Group Theory Calculations Involving Linear Molecules

Abstract

Most chemistry courses involving group theory do not treat the infinite point groups C∞v or D∞h. Even the character tables themselves are not transparent looking, with the profusion of ellipses. Because of this, it is not possible to deduce the vibrational symmetry modes of CO2, even though the symmetric, asymmetric stretch, and doubly-degenerate bending modes are discussed in almost all physical chemistry courses. In this paper we show how linear molecules such as CO2, C2H2, and HCN can be treated using the point groups Cnv or Dnh for general values of n. When determining which irreducible representations comprise the normal vibrational modes of a linear molecule such as CO2, we show that the n-dependence vanishes. The calculations presented here do not require advanced mathematical knowledge and could be incorporated into an undergraduate chemistry curriculum in which group theory is presented.