Abstract
Evolutionary algorithms, based on physically motivated forms of variation operators and local optimization, proved to be a powerful approach in determining the crystal structure of materials. This review summarized the recent progress of the USPEX method as a tool for crystal structure prediction. In particular, we highlight the methodology in (1) prediction of molecular crystal structures and (2) variable-composition structure predictions, and their applications to a series of systems, including Mg(BH4)2, Xe-O, Mg-O compounds, etc. We demonstrate that this method has a wide field of applications in both computational materials design and studies of matter at extreme conditions.
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Notes
- 1.
Two extended formulations of this problem include simultaneous searches for stable chemical compositions and structures in multicomponent systems, and finding the structures (and compositions) that possess required physical properties.
References
Maddox J (1988) Crystals from first principles. Nature 335:201
Gavezzotti A (1994) Are crystal structures predictable? Acc Chem Res 27:309–314
Oganov AR (ed) (2010) Modern methods of crystal structure prediction. Wiley, Weinheim
Pannetier J, Bassas-Alsina J, Rodriguez-Carvajal J et al (1990) Prediction of crystal structures from crystal chemistry rules by simulated annealing. Nature 346:343–345
Schon JC, Jansen M (1996) First step towards planning of syntheses in solid-state chemistry: determination of promising structure candidates by global optimization. Angew Chem Int Ed Engl 35:1286–1304
Martonak R, Laio A, Parrinello M (2003) Predicting crystal structures: the Parrinello–Rahman method revisited. Phys Rev Lett 90:075503
Zhu Q, Oganov AR, Lyakhov AO (2012) Evolutionary metadynamics: a novel method to predict crystal structures. CrystEngComm 14:3596–3601
Woodley MS, Battle DP, Gale DJ et al (1999) The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation. Phys Chem Chem Phys 1:2535–2542
Freeman CM, Newsam JM, Levine SM et al (1993) Inorganic crystal structure prediction using simplified potentials and experimental unit cells: application to the polymorphs of titanium dioxide. J Mater Chem 3:531–535
Wales DJ, Doye JPK (1997) Global optimization by basin-hopping and the lowest energy structures of Lennard–Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116
Goedecker S (2004) Minima hopping: searching for the global minimum of the potential energy surface of complex molecular systems without invoking thermodynamics. J Chem Phys 120:9911–9917
Curtarolo S, Morgan D, Persson K et al (2003) Crystal structures with data mining of quantum calculations. Phys Rev Lett 91:135503
Oganov AR, Glass CW (2006) Crystal structure prediction using evolutionary algorithms: principles and applications. J Chem Phys 124:244704
Lyakhov AL, Oganov AR, Valle M (2010) How to predict very large and complex crystal structures. Comput Phys Comm 181:1623–1632
Oganov AR, Lyakhov AO, Valle M (2011) How evolutionary crystal structure prediction works – and why. Acc Chem Res 44:227–237
Zhu Q, Oganov AR, Glass CW et al (2012) Constrained evolutionary algorithm for structure prediction of molecular crystals: methodology and applications. Acta Crystallogr B68:215–226
Lyakhov AO, Oganov AR, Stokes HT et al (2013) New developments in evolutionary structure prediction algorithm USPEX. Comput Phys Comm 184:1172–1182
Zhu Q (2013) Crystal structue prediction and its applications to Earth and materials sciences. Dissertation, Stony Brook University
Chaplot SL, Rao KR (2006) Crystal structure prediction – evolutionary or revolutionary crystallography? Curr Sci 91:1448–1450
