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Variable-cell double-ended surface walking method for fast transition state location of solid phase transitions.

To identify the low energy pathway for solid-to-solid phase transition has been a great challenge in physics and material science. This work develops a new theoretical method, namely, variable-cell double-ended surface walking (VC-DESW) to locate the transition state (TS) and deduce the pathway in solid phase transition. Inherited from the DESW method ( J. Chem. Theory Comput. 2013 , 9 , 5745 ) for molecular systems, the VC-DESW method implements an efficient mechanism to couple the lattice and atom degrees of freedom. The method features with fast pseudopathway building and accurate TS location for solid phase transition systems without requiring expensive Hessian computation and iterative pathway optimization. A generalized coordinate, consisting of the lattice vectors and the scaled atomic coordinates, is designed for describing the crystal potential energy surface (PES), which is able to capture the anisotropic behavior in phase transition. By comparing with the existing method for solid phase transition in different systems, we show that the VC-DESW method can be much more efficient for finding the TS in crystal phase transition. With the combination of the recently developed unbiased stochastic surface walking pathway sampling method, the VC-DESW is further utilized to resolve the lowest energy pathway of SiO2 α-quartz to quartz-II phase transition from many likely reaction pathways. These new methods provide a powerful platform for understanding and predicting the solid phase transition mechanism and kinetics.