Crystal Structure Prediction and Its Application in Earth and Materials Sciences

  • Qiang Zhu
  • Artem R. OganovEmail author
  • Xiang-Feng Zhou
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 345)


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.


Crystal structure prediction Molecular crystals Variable composition High pressure Novel compounds Ab initio simulations Density functional theory 



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).


  1. 1.
    Maddox J (1988) Crystals from first principles. Nature 335:201CrossRefGoogle Scholar
  2. 2.
    Gavezzotti A (1994) Are crystal structures predictable? Acc Chem Res 27:309–314CrossRefGoogle Scholar
  3. 3.
    Oganov AR (ed) (2010) Modern methods of crystal structure prediction. Wiley, WeinheimGoogle Scholar
  4. 4.
    Pannetier J, Bassas-Alsina J, Rodriguez-Carvajal J et al (1990) Prediction of crystal structures from crystal chemistry rules by simulated annealing. Nature 346:343–345CrossRefGoogle Scholar
  5. 5.
    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 35:1286–1304CrossRefGoogle Scholar
  6. 6.
    Martonak R, Laio A, Parrinello M (2003) Predicting crystal structures: the Parrinello–Rahman method revisited. Phys Rev Lett 90:075503CrossRefGoogle Scholar
  7. 7.
    Zhu Q, Oganov AR, Lyakhov AO (2012) Evolutionary metadynamics: a novel method to predict crystal structures. CrystEngComm 14:3596–3601CrossRefGoogle Scholar
  8. 8.
    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 1:2535–2542CrossRefGoogle Scholar
  9. 9.
    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 3:531–535CrossRefGoogle Scholar
  10. 10.
    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 101:5111–5116CrossRefGoogle Scholar
  11. 11.
    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 120:9911–9917CrossRefGoogle Scholar
  12. 12.
    Curtarolo S, Morgan D, Persson K et al (2003) Crystal structures with data mining of quantum calculations. Phys Rev Lett 91:135503CrossRefGoogle Scholar
  13. 13.
    Oganov AR, Glass CW (2006) Crystal structure prediction using evolutionary algorithms: principles and applications. J Chem Phys 124:244704CrossRefGoogle Scholar
  14. 14.
    Lyakhov AL, Oganov AR, Valle M (2010) How to predict very large and complex crystal structures. Comput Phys Comm 181:1623–1632CrossRefGoogle Scholar
  15. 15.
    Oganov AR, Lyakhov AO, Valle M (2011) How evolutionary crystal structure prediction works – and why. Acc Chem Res 44:227–237CrossRefGoogle Scholar
  16. 16.
    Zhu Q, Oganov AR, Glass CW et al (2012) Constrained evolutionary algorithm for structure prediction of molecular crystals: methodology and applications. Acta Crystallogr B68:215–226CrossRefGoogle Scholar
  17. 17.
    Lyakhov AO, Oganov AR, Stokes HT et al (2013) New developments in evolutionary structure prediction algorithm USPEX. Comput Phys Comm 184:1172–1182CrossRefGoogle Scholar
  18. 18.
    Zhu Q (2013) Crystal structue prediction and its applications to Earth and materials sciences. Dissertation, Stony Brook UniversityGoogle Scholar
  19. 19.
    Chaplot SL, Rao KR (2006) Crystal structure prediction – evolutionary or revolutionary crystallography? Curr Sci 91:1448–1450Google Scholar
  20. 20.
    Oganov AR, Chen J, Gatti C et al (2009) Ionic high-pressure form of elemental boron. Nature 457:863–867CrossRefGoogle Scholar
  21. 21.
    Ma Y, Eremets MI, Oganov AR et al (2009) Transparent dense sodium. Nature 458:182–185CrossRefGoogle Scholar
  22. 22.
    Li Q, Ma Y, Oganov AR et al (2009) Superhard monoclinic polymorph of carbon. Phys Rev Lett 102:175506CrossRefGoogle Scholar
  23. 23.
    Zhu Q, Oganov AR, Salvado MA et al (2011) Denser than diamond: ab initio search for superdense carbon allotropes. Phys Rev B 83:193410CrossRefGoogle Scholar
  24. 24.
    Lyakhov AO, Oganov AR (2011) Evolutionary search for superhard materials: methodology and applications to forms of carbon and TiO2. Phys Rev B 84:092103CrossRefGoogle Scholar
  25. 25.
