Crystal structure prediction of materials with high symmetry using differential evolution

Abstract

Crystal structure determines properties of materials. With the crystal structure of a chemical substance, many physical and chemical properties can be predicted by first-principles calculations or machine learning models. Since it is relatively easy to generate a hypothetical chemically valid formula, crystal structure prediction becomes an important method for discovering new materials. In our previous work, we proposed a contact map-based crystal structure prediction method, which uses global optimization algorithms such as genetic algorithms to maximize the match between the contact map of the predicted structure and the contact map of the real crystal structure to search for the coordinates at the Wyckoff positions (WP), demonstrating that known geometric constraints (such as the contact map of the crystal structure) help the crystal structure reconstruction. However, when predicting the crystal structure with high symmetry, we found that the global optimization algorithm has difficulty to find an effective combination of WP that satisfies the chemical formula, which is mainly caused by the inconsistency between the dimensionality of the contact map of the predicted crystal structure and the dimensionality of the contact map of the target crystal structure. This makes it challenging to predict the crystal structures of high-symmetry crystals. In order to solve this problem, here we propose to use PyXtal to generate and filter random crystal structures with given symmetry constraints based on the information such as chemical formulas and space groups. With contact map as the optimization goal, we use differential evolution algorithms to search for non-special coordinates at the WP to realize the structure prediction of high-symmetry crystal materials. Our experimental results show that our proposed algorithm CMCrystalHS can effectively solve the problem of inconsistent contact map dimensions and predict the crystal structures with high symmetry.

Keywords: crystal materials; crystal structure prediction; differential evolution; global optimization; materials.