THEORY OF ODD TORSIONAL TRANSITIONS IN THE V-N RESONANCE RAMAN-SPECTRUM OF ETHYLENE

The V-N resonance Raman spectrum of ethylene shows a long progression in even quanta of the ground-state torsional mode v(4)''(a(u)). Bands approximately midway between the even quanta have been assigned to tra nsitions to odd quanta of v(4)'', although such transitions are forbid den according to the usual g negated left right arrow u selection rule of Raman spectroscopy. We consider the theory of the intensity of suc h transitions allowing for the fact that the excited state is twisted by 90 degrees at equilibrium, using Hougen's double group theory for t he separation of the torsional and a-rotational motions. From approxim ate one-dimensional torsional potentials of the V and N electronic sta tes, it is shown that qualitative agreement between observed and calcu lated intensities is obtained. The electronic transition moment is ass umed to be proportional to cos2 gamma, where 2 gamma is the torsional angle, but the calculated relative intensities are not sensitive to th e precise torsional dependence. More detailed theory will require incl usion of the CC-stretching and CH2-scissoring degrees of freedom and c onsideration of an avoided crossing affecting the V state.