Chemical shielding anisotropy components, tensor

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. 

The shielding factor is a property of the molecule, but as we see in later examples, the ability of the magnetic field to influence the motion of electrons depends on the orientation of the molecule relative to B0. Hence, O is a second-rank tensor, not a simple scalar quantity. It is always possible to define three mutually orthogonal axes within a molecule such that o may be expressed in terms of three principal components, on, molecular symmetry requires that two of the components of o be equal (and in other instances it is possible to assume approximate equality), so that the components may be expressed relative to the symmetry axis as chemical shielding anisotropy defined (ct — cr,). 

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. 

Figure 16 Spectral lineshapes for powdered solids. (A) Peak doublet produced by dipole coupling between two spin 1/2 nuclei. The doublet is composed of two parts (shown dotted). They correspond to the observed proton flip occurring when its neighbor is spin up (left) or spin down (right). The indicated turning points correspond to the angle between the internuclear vector and 5b. (B) Chemical shift anisotropy pattern with shielding tensor components (Til, < 22. and (T33. (C) Combined DD and CSA spectrum. Note that this is not simply (A) -1- (B). (Reproduced with permission from Power WP and Wasylishen RE (1991) In Webb GA (ed.) Annual Reports in NMR Spectroscopy, vol. 23, p. 17. London Academic Press.)...

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