On the theory of barrierless electronic relaxation in solution

We report a theoretical study of the barrierless electronic relaxation in solution. The existing theoretical models are divided into two classes: (A) Instantaneous death models where the excited state decays with unit probability as soon as it attains certain critical conformations, and (B) finite decay models, where the decay from the critical geometries occur at a finite rate $(=k_0)$. All the models belonging to class (A) predict inverse friction (\zeta)dependence of the nonradiative decay rate if the radiative relaxation is neglected. These models predict that the long time decay rate is independent of the excitation wavelength although the average rate (so the quantum yield) show a strong dependence. The relaxation behavior of models (B) is controlled by the dimensionless parameter $^-_k_0(=k_0\zeta/\omega^2\mu$, where \omega is the frequency of the excited state surface and \mu is the effective mass of the reactive motion). A fractional friction dependence of the long time rate is obtained at low to intermediate values of $^-_k_0$, but an inverse friction dependence is predicted for large values of this parameter. The fractional dependence of the average rate on viscosity is found to depend critically on the wavelength of the exciting light. A small negative activation energy is found at small values of $^-_k_0$. A delta-function sink (DFS) is introduced to simplify numerical calculations. This DFS model retains the essential features of the more realistic Gaussian sink model. The DFS model is studied both analytically and numerically. We find that the asymmetry in the position of the sink function, with respect to the minimum of the excited state potential surface, can play an important (hidden) role in the relaxation process. Especially, it can give rise to a significant temperature coefficient of the rate and can lead to an erroneous conclusion on the "molecular" activation energy. Finally, systematics of fitting the experimental data to the present theories are discussed