Environmental effects on radiative rate constants with applications to linear polyenes

An expression for the solvent dependence of the radiative rate constant of a forbidden transition in the presence of vibronic mixing is derived from perturbation theory. The case of nonpolar solvents and nonpolar fluorophores is considered. It is shown that the radiative rate constant, corrected for local field effects, depends on solvent-fluorophore dispersion interactions whose effect is to modulate the energy separation between the vibronically coupled borrowing and lending states. Analysis of radiative rate data for the linear polyenes diphenylhexatriene and trans-retinol gives quantitative agreement with theory. Other linear polyenes with larger separations between their first two excited singlet states are predicted to have radiative rates which do not vary appreciably with solvent polarizability as is observed. The procedure used to derive an expression for the solvent dependence of the radiative rate is not restricted to the linear polyenes but is generally valid.