A symmetry-orientated divide-and-conquer method for crystal structure prediction

Abstract

Crystal structure prediction has been a subject of topical interest but remains a substantial challenge especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy surface. In this paper, a symmetry-orientated divide-and-conquer scheme was proposed to construct a symmetry tree graph, where the entire search space is decomposed into a finite number of symmetry dependent subspaces. An artificial intelligence-based symmetry selection strategy was subsequently devised to select the low-lying subspaces with high symmetries for global exploration and in-depth exploitation. Our approach can significantly simplify the problem of crystal structure prediction by avoiding exploration of the most complex P1 subspace on the entire search space and has the advantage of preserving the crystal symmetry during structure evolution, making it well suitable for predicting the complex crystal structures. The effectiveness of the method has been validated by successful prediction of the candidate structures of binary Lennard-Jones mixtures and the high-pressure phase of ice, containing more than 100 atoms in the simulation cell. The work therefore opens up an opportunity toward achieving the long-sought goal of crystal structure prediction of complex systems.

Crystal Transformer: Self-learning neural language model for Generative and Tinkering Design of Materials

“…While prediction models have been proposed for synthesizability prediction [53], formation energy prediction [54], and e-above-hull calculation, these models and algorithms usually require the availability of the crystal structures. Fortunately, recent progress in template based [55,52], deep learning based [56], and global optimization based crystal structure prediction tools [57,58] have made it possible to guess the crystal structures for increasing families of materials, which can be combined with our composition generators to explore and discover new materials.…”

Crystal Structure Prediction via Efficient Sampling of the Potential Energy Surface

“…To make the search process more efficient, instead of pursuing a direct sampling of PES associated with general spatial arrangements of atoms (e.g., PSO), we have developed a symmetry-oriented divide-and-conquer scheme via the construction of a symmetry tree graph that allows for the decomposition of a vast structure space into 230 subspaces based on the space group symmetry (Figure ). Each subspace can be further subdivided into a set of site-symmetry-related groups (crystallographic orbits) and individual structures that are geometry optimized toward related energy minima.…”

Tantalum Diboride: The Superhard and Metallic Boride

“…The structure prediction of TaB 2 under ambient pressure is performed by the CALYPSO method combined with the Vienna ab initio simulation package (VASP) . This effective method successfully searched the ground-state and metastable-state structures for various systems from zero-dimensional (0D) clusters to two-dimensional (2D) monolayers and to three-dimensional crystals. − During the structure prediction of TaB 2 , 70% of low-lying structures are collected as the specimens to create the candidate structures in the next generation, and the remaining 30% of structures are generated with some special restrictions, such as the symmetries, the bond lengths, and so forth. After 50 generations of structure searches, about 1200 to 1500 low-lying structures of TaB 2 are obtained at ambient pressure.…”

“…In this work, we perform comprehensive structure searches of TaB 2 by crystal structure analysis by the particle swarm optimization (CALYPSO) structural search method and first-principles calculations. − Our results show that two novel structures of TaB 2 with Cmmm and I 4 1 / amd symmetries can be metastable at ambient pressure, except for the well-known ground-state structure of the P 6/ mmm phase. The subsequent stress–strain calculations of the three structures indicate the abnormal stress responses of TaB 2 in many crystal planes, which are the apparent strain-stiffening behaviors along some main directions.…”