A useful theorem in simple molecular orbital theory

Abstract

In the general case, the energies of the molecular orbitals of a system A alternate with those of system B which has one less orbital but is otherwise identical with system A. Under certain circumstances, associated usually with symmetry, some m.o.s. of systems A and B may have a common energy.

This theorem goes some way towards rationalising many semiqualitative statements which have been made in the m.o. framework but which previously were not rigorously justified. It also has some interesting applications, in particular when molecules are built up by connecting identical groups together by single orbitals.