Electron intracule densities with correct electron coalescence cusps from Hiller–Sucher–Feinberg-type identities

Abstract

Identities for the electron intracule density I(R) in atoms and molecules are derived within the Hiller–Sucher–Feinberg (HSF) formalism. It is proven that, when applied to arbitrary (exact or approximate) electronic wave functions, these identities produce intracule densities that satisfy a modified condition for the electron coalescence cusp. A corollary of this proof provides a new, simplified derivation of the cusp condition for the exact I(R). An expression for the Hartree–Fock approximation to the HSF electron intracule density that contains only two- and three-electron terms is obtained and its properties are analyzed. A simple scaling of the three-electron contributions in this expression assures integrability of the approximate I(R) and improves its overall accuracy. Numerical tests carried out for the H−, He, Li+, Be2+, Li, and Be systems demonstrate that the application of the scaled HSF-type identity to Hartree–Fock wave functions affords dramatic improvements in the short-range behavior of the electron intracule density.