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

\underline{J. K. G. WATSON}, W. SIEBRAND, M. Z. ZGIERSKI, Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6.; M. PAWLIKOWSKI, Department of Computational Methods in Chemistry, Jagiellonian University, 30-060 Cracow, Poland..

The V − N resonance Raman spectrum of ethylene^{a} shows a long progression in even quanta of the groundstate torsional mode ν′′_{4}(a_{u}). Bands approximately midway between the even quanta have been assigned^{b} to transitions to odd quanta of ν′′_{4}. Such transitions are forbidden according to the usual g ↮ u selection 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^{∘} at equilibrium, using Hougen’s double group theory^{c}. From approximate onedimensional torsional potentials 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 θ, where θ 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 state^{d}.

aR. J. Sension and B. S. Hudson, J. Chem. Phys. 90, 1377 (1989).

bW. Siebrand and M. Z. Zgierski, J. Raman Spectrosc. 21, 263 (1990).

cA. J. Merer and J. K. G. Watson, J. Mol. Spectrosc. 47, 499 (1973).

dC. Petrongolo, R. J. Buenker, and S. D. Peyerimhoff, J. Chem. Phys. 76, 3655 (1982).