The summary of nonrigid molecules: the Schrödinger supergroup

Abstract

The symmetry groups of nonrigid molecules possess two subgroups: one is that of all the symmetry operations of the Schrödinger group of the molecule and the other is a group of a new type of operation called an isodynamic operation. The total group, which is called the Schrödinger supergroup, is a semidirect product of the Schrödinger group and the isodynamic group. Examples are given for borondifluoride methyl, ethane, dimethylacetylene and borontrimethyl. It is shown that in certain cases the double groups of the isodynamic group have to be used. The results do not agree always with those recently given by Longuet-Higgins: a careful analysis of the nature of symmetry and isodynamic operations indicates the origin of the discrepancy.