THE USE OF HIGH-ORDER EXTENDED GROUPS IN UNSYMMETRIC INTERNAL ROTATION PROBLEMS

Abstract

It is sometimes convenient when applying group theory to internal rotation problems in molecules composed of two identical halves$(e.g. H_{2}O_{2}, N_{2}H_{4}, C_{2}H_{6})$ to use a double group of the Longue-Huggins permutation inversion group for treating the rotational, internal-rotational, or vibrational problems separately. In the present work the possibility of applying the concept of extended groups to internal rotation problems in molecules with unequal halves $(e.g. CH_{3}OH)$ is investigated. Preliminary results indicate that a consistent formalism can be constructed which involves extended groups corresponding to very high, but finite multiples of the original Longuet-Higgins permutation inversion group of the molecule, and that this formalism can be used to rederive in an interesting fashion many results already well known from theoretical discussions in earlier infrared and microwave investigations. Work is proceeding on an attempt to use this formalism to understand the apparent intensity anomalies in an electronic spectrum of $CF_{3}NO$, which presumably arise from complications associated with a transition between an eclipsed and a staggered form of the molecule.