Sum-Over States Theory of SH Parameters

the SOC contribution has three terms that arise from excited states with the same total spin as the ground state and from terms that differ by unit of total spin-angular momentum. 

The first term is simply the spin-Zeeman term, the seeond term is the reduced mass correction, and the fliird term is a gauge correction to the SOC, which has been written in somewhat simplified form here (explained in detail elsewhere [60]). 

The first two terms are widely known, while the third term is a eontribution from the SOC and has only more recently received significant attention [9,46,61-63], d. Field gradients. Finally, the computation of field gradients is given by 

Note that this term is a simple spin-independent first-order property of the system. 

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