Effect of Spin–Orbit Interactions on Radiative Triplet–Singlet Transitions in Aromatic Hydrocarbons

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Abstract
The 3(ππ*) → 1(ππ) phosphorescence spectra of many aromatic hydrocarbons are out-of-plane polarized. The electric-dipole transition moment due to the indicated mechanism of σπ singlet–triplet mixing by the spin–orbit interaction is calculated as the sum of contributions from σπ excitations of the individual localized σ bonds. The singlet 1(ππ) is mixed with triplets produced by σ → π* and π → σ* excitations of 1(ππ). The triplet 3(ππ*) is mixed with singlets produced by σ → π and π* → σ* excitations of 3(ππ*). A general expression is obtained for the radiative triplet–singlet transition probability in terms of the π-electron charge distribution in the ground and triplet states. Semiempirical estimates of the σπ transition energies and other parameters in the expression for the transition moment give order-of-magnitude agreement between the computed and observed triplet-state lifetimes.