Stochastic surface walking method for crystal structure and phase transition pathway prediction.

The determination of crystal structures and the solid-to-solid phase transition mechanisms are two important and related subjects in material science. Here we develop an unbiased general-purpose potential energy surface (PES) searching method, namely, SSW-crystal method, for prediction of both the crystal structure and the crystal phase transition pathway. The SSW-crystal method features with stochastic surface walking (SSW) via repeated small structural perturbation by taking into account the second derivative information on both the lattice and the atom degrees of freedom. The SSW-crystal method is capable of overcoming the high barrier of phase transition and identifying the desirable phase transition reaction coordinates. By applying the SSW-crystal method to a set of examples, including SiO2 crystal up to 162 atoms per cell, Lennard-Jones model crystals up to 256 atoms, ternary SrTiO3 crystal of 50 atoms and the rutile-to-anatase TiO2 phase transition, we show that the SSW-crystal method can efficiently locate the global minimum (GM) from random initial structures without a priori knowledge of the system, and also allows for exhaustive sampling of the phase transition pathways, from which the lowest energy pathway can be obtained.