Self-consistent treatment of the frequency-independent Breit interaction in Dirac-Fock and MCSCF calculations of atomic structures: I. Theoretical considerations

The self-consistent treatment of the Breit interaction in fully numerical a tomic structure calculations is cumbersome due to the computationally deman ding evaluation of two-electron integrals as they occur in the original for mulation (Grant I P and Pyper N C 1976 J. Phys. B: At. Mel. Phys. 9 761). We present a reformulation of the frequency-independent Breit interaction o perator in spherical coordinates and derive the corresponding matrix elemen ts over spinors. With this formulation it becomes possible to compute the m atrix elements of the Breit interaction efficiently and analogously to thos e of the Coulomb interaction: i.e., by determining the corresponding intera ction potential functions using Poisson equations. The derived formulae will equally simplify computations using either basis sets or a numerical representation of the orbitals such that the Breit inte raction can be included effectively in CI and SCF calculations for atoms an d molecules. Of course, the computation of the Breit contribution to the to tal electronic energy as a first-order perturbation correction is also simp lified. Furthermore, the frequency-dependent Breit interaction could be tre ated analogously.