Small scale variational scheme incorporating local orbitals with fully flexible hybridization: A local orbital reconstruction of Walsh's rules

Abstract

The idea that chemical bonding is predominantly local, and can be captured at least qualitatively by mixing of orbitals at a single center (hybridization) and between two adjacent atoms (pair-bonding) has served chemistry very well. There are, to be sure, departures from the simplest expectations of bond angles, which we describe as arising from purely geometric constraints, local energy conditions, and long-range strain. To illustrate the flexibility of the one-center hybridization/pairwise interaction description of bonding, we have devised a small variational computation, based on a Lewis bonding scheme refined by constrained unitary transformation of the atomic orbital basis. In its simplest form the model permits full one-center hybridization but only two-center bonding. The model may be extended either by perturbation theoretic corrections for delocalization or by relaxing the constraints on the basis transforms. A simple parameterization of the model permits a demonstration that Walsh rules may be developed from the simplest realization of a local description of molecular electronic structure which can provide a quantitative description of the interplay between atomic energy states, hybridization, and molecular geometry.