The symmetry groups of non-rigid molecules

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Abstract
The concept of molecular symmetry is extended to molecules such as ethane and hydrazine which can pass from one conformation to another. The symmetry group of such a molecule is the set of (i) all feasible permutations of the positions and spins of identical nuclei and (ii) all feasible permutation-inversions, which simultaneously invert the coordinates of all particles in the centre of mass. According to the representations of this group one can classify not only the spin states and states of motions of the nuclei, but even the electronic states of the molecule. Examples are given to illustrate the use of this concept in determining the statistical weights of individual levels and selection rules for electric dipole transitions between them.