Shielding tensors principal values

The Haeberlen-Mehring-Spiess convention defines three parameters in terms of the three shielding tensor principal components, Cyy/ and cr z. The three parameters are the isotropic shielding value (ffiso), the shielding anisotropy (Ac), and the shielding asymmetry (77). Their definitions are provided below ... 

The static solid-state NMR can produce a broad pattern to give the three principal values of the shielding tensors for polyhedral silicons. Figures 15 and 16 show the static powder spectra of octasilacubane 22 and of the hexasilaprismane 12, respectively56. The values of the an, 022 and <733 tensors are given in Table 11 together with the calculated values for the methyl substituted compounds57. 

TABLE 11. Experimental and calculated principal values of shielding tensors for hexasilaprismane and octasilacubane... 

It is assumed that shielding is the only magnetic influence on spinning sideband intensities. The isotropic chemical shift criso = —<5 Si/ppm is defined as equal to one-third of the trace of the shielding tensor (Trcr/3). The principal values of the shielding tensor (an,... 

FIGURE 31. Summary chart of the principal components for the 29Si shielding tensors of the compounds studied. Axial symmetry is indicated by the double intensity of lines at The arrows indicate the isotropic values. The shielding scale is relative to the isotropic value for tetramethylsilane. Reproduced by permission of the Royal Society of Chemistry from Reference 140... 

Solid-state high-resolution NMR spectroscopy, combined with quantum chemistry, is able to provide detailed information on the electronic and stereochemical structures of molecules[l]. Quantum-chemical calculations produce three principal values of the nuclear shielding tensor. These principal values have more detailed information about structure of molecules as compared with isotropic chemical shifts. Comparison of the observed chemical shift and chemical shift tensor with the calculated shieldings, produced by quantum-chemical calculations, permits deep insight into the structures of the molecules under investigation. 

In Figure 7, the principal values for the C5-shielding tensor are plotted against the angle (p6 7. It is evident that the g22 component dominantly contributes to causing the periodic angular dependence of the C5 shielding. The a33 component also shows... 

It is apparent from the calculations in the model pyridine-methanol system, that various principal components of the chemical shift tensor are affected differently by the HB. Consequentely, the principal values perpendicular to the direction of the interaction will exhibit a greater effect than the shielding components along the direction of the interaction. This general argument is in agreement with the qualitative observations in purine. A full 3D study of the interaction in the pyridine-methanol complex is required to quantitatively interpret the results in purine. 

Most of the ab initio studies of NMR chemical shifts in peptides and proteins have focused on the average or isotropic value of the NMR chemical shift. The chemical shift is a tensor quantity and is, therefore, capable of providing six independent pieces of information, namely, the magnitude and direction of each of the three principal components. In general, the shielding tensor can be antisymmetric, leading to nine independent components. However, only the symmetric part of the shielding tensor is relevant to the experiments... 

Not all 9 components of a are typically reported when describing the chemical shielding tensor. Instead, the 3 principal components (or eigen values) in a principal axis system (PAS) are reported. The CSA tensor can also be described by three additional parameters 1) the isotropic value (or trace), aiso, of the shielding tensor and is defined as... 

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