Noninvariance Groups in Molecular Quantum Mechanics. I

Abstract

The problem of one electron moving in the field of many stationary nuclei is formulated in terms of the operations of the Lie algebras of E₄, R₅, and O_4,1, all noninvariance groups of quantal electrostatics. This makes it possible to carry through and completely analyze one‐electron molecular calculations using only concepts and operations of the theory of continuous groups. The approach is designed for the study of general laws of behavior of simple molecular systems. To exemplify it, it is used in its simplest form to uncover a suggestive approximate dynamical symmetry. This is related to a known angular momentum invariant that is instrumental in determining the properties of small molecules.