Accurate third-order correlation energies for closed-shell systems. II. Two- and four-electron systems

Abstract

For pt.I see ibid., vol.15, no.8, p.1137-59 (1982). Accurate third-order results for the partial-wave (PW) increments to the pair energies (E3(A)), the pair energies (E3K(T)), and the total energies (E3), for several members of the He and Be isoelectronic sequences are computed within the framework of the variational-perturbation method with H0=HHF. For Be-like systems off-diagonal terms, neglected in previous work, are taken into account. Extensive basis sets including all PLW up to l<or=9 are employed in the calculations. Particular attention is given to the problem of eliminating the radial and angular basis saturation errors. A discussion of the Z dependence of E3(A), E3K(T), and E3 is presented. Some attention is also paid to the transferability of E3(A) between systems of the same number of electrons (N transferability). It is found that the four-electron systems the 1s22s2-1s22p2 quasi-degeneracy makes the regularities for the Z dependence of the E3(A), E3K(T), and E3 energies weaker, and destroys completely the N transferability of E3(A) for the 2s2 pair. It is also found that with increasing nuclear charge, Z, the energies through third order become less accurate approximations of their exact counterparts, e.g., for Ar14+ E2+E3 amounts to only 83% of the accurate value of the correlation energy.