Ridge-based bias potentials to accelerate molecular dynamics.

An effective way to accelerate rare events in molecular dynamics simulations is to apply a bias potential which destabilizes minima without biasing the transitions between stable states. This approach, called hyperdynamics, is limited by our ability to construct general bias potentials without having to understand the reaction mechanisms available to the system, a priori. Current bias potentials are typically constructed in terms of a metric which quantifies the distance that a trajectory deviates from the reactant state minimum. Such metrics include detection of negative curvatures of the potential, an energy increase, or deviations in bond lengths from the minimum. When one of these properties exceeds a critical value, the bias potentials are constructed to approach zero. A problem common to each of these schemes is that their effectiveness decreases rapidly with system size. We attribute this problem to a diminishing volume defined by the metrics around a reactant minimum as compared to the total volume of the reactant state basin. In this work, we mitigate the dimensionality scaling problem by constructing bias potentials that are based upon the distance to the boundary of the reactant basin. This distance is quantified in two ways: (i) by following the minimum mode direction to the reactant boundary and (ii) by training a machine learning algorithm to give an analytic expression for the boundary to which the distance can be calculated. Both of these ridge-based bias potentials are demonstrated to scale qualitatively better with dimensionality than the existing methods. We attribute this improvement to a greater filling fraction of the reactant state using the ridge-based bias potentials as compared to the standard potentials.