Multipole analysis of electron repulsion energies in many-electron atoms

Abstract

The repulsion energy W between two electrons located at r ₁ and r ₂ can be expressed by the sum of the interaction energies W _k between an electron located at ${\bf r}_{>}$ and linear electric multipoles located at the coordinate origin along the vector ${\bf r}_{<}$, where ${\bf r}_{<}$ and ${\bf r}_{>}$ are the vectors with smaller and larger moduli, respectively, of the two vectors r ₁ and r ₂. All the existing multipole contributions W _k 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 |W _k | decreases rapidly with increasing k, W ₀  >  W, and W _k with k  ≥  1 work to reduce W ₀. The effect of electron correlation is also discussed for some helium-like atoms.