A Review of Recent Phase Transition Simulation Methods: Transition Path Search

Abstract

In this paper, we give a review of recent transition path search methods for nanoscale phase transition simulation A potential energy surface (PES) characterizes detailed information about phase transitions where the transition path is related to a minimum energy path on the PES. The minimum energy path connects reactant to product via saddle point(s) on the PES. Once the minimum energy path is generated, the activation energy required for transitions can be determined. Using transition state theory, one can estimate the rate constant of the transition. The rate constant is critical to accurately simulate the transition process with sampling algorithms such as kinetic Monte Carlo. NOMENCLATURE PESPotential energy surface MEP Minimum energy path Q O Vector of the molecular conformation of the reactant in reaction coordinates on the PES with respect to its time (t) in the reaction i.e. t=0 Q F Vector of the molecular conformation of the product in reaction coordinates on the PES with respect to its time (t) in the reaction i.e. t=F Q X Vector of the molecular conformation of a point in reaction coordinates on the PES with respect to its time (t) in the reaction i.e. t=X V Potential Energy ∇ Gradient INTRODUCTIONIn this paper, we give a review of recent transition path search methods for nanoscale phase transition simulation. It is not in the scope of this review to compare the methods against each other. Rather, we aim to provide the reader with the essence of each method reviewed. A phase transition is a geometric and topological transformation process of materials from one phase to another, each of which has a unique and homogeneous physical property. The most important step involved in modeling phase transition is the knowledge of the activation energy barrier and rate constant involved in the transition.In 1931, Erying and Polanyi proposed the transition state theory (TST) as a means to calculate the activation energy and rate constants [1,2] for characterizing reactions. An activation energy barrier always exists between phases. This activation energy characterizes the transition state. The methods reviewed are built on the theory prescribed by TST or some variants of TST (Variational Transition State Theory [3] and Reaction Path Hamiltonian [4])In an effort to simulate a reaction or transition, a potential energy surface (PES) that characterizes the process is first generated. Then, a minimum energy path (MEP) is computed which represents the transition pathway in the reaction coordinate space. Finally, the activation energy and rate constant that define the speed of the process (the rate of the reaction) can be calculated using TST and information about the saddle point(s).

An Efficient Saddle Point Search Method Using Kriging Metamodels

“…Refs. [5][6][7][8] provide a detailed review. The existing saddle point search methods can generally be categorized into two groups: single-ended methods and double-ended methods.…”

“…A number of methods [5][6][7][8] that search for saddle points on a PES have been developed. However, they require a large number of costly functional evaluations, which is usually conducted by first-principles such as using the density functional theory (DFT).…”

Controlled Kinetic Monte Carlo Simulation for Computer-Aided Nanomanufacturing

“…During KMC simulation, discrete events are generated and fired sequentially based on their respective probabilities of occurrence, which are exponential distributions in general. The transition rate (also called propensity function) a j from current state to state j is a j ¼ j expðÀDE j =k B TÞ, where k B is the Boltzmann constant, T is the temperature, DE j is the energy barrier between the current state and state j, and j is the pre-exponential factor that can be measured or calculated from the vibrational frequencies, e.g., based on the harmonic transition state theory [19,20].…”

A Concurrent Search Algorithm for Multiple Phase Transition Pathways

“…A number of methods [4,5] already exist to search the transition path and saddle points on a PES. All of the current methods need the prior knowledge of either the reactant or product, or both, in order to search a MEP.…”