The vibronically induced phosphorescence in benzene

Abstract

The phosphorescence spectrum of benzene is particularly rich in vibronic structure and provides the best-known example of a spectrum of electronic transitions that by symmetry is both spin and orbital forbidden. Such transitions, only allowed through the coupling of nuclear and electronic motions, are notoriously difficult to analyze both on theoretical and experimental grounds. We investigate the vibronically induced phosphorescence by means of multi-configuration quadratic response theory calculations and explore vibronic intensities, polarization directions, transition moments for benzene phosphorescence and the radiative lifetime of triplet benzene. We find that the radiative decay of the 3B 1u state takes place predominantly through vibronic coupling among the e 2g CC stretching modes ν 8=1601 cm −1 and ν 9=1178 cm −1, with a close to complete out-of-plane polarization. The calculations predict relative intensities of different vibronic bands in good agreement with experiment. The oscillator strength for the 3B 1u← 1A 1g absorption is predicted to 0.74×10 −10, to be compared with the experimental value of ≈10 −10. The computed averaged radiative lifetime falls in the interval of 22 to 96 seconds, depending on the quality of the basis set, with the best prediction being 64 seconds.