Radiative Triplet Lifetimes in Benzene and Azabenzenes with Particular Reference to Phosphorescence Mechanisms in Benzene

Calculations of radiative triplet lifetimes of benzene and azabenzenes are carried out by making use of an INDO/S method in which the parametrization of the CNDO/S method is used, retaining the semi-empirical Slater-Condon parameters determined in the INDO/2 method. The calculated excitation energies, oscillator strengths, and radiative lifetimes are in reasonable agreement with experimental values. The possible phosphorescence mechanisms for the 3B1u state of benzene are discussed rather in detail, considering the first-order vibronic as well as the first-order spin-orbit and the second-order spin-vibronic couplings. It is concluded that the strong first-order vibronic coupling between the triplet manifolds, 3B1u and 3E1u, is responsible for the almost purely out-of-plane polarized phosphorescence of benzene, borrowing an intensity from the 3E1u-1A1g intercombination, and that the effects of the first-order spin-orbit and the second-order spin-vibronic couplings are small. The conclusion is in accord with the analyses of the Zeeman and MI DP spectra presented by van Egmond and van der Waals.