Generalization of analytic energy derivatives for configuration interaction wave functions

Abstract

This paper takes the form of a review including some original contributions. A fresh derivation of analytic energy derivative expressions for configuration interaction (CI) wave functions is presented. In this method the CI energy is described by σIJCICJ(H IJ-δIJE) so that the orthonormality condition is explicitly included therein. In the sequence of differentiations up to fourth order it will be demonstrated that each derivative may be expressed in terms of (HIJ-δIJE) and its derivatives in a symmetric way with respect to the interchange of differential variables. In a similar manner, the CI variational condition may be described in an equation which explicitly includes the normalization condition. It is shown that the differentiation of the modified variational condition produces the coupled perturbed configuration interaction (CPCI) equations in directly soluble and compact forms. The necessary formulae for the energy derivatives up to fourth order and the CPCI equations up to second order are explicitly given.