Crystal Structure Prediction Using an Age-Fitness Multiobjective Genetic Algorithm and Coordination Number Constraints.

Crystal structure prediction (CSP) has emerged as one of the most important approaches for discovering new materials. CSP algorithms based on evolutionary algorithms and particle swarm optimization have discovered a great number of new materials. However, these algorithms based on ab initio calculation of free energy are inefficient. Moreover, they have severe limitations in terms of scalability. We recently proposed a promising crystal structure prediction method based on atomic contact maps, using global optimization algorithms to search for the Wyckoff positions by maximizing the match between the contact map of the predicted structure and the contact map of the true crystal structure. However, our previous contact-map-based CSP algorithms have two major limitations: (1) the loss of search capability due to getting trapped in local optima; (2) it only uses the connection of atoms in the unit cell to predict the crystal structure, ignoring the chemical environment outside the unit cell, which may lead to unreasonable coordination environments. Herein, we propose a novel multiobjective genetic algorithm for contact-map-based crystal structure prediction by optimizing three objectives, including contact map match accuracy, individual age, and coordination number match. Furthermore, we assign the age values to all the individuals of the GA and try to minimize the age, aiming to avoid the premature convergence problem. Our experimental results show that compared to our previous CMCrystal algorithm, our multiobjective crystal structure prediction algorithm (CMCrystalMOO) can reconstruct the crystal structure with higher quality and alleviate the problem of premature convergence. The source code is open sourced and can be accessed at https://github.com/usccolumbia/MOOCSP.

Distance Matrix-Based Crystal Structure Prediction Using Evolutionary Algorithms.

Crystal structure prediction (CSP) for inorganic materials is one of the central and most challenging problems in materials science and computational chemistry. This problem can be formulated as a global optimization problem in which global search algorithms such as genetic algorithms (GAs) and particle swarm optimization have been combined with first-principles free-energy calculations to predict crystal structures given only the material composition or a chemical system. These DFT-based ab initio CSP algorithms are computationally demanding and can usually be used only to predict crystal structures of relatively small systems. The vast coordinate space and the expensive DFT free-energy calculations limit their inefficiency and scalability. On the other hand, a similar structure prediction problem has been intensively investigated in parallel in the protein structure prediction (PSP) community of bioinformatics, in which the dominating predictors are knowledge-based approaches including homology modeling and threading that exploit known protein structures. Surprisingly, the CSP field has mainly focused on ab initio approaches in the past decade. Inspired by the knowledge-rich PSP approaches, herein, we explore whether known geometric constraints such as the pairwise atomic distances of a target crystal material can help predict/reconstruct its structure given its space group and lattice information. We propose DMCrystal, a GA-based crystal structure reconstruction algorithm based on predicted pairwise atomic distances. Based on extensive experiments, we show that the predicted distance matrix can dramatically help reconstruct the crystal structure and usually achieves much better performance than that of CMCrystal, an atomic contact map-based CSP algorithm. This implies that the knowledge of atomic interaction information learned from the existing materials can be used to significantly improve the CSP in terms of both speed and quality.

Crystal structure prediction of materials with high symmetry using differential evolution.

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.