Oganov AR, Chen J, Gatti C et al (2009) Ionic high-pressure form of elemental boron. Nature 457:863–867
Ma Y, Eremets MI, Oganov AR et al (2009) Transparent dense sodium. Nature 458:182–185
Li Q, Ma Y, Oganov AR et al (2009) Superhard monoclinic polymorph of carbon. Phys Rev Lett 102:175506
Zhu Q, Oganov AR, Salvado MA et al (2011) Denser than diamond: ab initio search for superdense carbon allotropes. Phys Rev B 83:193410
Lyakhov AO, Oganov AR (2011) Evolutionary search for superhard materials: methodology and applications to forms of carbon and TiO2. Phys Rev B 84:092103
Zhu Q, Jung DY, Oganov AR et al (2013) Stability of xenon oxides at high pressures. Nat Chem 5:61–65
Zhu Q, Oganov AR, Lyahkov AO (2013) Novel stable compounds in the Mg–O system under high pressure. Phys Chem Chem Phys 15:7696–7700
Zhou XF, Oganov AR, Qian GR et al (2012) First-principles determination of the structure of magnesium borohydride. Phys Rev Lett 109:245503
Qian GR, Dong X, Zhou XF et al (2013) Variable cell nudged elastic band method for studying solid–solid structural phase transitions. Comput Phys Comm 184:2111–2118
Oganov AR, Valle M (2009) How to quantify energy landscapes of solids. J Chem Phys 130:104504
Price SL (2004) The computational prediction of pharmaceutical crystal structures and polymorphism. Adv Drug Deliv Rev 56:301–319
Lommerse JPM, Motherwell WDS, Ammon HL et al (2000) A test of crystal structure prediction of small organic molecules. Acta Crystallogr B56:697–714
Motherwell WDS, Ammon HL, Dunitz JD et al (2002) Crystal structure prediction of small organic molecules: a second blind test. Acta Crystallogr B58:647–661
Day GM, Motherwell WDS, Ammon HL et al (2005) A third blind test of crystal structure prediction. Acta Crystallogr B61:511–527
Day GM, Cooper TG, Cruz-Cabeza AJ et al (2009) Significant progress in predicting the crystal structures of small organic molecules: a report on the fourth blind test. Acta Crystallogr B65:107–125
Bardwell DA, Adjiman CS, Arnautova YA et al (2011) Towards crystal structure prediction of complex organic compounds: a report on the fifth blind test. Acta Crystallogr B67:535–551
Day GM (2011) Current approaches to predicting molecular organic crystal structures. Crystallogr Rev 17:3–52
Brock CP, Dunitz JD (1994) Towards a grammar of crystal packing. Chem Mater 6:1118–1127
Baur WH, Kassner D (1992) The perils of CC: comparing the frequencies of falsely assigned space groups with their general population. Acta Crystallogr B48:356–369
Johannesson GH, Bligaard T, Ruban AV et al (2002) Combined electronic structure and evolutionary search approach to materials design. Phys Rev Lett 88(255506):2002
Oganov AR, Ma Y, Lyakhov AO et al (2010) Evolutionary crystal structure prediction as a method for the discovery of minerals and materials. Rev Mineral Geochem 71:271–298
Lyakhov AO, Oganov AR (2010) Crystal structure prediction using evolutionary approach. In: Oganov AR (ed) Modern methods of crystal structure prediction. Wiley, Weinheim, pp 147–180
Kresse G, Furthmuller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186
Perdew JP, Burke K, Ernzerhof M (1996) Generalize gradient approximation made simple. Phys Rev Lett 77:3865–3868
Blochl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979
Tekin A, Caputo R, Zuttel A (2010) First-principles determination of the ground-state structure of LiBH4. Phys Rev Lett 104:215501
George L, Drozd V, Saxena SK et al (2009) Structural phase transitions of Mg(BH4)2 under pressure. J Phys Chem C 113:15087–15090
Cerny R, Filinchuk Y, Hagemann H et al (2007) Magnesium borohydride: synthesis and crystal structure. Angew Chem Int Ed 46:5765–5767
