Adiabatic elimination in multidimensional diffusive barrier crossing

We consider the (reaction-coordinate) viscosity dependence of reaction-rate coefficients for the two-dimensional Agmon-Kosloff surface. We show that rate coefficients calculated from the Agmon-Hopfield sink-Smoluchowski equation are a lower bound, approaching asymptotically the two-dimensional result for fast reactive-mode diffusion. A modified equation, employing an effective potential in the spirit of a recent suggestion by the Karpov group, yields a promising approximation over most of the viscosity range.