The hydrogenic limit of many-electron atoms

Abstract

The properties of many-electron atoms in the limit of infinite nuclear charge Z and a constant degree of ionization 1−N/Z (N being the total number of electrons) are investigated. The hydrogenic limit of such atoms, defined as a system of N noninteracting electrons moving about a nucleus of charge Z, is studied in detail. In addition to the well-known formulas for the energy components we derive closed form expressions for all the moments of the charge density ∫dτrkρ(r) where k⩾−1. These results serve as a starting point for the comparison of two density functional theories: the Thomas–Fermi (TF) theory and the local density functional (LDF) theory. It is shown that in both cases the energy components, as well as the moments of the charge density, converge to the hydrogenic limit as N/Z→ 0. We further compare the TF and LDF predictions for the total energy E over the whole range 0⩽N/Z⩽1. It is shown that LDF may closely approach the TF theory for an appropriate choice of the electronic repulsion parameter.