Mathematical foundations of Accelerated Molecular Dynamics methods
For computational chemists and physicists, this work provides a theoretical foundation for widely used accelerated dynamics methods, though it is a review of existing results rather than novel contributions.
This review presents rigorous mathematical justification for Accelerated Molecular Dynamics methods, showing that exit events from metastable states can be modeled by kinetic Monte Carlo and parameterized using Eyring-Kramers formulas, providing a foundation for analyzing and improving these algorithms.
The objective of this review article is to present recent results on the mathematical analysis of the Accelerated Dynamics algorithms introduced by A.F. Voter in collaboration with D. Perez and M. Sorensen. Using the notion of quasi-stationary distribution, one is able to rigorously justify the fact that the exit event from a metastable state for the Langevin or overdamped Langevin dynamics can be modeled by a kinetic Monte Carlo model. Moreover, under some geometric assumptions, one can prove that this kinetic Monte Carlo model can be parameterized using Eyring-Kramers formulas. These are the building blocks required to analyze the Accelerated Dynamics algorithms, to understand their efficiency and their accuracy, and to improve and generalize these techniques beyond their original scope.