Strategies for Spin-Orbit Methods

The first two strategies require two distinct steps to include both correlation and spin-orbit effects in the overall result whereas the third does both in one step. These strategies are therefore referred to as two-step and one-step methods. 

This strategy, however, leads to at least two problems. First, to treat the spin-orbit interaction properly, correlated wave functions must be obtained for all the states that interact with the reference via the spin-orbit interaction, and as a consequence, the number of states now involved in calculating the spin-orbit interaction matrix may be much larger than the reference space. Second, the reference space used for the correlation might be unrealistic or unsuitable for systems with large spin-orbit interaction. 

As already mentioned, correlation methodology is a highly technical subject, and we do not intend to review this field here. Furthermore, even within the rather narrow scope of spin-orbit methods there is a fair number of approaches, differing to a large extent in their technical approaches to the problem. Here, we will try to concentrate on the typical features of some of these methods, and refer the reader to the rather extensive literature in the field, including a number of good review articles. 

we discuss specific examples of the one-step and two-step approaches. Although most of these have been applied with pseudopotentials or model potentials, they are by no means dependent on this, and they may also be adapted to all-electron calculations. The discussion is not exhaustive, and among the topics not covered below are the approaches pioneered by Yarkony (1992) (based on quasidegenerate perturbation theory) and Agren et al. (1996) (based on response theory), both of which have found 

This is not true if we include the two-electron terms in the spin-orbit operator. 

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