Monte Carlo Sampling in Path Space: Calculating Time Correlation Functions by Transforming Ensembles of Trajectories

Computational studies of processes in complex systems with metastable states are often complicated by a wide separation of time scales. Such processes can be studied with transition path sampling, a computational methodology based on an importance sampling of reactive trajectories capable of bridging this time scale gap. Within this perspective, ensembles of trajectories are sampled and manipulated in close analogy to standard techniques of statistical mechanics. In particular, the population time correlation functions appearing in the expressions for transition rate constants can be written in terms of free energy differences between ensembles of trajectories. Here we calculate such free energy differences with thermodynamic integration, which, in effect, corresponds to reversibly changing between ensembles of trajectories.