Interelectronic angular analysis of electron repulsion energies in many-electron atoms

Abstract

For many-electron systems, the electron repulsion energy density w(θ12) is introduced to study the distribution of the electron repulsion energy W = ⟨r−112⟩ as a function of the interelectronic angle θ12. It is shown that in general the electron repulsion energy density w(θ12) is expressed by a linear combination of Legendre polynomials Pm(cos θ12). Explicit formulae for the expansion coefficients are presented for many-electron atoms described by determinantal wavefunctions. The results are applied to the ground-state helium atom at the Hartree–Fock and correlated levels.