    Zhu Q, Jung DY, Oganov AR et al (2013) Stability of xenon oxides at high pressures. Nat Chem 5:61–65CrossRefGoogle Scholar
  26. 26.
    Zhu Q, Oganov AR, Lyahkov AO (2013) Novel stable compounds in the Mg–O system under high pressure. Phys Chem Chem Phys 15:7696–7700CrossRefGoogle Scholar
  27. 27.
    Zhou XF, Oganov AR, Qian GR et al (2012) First-principles determination of the structure of magnesium borohydride. Phys Rev Lett 109:245503CrossRefGoogle Scholar
  28. 28.
    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 184:2111–2118CrossRefGoogle Scholar
  29. 29.
    Oganov AR, Valle M (2009) How to quantify energy landscapes of solids. J Chem Phys 130:104504CrossRefGoogle Scholar
  30. 30.
    Price SL (2004) The computational prediction of pharmaceutical crystal structures and polymorphism. Adv Drug Deliv Rev 56:301–319CrossRefGoogle Scholar
  31. 31.
    Lommerse JPM, Motherwell WDS, Ammon HL et al (2000) A test of crystal structure prediction of small organic molecules. Acta Crystallogr B56:697–714CrossRefGoogle Scholar
  32. 32.
    Motherwell WDS, Ammon HL, Dunitz JD et al (2002) Crystal structure prediction of small organic molecules: a second blind test. Acta Crystallogr B58:647–661CrossRefGoogle Scholar
  33. 33.
    Day GM, Motherwell WDS, Ammon HL et al (2005) A third blind test of crystal structure prediction. Acta Crystallogr B61:511–527CrossRefGoogle Scholar
  34. 34.
    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 B65:107–125CrossRefGoogle Scholar
  35. 35.
    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 B67:535–551CrossRefGoogle Scholar
  36. 36.
    Day GM (2011) Current approaches to predicting molecular organic crystal structures. Crystallogr Rev 17:3–52CrossRefGoogle Scholar
  37. 37.
    Brock CP, Dunitz JD (1994) Towards a grammar of crystal packing. Chem Mater 6:1118–1127CrossRefGoogle Scholar
  38. 38.
    Baur WH, Kassner D (1992) The perils of CC: comparing the frequencies of falsely assigned space groups with their general population. Acta Crystallogr B48:356–369CrossRefGoogle Scholar
  39. 39.
    Johannesson GH, Bligaard T, Ruban AV et al (2002) Combined electronic structure and evolutionary search approach to materials design. Phys Rev Lett 88(255506):2002Google Scholar
  40. 40.
    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 71:271–298CrossRefGoogle Scholar
  41. 41.
    Lyakhov AO, Oganov AR (2010) Crystal structure prediction using evolutionary approach. In: Oganov AR (ed) Modern methods of crystal structure prediction. Wiley, Weinheim, pp 147–180CrossRefGoogle Scholar
  42. 42.
    Kresse G, Furthmuller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169–11186CrossRefGoogle Scholar
  43. 43.
    Perdew JP, Burke K, Ernzerhof M (1996) Generalize gradient approximation made simple. Phys Rev Lett 77:3865–3868CrossRefGoogle Scholar
  44. 44.
    Blochl PE (1994) Projector augmented-wave method. Phys Rev B 50:17953–17979CrossRefGoogle Scholar
  45. 45.
    Tekin A, Caputo R, Zuttel A (2010) First-principles determination of the ground-state structure of LiBH4. Phys Rev Lett 104:215501CrossRefGoogle Scholar
  46. 46.
    George L, Drozd V, Saxena SK et al (2009) Structural phase transitions of Mg(BH4)2 under pressure. J Phys Chem C 113:15087–15090CrossRefGoogle Scholar
  47. 47.
    Cerny R, Filinchuk Y, Hagemann H et al (2007) Magnesium borohydride: synthesis and crystal structure. Angew Chem Int Ed 46:5765–5767CrossRefGoogle Scholar
  48. 48.
    Her J, Stephens PW, Gao Y et al (2007) Structure of unsolvated magnesium borohydride Mg(BH4)2. Acta Crystallogr B63:561–568CrossRefGoogle Scholar
  49. 49.
    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 116:1563–1571CrossRefGoogle Scholar
  50. 50.
    Ozolins V, Majzoub EH, Wolverton C (2008) First-principles prediction of a ground state crystal structure of magnesium borohydride. Phys Rev Lett 100:135501CrossRefGoogle Scholar
  51. 51.
