Internal symmetry groups of non‐rigid molecules

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Abstract
Hougen has established, for quasi‐rigid molecules, the relationship between permutationinversions acting on the molecular Hamiltonians written in Cartesian co‐ordinates and permutation‐rotations (perrotations) of symmetry acting on nuclear equilibrium configurations. We extend these relations to the case of non‐rigid molecules. For this, we introduce kinetic perrotations which act on nuclear equilibrium configurations in the same way as do Altmann's isodynamic operators. We show that isodynamic operators do not always form a group. Moreover, their action cannot be extended to the electrons. They cannot be used for the classification of molecular wave functions. This classification is achieved by using the group of Longuet‐Higgins and the group of the corresponding feasible perrotations.