Divide and conquer algorithms

Theoretical physics

Algorithm

Theoretical computer science

Crystal structure

Computer science

Statistical physics

Linear subspace

Physics

Crystal structure prediction

Mathematics

Homogeneous space

Artificial intelligence

Geometry

Crystallography

Chemistry

Symmetry (geometry)

Subspace topology

Binary number

Arithmetic

The Journal of Chemical Physics

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.

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