Theory of odd torsional transitions in the V-N resonance Raman spectrum of ethylene

Abstract

The V-N resonance Raman spectrum of ethylene shows a long progression in even quanta of the ground-state torsional mode v″4(au). Bands approximately midway between the even quanta have been assigned to transitions to odd quanta of v″4, although such transitions are forbidden according to the usual g↔u selection rule of Raman spectroscopy. We consider the theory of the intensity of such transitions allowing for the fact that the excited state is twisted by 90° at equilibrium, using Hougen's double group theory for the separation of the torsional and a-rotational motions. From approximate one-dimensional torsional potentials of the V and N electronic states, it is shown that qualitative agreement between observed and calculated intensities is obtained. The electronic transition moment is assumed to be proportional to cos2γ, where 2γ is the torsional angle, but the calculated relative intensities are not sensitive to the precise torsional dependence. More detailed theory will require inclusion of the CC-stretching and CH2-scissoring degrees of freedom and consideration of an avoided crossing affecting the V state.