Fractional Viscosity Dependence of Relaxation Rates and Non-Steady-State Dynamics in Barrierless Reactions in Solution

A finite decay model of barrierless electronic relaxation in solution is studied both analytically and numerically. The fractional viscosity $(\eta)$ dependence of the rate $(k\propto \eta^{-\alpha} with 1 > \alpha > 0)$ is shown to be strongly correlated with non-steady-state dynamics on the reaction potential surface. We also find that the exponent \alpha may depend strongly on the wavelength of the exciting light