Deterministic Path Search Algorithm on Free-Energy Landscape using Random Grids

Given a multidimensional free-energy or potential-energy landscape, finding reaction paths that connect an initial (or reactant) state and a final (or product) state is important for biophysics and materials science. The likelihood of a path can be evaluated using an objective function, and the most likely reaction path can be found by optimizing its objective function. However, nonlinear optimization on a complex free-energy or potential-energy landscape may lead to suboptimal solutions. In this study, this drawback is avoided using deterministic path-finding methods such as Dijkstra's algorithm on a graph by assigning grids on the coordinate system to graph nodes and relating the objective function of the path to the edge cost between the nodes. Furthermore, the use of random grids is proposed because they more accurately represent paths than regular grids. As a demonstration, the proposed method is successfully applied to find the minimum resistance path on a three-hole potential model, demonstrating that the proposed method is promising.