Anisotropy dipolar coupling

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

Dipolar coupling and 3C shielding anisotropy cause unequal intensity of spinning side bands. The scalar coupling enabled magic angle rotation to distinguish two sets of sub-spectra.58... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

As another example, the three-dimensional structure of Cytochrome c has been determined on the basis of structural information from pseudocontact paramagnetic chemical shifts, Curie-Dipolar cross-correlation, secondary structure constraints, dipolar couplings and 15N relaxation data [103]. This protein has a paramagnetic center, and therefore the above-mentioned conformational restraints can be derived from this feature. Dipolar couplings do not average to zero because of the susceptibility tensor anisotropy of the protein. The structure determination of this protein without NOE data gives an RMSD (root... 

The isotropic shift. The isotropic shift is the sum of two contributions the contact and the dipolar contributions. The former is due to the presence of unpaired electron density on the resonating nucleus. The latter arises from the anisotropy of the magnetic susceptibility tensor, modulated by the distance between the unpaired electron and the resonating nucleus, and is also dependent on the orientation of the metal nucleus vector with respect to the principal axes of the magnetic susceptibility tensor. Some problems arise when the spin delocalization is taken into account in calculating the dipolar coupling, but we will not address this problem except when strictly necessary. 

Solids—Many polymers are either soluble or insoluble. NMR of solids generally give broad lines because of the effects of dipolar coupling between nuclei and the effect of chemical shift anisotropy (CSA). Both of these effects are greatly reduced for polymers in solution and allow for decent spectra of soluble polymers in solution. 

The specific heat for uncoupled spins does not depend on the orientations of the anisotropy axes however, the corrections due to the dipolar coupling do, as can be seen in Figure 3.4. As for the linear susceptibility, the effect of dipolar interaction is stronger in the case of parallel anistropy than for random anistropy. 

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