Bond Order in LCAO Molecular Orbital Theory

Abstract

On the basis of LCAO theory, the following intrinsic definition of bond order is derived: B ij =p ij S ij +p ij f ij g ij , where i and j index basis functions on different centers, pij is the corresponding charge‐and‐bond‐order matrix element, Sij is the overlap integral, fij is a long range factor, and gij is an atomic hybridization and nonorthogonality factor. The term pijSij is the overlap population and the term pijfijgij is the associated net atomic population; the latter is defined by a reference homopolar bond constructed from normalized hybrids of compositions determined by the LCAO wavefunction. The bond order, Bij , reduces in the appropriate special cases to the Coulson, Mulliken, and Wiberg bond orders. However, Bij is not limited to these cases but is also valid for analysis of any LCAO wavefunction. It may also be combined with a Mulliken population analysis to resolve the total electron population into bonding terms and residual lone pair terms. Similarly, the valence electron population may be resolved into covalence, electrovalence, and free valence. Applications are given to HF, the Group I fluorides, and some organic molecules.