Pseudopotentials spin-free

So far we have made no mention of relativistic effects, apart from a development in terms of pseudospinors rather than pseudoorbitals. Since the intended use of most pseudopotentials is in code based on a nonrelativistic formulation of quantum chemistry, the separation of the spin-free and spin-orbit terms is essential. Two approaches are again possible. 

The other approach is to use a spin-dependent equation, such as the Dirac-Hartree-Fock or Wood-Boring equation, to obtain spin-dependent pseudopotentials, and take the appropriate averages and differences to obtain a spin-free relativistic pseudopotential and a spin-orbit pseudopotential. The formalism for the latter approach is as follows. 

By far the majority of relativistic pseudopotential calculations include only the spin-free pseudopotential at the SCF stage, and add the spin-orbit potential afterwards if they add it at all. There are a few where both the spin-free and spin-orbit effects are included at the SCF stage and the calculations performed with double-group symmetry, just like four-component calculations. 

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