Physical behavior, symmetry classification and quantum numbers of vibrational–torsional states in ethane-like molecules

Abstract

The symmetry species of vibrational and vibrational–torsional states of ethane-like molecules are labeled and classified by the values of quantum numbers related to the vibrational contribution to the z-axis rotational and torsional angular momenta. It is emphasized that the symmetry behavior of degenerate vibrational states of this class of molecules depends on the joint action of end-to-end and torsional Coriolis coupling by a complex mechanism, with group theoretical implications. A new vibration–torsion quantum number is defined, to account for the arbitrariness of the symmetry classification of the degenerate vibrational modes. The classification of the vibrational states of a G s+ G s combination is studied in detail. The limit case where the value of the Coriolis coefficient is equal to one in both partners of the combination is examined, accounting for the effects of end-to-end and torsional Coriolis interactions, and the results are shown to be in agreement with the predictions from group theory. The occurrence of vibrational ℓ and ℓ i splittings in a G s+ G s combination, analogous to the vibrational ℓ-doubling in E+ E combinations, is also discussed. It is pointed out that the complex mechanisms of end-to-end and torsional Coriolis coupling, which can affect the torsional splittings significantly, might contain relevant general features also applicable to other classes of molecules with internal rotation.