Perturbation theory of the electron correlation effects for atomic and molecular properties

Two alternative perturbation approaches to the calculation of the correlation corrections to atomic and molecular properties are analyzed. One of them is based on the double-perturbation treatment of the external field and the correlation effects with reference to the Hartree–Fock (HF) Hamiltonian of the unperturbed system. This approach is equivalent to the calculation of correlation corrections to the results of the uncoupled Hartree–Fock (UCHF) perturbation scheme of Dalgarno. The other method consists of calculating the correlation corrections to the results of the coupled Hartree–Fock (CHF) perturbation theory. The diagrammatic analysis of the two perturbation methods reveals that in the case of the UCHF-based treatment the so-called correlation corrections involve both the self-consistency effects and the genuine correlation contributions. Since both these quantities follow from the correlation energy operator, it is proposed they be called the apparent and the true correlation effects, respectively. The structure of the CHF-based perturbation theory shows that the correlation corrections involve solely the true correlation effects. The relative role of the apparent and the true correlation contributions is analyzed for the UCHF-based theory by using the recent data of Itagaki and Saika. It is concluded that the true correlation effects can be expected to be much smaller than the apparent ones. It is proposed that a reliable estimate of the true perturbed energy can be obtained by adding the second-order correlation correction to the corresponding CHF result. As illustrated by the calculations of polarizabilities for He, Be, and Ne the correlation-corrected CHF values agree within a few percent with the best recommended data. The results of the diagrammatic analysis of the structure of the UCHF- and CHF-based perturbation theories are used to resolve some controversy concerning the cancellation of the higher-order self-consistency terms. It is explicitly shown that both theories contain all self-consistency contributions and that there is no cancellation of these terms. This permits one once again to conclude that the CHF-based perturbation theory of the correlation effects should be more efficient than the double-perturbation approach. The former corresponds to the HF level of accuracy for both the unperturbed and the perturbed system, while the latter satisfies this condition only in the absence of the external perturbation.