On the symmetry properties of non-rigid molecules

Abstract

A recent theorem states that the complete isometric symmetry group of a non-rigid molecule is a semi-direct product of the point group and the internal isometric group. It is shown that, although the point group is an invariant subgroup of the complete isometric group, the theorem is not generally valid. A counter-example is presented and a necessary condition is given for the validity of the general theorem. The counter-example is also discussed in terms of the symmetry group of the molecular model.