Report 78-14 Applications of the Permutation Group

A typical problem in dynamic stereochemistry is to determine the mechanism of the rearrangement of a chemical structure such as 1. (I 352) Many of the problems already studied have involved degenerate rearrangements (those which interconvert chemical structures of the same geometry apart from any difference in the ligands) and only these will be considered here. Two groups and the mapping (homomorphism) between them are crucial to the proper description of problems of this kind. The first of these is the symmetry group of the chemical structure's skeleton (i.e, without ligands) and is designated P. This may be a point group, the rotation subgroup of a point group, or a nonrigid symmetry group [1]. Generally, this group can be represented as a permutation group on the ligands or on the skeletal sites however, in the most general case, this group is best represented as a permutation-inversion group [1].