Different perturbed uncoupled Hartree--Fock methods for physical properties of atomic systems

In order to gain an understanding of the problem of the self-potential and to study the accuracy of the different methods at different stages of approximations, in this work two new PUCHF methods are introduced. One defines Dalgarno's PUCHF method as PUCHF method C1 and the proposed methods as PUCHF method C/sub 1/2/ and PUCHF method C0, because they include all of the self-potential, half of the self-potential, and none of the self-potential, respectively. PUCHF methods C0 and C/sub 1/2/ are similar to PUCHF method C1 in two ways. First, since they are all formulated with an explicitly known zeroth-order many-electron Hamiltonian which corresponds to the unperturbed Hartree-Fock wavefunction, all these PUCHF methods can be improved by using perturbation theory. Secondly, if only first-order corrections are needed, these corrections can be obtained without knowledge of the second-order orbitals. To provide a quantitative illustration of the significance of the difference in self-potential terms for the He, Li, and Be isoelectronic sequences one has calculated the dipole polarizabilities, α = α0 + α1, and dipole shielding factors, γ + γ0 + γ1, and used the coupled perturbed Hartree-Fock (CPHF) dipole polarizabilities, α/sub CPHF/, and dipole shielding factors, γ/sub CPHF/, as the standards for comparisons. Among these three PUCHF methods, it is concluded PUCHF method C/sub 1/2/ is the best. When the self-consistent-field Hartree-Fock orbitals of Roothaan, Sachs, and Weiss are used as zeroth-order orbitals i0's, PUCHF method C/sub 1/2/ yields α(=α0 + α1)'s which differ from α(sub CPHF/'s) by 1.29 to 0.08% in the case of the He sequence, and 2.50 to 1.06% in the case of the Be sequence. It also yields γ(=γ0 + γ1)'s which differ from γ/sub CPHF/'s by 0.13 to 0.01% in the case of He sequence, 8.89 to 0.95% in the case of the Li sequence, and 11.0 to 0.99% in the case of the Be sequence