Dominant reaction pathways in high-dimensional systems

This paper is devoted to the development of a theoretical and computational framework denominated dominant reaction pathways (DRPs) to efficiently sample the statistically significant thermally activated reaction pathways, in multidimensional systems. The DRP approach is consistently derived from the Langevin equation through a systematic expansion in the thermal energy, k_BT. Its main advantage with respect to existing simulation techniques is that it provides a natural and rigorous framework to perform the path sampling using constant displacement steps, rather than constant time steps. In our previous work, we have shown how to obtain the set of most probable reaction pathways, i.e., the lowest order in the k_BT expansion. In this work, we show how to compute the corrections to the leading order due to stochastic fluctuations around the most probable trajectories. We also discuss how to obtain predictions for the evolution of arbitrary observables and how to generate conformations, which are representative of the transition state ensemble. We illustrate how our method works in practice by studying the diffusion of a point particle in a two-dimensional funneled external potential.