Asymmetry, chemical shielding tensor

Here, ak is the isotropic chemical shift referenced in ppm from the carrier frequency co0, SkSA is the anisotropy and tfk SA the asymmetry of the chemical-shielding tensor, here also expressed in ppm. Note that for heteronuclear cases different reference frequencies co0 are chosen for different nuclei (doubly rotating frame of reference). The two Euler angles ak and pk describe the orientation of the chemical-shielding tensor with respect to the laboratory-fixed frame of reference. The anisotropy dkSA defines the width and the asymmetry t]kSA the shape of the powder line shape (see Fig. 11.1a). 

One potential problem with chemical shift anisotropy lineshape analysis (or indeed analysis of lineshapes arising from any nuclear spin interaction) is that the analysis results in a description of the angular reorientation of the chemical-shielding tensor during the motion, not the molecule. To convert this information into details of how the molecule moves, we need to know how the chemical-shielding tensor (or other interaction tensor) is oriented in the molecular frame. A further possible complication with the analysis is that it may not be possible to achieve an experiment temperature at which the motion is completely quenched, and thus it may not be possible to directly measure the principal values of the interaction tensor, i.e. anisotropy, asymmetry and isotropic component. If the motion is complex, lack of certainty about the input tensor parameters leads to an ambiguous lineshape analysis, with several (or even many) possible fits to the experimental data. 

This mechanism arises from the asymmetry of the shielding tensor. Let us recall that the chemical shift in NMR has its origin in the screening (shielding) of the static magnetic field B0 by the electronic distribution at... 

The chemical shielding anisotropy (CSA) tensors for the simple phosphate structures listed in Table I, were calculated using ab initio methods. The isotropic tensor value (aiso), the three principal components (aa), the CSA anisotropy (Act) and asymmetry parameter (rj) were evaluated and are given in Table II. 

Solid-state Hg NMR can clearly resolve several issues raised by solution NMR studies. If the solid-state isotropic shift is equal to the solution shift, then the solution chemical shift does not represent an average of several species in rapid exchange. As has been shown with Cd NMR (186), correspondence between solution and solid-state chemical shifts greatly increases the ability of the inorganic chemist to use solution spectra to classify molecular structure and bonding. Equally important, analysis of the solid-state chemical shift and the shielding tensor components can provide information about coordination number and asymmetry at the metal center in solids, even when other structural information is lacking. 

B3LYP level with the 6-311+- -G (d,P) standard basis set, have been used to characterize the and electric field gradient (EFG) in various bisphosphonate derivatives. The calculated EFG tensors were used to determine the and nuclear quadrupole coupling constant (y) and asymmetry parameter (/ ). For a better understanding of the bonding and electronic structure of bisphosphonates, the isotropic and anisotropic NMR chemical shieldings were calculated for the and P nuclei... 

The beauty of CP MAS solid-sate NMR spectra comes from the useful chemical information can be extracted from the envelope of narrow lines. Using methods developed by Maricq and Waugh (126) or by Herzfeld and Berger (91), the diagonal tensor elements an, 022, and CT33 can be extracted when the isotropic shift is known. Using the tensor elements, the shielding anisotropy and asymmetry are calculated, as shown in Eqs. 5 and 6. 

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