Evolutionary Crystal Structure Prediction Research Articles

How Evolutionary Crystal Structure Prediction Works—and Why

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, systems of variable composition, and the targeted optimization of specific physical properties.

How to predict very large and complex crystal structures

Evolutionary crystal structure prediction proved to be a powerful approach in discovering new materials. Certain limitations are encountered for systems with a large number of degrees of freedom (“large systems”) and complex energy landscapes (“complex systems”). We explore the nature of these limitations and address them with a number of newly developed tools. For large systems a major problem is the lack of diversity: any randomly produced population consists predominantly of high-energy disordered structures, offering virtually no routes toward the ordered ground state. We offer two solutions: first, modified variation operators that favor atoms with higher local order (a function we introduce here), and, second, construction of the first generation non-randomly, using pseudo-subcells with, in general, fractional atomic occupancies. This enhances order and diversity and improves energies of the structures. We introduce an additional variation operator, coordinate mutation, which applies preferentially to low-order (“badly placed”) atoms. Biasing other variation operators by local order is also found to produce improved results. One promising version of coordinate mutation, explored here, displaces atoms along the eigenvector of the lowest-frequency vibrational mode. For complex energy landscapes, the key problem is the possible existence of several energy funnels – in this situation it is possible to get trapped in one funnel (not necessarily containing the ground state). To address this problem, we develop an algorithm incorporating the ideas of abstract “distance” between structures. These new ingredients improve the performance of the evolutionary algorithm USPEX, in terms of efficiency and reliability, for large and complex systems.

Evolutionary Crystal Structure Prediction as a Method for the Discovery of Minerals and Materials

Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed “crystal structure prediction problem,” and recently developed evolutionary algorithm USPEX (Universal Structure Predictor: Evolutionary Xtallography) made an important progress in solving it, enabling efficient and reliable prediction of structures with up to ~40 atoms in the unit cell using ab initio methods. Here we review this methodology, as well as recent progress in analyzing energy landscape of solids (which also helps to analyze results of USPEX runs). We show several recent applications – (1) prediction of new high-pressure phases of CaCO3, (2) search

Iron silicides at pressures of the Earth's inner core

The Earth's core is expected to contain around 10 wt % light elements (S, Si, O, possibly C, H, etc.) alloyed with Fe and Ni. Very little is known about these alloys at pressures and temperatures of the core. Here, using the evolutionary crystal structure prediction methodology, we investigate Fe‐Si compounds at pressures of up to 400 GPa, i.e. covering the pressure range of the Earth's core. Evolutionary simulations correctly find that at atmospheric pressure the known non‐trivial structure with P213 symmetry is stable, while at pressures above 20 GPa the CsCl‐type structure is stable. We show that among the possible Fe silicides (Fe3Si, Fe2Si, Fe5Si3, FeSi, FeSi2 and FeSi3) only FeSi with CsCl‐type structure is thermodynamically stable at core pressures, while the other silicides are unstable to decomposition into Fe + FeSi or FeSi + Si. This is consistent with previous works and suggests that Si impurities contribute to stabilization of the body‐centered cubic phase of Fe in the inner core.

Evolutionary crystal structure prediction and its applications to materials at extreme conditions

Evolutionary crystal structure prediction and its applications to materials at extreme conditions

High-pressure phase transformations of FeS: Novel phases at conditions of planetary cores

Iron sulfide (FeS) was investigated using first-principles calculations up to a pressure of 400 GPa. A number Of new phase transitions were found. An antiferromagnetic MnP-type structure, FeS 11, was confirmed to be stable at low pressures, whereas at high pressures (40-135 GPa) we find a new stable phase, with a nonmagnetic MnP-type structure, FeS VI. The observed first-order change in the cell shape between the two phases can be explained by the difference in magnetic configurations. The calculated cell Parameters, atomic coordinates, and bulk modulus of non-magnetic MnP-type phase are consistent with those determined from experiment. The upper pressure limit of the stability of the non-magnetic MnP-type phase was calculated to be 135 GPa. A hitherto unsuspected phase transition from the non-magnetic MnP-type to a phase with Primin symmetry, FeS VII, was identified using the evolutionary crystal structure prediction (USPEX) method. The structure of the Pmmn phase has no known analogues, but can be described as a distortion of the NaCl-type structure. The Pmmn phase with the distorted NaCl-type structure is stable from 135 GPa at least up to 400 GPa. According to previous experiments and the present study, the transition sequence of FeS at low temperatures is as follows: troilite -> antiferromagnetic MnP-type phase -> monoclinic phase -> nonmagnetic MnP-type phase 4 Pmmn phase. The calculated volume reduction from the monoclinic to the nonmagnetic MnP-type phase is 1.0% at 40 GPa, which is in good agreement with experimental observations. The Calculated volume reduction from the non-magnetic MnP-type to the Pmmn phase is 3.7% at 135 GPa. (C) 2008 Elsevier B.V. All rights reserved.

Evolutionary crystal structure prediction as a tool in materials design

Ab initio methods allow a more or less straightforward prediction of numerous physicalproperties of solids, but require the knowledge of their crystal structure. The evolutionaryalgorithm USPEX, developed by us in 2004–2006, enables reliable prediction of thestable crystal structure without relying on any experimental data. Numerous tests(mostly for systems with up to 28 atoms in the unit cell, and a few tests with up to128 atoms/cell) showed a success rate of nearly 100%. USPEX has resulted in a number ofpredictions of hitherto unknown stable structures. We give a short overview ofthe method, introducing some new developments and results, and discuss a fewalternative approaches. The method is illustrated by a test on an 80 atom supercell ofMgSiO3 and by the search for new materials with compositionsAl13K and Al12C.