Shift tensor

D. Tinet, A. M. Faugere, and R. Prost, Cd NMR chemical shift tensor analysis of cadmium-exchanged clays and clay gels, J. Phys. Chem. 95 8804 (1991). 

In liquid-state NMR spectroscopy only the isotropic component of the chemical shift tensor is measurable. Upon ahgnment the situahon changes and the so-called zz-component of the chemical shift tensor includes anisotropic components. 

Principal Values of 29Si Chemical Shift Tensors for Disilenes (ppm)... 

The correlation of the chemical shift tensors of two neighboring carbonyl carbons, say, C (,) and can be exploited to determine the backbone torsion [Pg.76]

Despite the benefits of high resolution, measurements of wideline spectra of quadrupolar nuclei under static or MAS conditions are still commonly used in a variety of applications. For both integer and half-integer spins, simulations of quadrupolar lineshapes can yield full sets of NMR parameters associated with quadrupolar and chemical shift tensors and can be used for studying molecular dynamics. 

Several methods have been developed to determine the chemical shift anisotropies in the presence of small and large quadrupolar broadenings, including lineshape analysis of CT or CT plus ST spectra measured under static, MAS, or high-resolution conditions [206-210]. These methods allow for determination of the quadrupolar parameters (Cq, i)q) and chemical shift parameters (dcs, //cs> <5CT), as well as the relative orientation of the quadrupolar and chemical shift tensors. In this context, the MQMAS experiment can be useful, as it scales the CSA by a factor of p in the isotropic dimension, allowing for determination of chemical shift parameters from the spinning sideband manifold [211],... 

The isotropic chemical shift, the trace of the chemical shift tensor, is one of the basic NMR parameters often measured for both spin-1/2 and quadrupolar nuclei. The CSA can also be measured in non-cubic environments, such as the n3Cd nuclei experience in the chalcopyrite structure of crystalline CdGeAs2 [141] or CdGeP2 [142], and the 31P nuclei in the latter compound [142], Although the isotropic chemical shift can be measured from the NMR spectrum of a static powder because the CSA is zero in many cases because of cubic symmetry of the lattice, improved resolution is obtained by using MAS to remove dipolar couplings. Two particular areas where the isotropic chemical shifts have proven very informative will now be discussed, semiconductor alloys and semiconductor polytypes. 

Fig. 10.20. Theoretical spectral patterns for NMR of solid powders. The top trace shows the example of high symmetry, or cubic site symmetry. In this case, all three chemical shift tensor components are equal in value, a, and the tensor is best represented by a sphere. This gives rise to a single, narrow peak. In the middle trace, two of the three components are equal, so the tensor is said to have axial site symmetry. This tensor is best represented by an ellipsoid and gives rise to the assymetric lineshape shown. If all three chemical shift components are of different values, then the tensor is said to have low-site symmetry. This gives rise to the broad pattern shown in the bottom trace.

Tab. 6.2 Calculated principle values nucleic acid bases and base pairs and orientations of chemical shift tensors of the imino nitrogens in...

Tab. 6.3 Calculated carbon chemical shift tensors in nucleosides.

The nature of the chemical shift tensor is a potential source of complications in relaxation studies. For sugar carbons, the CSAs are around 40 ppm and their contribution to relaxation of protonated carbons is nearly negligible. On the other hand, CSA values of the protonated carbons of the bases are between 120 and 180 ppm, the tensors deviate quite significantly from axial symmetry and none of their principal components is colli-near with the C-H bond. This makes interpretation of the relaxation rates in terms of molecular dynamics prohibitively complicated or, if neglected, introduces an error whose magnitude has not yet been evaluated. 

The DD-CSA cross-correlated relaxation, namely that between 13C-1H dipole and 31P-CSA, can also be used to determine backbone a and C angles in RNA [65]. The experiment requires oligonucleotides that are 13C-labeled in the sugar moiety. First, 1H-coupled, / - DQ//Q-II CP spectra are measured. DQ and ZQ spectra are obtained by linear combinations of four subspectra recorded for each q-increment. Then, the cross-relaxation rates are calculated from the peak intensity ratios of the doublets in the DQ and ZQ spectra. The observed cross-correlation rates depend on the relative orientations of CH dipoles with respect to the components of the 31P chemical shift tensor. As the components of the 31P chemical shift tensor in RNA are not known, the barium salt of diethyl phosphate was used as a model compound with the principal components values of -76 ppm, -16 ppm and 103 ppm, respectively [106]. Since the measured cross-correlation rates are a function of the angles / and e as well, these angles need to be determined independently using 3/(H, P) and 3/(C, P) coupling constants. 

Fushman, D. and D. Cowburn, Nuclear magnetic resonance relaxation in determination of residue-specific 1SN chemical shift tensors in proteins in solution protein dynamics, structure, and applications of transverse relaxation optimized spectroscopy, in Methods Enzymol. T. James, U. Schmitz, and V. Doetsch, Editors. 2001. p.109-126. 

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