Different Perturbed Uncoupled Hartree–Fock (PUCHF) Methods for Physical Properties. I. Theory and Dipole Polarizabilities

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Abstract
Two different kinds of uncoupled Hartree–Fock (UCHF) Methods, Method C1/2 and Method C0, for the calculation of second-order physical properties are proposed. They differ from Dalgarno's uncoupled Hartree–Fock method (Method C1) by including half of the self-potential or not including the self-potential at all. They are formulated with a zeroth-order many-electron Hamiltonian, and first-order correction of both methods can be obtained without knowledge of the second-order orbitals. This situation is similar to the case studied by Tuan and co-workers for Method C1. The dipole polarizabilities for the He and Be isoelectronic sequences have been calculated by the three UCHF methods, αUCHF = α0, by the three UCHF methods with the first-order perturbation correction (PUCHF methods), αPUCHF = α0 + α1, and by the geometric approximation based on these three PUCHF methods, αgeom = α0(1 − α1 / α0)−1. The significance of the difference in the self-potential is demonstrated by comparing the results with results from the coupled Hartree–Fock (CHF) method. Method C1/2, which included the intermediate amount of self-potential, gave the best comparison of α0, α0 + α1 and αgeom with αCHF. For the He isoelectronic sequence from Method C1/2, α0 differs from αCHF by 9.71%–2.26%, α0 + α1 differs from αCHF by 1.29%–0.08%, and αgeom differs from αCHF by 0.42%–0.03%. Errors in the Be isoelectronic sequence are larger than those in the He isoelectronic sequence. Explanations in terms of the restricted forms of the Hartree–Fock wavefunction and of the variational first-order orbitals are given. The relative computing times for the CHF method and the perturbed version of Method C1/2 are in the ratio of 5 to 1. It is suggested that for evaluating the physical properties of larger and complicated systems the geometric approximation based on the PUCHF Method C1/2 can replace the CHF method as a simple and accurate method.