One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions

For multidimensional activated rate processes controlled by diffusive crossing of a saddle point region, we show that a one-dimensional reaction coordinate can be constructed even when the diffusion anisotropy is arbitrary. The rate constant, found using the potential of mean force along this coordinate, is identical to that predicted by the multidimensional Kramers-Langer theory. This reaction coordinate minimizes the one-dimensional rate constant obtained using a trial reaction coordinate and is orthogonal to the stochastic separatrix, the transition state that separates reactants from products.