Transition Path Sampling

Abstract

Often, the dynamics of complex condensed materials is characterized by the presence of a wide range of different time scales, complicating the study of such processes with computer simulations. Consider, for instance, dynamical processes occurring in liquid water. Here, the fastest molecular processes are intramolecular vibrations with periods in the 10-20 fs range. The translational and rotational motions of water molecules occur on a significantly longer time scale. Typically, the direction of translational motion of a molecule persist for about 500 fs, corresponding to 50 vibrational periods. Hydrogen bonds, responsible for many of the unique properties of liquid water, have an average lifetime of about 1 ps and the rotational motion of water molecules stays correlated for about 10 ps. Much longer time scales are typically involved if covalent bonds are broken and formed. For instance, the average lifetime of a water molecule in liquid water before it dissociates and forms hydroxide and hydronium ions is on the order of 10 hours. This enormous range of time scales, spanning nearly 20 orders of magnitude, is a challenge for the computer simulator who wants to study such processes.

Nonequilibrium ab initio molecular dynamics determination of Ti monovacancy migration rates in B1 TiN

“…Transition path sampling (TPS) [65][66][67] and transition interface sampling (TIS) [68,69] are examples of techniques employing the PSS. Both can provide the occurrence-probability of reaction pathways connecting known initial and final states by following any possible trajectory.…”

Elaborating Transition Interface Sampling Methods

“…which is identical to the weight for a path in the TPS-ensemble [14] with x −τ b ∆t instead of x 0 . Note that so far, we have assumed nothing about the nature of dynamics (irreversible or reversible, stochastic or deterministic).…”

“…In this appendix we derive the acceptance probability for the shooting algorithm for arbitrary dynamics along the same lines as in Ref. [14]. At start, we try to be as general as possible making the least possible assumptions on the type of dynamics or on whether the system is in equilibrium or not.…”

Metastability, conformation dynamics, and transition pathways in complex systems

“…The Transition Path Sampling (TPS) method, developed by Bolhuis, Chandler, Dellago, and Geissler, is a practical way of implementing such a strategy [DBG02,BCDG02].…”

“…How to implement such a procedure in practice after timediscretization of (23) -i.e. how to generate new paths with reasonable acceptance rate in a Metropolis algorithm, etc -is explained in [DBG02,BCDG02]. In principle, TPS removes all pre-assumptions about the mechanism of transition by sampling all the paths that may be involved in such transitions.…”