Theory of electronic relaxation in solution in the absence of an activation barrier

Abstract

We present a theory which describes the effects of viscosity on those electronic relaxation processes in solution in which the intramolecular potential surface does not present a barrier to the motion leading to the decay of the initially formed excited state. We model the reactive motion as the motion of a solute particle on the excited state potential surface with a position dependent sink which gives rise to the decay of the excited state population. Three different types of sinks are considered: (A) a pinhole sink at the minimum of the potential surface; this models the situation when the molecule decays to ground state as soon as it reaches the potential minimum; (B) a Gaussian sink with probability of decay maximum at the potential minimum; (C) a Lorentzian sink with maximum decay at the potential minimum. For case (A) an explicit analytic solution is obtained for the decay rate, but for cases (B) and (C) we obtained the decay rate numerically. Model (A) predicts nonexponential decay at all viscosities except at long times when the decay is single exponential. For cases (B) and (C) the decay is single exponential at low viscosities but becomes multiexponential at high viscosities. We show that the experimentally observed fractional viscosity dependence of fluorescence quantum yield arises naturally in this theory due to the position dependence of the sink as well as due to the competition between radiative and nonradiative relaxation. Our model also predicts a crossover from an apparent negative (constant viscosity) activation energy at low viscosities to a positive activation energy at high viscosity. The physical significance of these results is discussed in light of the available experimental results on TPM dye relaxation. Some possible generalizations of our theory to more realistic cases are indicated.