Nuclear magnetic shielding tensor, components

The GIAO method is used in conjunction with analytical derivative theory in this approach the magnetic field perturbation is treated in an analogous way to the perturbation produced by changes in the nuclear coordinates. In this framework, the components of the nuclear magnetic shielding tensor are obtained as ... 

Prom the expansion in Eq. (5.30) we can define the components of the magnetizability and nuclear magnetic shielding tensor of nucleus K as first derivatives of the perturbed electronic magnetic dipole moment with respect to a component of the magnetic induction or the nuclear magnetic dipole moment of nucleus if ... 

Applying then the general expression for the first derivative of a perturbation-dependent expectation value, Eq. (3.41), to a component of the molecular magnetic induction B Rk,B) at the position of nucleus K in the presence of an external magnetic induction we obtain expressions for the tensor components of the nuclear magnetic shielding tensor of nucleus K involving first derivatives of the perturbed wavefunction... 

It is quite worth noting that all the components of total CTOCD-DZ nuclear magnetic shielding tensors are independent of the coordinate system, as there is complete cancellation between corresponding terms arising from variation of the p paramagnetic and A diamagnetic components. Compare this with the case for equations (54) and (153) and equations... 

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