Spin–Orbit Coupling in Aromatic Hydrocarbons. Analysis of Nonradiative Transitions between Singlet and Triplet States in Benzene and Naphthalene

Rate expressions for intersystem crossings in aromatic hydrocarbons are formulated by treating both the spin–orbit coupling and the nuclear kinetic-energy operators as perturbations causing the nonradiative transition. General expressions are derived for the corresponding matrix elements, which are shown to fall into three groups, corresponding to three different mechanisms. In the first, which is subject to an electronic orbital selection rule, the transition is caused by spin–orbit coupling only. In the second and third, spin–orbit coupling and vibronic coupling act together, namely, Herzberg–Teller vibronic coupling in the second, and diabatic (non-Born–Oppenheimer) coupling, caused by the nuclear momenta, in the third mechanism. It is shown that in aromatic hydrocarbons spin–orbit coupling between π states governs the second mechanism and spin–orbit coupling between π and σ states the third mechanism. The three mechanisms are distinguished by the effect of partial deuteration on the rate constant, which may or may not give rise to a position-dependent deuterium effect, and by the different rate constants associated with the three sublevels of the triplet state. From these observations and quantitative calculations of the spin–orbit and vibronic matrix elements in benzene and naphthalene, it is concluded that in naphthalene T1↝S0 is governed by the third mechanism, and that in benzene the first and second mechanism may play a role in S1↝T1 and T1↝S0, respectively.