Bopp's approximation to the energy of an<i>N</i>-electron system

Abstract

The connection between Bopp's approximation to the energy of N-electron atoms and ions, and [infinity]-order perturbation theory is established. The approximation gives the first two terms in the perturbation series correctly, but contains only parts of all higher-order terms. Calculations show that Bopp's approximation is superior to first-order perturbation theory, but inferior both to second-order perturbation theory and to the Hartree-Fock method. For three-electron systems Bopp's approximation is a lower bound for the exact energy. Certain conditions on the second-order density matrix for atoms and atomic ions are noted, and a brief comment is made on the electron correlation problem in molecules.