Practical and conceptual path sampling issues

Abstract

In the past 15 years transition path sampling (TPS) has evolved from its basic algorithm to an entire collection of methods and a framework for investigating rare events in complex systems. The methodology is applicable to a wide variety of systems and processes, ranging from transitions in small clusters or molecules to chemical reactions, phase transitions, and conformational changes in biomolecules. The basic idea of TPS is to harvest dynamical unbiased trajectories that connect a reactant with a product, by a Markov Chain Monte Carlo procedure called shooting. This simple importance sampling yields the rate constants, the free energy surface, insight in the mechanism of the rare event of interest, and by using the concept of the committor, also access to the reaction coordinate. In the last decade extensions to TPS have been developed, notably the transition interface sampling (TIS) methods, and its generalization multiple state TIS. Combination with advanced sampling methods such as replica exchange and the Wang-Landau algorithm, among others, improves sampling efficiency. Notwithstanding the success of TPS, there are issues left to discuss, and, despite the method's apparent simplicity, many pitfalls to avoid. This paper discusses several of these issues and pitfalls: the choice of stable states and interface order parameters, the problem of positioning the TPS windows and TIS interfaces, the matter of convergence of the path ensemble, the matter of kinetic traps, and the question whether TPS is able to investigate and sample Markov state models. We also review the reweighting technique used to join path ensembles. Finally we discuss the use of the sampled path ensemble to obtain reaction coordinates.