Multispin systems

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. 

To investigate multispin systems, the so-called electron spin transient nutation (ESTN) spectroscopy is recently elaborated. This is a version of pulsed ESR. Nutation is the precessional motion of spin. The method and its applications are detailed in the paper of Itoh et al. (1997). Chapters 1 and 8 describes that the determination of spin multiplicity becomes a very important problem in organic chemistry of ion-radicals. 

In this field, the resolution of DMR is promising. However, experiments on deuterated molecules have just begun, and the nuclear relaxation was not yet analyzed. We can just present here some preliminary ideas that were obtained from proton relaxation experiments (19). Because of the nature of dipolar interaction, we are dealing with a multispin system this entails some complex problems of nuclear spin dynamics which are beyond the scope of this discussion. The quantitative analysis of proton relaxation data is thus far from straight-forward (20). We shall limit ourselves to a qualitative interpretation of the frequency dependence of the relaxation rate that is summarized schematically in Figure 4. Important relaxation effects appear in both high and low frequency regions. 

Multispin systems 242 Anisotropic motion 242 The methyl group 244... 

Current theoretical work on relaxation apparently centres on two issues, the problems of cross relaxation and cross correlation in multispin systems and the effect of anisotropic motion on nuclear relaxation. Both lines of effort come together in very recent theoretical and experimental work on the relaxation behaviour of the methyl group to which in the past three years alone more than 10 papers have been devoted. 

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. 

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. 

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. 

In a more realistic multispin system, neighbouring nuclei, N, that are close to I can also contribute to its Wj relaxation pathway. The magnitude of the NOE then becomes dependent on the I-S intemuclear separation (inversely as rjs ), but also has a dependence on the distance(s) between I and its near neighbour(s) (inversely as rjjlf), amongst other factors. 

Following the (assumed) instantaneous inversion of the S-spin resonance, the initial growth rate of the NOE at I depends linearly on the cross-relaxation rate between these two spins even in multispin systems, such that ... 

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