On the electron-pair radial coalescence density of atoms

Abstract

The electron-pair radial density D2(r1, r2) is the probability density of any two electrons that are located at radii r1 and r2, respectively. The electron-pair radial coalescence density D2(r, r) is the diagonal element function of D2(r1, r2) and represents the probability density of two electrons being on the same sphere with a radius r. Theoretical analysis of atomic coalescence densities shows that the Hartree–Fock (HF) radial coalescence density D2(r, r) is rigorously bounded by functions immediately obtained from the familiar single-electron radial density D(r). The results also imply inequality relations between the electron-pair radial difference density at the origin and the average single-electron radial density value. Numerical results are given for the 53 atoms He through Xe. It is also examined how the inclusion of the electron correlation modifies the HF relations.