Her J, Stephens PW, Gao Y et al (2007) Structure of unsolvated magnesium borohydride Mg(BH4)2. Acta Crystallogr B63:561–568
Cerny R, Ravnsbak DB, Schouwink P et al (2012) Potassium zinc borohydrides containing triangular [Zn(BH4)3]− and tetrahedral [Mg(BH4)xCl4-x]2− anions. J Phys Chem C 116:1563–1571
Ozolins V, Majzoub EH, Wolverton C (2008) First-principles prediction of a ground state crystal structure of magnesium borohydride. Phys Rev Lett 100:135501
Voss J, Hummelshj JS, Odziana Z et al (2009) Structural stability and decomposition of Mg(BH4)2 isomorphsan ab initio free energy study. J Phys Condens Matter 21:012203
Zhou XF, Qian GR, Zhou J et al (2009) Crystal structure and stability of magnesium borohydride from first principles. Phys Rev B 79:212102
Filinchuk Y, Richter B, Jensen TR (2011) Porous and dense magnesium borohydride frameworks: synthesis, stability, and reversible absorption of guest species. Angew Chem Int Ed 50:11162–11166
Fan J, Bao K, Duan DF et al (2012) High volumetric hydrogen density phases of magnesium borohydride at highpressure: a first-principles study. Chin Phys B 21:086104
Bil A, Kolb B, Atkinson R et al (2011) Van der Waals interactions in the ground state of Mg(BH4)2 from density functional theory. Phys Rev B 83:224103
Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799
Henkelman G, Arnaldsson A, Jonsson H (2006) A fast and robust algorithm for Bader decomposition of charge density. Comput Mater Sci 36:354–360
Levy HA, Agron PA (1963) The crystal and molecular structure of xenon difluoride by neutron diffraction. J Am Chem Soc 85:241–242
Templeton DH, Zalkin A, Forrester JD et al (1963) Crystal and molecular structure of xenon trioxide. J Am Chem Soc 85:817
Hoyer S, Emmler T, Seppelt K (2006) The structure of xenon hexafluoride in the solid state. J Fluorine Chem 127:1415–1422
Kim M, Debessai M, Yoo CS (2010) Two- and three-dimensional extended solids and metallization of compressed XeF2. Nat Chem 2:784–788
Somayazulu M, Dera P, Goncharov AF et al (2010) Pressure-induced bonding and compound formation in xenon-hydrogen solids. Nat Chem 2:50–53
Smith DF (1963) Xenon trioxide. J Am Chem Soc 85:816–817
Selig H, Claassen HH, Chernick CL et al (1964) Xenon tetroxide: preparation and some properties. Science 143:1322–1323
Brock DS, Schrobilgen GJ (2011) Synthesis of the missing oxide of xenon, XeO2, and its implications for Earth missing xenon. J Am Chem Soc 133:6265–626
Grochala W (2007) Atypical compounds of gases, which have been called 'noble'. Chem Soc Rev 36:1632–1655
Anders E, Owen T (1977) Mars and Earth: origin and abundance of volatiles. Science 198:453–465
Sanloup C, Hemley RJ, Mao HK (2002) Evidence for xenon silicates at high pressure and temperature. Geophys Res Lett 29:1883–1886
Sanloup C, Schmidt BC, Perez EMC (2005) Retention of xenon in quartz and Earth’s missing xenon. Science 310:1174–1177
Oganov AR, Ma Y, Glass CW et al (2007) Evolutionary crystal structure prediction: overview of the USPEX method and some of its applications. Psi-K Newsletter 84:142–171
Caldwell WA, Nguyen JH, Pfrommer BG et al (1997) Structure, bonding, and geochemistry of xenon at high pressures. Science 277:930–933
Urusov VS (1977) Theory of isomorphous miscibility. Nauka, Moscow
Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403
Frost DJ, Liebske C, Langenhorst F et al (2004) Experimental evidence for the existence of iron-rich metal in the Earth’s lower mantle. Nature 428:409–412
Zhang FW, Oganov AR (2006) Valence state and spin transitions of iron in Earth's mantle silicates. Earth Planet Sci Lett 249:436–443
Lin J, Heinz DL, Mao HK et al (2003) Stability of magnesiowstite in Earth's lower mantle. Proc Natl Acad Sci U S A 100:4405–4408
