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...

, has yet to be experimentally confirmed.Here we show that at pressures of ~200 GPa (∼5.0 fold compression), Na becomes

Abstract. We explore whether the topology of energy landscapes in chemical systems obeys any rules, and what these rules are. To answer this and related questions we use several tools: (i) reduced energy surface and its density of states, (ii) descriptor of structure called fingerprint function, which can be represented as a one-dimensional function or a vector in abstract multidimensional space, (iii) definition of a "distance" between two structures, enabling quantification of energy landscapes, (iv) definition of a degree of order of a structure, (v) definitions of the quasi-entropy, quantifying structural diversity. Our approach can be used for rationalizing large databases of crystal structures and for tuning computational algorithms for structure prediction. It enables quantitative and intuitive representations of energy landscapes and reappraisal of some of the traditional chemical notions and rules. Our analysis confirms the expectations that low-energy minima are clustered in compact regions of configuration space ("funnels") and chemical systems tend to have very few funnels, sometimes only one. This analysis can be applied to the physical properties of solids, opening new ways of discovering structure-property relations. We quantitatively demostrate that crystals tend to adopt one of the few simplest structures consistent with their chemistry, providing a thermodynamic justification of Pauling's 5 th rule.

No abstract

No abstract