Abstract
Transition path sampling is a powerful tool in the study of rare events. Shooting trial trajectories from configurations along existing transition paths proved particularly efficient in the sampling of reactive trajectories. However, most shooting attempts tend not to result in transition paths, in particular in cases where the transition dynamics has diffusive character. To overcome the resulting efficiency problem, we developed an algorithm for "shooting from the top." We first define a shooting range through which all paths have to pass and then shoot off trial trajectories only from within this range. For a well chosen shooting range, nearly every shot is successful, resulting in an accepted transition path. To deal with multiple mechanisms, weighted shooting ranges can be used. To cope with the problem of unsuitably placed shooting ranges, we developed an algorithm that iteratively improves the location of the shooting range. The transition path sampling procedure is illustrated for models of diffusive and Langevin dynamics. The method should be particularly useful in cases where the transition paths are long so that only relatively few shots are possible, yet reasonable order parameters are known.
Highlights
Dynamics in complex systems is often dominated by rare events, from the nucleation of crystals to the folding of proteins.1,2 The typical waiting time for the events of interest is much longer than the event itself
We described an algorithm that uses shooting ranges to improve the efficiency in transition path sampling of rare events
The key idea is that shooting off trajectories from points in the transition state region is more likely to produce transition paths than shooting trajectories from points close to the reactant and product states
Summary
Dynamics in complex systems is often dominated by rare events, from the nucleation of crystals to the folding of proteins. The typical waiting time for the events of interest is much longer than the event itself. Even if it is technically possible to propagate large systems long enough in simulation time to witness a rare event, this direct sampling is not efficient when the relevant transition makes up only a tiny fraction of the trajectory. Transition path sampling (TPS) tries to overcome the disparity of time scales through importance sampling in trajectory space.. A point along an existing TP is chosen at random, its velocities are perturbed, and trajectory segments are propagated forward and backward in time starting from the perturbed phase point. If the two trajectory segments end up in different metastable states, the new path is accepted, after reversing time on the backward segment.
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