How Evolutionary Crystal Structure Prediction Works—and Why

Abstract

Once the crystal structure of a chemical substance is known, many properties can be predicted reliably and routinely. Therefore if researchers could predict the crystal structure of a material before it is synthesized, they could significantly accelerate the discovery of new materials. In addition, the ability to predict crystal structures at arbitrary conditions of pressure and temperature is invaluable for the study of matter at extreme conditions, where experiments are difficult. Crystal structure prediction (CSP), the problem of finding the most stable arrangement of atoms given only the chemical composition, has long remained a major unsolved scientific problem. Two problems are entangled here: search, the efficient exploration of the multidimensional energy landscape, and ranking, the correct calculation of relative energies. For organic crystals, which contain a few molecules in the unit cell, search can be quite simple as long as a researcher does not need to include many possible isomers or conformations of the molecules; therefore ranking becomes the main challenge. For inorganic crystals, quantum mechanical methods often provide correct relative energies, making search the most critical problem. Recent developments provide useful practical methods for solving the search problem to a considerable extent. One can use simulated annealing, metadynamics, random sampling, basin hopping, minima hopping, and data mining. Genetic algorithms have been applied to crystals since 1995, but with limited success, which necessitated the development of a very different evolutionary algorithm. This Account reviews CSP using one of the major techniques, the hybrid evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary Xtallography). Using recent developments in the theory of energy landscapes, we unravel the reasons evolutionary techniques work for CSP and point out their limitations. We demonstrate that the energy landscapes of chemical systems have an overall shape and explore their intrinsic dimensionalities. Because of the inverse relationships between order and energy and between the dimensionality and diversity of an ensemble of crystal structures, the chances that a random search will find the ground state decrease exponentially with increasing system size. A well-designed evolutionary algorithm allows for much greater computational efficiency. We illustrate the power of evolutionary CSP through applications that examine matter at high pressure, where new, unexpected phenomena take place. Evolutionary CSP has allowed researchers to make unexpected discoveries such as a transparent phase of sodium, a partially ionic form of boron, complex superconducting forms of calcium, a novel superhard allotrope of carbon, polymeric modifications of nitrogen, and a new class of compounds, perhydrides. These methods have also led to the discovery of novel hydride superconductors including the "impossible" LiH(n) (n=2, 6, 8) compounds, and CaLi(2). We discuss extensions of the method to molecular crystals, syst...

Synthesis of β-Mg2C3: A Monoclinic High-Pressure Polymorph of Magnesium Sesquicarbide

“…This method was previously shown to be powerful for complicated low-symmetry structures, such as orthorhombic boron 45 and unexpected sodium chlorides 46 and has become a more and more widely used technique. 47,48 Figure 3a compares the pressure dependence of the relative enthalpies of the four lowest energy Mg 2 C 3 structures predicted by USPEX. The known α-Mg 2 C 3 (Pnnm) structure was predicted to be the most stable at ambient pressure.…”

Pressure-induced novel compounds in the Hf-O system from first-principles calculations

“…In our work, variablecomposition structure searches [23] for the Hf-O system with up to 32 atoms in the unit cell were performed at 0 GPa, 10 GPa, 20 GPa, 30 GPa, 40 GPa, 50 GPa, 60 GPa, 70 GPa, 80 GPa, 90 GPa, 100 GPa, 110 GPa and 120 GPa. The initial generation of structures was produced randomly using space group symmetry, each subsequent generation was obtained by variation operators including heredity (40%), lattice mutation (20%), random (20%) and transmutation (20%).…”

Quantum topology phase diagrams for molecules, clusters, and solids

“…[20][21][22] A simple example of such an application, a variety of phases of water ice [23][24][25] subjected to varying pressure, is presented in this perspective, see Figure 3 and the accompanying figure caption. The phase diagram is constructed by using Eq.…”