A mean-field spin-orbit method applicable to correlated wavefunctions

Starting from the full microscopic Breit-Pauli or no-pair spin-orbit Hamiltonians, we have devised an effective one-electron spin-orbit Hamiltonian in a well defined series of approximations by averaging the two-electron contributions to the spin-orbit matrix element over the valence shell. In addition the two-electron integrals were restricted to comprise only one-centre terms. The validity of these approximations has been tested on several palladium containing compounds. Excellent agreement of the matrix elements of the mean-field operator with corresponding full results is observed; deviations amount to a few cm−1 in absolute value or at most 0.2% on a relative scale. The newly defined mean-field operator can thus safely be employed to evaluate spin-orbit effects in transition metal containing compounds.