The calculation of vibrational intensities in forbidden electronic transitions.

A method is described for the use of electronic structure and Franck-Condon factor programs in the calculation of the vibrational intensities in forbidden electronic transitions. Using the B 2B2-X 2B1 electronic transition of benzonitrile cation as a test case, transition moments were calculated using the symmetry adapted cluster/configuration interaction method at various points along the normal mode displacements of the molecule, from which transition moment derivatives were obtained. The transition moments were found to vary almost linearly with respect to the normal mode displacements. Using these, along with Franck-Condon factors, an expansion of the transition moment with respect to the normal coordinates provides a measure of vibrational intensities, including the effects of geometry change and Duschinsky rotation [Acta Physicochim. URSS 7, 551 (1937)]. Second order terms in the moment expansion are calculated, and it is determined that they must be included if the intensity of combination bands is to be properly obtained.