Calculations of resonance Raman cross sections in forbidden electronic transitions: Scattering of the 992 cm−1 mode in the 1B2u band of benzene

Strictly dipole forbidden electronic states are shown to be possible sources of Raman cross section for the scattering of totally symmetric fundamentals. In particular, the absolute scattering cross section and depolarization ratio of the 992 cm−1 a1g mode in benzene are calculated in the region of the electronically forbidden 1B2u transition. The molecular polarizability in this region is derived from two principle sources. One is the preresonance contribution of an effective electronic transition in the deep vacuum ultraviolet. The other is due to contributions from the vibrational substructure of the 1B2u transition which vary in sign. Interference effects lead to interesting resonance profiles for both the scattering cross section and the depolarization ratio. The in-resonance contributions to the polarizability are determined by a semiempirical approach to the summation over all vibrational subspaces. The damping constant need not serve as an artifical breadth parameter when that breadth is not lifetime limited. Once the complete vibrational subspace has been included in the theory much smaller values of the damping constant than previously used can be accommodated.