BUNSENMAGAZIN - Deutsche Bunsengesellschaft für ...

DEUTSCHE BUNSEN-GESELLSCHAFT
Figure 5: Schematic 2D-DQ-spectrum of a two-spin system with spin A (w A )
and spin B (w B ), recorded in rotor-synchronized fashion. All correlation
peaks in the DQ dimension appear at the sum frequency of the coupled
spins, where we can distinguish auto-correlation peaks at the diagonal
from cross-peaks that are off-diagonal. 13a
In addition, we exploit the fact that observable DQ signal intensi-
2 -6 ties are proportional to D or rij , respectively (Dij is the homo-
ij
nuclear dipolar coupling constant, r the internuclear distance).
ij
Strong signal intensities in the corresponding (rotor-synchronized)
double-quantum spectrum therefore reveal protons in rather
close spatial proximity (e.g., distances up to 3.5 Å). This can be
used in a qualitative way to derive fi rst distance constrains of the
coupled protons and thus provide a glimpse on possible arrangements.
Notably, DQ MAS NMR is based on analyzing signals
resulting from a coherence originating from two spatially separated
nuclei. Thus, the basic physics is analogous to coherent
X-ray or neutron scattering, where the coherent superposition
of scattered waves is exploited to deduce the distance between
the scattering centers. In NMR, however, no translational symmetry
is necessary to determine distances in the range of 100
to 1000 pm. 31 More accurate values for dipole-dipole couplings
may be obtained from so-called build-up curves of DQCs, which
for isolated spin pairs, such as doubly labeled 13C-13C, exhibit an
oscil latory behavior. 32 Strongly coupled 1H-1H systems, however,
quickly develop a multi-spin character and the oscillations are
damped out. Nevertheless, even there the initial build-up is dominated
by DQCs and can be analyzed quantitatively. 33,34
Figure 6: Comparison of a rotor-synchronized 2D DQMAS spectrum and its rotor-encoded
spinning sideband pattern. Note that the frequency distribution
(and thus intensity distribution) can be pumped according to the product of the
DQ excitation time (t exc ) and the respective homonuclear dipolar coupling D ij . 35
UNTERRICHT
For spin pairs, and even more so for dipolar coupled clusters
(e.g. triple- or quadruple hydrogen-bonded moieties), the underlying
dipolar couplings and hence the geometry of the spin
system can be much better elucidated if DQ spinning sidebands
are generated. This can be achieved by choosing t time 1
20,30 increments well below t where the reconversion is rotor
R
encoded because the dipolar Hamiltonian that is modulated
by MAS differs at the beginning of both the excitation and reconversion
periods (cf. fi gure 7). This mechanism is termed
Reconversion Rotor Encoding (RRE) and occurs, whenever the
Hamiltonians involved have an amplitude modulation on the
rotor phase. Notably, RRE produces odd-order spinning sidebands
only. In actual applications, the rotor frequency w and R
the excitation time t will be chosen such that up to third order
exc
sidebands are generated thereby achieving suffi cient signalto-noise
ratios. In contrast, multi-spin effects (e.g. a spin pair
is coupled to a third spin) give rise to additional (even order)
sidebands and are therefore easily recognized. 35,36
Figure 7: Schematic representation of the reconversion rotor encoding
(RRE) in case of t 1 increments different from a rotor period t R . As indicated
by the sinusoidal wave, an additional phase factor that depends on the rotor
frequency is added to the reconversion Hamiltonian. 20
Though two-dimensional 1 H DQ MAS experiments have found
manifold application, such experiments still suffer from the
rather limited spectral resolution in solid-state 1 H NMR even
at currently available fastest MAS frequencies of up to 70 kHz
and highest magnetic fi elds (≥ 20 T). Indeed, in favorable cases
of structurally well-ordered (mainly crystalline) samples, where
the experimentally observed 1 H MAS NMR line shapes are solely
broadened by strong homonuclear dipolar couplings among
abundant protons, remarkable resolution can in principle be
obtained using so-called homonuclear dipolar decoupling sequences
like windowed phase-modulated LEE-GOLDBURG
(wPMLG) 37 or windowed DUMBO-1 38 that also constitute the
key part of high-resolution DQ spectra (DQCRAMPS). 39 This approach,
however, is often limited to model compounds 40 but has
also been successfully applied to biologically relevant systems. 41
Despite the fact that the technical implementation of such dipolar
decoupling sequences on the actual NMR console varies
substantially, the basic idea to align the magnetization along an
effective radiofrequency fi eld at the magic angle with respect
to the static magnetic fi eld is retained. In oversimplifi ed words,
reduction (or even complete removal) of line-broadening due to
65