A Theoretical Study of the Radiationless Decay Mechanism of Cyclic Alkenes in the Lowest Triplet State

Abstract

The radiationless decay mechanisms of cyclic alkenes CnH2n-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.