Mazin II, Fei Y, Downs R et al (1998) Possible polytypism in FeO at high pressures. Am Mineral 83:451–457
Oganov AR, Martonak R, Laio A et al (2005) Anisotropy of Earth’s D” layer and stacking faults in the MgSiO3 postperovskite phase. Nature 438:1142–1144
Duffy TS, Hemley RJ, Mao HK (1995) Equation of state and shear strength at multimegabar pressures: magnesium oxide to 227 GPa. Phys Rev Lett 74:1371–1374
Mehl MJ, Cohen RE, Krakauer H (1988) Linearized augmented plane wave electronic structure calculations for MgO and CaO. J Geophys Res 118:8009–8022
Oganov AR, Gillan MJ, Price GD (2003) Ab initio lattice dynamics and structural stability of MgO. J Chem Phys 118:10174–10182
Belonoshko AB, Arapan S, Martonak R et al (2010) MgO phase diagram from first principles in a wide pressure–temperature range. Phys Rev B 81:054110
Wriedt H (1987) The MgO (magnesium-oxygen) system. J Phase Equil 8:227–233
Recio JM, Pandey R (1993) Ab initio study of neutral and ionized microclusters of MgO. Phys Rev A 47:2075–2082
Wang ZL, Bentley J, Kenik EA (1992) In-situ formation of MgO2 thin films on MgO single-crystal surfaces at high temperatures. Surf Sci 273:88–108
Vannerberg N (2007) Peroxides, superoxides, and ozonides of the metals of groups Ia, IIa, and IIb. In: Cotton FA (ed) Progress in inorganic chemistry. Wiley, New York, p 2007. ISBN 9780470166055
Abrahams SC, Kalnajs J (1954) The formation and structure of magnesium peroxide. Acta Crystallogr 7:838–842
Efthimiopoulos I, Kunc K, Karmakar S et al (2010) Structural transformation and vibrational properties of BaO2 at high pressures. Phys Rev B 82(134125):2010
Vannerberg NG (1959) The formation and structure of magnesium peroxide. Ark Kemi 14:99–105
Togo A, Oba F, Tanaka I (2008) First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Phys Rev B 78:134106
Olijnyk H, Holzapfel WB (1985) High-pressure structural phase transition in Mg. Phys Rev B 31:8412–4683
Wentzcovitch RM, Cohen ML (1988) Theoretical model for the hcp-bcc transition in Mg. Phys Rev B 37:5571–5576
Li P, Gao G, Wang Y et al (2010) Crystal structures and exotic behavior of magnesium under pressure. J Phys Chem C 114:21745–21749
Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B25:925–946
Waber JT, Cromer DT (1965) Orbital radii of atoms and ions. J Chem Phys 42:4116–4123
Neumann MA, Perrin M (2005) The computational prediction of pharmaceutical crystal structures and polymorphism. J Phys Chem B 109:15531
Dion M, Rydberg H, Schroder E et al (2004) Van der Waals density functional for general geometries. Phys Rev Lett 92:246401
Román-Pérez G, Soler JM (2009) Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotube. Phys Rev Lett 103:096102
Zhu Q, Li L, Oganov AR et al (2013) Evolutionary method for predicting surface reconstructions with variable stoichiometry. Phys Rev B 87:195317
Acknowledgments
Calculations were performed at the supercomputer of the Center for Functional Nanomaterials, Brookhaven National Laboratory. We gratefully acknowledge funding from DARPA (Grants No. W31P4Q1210008 and No. W31P4Q1310005), NSF (No. EAR-1114313 and No. DMR-1231586), the AFOSR (No. FA9550-13-C-0037), CRDF Global (No. UKE2-7034-KV-11), and Government of the Russian Federation (No. 14.A12.31.0003). X.F.Z thanks National Science Foundation of China (Grant No. 11174152).
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Zhu, Q., Oganov, A.R., Zhou, XF. (2014). Crystal Structure Prediction and Its Application in Earth and Materials Sciences. In: Atahan-Evrenk, S., Aspuru-Guzik, A. (eds) Prediction and Calculation of Crystal Structures. Topics in Current Chemistry, vol 345. Springer, Cham. https://doi.org/10.1007/128_2013_508
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