On the calculation of reaction rate constants in the transition path ensemble

We present improved formulas for the calculation of transition rate constants in the transition path ensemble. In this method transition paths between stable states are generated by sampling the distribution of paths with a Monte Carlo procedure. With the new expressions the computational cost for the calculation of transition rate constants can be reduced considerably compared to our original formulation. We demonstrate the method by studying the isomerization of a diatomic molecule immersed in a Weeks–Chandler–Andersen fluid. The paper is concluded by an efficiency analysis of the path sampling algorithm.