A theoretical study of the radiationless decay mechanism of cyclic alkenes in the lowest triplet state

The radiationless decay mechanisms of cyclic alkenes C_nH_2n-2 (n = 4, 5, 6), norbornene, their phenyl derivatives, and styrene in their lowest triplet state have been investigated by unrestricted density functional, ab initio CASSCF, and MRD-CI calculations. The potential energy surfaces of the ground (S₀) and lowest triplet state (T₁) have been explored along double bond twisting and anti pyramidalization reaction pathways to explain the experimentally observed inverse proportionality between ring size and triplet-state lifetime. The calculations for the transition probabilities between T₁ and S₀ states are based on Fermi's golden rule including spin-orbit coupling (SOC) constants. According to the older "free-rotor model", the hindered twist around the double bond in small ring alkenes has been assumed so far to be the main factor determining the T₁-state lifetimes. All computational results show, however, that only a combined reaction coordinate of anti pyramidalization and twisting at the double bond provides a low-energy pathway which reproduces the experimentally observed transition probabilities. For the relative transition rates, the different Franck-Condon (FC) factors in the series of compounds are found to be much more important than the SOC constants (FC-controlled mechanism). On the basis of the theoretical model, the effect of substitution of vinylic hydrogen atoms by phenyl groups is discussed.