Knowledge Bank

The radiative rate constants of diphenylhexatriene and transretinol are calculated from published values of the fluorescence lifetime and quantum $yield.1,2$ The variations in the calculated rate constants with solvent and temperature are quantitatively explained by a theoretical expression, relating the radiative rate constant of a forbidden transition to the amount of mixing with a single allowed $transition.3$ The mixing is inversely proportional to the energy separation of the two states. Increasing the solvent polarizability decreases the energy gap leading to increased mixing. Extension of a relation between radiative lifetime and absorption $intensity4$ permits an estimate of the energy gap between the states and the magnitude of the mixing matrix element.