Analysis of the Karplus-Kolker approximation to Hartree-Fock perturbation theory

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Abstract
The Karplus-Kolker approximate uncoupled Hartree-Fock perturbation scheme is compared with the corresponding coupled variation-perturbation approach. The first-order perturbation-like corrections to the Karplus-Kolker second-order energies are defined and their meaning and relative importance are discussed. Also a geometric approximation to the coupled Hartree-Fock perturbation theory, based on the Karplus-Kolker method, is examined. To account properly for the coupling effects an alternative approach, called the coupled geometric approximation, is proposed. Appropriate numerical calculations were performed for the electric dipole polarizabilities and dipole shielding factors of two-, four- and ten-electron atomic systems. The first-order corrected Karplus-Kolker second-order energies are usually far from the corresponding coupled Hartree-Fock results. When the coupling effects are negligible, the geometric approximation gives quite satisfactory results. In the case of large coupling terms, the coupled geometric approach leads to an essential improvement of the calculated second-order atomic properties. These final results are very close to the corresponding coupled Hartree-Fock values.