For multispin system

Study of line shapes in solids often provides valuable information on molecular motion—gross phase changes, overall tumbling of molecules, or internal rotations and other motions. For a limited number of spins the dipolar, CSA, or quadrupo-lar interactions may be simulated and compared with experiment, whereas for multispin systems the line shape is often rather featureless and only the overall shape can be characterized. 

For multispin systems in which mixing of nuclear spin states occurs owing to dipolar couplings among deuterons, the relaxation is influenced by crosscorrelation terms between individual quadrupolar interaction tensors in addition to the auto-correlation terms [5.17, 5.30]. It is reasonable to expect that these cross-correlation terms may provide additional information on the motional processes. The static Hamiltonian Hq for two deuterons is... 

The second reason is related to the misconception that proton dipolar relaxation-rates for the average molecule are far too complicated for practical use in stereochemical problems. This belief has been encouraged, perhaps, by the formidable, density-matrix calculations " commonly used by physicists and physical chemists for a rigorous interpretation of relaxation phenomena in multispin systems. However, proton-relaxation experiments reported by Freeman, Hill, Hall, and their coworkers " have demonstrated that pessimism regarding the interpretation of proton relaxation-rates may be unjustified. Valuable information of considerable importance for the carbohydrate chemist may be derived for the average molecule of interest from a simple treatment of relaxation rates. 

Eq. 16 is an extremely useful criterion for examining the extent of dipolar interaction in a multispin system, and gives the relaxation method a major advantage over the n.O.e. method. The equivalent quantitative test for the n.O.e. experiment requires all but the receptor nucleus to be saturated and this is not readily performed in practice. 

These variables, connecting all possible pairs of spins in a multispin system, are used for the evaluation of the second moment Mt. 

FIGURE 7.6 Powder patterns for homonuclear dipole coupling. Dashed line represents a two-spin system. Solid line shows broadening from other nearby nuclei in a multispin system. 

When more than two spins are present, the relationships for steady-state nOe become complicated by transfer of magnetization. However, the initial rate of buildup of nOe in multispin systems depends only on ajs, which for homonuclear relaxation is proportional to 7s- It is convenient to compare the initial ajs for a pair of protons of interest with those for a reference pair where the internuclear distance is known [433,440,441]. Then,... 

If quadrupolar nuclei are involved, a number of complications must be accounted for by appropriate procedures. In principle, one can distinguish four cases (a) the standard case S=I=l/2 as discussed above (b) S>l/2,1=1/2 (c) S=l/2, I>l/2 and (d) S>l/2, I>l/2. Cases (a) and (b) are handled well by the pulse sequence of Fig. 8a for either two- or multispin systems. Provided the length of the n(S) pulse is well-defined (in the hmits either of entirely non-se-lective or entirely selective excitation of the central transition) any effect of nuclear electric quadrupolar couphng that is present in case (b) will have identical influence on the intensities So and S, resulting in overall cancellation. 

Even so, there are numerous experimental and theoretical difficulties to overcome relating directly to the measurement. For example, the reliable quantification of homonuclear dipole-dipole interactions under high-resolution conditions (with MAS) in multispin systems is still an unsolved problem, in particular when quadrupolar nuclei are involved. Likewise, no rigorous strategy seems to be available at present for the REDOR measurement of heteronuclear dipolar coupling between two quadrupolar nuclear species. In this connection, it is of the utmost importance that NMR spectroscopy remains a vital and attractive research area in its own right. Assuredly, the continued influx of new solid state NMR technology into this research area will provide an... 

The previous section considered the NOE for the hypothetical case of a two-spin system in which the spins relax exclusively via mutual dipole-dipole relaxation. In progressing to consider more realistic multispin systems two key issues will be addressed how the presence of other spins affects the magnitudes of steady-state NOEs and how these reintroduce distance dependence to the NOE. These considerations lead to the conclusion that steady-state NOE measurements must be used in a comparative way to provide structural data, and that they do not generally provide estimates of intemuclear distances per se. 

The previous section considered the NOE for the hypothetical case of a two-spin system in which the spins relax exclusively via mutual dipole-dipole relaxation. In progressing to consider more realistic multispin systems, two key issues will be... 

J. Ren, H. Eckert, A homonuclear rotational echo double-resonance method for measuring site-resolved distance distributions in 1=1/2 spin pairs, clusters, and multispin systems, Angew. Chem. Int. Ed. 51 (2012) 12888—12891. 

Only the longitudinal spin term is present in Eq. (14) and aU heteronuclear dipole-dipole coupling interactions commute in a multispin system making the analysis much more straightforward. One of the best known pulse sequences in solid-state NMR spectroscopy, the rotational-echo double-resonance NMR (REDOR) experiment [44], employs appropriately placed pulses to avoid averaging of the heteronuclear dipolar coupling interactions by MAS. REDOR has been used in numerous cases to extract precise dipolar couplings and the inventor. Prof Schaefer, was commemorated recently for his contributions to solid-state NMR spectroscopy [45]. 

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