A forward flux sampling based iterative method to reconstruct recrossing eliminated evaluation of reaction rate

Abstract

Rare events are a common yet challenging topic in many fields of interest. Among many importance-sampling-based rare event simulation methods, forward flux sampling (FFS), established on the effective positive flux framework, is a widely used rare event sampling method due to its simplicity and less restrictive nature. FFS is commonly assumed to work well under diffusive regimes, whereas for correlated systems, the initial flux simulation needs to be either sufficiently long or initiated from multiple uncorrelated starting points to sample a sufficient number of uncorrelated points, and the short timescale recrossing over the energy barrier may result in a potentially overestimated reaction rate. To solve the above-mentioned problems, the author(s) propose an iterative method by regarding the space of the initial outgoing trajectory distribution as the state space of a discrete time Markov Chain (DTMC) process. Upon convergence of the DTMC process by iteratively applying the probability kernel, the initial outgoing trajectory distribution converges to the stationary distribution, and the associated measurable converges to the expected value. Numerical results show that the system is able to converge to its stationary distribution with poor initial outgoing trajectory distribution leading to either orders of magnitude higher or lower estimations of reaction rate compared to its expected value. Meanwhile, the proposed method is able to obtain the recrossing free reaction rate in strongly correlated systems, which could be an order of magnitude smaller than that obtained via the standard FFS method.