Accurate third-order correlation energies for closed-shell systems. I. Ten-electron systems

Abstract

Third-order values of the partial-wave (PW) increments to the pair energies, pair energies and total energies, E3, for members of the Ne isoelectronic sequence are obtained using a ponderated ab initio perturbation approach. The variational-perturbation method is applied within the framework of the Rayleigh-Schrodinger Hartree-Fock perturbation theory. The N-electron first-order wavefunction is defined in terms of orbital configurations of one-electron functions and symmetry-adapted pair functions in the form of PW expansions. Since the third-order values depend critically on the accuracy of the first-order wavefunction, the authors use extensive basis sets including all PW up to l, l'<or=9 and perform careful radial and angular extrapolations. The extrapolated third-order energies for E3F-, E3Na+, E3Mg2+ and E3Ar8+ are 0.0176, 0.0005, -0.0010 and -0.0022 Hartree, respectively. The authors have found that the role of the third-order corrections consists mainly in a modification of the distribution of the portions of the correlation energy among the individual pairs without essential impact on the total energy. Special attention is paid to the study of the Z dependence of all the quantities considered. It is found that unlike the second-order energies, E2, the correlation energies calculated through third order (E2+E3) decrease in a monotonic way with increasing Z. Whenever possible, the results are compared with their theoretical and semiempirical counterparts.