Enumeration of Permutational Isomerization Reactions

Abstract

Rearrangement reactions of certain stereochemically nonrigid molecules may be described by permutation operations. The usefulness of these permutation operations in solving quantum mechanical and stereo-chemical problems has already been demonstrated. In this paper it is shown how the point group of a molecule renders certain permutations equivalent. This equivalence is used to generate classes of equivalent permutations, i.e., classes of equivalent isomerization reactions. Two types of equivalent reactions are defined: indistinguishable permutational isomerization reactions and nondifferentiable permutational isomerization reactions. The classes of equivalent permutations generated are shown to be conjugacy classes and double cosets, respectively, of the symmetric group without respect to a subgroup. Formulas are provided which enumerate these classes. Nonrigid trigonal bipyramidal and octahedral molecules are treated as examples.