Theoretical and Experimental Investigation of the Electronic Propensity Rule: A Linear Relationship between Radiative and Nonradiative Decay Rates of Molecules

The electronic propensity rule, which suggests a proportional relationship between radiative and nonradiative electronic coupling elements in fluorescent molecules, has been postulated for some time. Despite its potential significance, the rule has not been rigorously derived and experimentally validated. In this work, we draw upon the theoretical framework established by Schuurmans et al. for the relation between the radiative and nonradiative electronic coupling elements of the rare earth metal in the crystal at low temperature and extend their approach to the fluorescent molecules under external electric field perturbation at a fixed energy gap and varied temperatures, with a further single-electron approximation (Schuurmans, M. F. H., et al. Physica B & C1984, 123, 131-155). We obtained a linear relation between the radiative decay rates and nonradiative decay rates for internal conversion, which is verified by experimental data from two types of dextran-dye complexes and the light-harvesting antenna complex in photosynthetic bacteria.