Knowledge Bank

The $V-N$ resonance Raman spectrum of $ethylenea$ shows a long progression in even quanta of the ground-state torsional mode $\nu 40(av)$. Bands approximately midway between the even quanta have been $assignedb$ to transitions to odd quanta of $\nu 40$. Such transitions are forbidden according to the usual $9\leftrightarrow u$ slection rule of Raman spectroscopy. Here we consider the theory of the intensity of such transitions allowing for the fact that the excited state is twisted by $90\circ$ at equilibrium, using Hougen#### double group $theoryc$. From approximate one dimensional torsional potensials of the $V$ and $N$ electronic states, it is shown that good qualitative agreement between observed and calculated intensities is obtained. The electronic transition moment is assumed to be proportional to cos$\theta$, where $\theta$ is the torsional angle, but the calculated relative intensities are not sensitive to the precise torsional dependence. More detailed theory will require consideration of the avoided crossing affecting the $V$ $stated$.