Uncoupled Hartree-Fock perturbation theory and the Pople-Schofield approximation

Abstract

The first-order perturbation equation in UCPT is derived in a form which reflects the essential lack of uniqueness of the perturbed orbital. The functionals leading to this equation and the other forms of the first-order equation are compared and this functional found to be best, although equivalent to the others if additional conditions are applied to their variation. The Pople-Schofield approximation, which is frequently applied to simplify the computation of the variational functional, is examined and found to be exact in the sense that H0 can be constructed to make it so. A simpler way of regarding the Pople-Schofield approximation is presented using a method due to Hirschfelder and originally designed to deal with exchange forces.

Why the Kirkwood-Pople-Schofield method works so well

“…The use of the Sternheimer potential [29] brings about some difficult problems related to its singularities and the recipe for constructing the appropriate local HF operator, which has been proposed by Amos and Crispin [30], does not seem to be easy to follow. On the other hand, if one uses the standard HF operator, then the derivations of the KPS functional presented by Lekkerkerker et al [7] and Rivail and Cartier [10,11] are incomplete.…”