Group Theory Calculations Involving Linear Molecules

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 Dnv 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.