A simple method to calculate the correlation energy in molecules based on the bond orbital approximation

Abstract

It is the main scope of this work to present a transparent numerical approach for the determination of interatomic correlation energies in molecules. The analysis is of model character, i.e. the presentation of quantitative numerical data is not intended. Our simple analytical method to calculate the correlation energy is based on the bond orbital approximation (BOA) for the mean-field ground state and on the local approach (LA) to electron correlation. The interatomic correlation energy is obtained as a sum of various intrabond and interbond contributions, for which simple analytic formulae are derived. In this way, the dependence of electron correlation on bond polarities, two-electron integrals and kinetic hopping elements becomes transparent. The remaining intra-atomic part of the correlation energy is described by analytic expressions which depend only on the total charge and the number of p and s electrons on a given atom. Therefore, the total correlation energy may be estimated by using the information available from the self-consistent field calculation. As an example, an application of the method to a number of molecules of the general topology X-Y≡Y-Z is presented. The correlation energies obtained in an analytic way agree rather well with those given by a direct numerical evaluation within the LA.