Many-Body Perturbation Theory Applied to Open-Shell Atoms

Abstract

It is shown how many-body perturbation theory may be applied to the problem of correcting Hartree-Fock energies and wave functions for the degenerate ground states of open-shell atoms. The choice of an appropriate potential for the calculation of the single-particle states of the perturbation expansion is discussed in detail. As an example of these methods, the correlation energies among all pairs of electrons in the neutral oxygen atom are calculated for excitations into 1=0, 1, 2, and 3 states. The total calculated pair correlation energy is -0.274 atomic units (a.u.) as compared with the total correlation energy -0.258 a.u. which is deduced from experiment. The correlation energy among $2p\ensuremath{-}2p$ electron pairs is -0.0906 a.u.; among $2s\ensuremath{-}2p$ pairs, -0.1004 a.u.; $2s\ensuremath{-}2s$, -0.0150 a.u.; $1s\ensuremath{-}2p$, -0.014996 a.u.; $1s\ensuremath{-}2s$, -0.00629 a.u.; $1s\ensuremath{-}1s$, -0.0438 a.u. There is also a contribution -0.0028 a.u. which corrects for the use of a restricted Hartree-Fock solution.