Dynamics of two-dimensional diffusional barrier crossing

The time-dependent diffusion equation is solved directly, by a new numerical algorithm, for a two-dimensional potential energy surface. The dynamics gives a qualitative description of isomerization reactions in solution. Along the reaction coordinate, the potential has a double-well shape, and the diffusion coefficient is inversely proportional to solvent viscosity. Along the perpendicular coordinate there are also two wells, the barrier height varies and the diffusion coefficient is assumed independent of viscosity. Under these conditions, in the high-viscosity regime, the diffusional flux can bypass the reaction-coordinate barrier, achieving a higher reaction rate. The calculated rate coefficient shows a non-Kramers, fractional viscosity dependence, in agreement with the isomerization experiments.