Symmetry constraints on the Hartree-Fock model

Abstract

It is shown that the removal of the ‘spherical approximation’ from the Atomic Hartree-Fock equations generates a set of atomic orbitals which are not always eigenfunctions of L ². In particular, the s-type and d-type orbitals ‘mix’. The result of this mixing is to generate a set of ‘valence’ orbitals for these atoms which solves the old problem of why, if the 3d lies below the 4s, does the 3d not always fill up first.