Vibronic—Spin-Orbit Perturbations and the Assignment of the Lowest Triplet State of Benzene

Abstract

Second-order perturbation theory in electron configuration and spin space using both vibronic and spin-orbit perturbations reveals a number of routes for bringing dipole allowed character into a spin-forbidden transition. Apart from direct spin-orbit interaction, there are three additional mechanisms: (1) direct spin-vibronic coupling (a very weak, though first-order term), (2) spin-orbit coupling with vibronic coupling in the singlet manifold, and (3) vibronic coupling in the triplet manifold with spin-orbit coupling. In the case of benzene, vibrational analysis alone of the phosphorescence spectrum can neither discern the route for bringing allowed singlet character into the triplet state nor can it lead to an assignment of that state. It happens that polarized luminescence data are able to show that route (3) is dominant, and, given this, vibrational analysis leads to a 3B1u assignment. The vibronic characteristics of the various routes are discussed. Estimates are made of the relative importance of the various routes based on energy considerations within the framework of second-order perturbation theory. Approximate oscillator strengths are obtained and compared with the experimental value showing, independently, that route (3) is dominant and that the assignment must be 3B1u. Other possible examples where mixed vibronic—spin-orbit terms are important to phosphoresence are mentioned suggesting the fruitfulness of detailed polarized phosphorescence experiments, both to aid in assigning excited states and to test vibronic theories.