Symmetry in Molecules

Abstract

This article reviews and illustrates our understanding of the interplay between group theory and the theory of atomic and molecular electronic structure. It begins by demonstrating how the quest for group theory already emerged from the classical chemistry and crystallography of the nineteenth century, and goes on to describe the geometrical and dynamical symmetries met in the quantum mechanical one-electron problem. Next, detailed attention is paid to atoms and molecules with two or more electrons and hence to the permutation symmetry induced by the indistinguis-hability of electrons. Many-electron wave functions must span the antisymmetric representation of the permutation group, and the problem of constructing such functions is considered from various angles. Thus, contact is made to modern methods of determining many-electron wave functions by large scale computations. The article addresses itself to the student of chemistry who has but little knowledge of group theory, and hence it also includes a brief discussion of the theory of group representations.