Non-equilibrium Trajectory Sampling (NETS) method for generating free-energy landscapes and steady-state distributions

Abstract

This study presents a novel method for constructing free-energy profiles and steady-state distributions from either equilibrium or non-equilibrium trajectories along a defined reaction coordinate. The method works by tracking the final states of a swarm of short simulations launched under different initial conditions with no prior knowledge of the free energy landscape. Subsequently, this trajectory information is used to build a transition matrix whose primary eigenvector captures the steady-state occupation probability for each value of the reaction coordinate, yielding the free energy profile in equilibrium. This innovative method holds potential for many new materials and engineering applications where it is desired to know the free energy of rate-limiting configurations as may be relevant for transport processes (in, e.g., battery electrolytes and nano-filtration membranes), complexation (in, e.g., self-assembly and ligand-binding interactions), or in tuning properties such as adsorption. We illustrate the effectiveness of the method by capturing the free energy associated with a one-dimensional barrier potential modeling a separation membrane and the particle distribution associated with thermophoresis under a temperature gradient. Further extensions and applications of the method are also discussed.