A Concurrent Search Algorithm for Multiple Phase Transition Pathways

Abstract

The challenge of accurately predicting a phase transition in computer-aided nano-design is estimating the true value of transition rate, which is determined by the saddle point with the minimum energy barrier between stable states on the potential energy surface (PES). In this paper, a new algorithm for searching the minimum energy path (MEP) is presented. Unlike existing pathway search methods, the new algorithm is able to locate both the saddle points and local minima simultaneously. Therefore no prior knowledge of the precise positions for the reactant and product on the PES is required. In addition, the algorithm is able to search multiple transition paths on the PES simultaneously. In this method, a Bézier curve is used to represent each transition path. Starting from a single Bézier curve, multiple curves with ends connected can be generated during the search process. For each Bézier curve, the reactant and product states are located by minimizing the two end control points of the curve, while the transition pathway is refined by moving the intermediate control points of the curve in the conjugate directions. A curve subdivision scheme is developed so that multiple transition paths can be located. The algorithm is demonstrated by examples.