two ways: 15-18 If only the echo-height is monitored (e.g. in
a rotor-synchronized acquisition) a single line results in the
NMR spectrum for each spectroscopically resolved site and
(most) information about anisotropic couplings is lost. On the
other hand, if the whole echo-train is monitored, a (spinning)
sideband pattern results that contains information about the
anisotropic couplings, yet with spectral resolution of the different
sites (Fig. 2). This is important for a precise structural
elucidation based on dipole-dipole couplings as well as using
this interaction to study molecular dynamics. Moreover, on account
of its angular dependence, molecular motion leads to an
averaging of observable dipolar couplings. Monitoring this reduction
of the dipolar coupling thus allows an identifi cation of
dynamic processes present in the sample. Indeed, this is well
known, e.g., from NMR investigations of liquid crystals, where
the reduced NMR couplings yield site-specifi c values for the
Maier-Saupe order parameter S = . 27 The
extreme case is given by a solution, where fast isotropic tumbling
of the molecules (Brownian motion) leads to an almost
complete averaging of line-broadening due to dipolar couplings
and other anisotropic interactions.
2.3 DOUBLE-QUANTUM NMR
The Hamiltonian that describes a particular spin interaction can
be separated into a space and a spin part. While MAS solely
affects the space part, it is possible to manipulate the spin
part by radiofrequency pulse techniques. 20,28,29 Depending on
the applied pulse sequence, a given spin interaction can be
selectively switched on and off in order to discriminate different
contributions to the desired spectral information. In order
to obtain structural information, homonuclear dipolar couplings
that relate protons of different chemical entities are highly informative.
They can be conveniently probed applying so-called
double-quantum MAS NMR spectroscopy, 30 which relies on
the selective excitation of quantum-mechanically “forbidden”
double-quantum coherences (DQC). In fact, this simply means
that such double-quantum coherences cannot be detected by
conventional means but have to be converted into detectable
single-quantum (SQ) signal. Considering a pair of two protons
(each spin-1/2), DQCs can easily be generated by two successive
90° pulses (cf. fi gure 3): the fi rst 90° pulse labels the spins
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BUNSEN-MAGAZIN · 11. JAHRGANG · 2/2009
with their 1 H chemical shifts while the evolution under the dipolar
coupling produces so-called two-spin correlations, which
are turned into DQCs by the second 90° pulse. In other words,
a DQC means that both coupled protons change their spin state
simultaneously in a correlated fashion so that the sum of changes
in magnetic quantum number amounts to two.
Figure 3: Generation of double-quantum coherences (DQCs) by two successive
90° pulses acting on a quadruple spin system (spins A-D). Note that a
dipolar coupling D ij > 0 is required. 30
After excitation, the DQC evolves during an incremented time
period t 1 and is then converted into observable signal that can
be detected in an acquisition period. If this pulse sequence
is applied as so-called 1D-experiment (e.g. t 1 is constant), the
resulting 1 H NMR spectrum refl ects pair-wise dipolar-coupled
proton sites that experience suffi ciently strong dipolar couplings.
As stated above, molecular motions (like e.g. axial C 3 -
rotation of methyl group protons) can reduce the dipolar coupling
among two spins and thus lead to signal losses in such
DQ-fi ltered spectra.
Figure 4: Schematic representation of the back-to-back pulse sequence for
double-quantum excitation. The t 1 period can be kept constant (1D version,
DQ-filtering) or incremented in either a rotor-synchronized fashion (e.g. an increment
corresponds to a rotor period (t R = 1/rotation frequency) or in arbitrary
increments. The sinusoidal wave reflects the rotor modulation due to MAS. 30
Effective averaging of the underlying dipolar couplings and
hence missing of peaks in comparison to the regular 1D- 1 H
MAS NMR spectrum, typically indicate motions that are fast
on the NMR time scale (e.g. motional correlation times below
μs). This can be used to detect mobile proton sites. For the
investigation of local structures, however, the 2D version is
preferred. In such a two-dimensional experiment, DQCs due
to pairs of dipolar coupled protons are correlated with SQCs
resulting in characteristic correlation peaks. DQCs between
like spins appear as a single correlation peak on the diagonal
while a pair of cross-peaks that are symmetrically arranged
on either side of the diagonal refl ect couplings among unlike
spins (cf. fi gure 5). 13a