DEDUCING THE SYMMETRY OPERATIONS GENERATED AT A TRANSITION-STATE

The problem of transition state symmetry determination is investigated. It is shown how the symmetry operations generated at the transition state for an interconversion between two versions of the same (non-planar) structure may be found. We assume that a reaction follows steepest descent paths on either side of the transition state and that there is a single symmetry-equivalent path between the two minima. The representation of point group operations by permutations and permutation-inversions of identical nuclei is used so that the point group of each version is isomorphic to a subgroup of the CNPI group. The operations which relate each version to the other are then cosets in the CNPI group. The symmetry operations unique to the transition state between them are those common to both cosets. The discussion is extended to cover the interconversion of planar structures and single-step paths between labelled-atom enantiomers.