Second-order correlation energies forF1−,Na1+,Mg2+, andAr8+:Zdependence of irreducible-pair energies

Abstract

Second-order correlation energies for some ions of the Ne isoelectronic series are evaluated within the framework of the Rayleigh-Schr\"odinger Hartree-Fock perturbation theory (RS-HEPT). The variational-perturbation method is applied. Pair functions of definite orbital and spin symmetry are expressed in the form of partial-wave expansions. Special attention is paid to the determination of the $Z$ dependence of both the partial-wave increments to the pair energies and the second-order pair energies, which represent very close approximation to the "all-external" pair-correlation energies. It is found that the partial-wave increments depend in a strictly monotone way on the nuclear charge, whereas the $Z$ dependence of the pair energies is more complicated. A comparison with relevant results of the most extensive variational computation for ${\mathrm{F}}^{1\ensuremath{-}}$ confirms our previous conclusion that for Ne-like atoms the RS-HFPT yields very accurate correlation energies. A very accurate value for the electron affinity of F (3.534 eV) has also been obtained.