A Review of Recent Phase Transition Simulation Methods: Saddle Point Search

A review of saddle point search methods on a potential energy surface is presented in this paper. Finding saddle points on a complex potential energy surface is the major challenge in modeling and simulating the kinetics of first-order phase transitions. Once the saddle points have been identified and the activation energy for the transition is known, one can apply the kinetic Monte Carlo method to simulate the transition process. We consider some factors while reviewing the methods, such as whether the solution is global, the knowledge of the Hessian during the search, the capability to locate multiple saddle points and higher order saddle points, the kind of approximations used for potential energy surface, if any; and the convergence of the methods.