Correlation effects on spin-orbit splitting

To conclude this discussion on spin-orbit effective core potentials, it is interesting to discuss how correlation effects (namely the core-core, core-valence and valence correlations), influence SO-coupling with respect to core-valence separation. 

Although this does not enter into the discussion of correlation effects, we point out the role of higher-order relativistic effects, such as the Breit interaction, on the spin-orbit splitting, which are not explicitly included. For the neutral Pb atom, the Breit interaction estimated by a four-component all-electron calculation using first order perturbation theory lowers the SCF spin-orbit splitting by 166 cm thus compensating partially the increase due to core-core and core-valence interactions [60]. 

To summarise, the pure valence correlation (double excitations) tends to lower the spin-orbit splitting while the valence spinors relaxation (single excitations) tends to increase the splitting. Concerning the role of the core orbitals, the whole core polarisation, core-core and core-valence correlations taken into account via a semi-empirical CPP tend to enhance this splitting.  

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