Short-range behavior of some electron-pair densities

The short-range behavior of several electron-pair densities is reported to be governed in common by a quantity ρ2(0, 0), which is a special value at the origin r1 = r2 = 0 of the spherically averaged two-electron density function ρ2(r1, r2). Such electron-pair densities include the radial sum density, the outer density, the coalescence density, and the counterbalance density, appearing in the literature to clarify different aspects of the electron–electron interaction. Moreover, the two-electron value ρ2(0, 0) is shown to be exactly determined by the one-electron value ρ(0) in the Hartree–Fock theory of atoms with closed s subshells, where ρ(0) is the value at the origin r = 0 of the spherically averaged single-electron density function ρ(r). A small correction is added for open s subshell cases.