Theory of Polyhedral Molecules. II. A Crystal Field Model

Abstract

A crystal field model is developed for finding the molecular orbitals of polyhedra of identical atoms. The valence electrons are taken as moving in a one-electron crystal field set up by an effective nuclear charge centered at each atom. The field is expanded in spherical harmonics. Zeroth-order solutions are found from the spherically symmetric term, while higher terms are treated as a first-order crystal field perturbation. Polyhedra of hydrogen and of boron or carbon are considered. For the latter special attention is given to the identification of out-pointing orbitals, i.e., the orbitals used in bonding. Comparison is made between crystal field and LCAO energy levels. It is shown that they become more alike when, in the latter, α(2s) is made much lower than α(2p).