Isometric group of semi-rigid models: relation to the permutation-inversion group and extension of the concept to non-rigid molecules

Abstract

After a short recapitulation of the basic assumptions underlying the isometric group concept for semi-rigid molecules a relation to the permutation-inversion group (Longuet-Higgins group) is established. Conditions will be put forward under which the permutation-inversion group is homomorphic (not isomorphic) to the isometric group. It will be shown that the familiar symmetry concept of quasi-rigid molecules is identical with the isometric group concept. Finally the latter will be generalized to non-rigid molecules; the isometric group of such systems will be shown to be isomorphic with the isometric group of the associated semi-rigid model. For semi-rigid models with proper covering group the isometric group is shown to be a semi-direct product of the covering group and the internal isometric group.