The phosphorescence of benzene obtained by ab initio and semi-empirical calculations

Radiative decay and phosphorescence of triplet stare benzene is doubly -orbital and spin- forbidden and is only activated through vibronic coupling among the manifold of triplet states. For this reason the determination of lifetime and transition moments for the decay of triplet benzene has posed a considerable challenge to both theory and experiment. In the present work we have addressed the triplet benzene problem at several levels of theory; by truncated perturbation theory and semiempirical, CNDO/S-CI, calculations; by complete sum-over-state calculations as implemented in recent ab initio multiconfiguration quadratic response (MCQR) theory; and by direct MCQR calculations of vibronic phosphorescence. The vibronic coupling is in the two former cases treated by the Herzberg-Teller (H-T) perturbation theory, involving four main mechanisms for the phosphorescent decay of triplet benzene. The results and interpretations given by these approaches as well as their merits and limitations are presented and discussed in some detail. Our calculations indicate that the phosphorescent decay of the³B_{1 u} state takes place predominantly through vibronic coupling along the e_{2 g} mode. We obtain a phosphorescence that is almost completely out-of-plane polarized, which is in line with more recent measurements by the microwave-induced delayed phosphorescence technique, and could reproduce quite well the intensity ratios for different vibronic bands obtained in that experiment. The final triplet state lifetime is the result of a delicate sum of contributions from several vibronic degenerate and non-degenerate modes. The direct vibronic phosphorescence calculations predict a long lifetime, about one minute - 68 seconds for the best wavefunction - and seem to focus on a doubling of the assumed, albeit not established, "best experimental" value for the radiative lifetime of triplet benzene; {reversed tilde equals} 30 seconds.