Temperature dependent reaction coordinates

Temperature-dependent reaction-coordinates are investigated using Brownian dynamics. A functional of the reaction coordinate, which does not have explicit time dependence, is derived. The path that minimizes the functional is defined as the reaction coordinate. The optimal coordinate varies from the steepest descent path at zero temperature to a straight line connecting “reactants” and “products” at high temperatures. An estimate of the time scale of the process is an output of the optimization. A numerical example is provided and adjustments for the Stratonovich calculus are discussed.