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Valle M.,Data Analysis and Visualization Group | Oganov A.R.,State University of New York at Stony Brook | Oganov A.R.,Moscow State University
Acta Crystallographica Section A: Foundations of Crystallography | Year: 2010

The initial aim of the crystal fingerprint project was to solve a very specific problem: to classify and remove duplicate crystal structures from the results generated by the evolutionary crystal-structure predictor USPEX. These duplications decrease the genetic diversity of the population used by the evolutionary algorithm, potentially leading to stagnation and, after a certain time, reducing the likelihood of predicting essentially new structures. After solving the initial problem, the approach led to unexpected discoveries: unforeseen correlations, useful derived quantities and insight into the structure of the overall set of results. All of these were facilitated by the projects underlying idea: to transform the structure sets from the physical configuration space to an abstract, high-dimensional space called the fingerprint space. Here every structure is represented as a point whose coordinates (fingerprint) are computed from the crystal structure. Then the spaces distance measure, interpreted as structure closeness, enables grouping of structures into similarity classes. This model provides much flexibility and facilitates access to knowledge and algorithms from fields outside crystallography, e.g. pattern recognition and data mining. The current usage of the fingerprint-space model is revealing interesting properties that relate to chemical and crystallographic attributes of a structure set. For this reason, the mapping of structure sets to fingerprint space could become a new paradigm for studying crystal-structure ensembles and global chemical features of the energy landscape. © 2010 International Union of Crystallography Printed in Singapore - all rights reserved. Source


Oganov A.R.,State University of New York at Stony Brook | Oganov A.R.,Moscow State University | Ma Y.,Jilin University | Lyakhov A.O.,State University of New York at Stony Brook | And 2 more authors.
Reviews in Mineralogy and Geochemistry | Year: 2010

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 for the structure of the polymeric phase of CO2 ("phase V"), (3) high-pressure phases of oxygen, (4) exploration of possible stable compounds in the Xe-C system at high pressures, (5) exotic high-pressure phases of elements boron and sodium, as well as extension of the method to variable-composition systems. Copyright © Mineralogical Society of America. Source


Oganov A.R.,State University of New York at Stony Brook | Oganov A.R.,Moscow State University | Ma Y.,Jilin University | Lyakhov A.O.,State University of New York at Stony Brook | And 2 more authors.
NATO Science for Peace and Security Series B: Physics and Biophysics | Year: 2010

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 for the structure of the polymeric phase of CO2 ("phase V"), (3) high-pressure phases of oxygen, (4) exploration of possible stable compounds in the Xe-C system at high pressures, (5) exotic high-pressure phases of elements boron and sodium. © 2010 Springer Science+Business Media B.V. Source


Oganov A.R.,State University of New York at Stony Brook | Oganov A.R.,Moscow State University | Lyakhov A.O.,State University of New York at Stony Brook | Valle M.,Data Analysis and Visualization Group
Accounts of Chemical Research | Year: 2011

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" LiHn (n = 2, 6, 8) compounds, and CaLi2. We discuss extensions of the method to molecular crystals, systems of variable composition, and the targeted optimization of specific physical properties. © 2011 American Chemical Society. Source

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