    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 21:012203CrossRefGoogle Scholar
  52. 52.
    Zhou XF, Qian GR, Zhou J et al (2009) Crystal structure and stability of magnesium borohydride from first principles. Phys Rev B 79:212102CrossRefGoogle Scholar
  53. 53.
    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 50:11162–11166CrossRefGoogle Scholar
  54. 54.
    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 21:086104CrossRefGoogle Scholar
  55. 55.
    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 83:224103CrossRefGoogle Scholar
  56. 56.
    Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799CrossRefGoogle Scholar
  57. 57.
    Henkelman G, Arnaldsson A, Jonsson H (2006) A fast and robust algorithm for Bader decomposition of charge density. Comput Mater Sci 36:354–360CrossRefGoogle Scholar
  58. 58.
    Levy HA, Agron PA (1963) The crystal and molecular structure of xenon difluoride by neutron diffraction. J Am Chem Soc 85:241–242CrossRefGoogle Scholar
  59. 59.
    Templeton DH, Zalkin A, Forrester JD et al (1963) Crystal and molecular structure of xenon trioxide. J Am Chem Soc 85:817CrossRefGoogle Scholar
  60. 60.
    Hoyer S, Emmler T, Seppelt K (2006) The structure of xenon hexafluoride in the solid state. J Fluorine Chem 127:1415–1422CrossRefGoogle Scholar
  61. 61.
    Kim M, Debessai M, Yoo CS (2010) Two- and three-dimensional extended solids and metallization of compressed XeF2. Nat Chem 2:784–788CrossRefGoogle Scholar
  62. 62.
    Somayazulu M, Dera P, Goncharov AF et al (2010) Pressure-induced bonding and compound formation in xenon-hydrogen solids. Nat Chem 2:50–53CrossRefGoogle Scholar
  63. 63.
    Smith DF (1963) Xenon trioxide. J Am Chem Soc 85:816–817CrossRefGoogle Scholar
  64. 64.
    Selig H, Claassen HH, Chernick CL et al (1964) Xenon tetroxide: preparation and some properties. Science 143:1322–1323CrossRefGoogle Scholar
  65. 65.
    Brock DS, Schrobilgen GJ (2011) Synthesis of the missing oxide of xenon, XeO2, and its implications for Earth missing xenon. J Am Chem Soc 133:6265–626CrossRefGoogle Scholar
  66. 66.
    Grochala W (2007) Atypical compounds of gases, which have been called 'noble'. Chem Soc Rev 36:1632–1655CrossRefGoogle Scholar
  67. 67.
    Anders E, Owen T (1977) Mars and Earth: origin and abundance of volatiles. Science 198:453–465CrossRefGoogle Scholar
  68. 68.
    Sanloup C, Hemley RJ, Mao HK (2002) Evidence for xenon silicates at high pressure and temperature. Geophys Res Lett 29:1883–1886CrossRefGoogle Scholar
  69. 69.
    Sanloup C, Schmidt BC, Perez EMC (2005) Retention of xenon in quartz and Earth’s missing xenon. Science 310:1174–1177CrossRefGoogle Scholar
  70. 70.
    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 84:142–171Google Scholar
  71. 71.
    Caldwell WA, Nguyen JH, Pfrommer BG et al (1997) Structure, bonding, and geochemistry of xenon at high pressures. Science 277:930–933CrossRefGoogle Scholar
  72. 72.
    Urusov VS (1977) Theory of isomorphous miscibility. Nauka, MoscowGoogle Scholar
  73. 73.
    Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403CrossRefGoogle Scholar
  74. 74.
    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 428:409–412CrossRefGoogle Scholar
  75. 75.
    Zhang FW, Oganov AR (2006) Valence state and spin transitions of iron in Earth's mantle silicates. Earth Planet Sci Lett 249:436–443CrossRefGoogle Scholar
  76. 76.
    Lin J, Heinz DL, Mao HK et al (2003) Stability of magnesiowstite in Earth's lower mantle. Proc Natl Acad Sci U S A 100:4405–4408CrossRefGoogle Scholar
  77. 77.
    Mazin II, Fei Y, Downs R et al (1998) Possible polytypism in FeO at high pressures. Am Mineral 83:451–457Google Scholar
  78. 78.
