Energetic Contributions to the Two-Electron Bond: A Simplified Group Function (SGF) Analysis

Abstract

The group function (GF) formalism coupled with the limit in which intergroup electron interchange symmetry is rigorously neglected (the simplified group function (SGF) approach) is shown to lead to a resolution of intergroup bonding as an effective power series in overlap density. The successive orders are shown to correspond to a concomitant resolution into traditional bonding contributions: zeroth order leads to the conventional excitonic description (no electron transfer or interchange); first-order terms may be interpreted as dative bonding, in which electron transfer configurations mix with the excitonic states; and finally, second-order terms correspond directly to the incorporation of electron interchange symmetry and hence to pure covalent bonding. A conceptual parallelism of the division of long range (static, inductive and dispersive) interactions with short range (ionic, dative and covalent) interactions is drawn to emphasize the unity of these apparently disparate limits in the SGF/GF analysis. Explicit application to the archetypical two-electron bond highlights the conceptual simplicity of the approach, and is compared to a commensurate MO and VB analysis expressed in terms of the same integrals. The results show clearly why such a simple resolution is difficult to extract from MO and VB approaches, which are philosophically biased towards the strong bonding limit.