Cartesian coordinates chemical shift tensor

The principal values of the chemical shift tensor (or, <722, 0 33) give the magnitude of the tensor <7 in three mutually perpendicular directions (Cartesian coordinates), and the As are direction cosines specifying the orientation of the molecular principal coordinate system with respect to the applied field Bq. The rapid molecular motion experienced by polymer segments in solution results in the observation of their isotropic chemical shifts, <7j, obtained by averaging the chemical shift tensor <7 over all orientations ... 

The bond polarization model gives the chemical shift of an atom a as the sum over the Na bonds of this bond. The bond contributions are formed of a component for the unpolarized bond (which also includes the inner shell contributions to the magnetic shielding) and a polarization term. The bond contributions are represented by a tensor with its principal axes along the basis vectors of the bond coordinate system. The transformation from the bond coordinate system into a common cartesian system is given by the transformation matrix Z). ... 

In this expression, C is a constant specific for each interaction, depending on gyromag-netic ratios and nuclear electric quadrupole moments. la is a Cartesian component of the nuclear spin, with the sum extended to all three Cartesian coordinates. Rap represents the components of a 3 x 3 Cartesian tensor of second rank that specifies the detailed nature of each interaction, some examples of which appeared in the expressions given previously (a, V, and J). Finally, Ap is a Cartesian component of a vector that can be the same nuclear spin vector (quadmpolar interaction), another nuclear spin vector (dipolar interaction or /-coupling), or the external magnetic field (chemical shiff interaction). Some of the tensors represented by Rap are traceless (cases of dipolar and quadmpolar interactions), whereas others (cases of chemical shift and /-coupling) posses non-vanishing trace. 

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