Electron-pair radial densities from shell densities of atoms

Abstract

Based on subshell and shell analysis of the electron-pair radial density D(2)(r1, r2) of atoms, we report that D(2)(r1, r2) is well expressed by a set of shell densities dn(r) in the Hartree–Fock theory, where n denotes the principal quantum number. Numerical tests on the 53 atoms, He through Xe, show that the quantum similarity index, bounded by 0 (complete dissimilarity) and 1 (complete similarity), is never smaller than 0.9995 between the original and approximate electron-pair densities. The relation implies a construction of a two-electron property from single-electron properties. The result is applied to the derivation of an improved upper bound to the radial coalescence density in terms of the single-electron radial density D(r). Numerical tests for the 53 atoms demonstrate the usefulness of the new bound.