EÅ cient schemes to compute diÄ usive barrier crossing rates

The formulation of the classical barrier-crossing problem is reviewed in the context of numerical simulations, with the focus on barrier crossing problems where the reaction coordinate depends in a non-trivial way on the Cartesian coordinates of many particles. Often it is convenient to measure the barrier height using constrained dynamics. Such a calculation requires a knowledge of the Jacobian for the coordinate transformation between Cartesian and generalized (`reaction’) coordinates, and it is shown that the calculation of this Jacobian can be simpli® ed. The conventional expression for the crossing rate is found to become computationally ineA cient when the barrier crossing is diA usive. An alternative formulation of the barrier-crossing rate is given that leads to much better statistical accuracy in the computed crossing rates.