Symmetry Considerations Concerning the Splitting of Vibration-Rotation Levels in Polyatomic Molecules

The interaction of rotation and vibration and perhaps other effects may split degenerate vibration-rotation energy levels of symmetrical polyatomic molecules into a number of components. The permutation symmetry of molecules containing several identical atoms provides certain restrictions on this splitting. This paper discusses the maximum number of fine-structure components, their quantum weights when nuclear spins are taken into account, and the selection rule for transitions. All arguments are based solely on symmetry considerations so that no estimate of the magnitude of the splitting is given.