    Oganov AR, Martonak R, Laio A et al (2005) Anisotropy of Earth’s D” layer and stacking faults in the MgSiO3 postperovskite phase. Nature 438:1142–1144CrossRefGoogle Scholar
  79. 79.
    Duffy TS, Hemley RJ, Mao HK (1995) Equation of state and shear strength at multimegabar pressures: magnesium oxide to 227 GPa. Phys Rev Lett 74:1371–1374CrossRefGoogle Scholar
  80. 80.
    Mehl MJ, Cohen RE, Krakauer H (1988) Linearized augmented plane wave electronic structure calculations for MgO and CaO. J Geophys Res 118:8009–8022CrossRefGoogle Scholar
  81. 81.
    Oganov AR, Gillan MJ, Price GD (2003) Ab initio lattice dynamics and structural stability of MgO. J Chem Phys 118:10174–10182CrossRefGoogle Scholar
  82. 82.
    Belonoshko AB, Arapan S, Martonak R et al (2010) MgO phase diagram from first principles in a wide pressure–temperature range. Phys Rev B 81:054110CrossRefGoogle Scholar
  83. 83.
    Wriedt H (1987) The MgO (magnesium-oxygen) system. J Phase Equil 8:227–233Google Scholar
  84. 84.
    Recio JM, Pandey R (1993) Ab initio study of neutral and ionized microclusters of MgO. Phys Rev A 47:2075–2082CrossRefGoogle Scholar
  85. 85.
    Wang ZL, Bentley J, Kenik EA (1992) In-situ formation of MgO2 thin films on MgO single-crystal surfaces at high temperatures. Surf Sci 273:88–108CrossRefGoogle Scholar
  86. 86.
    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 9780470166055Google Scholar
  87. 87.
    Abrahams SC, Kalnajs J (1954) The formation and structure of magnesium peroxide. Acta Crystallogr 7:838–842CrossRefGoogle Scholar
  88. 88.
    Efthimiopoulos I, Kunc K, Karmakar S et al (2010) Structural transformation and vibrational properties of BaO2 at high pressures. Phys Rev B 82(134125):2010Google Scholar
  89. 89.
    Vannerberg NG (1959) The formation and structure of magnesium peroxide. Ark Kemi 14:99–105Google Scholar
  90. 90.
    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 78:134106CrossRefGoogle Scholar
  91. 91.
    Olijnyk H, Holzapfel WB (1985) High-pressure structural phase transition in Mg. Phys Rev B 31:8412–4683CrossRefGoogle Scholar
  92. 92.
    Wentzcovitch RM, Cohen ML (1988) Theoretical model for the hcp-bcc transition in Mg. Phys Rev B 37:5571–5576CrossRefGoogle Scholar
  93. 93.
    Li P, Gao G, Wang Y et al (2010) Crystal structures and exotic behavior of magnesium under pressure. J Phys Chem C 114:21745–21749CrossRefGoogle Scholar
  94. 94.
    Shannon RD, Prewitt CT (1969) Effective ionic radii in oxides and fluorides. Acta Crystallogr B25:925–946CrossRefGoogle Scholar
  95. 95.
    Waber JT, Cromer DT (1965) Orbital radii of atoms and ions. J Chem Phys 42:4116–4123CrossRefGoogle Scholar
  96. 96.
    Neumann MA, Perrin M (2005) The computational prediction of pharmaceutical crystal structures and polymorphism. J Phys Chem B 109:15531CrossRefGoogle Scholar
  97. 97.
    Dion M, Rydberg H, Schroder E et al (2004) Van der Waals density functional for general geometries. Phys Rev Lett 92:246401CrossRefGoogle Scholar
  98. 98.
    Román-Pérez G, Soler JM (2009) Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotube. Phys Rev Lett 103:096102CrossRefGoogle Scholar
  99. 99.
    Zhu Q, Li L, Oganov AR et al (2013) Evolutionary method for predicting surface reconstructions with variable stoichiometry. Phys Rev B 87:195317CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Qiang Zhu
    • 1
  • Artem R. Oganov
    • 1
    • 2
    • 3
    Email author
  • Xiang-Feng Zhou
    • 1
    • 4
  1. 1.Department of Geosciences, Center for Materials by DesignInstitute for Advanced Computational Science, SUNY Stony BrookNew YorkUSA
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudny CityRussia
  3. 3.School of Materials ScienceNorthwestern Polytechnical UniversityXi’anChina
  4. 4.School of PhysicsNankai UniversityTianjinChina

Personalised recommendations