Ab initio g-Hartree calculations on the atoms Be and Ne that employ fully numerical and basis-set techniques.

Abstract

We report fully numerical calculations of correlation energies in second-order perturbation theory based on Hartree-Fock and g-Hartree mean fields for Be and Ne atoms and show that basis-set techniques give essentially the same results. An extension to higher-order perturbation theory is relatively straightforward in the basis-set approach. We report third-order calculations that yield in the case of Be significantly improved values for the g-Hartree correlation energy which now agrees within 4% with the total correlation energy known from complete configuration-interaction estimates, while third-order Hartree-Fock correlation energies calculated in the same basis set still disagree by 10% due to difficulties in describing the near degeneracy of the 2s and 2p orbitals. In the case of the Ne atom, we find that for the g-Hartree mean field still higher orders of perturbation theory are required to obtain agreement with experiment.