Stochastic formalism for thermally driven distribution frontier: A nonempirical approach to the potential escape problem

Abstract

We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the potential valleys. This method employs only the local gradient and diagonal part of the Hessian matrix of the potential. An application to a two-dimensional model potential is presented to demonstrate the successful finding of the paths to the saddle points. The present scheme could serve as a starting point toward first-principles simulation of rare events across the potential basins free from empirical collective variables.

arXiv comment5 pages, 3 figures; submitted

References in corpus (9)

• Escaping free-energy minima
• Sampling rare switching events in biochemical networks
• Direct evaluation of large-deviation functions
• Simulating rare events in dynamical processes
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Population dynamics method with a multi-canonical feedback control
• The instanton method and its numerical implementation in fluid mechanics
• Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
• Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process

Cited by in corpus (2)

• Non-empirical weighted Langevin mechanics for the potential escape problem: parallel algorithm and application to the Argon clusters
• AtomREM: Non-empirical seeker of the minimum energy escape paths on many-dimensional potential landscapes without coarse graining