Multipole analysis of electron repulsion energies in many-electron atoms

Abstract

The repulsion energy W between two electrons located at r1 and r2 can be expressed by the sum of the interaction energies Wk between an electron located at \({\bf r}_{>} \) and linear electric multipoles located at the coordinate origin along the vector \({\bf r}_{ } \) are the vectors with smaller and larger moduli, respectively, of the two vectors r1 and r2. All the existing multipole contributions Wk to the Hartree–Fock electron repulsion energy W are examined for the 102 atoms He through Lr in their ground states. It is found that |Wk| decreases rapidly with increasing k, W0 > W, and Wk with k ≥ 1 work to reduce W0. The effect of electron correlation is also discussed for some helium-like atoms.