Core Rearrangement and Hartree-Fock Ionization Energies

Abstract

The energy to strip all the valence electrons from an atom consists not only of the one-electron valence energies minus ½ the valence-electron-valence-electron interaction energy but also contains a contribution from the rearrangement of the core electrons upon ionization. Although this is a second-order contribution, it is second order in the core energy and therefore not necessarily negligible compared with valence energies. We have therefore made self-consistent Hartree-Fock calculations for Li, ${\mathrm{Li}}^{+}$, Be, ${\mathrm{Be}}^{++}$, Mg, and ${\mathrm{Mg}}^{++}$, computing separately for each electron its kinetic energy, nuclear Coulomb energy, core-electron Coulomb energy, valence-electron Coulomb energy, core-electron exchange energy, and valence-electron exchange energy. In Li and Be, core rearrangement decreased the ionization energy by less than 0.0001 Ry. In Mg, the $s$-core electron rearrangement increased the ionization energy by 0.1134 Ry while the $p$-core electron rearrangement decreased it by 0.1156 Ry for a total decrease of 0.0022 Ry.