An ab initio effective potential for two particles in the field of the core: a reduction of (N + 2)-electron problem to two-electron problem

We have used many-body Green function theory and the two-electron Bethe—Salpeter equation to derive an approximate two-electron position space hamiltonian eigenvalue equation for two electrons in the presence of a closed shell core. The resulting effective hamiltonian is nonlocal, energy independent, hermitian and nonadiabatic. It includes all the core—valence, valence—valence exchange effects, core screening effects and electron—electron correlation effects. If a closed form solution of the equation is difficult because of the need to construct the hamiltonian, a semi-empirical approach can be taken which expresses much of the hamiltonian in terms of known properties of the core. A semi-empirical analysis of this effective hamiltonian is shown to give well-known phenomenological effective hamiltonians and the connections to them. Thus this work can also be viewed as a theoretical justification and extension of the two-electron model potential or pseudopotential theories.