Group Theory Calculations Involving Linear Molecules

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 1 Issue 1 (1996), S1430-4171(96)01005-9

Group Theory Calculations Involving Linear Molecules

Jeffery A. Greathouse

University of California-Davis, Davis, CA 95616, USA

Published online: 25 March 1996

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 CO_₂, 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 C_nv or D_nv 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.

Key Words: In the Classroom; group theory; inorganic; normal mode; vibrational; point group; character table; linear; lecture; infinite

(*) Corresponding author. (E-mail: greathou@nature.berkeley.edu )

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