We have developed a powerful method for crystal structure prediction from "scratch" through particle swarm optimization (PSO) algorithm within the evolutionary scheme.PSO technique is dramatically different with the genetic algorithm and has apparently avoided the use of evolution operators (e.g., crossover and mutation). The approach is based on a highly efficient global minimization of free energy surfaces merging total-energy calculations via PSO technique and requires only chemical compositions for a given compound to predict stable or metastable structures at given external conditions (e.g., pressure). A particularly devised geometrical structure factor method which allows the elimination of similar structures during structure evolution was implemented to enhance the structure search efficiency. The application of designed variable unit cell size technique has greatly reduced the computational cost. Moreover, the symmetry constraint imposed in the structure generation enables the realization of diverse structures, leads to significantly reduced search space and optimization variables, and thus fastens the global structural convergence. The PSO algorithm has been successfully applied to the prediction of many known systems (e.g., elemental, binary and ternary compounds) with various chemical bonding environments (e.g., metallic, ionic, and covalent bonding). The remarkable success rate demonstrates the reliability of this methodology and illustrates the great promise of PSO as a major technique on crystal structure determination. 11 R. Martonak, A. Laio, and M. Parrinello, Physical review letters 90, 75503 (2003).

We have developed a software package CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) to predict the energetically stable/metastable crystal structures of materials at given chemical compositions and external conditions (e.g., pressure). The CALYPSO method is based on several major techniques (e.g.particle-swarm optimization algorithm, symmetry constraints on structural generation, bond characterization matrix on elimination of similar structures, partial random structures per generation on enhancing structural diversity, and penalty function, etc) for global structural minimization from scratch. All of these techniques have been demonstrated to be critical to the prediction of global stable structure. We have implemented these techniques into the CALYPSO code. Testing of the code on many known and unknown systems shows high efficiency and high successful rate of this CALYPSO method [Wang et al., Phys. Rev. B 82 (2010) 094116][1]. In this paper, we focus on descriptions of the implementation of CALYPSO code and why it works.

We have developed an efficient method for cluster structure prediction based on the generalization of particle swarm optimization (PSO). A local version of PSO algorithm was implemented to utilize a fine exploration of potential energy surface for a given non-periodic system. We have specifically devised a technique of so-called bond characterization matrix (BCM) to allow the proper measure on the structural similarity. The BCM technique was then employed to eliminate similar structures and define the desirable local search spaces. We find that the introduction of point group symmetries into generation of cluster structures enables structural diversity and apparently avoids the generation of liquid-like (or disordered) clusters for large systems, thus considerably improving the structural search efficiency. We have incorporated Metropolis criterion into our method to further enhance the structural evolution towards low-energy regimes of potential energy surfaces. Our method has been extensively benchmarked on Lennard-Jones clusters with different sizes up to 150 atoms and applied into prediction of new structures of medium-sized Li(n) (n = 20, 40, 58) clusters. High search efficiency was achieved, demonstrating the reliability of the current methodology and its promise as a major method on cluster structure prediction.

Being a best known thermoelectric material and a topological insulator at ambient condition, magic bismuth telluride (Bi2Te3) under pressure transforms into several superconducting phases, whose structures remain unsolved for decades. Here, we have solved the two long-puzzling low high-pressure phases as seven- and eightfold monoclinic structures, respectively, through particle-swarm optimization technique on crystal structure prediction. Above 14.4 GPa, we experimentally discovered that Bi2Te3 unexpectedly develops into a Bi-Te substitutional alloy by adopting a body-centered cubic disordered structure stable at least up to 52.1 GPa. The continuously monoclinic distortion leads to the ultimate formation of the Bi-Te alloy, which is attributed to the Bi→Te charge transfer under pressure. Our research provides a route to find alloys made of nonmetallic elements for a variety of applications.

Under high pressure, "simple" lithium (Li) exhibits complex structural behavior, and even experiences an unusual metal-to-semiconductor transition, leading to topics of interest in the structural polymorphs of dense Li. We here report two unexpected orthorhombic high-pressure structures Aba2-40 (40 atoms/cell, stable at 60-80 GPa) and Cmca-56 (56 atoms/cell, stable at 185-269 GPa), by using a newly developed particle swarm optimization technique on crystal structure prediction. The Aba2-40 having complex 4- and 8-atom layers stacked along the b axis is a semiconductor with a pronounced band gap >0.8 eV at 70 GPa originating from the core expulsion and localization of valence electrons in the voids of a crystal. We predict that a local trigonal planar structural motif adopted by Cmca-56 exists in a wide pressure range of 85-434 GPa, favorable for the weak metallicity.

Studies of the Earth

A structure prediction method for layered materials based on two-dimensional (2D) particle swarm optimization algorithm is developed. The relaxation of atoms in the perpendicular direction within a given range is allowed. Additional techniques including structural similarity determination, symmetry constraint enforcement, and discretization of structure constructions based on space gridding are implemented and demonstrated to significantly improve the global structural search efficiency. Our method is successful in predicting the structures of known 2D materials, including single layer and multi-layer graphene, 2D boron nitride (BN) compounds, and some quasi-2D group 6 metals(VIB) chalcogenides. Furthermore, by use of this method, we predict a new family of monolayered boron nitride structures with different chemical compositions. The first-principles electronic structure calculations reveal that the band gap of these N-rich BN systems can be tuned from 5.40 eV to 2.20 eV by adjusting the composition.

The structure prediction at the atomic level is emerging as a state-of-the-art approach to accelerate the functionality-driven discovery of materials. By combining the global swarm optimization algorithm with first-principles thermodynamic calculations, it exploits the power of current supercomputer architectures to robustly predict the ground state and metastable structures of materials with only the given knowledge of chemical composition. In this Review, we provide an overview of the basic theory and main features of our as-developed CALYPSO structure prediction method, as well as its versatile applications to design of a broad range of materials including those of three-dimensional bulks, two-dimensional reconstructed surfaces and layers, and isolated clusters/nanoparticles or molecules with a variety of functional properties. The current challenges faced by structure prediction for materials discovery and future developments of CALYPSO to overcome them are also discussed.