DPT of magnetic properties

The difference to the last section is that now the perturbation is of the nondiagonal form 

On 4-component-spinor level we can use the results of the last subsection (4.7), just replacing Qq by O and ignoring Q2- We get in particular 

We have commented on the nrl Eqi of a first-order magnetic property in section 2.11. For the second-order magnetic property 02 a reformulation is possible, if the turn-over rule can safely be used (otherwise additional terms due to differentiation in the distribution sense are necessary). The perturbation functions 01 and yoi are obtained from (330, 331). 

It is important that the exact relation between the upper and lower components of the Dirac bispinor is, in the presence of a magnetic field with vector potential A modified to 

A detailed presentation of relativistic effects on magnetic properties is found in Ref. [60], especially for the H-atom in a homogeneous magnetic field in Ref. [61] Application of DPT to first-order magnetic properties were published by Hennum, et al. [62]. An earlier, more intuitive formulation, especially for NMR chemical shifts was given by Nomura et al. [63]. The fully relativistic theory has been studied by Pyykko [64] and Pyper [65]. 

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