Does reaction path curvature play a role in the diffusion theory of multidimensional activated rate processes?

The two-dimensional Kramers' barrier crossing problem in the overdamped (diffusion) limit is investigated with particular attention given to possible effects of the geometry of the potential surface on the rate. Previous work ascribes corrections to the two-dimensional Kramers' formula to curvature of the reaction path. In contrast, we find that these corrections are due to the anharmonicity of the potential surface at the saddle and may become appreciable for small window frequency, i.e., flat potential surface at the saddle in the direction perpendicular to the reaction path. A general formalism to calculate such corrections is described.