Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Structure prediction drives materials discovery


Progress in the discovery of new materials has been accelerated by the development of reliable quantum-mechanical approaches to crystal structure prediction. The properties of a material depend very sensitively on its structure; therefore, structure prediction is the key to computational materials discovery. Structure prediction was considered to be a formidable problem, but the development of new computational tools has allowed the structures of many new and increasingly complex materials to be anticipated. These widely applicable methods, based on global optimization and relying on little or no empirical knowledge, have been used to study crystalline structures, point defects, surfaces and interfaces. In this Review, we discuss structure prediction methods, examining their potential for the study of different materials systems, and present examples of computationally driven discoveries of new materials — including superhard materials, superconductors and organic materials — that will enable new technologies. Advances in first-principle structure predictions also lead to a better understanding of physical and chemical phenomena in materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Mapping the materials space.
Fig. 2: Compound prediction with crystal structure prediction methods.
Fig. 3: Applications of crystal structure prediction to systems beyond bulk crystals.
Fig. 4: Superconducting materials.


  1. 1.

    Oganov, A. R. (ed.) Modern Methods of Crystal Structure Prediction (John Wiley & Sons, 2011).

  2. 2.

    Atahan-Evrenk, S. & Aspuru-Guzik, A. Topics in Current Chemistry Vol. 345 (Springer, 2014).

  3. 3.

    Oganov, A. R., Saleh, G. & Kvashnin, A. G. Computational Materials Discovery (Royal Society of Chemistry, 2018).

  4. 4.

    Bergerhoff, G., Hundt, R., Sievers, R. & Brown, I. D. The inorganic crystal structure data base. J. Chem. Inf. Comput. Sci. 23, 66–69 (1983).

    CAS  Google Scholar 

  5. 5.

    Villars, P. et al. The Pauling file, binaries edition. J. Alloys Compd. 367, 293–297 (2004).

    CAS  Google Scholar 

  6. 6.

    Curtarolo, S. et al. The high-throughput highway to computational materials design. Nat. Mater. 12, 191–201 (2013).

    CAS  Google Scholar 

  7. 7.

    Nosengo, N. Can artificial intelligence create the next wonder material? Nature 533, 22–25 (2016).

    CAS  Google Scholar 

  8. 8.

    Jain, A., Shin, Y. & Persson, K. A. Computational predictions of energy materials using density functional theory. Nat. Rev. Mater. 1, 15004 (2016).

    CAS  Google Scholar 

  9. 9.

    Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559, 547–555 (2018).

    CAS  Google Scholar 

  10. 10.

    Liu, H., Naumov, I. I., Hoffmann, R., Ashcroft, N. W. & Hemley, R. J. Potential high-Tc superconducting lanthanum and yttrium hydrides at high pressure. Proc. Natl Acad. Sci. USA 114, 6990–6995 (2017).

    CAS  Google Scholar 

  11. 11.

    Drozdov, A. P. et al. Superconductivity at 250 K in lanthanum hydride at high pressures. Preprint at arXiv (2018).

  12. 12.

    Somayazulu, M. et al. Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures. Phys. Rev. Lett. 122, 027001 (2019).

    CAS  Google Scholar 

  13. 13.

    Martin, R. M. Electronic Structure: Basic Theory and Practical Methods (Cambridge Univ. Press, 2004).

  14. 14.

    Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses (Cambridge Univ. Press, 2004).

  15. 15.

    Pickard, C. J. & Needs, R. J. Ab initio random structure searching. J. Phys. Condens. Matter 23, 053201 (2011).

    Google Scholar 

  16. 16.

    Martiniani, S., Schrenk, K. J., Stevenson, J. D., Wales, D. J. & Frenkel, D. Structural analysis of high-dimensional basins of attraction. Phys. Rev. E 94, 031301 (2016).

    Google Scholar 

  17. 17.

    Stevanovic, V. Sampling polymorphs of ionic solids using random superlattices. Phys. Rev. Lett. 116, 075503 (2016).

    Google Scholar 

  18. 18.

    Oganov, A. R. & Valle, M. How to quantify energy landscapes of solids. J. Chem. Phys. 130, 104504 (2009).

    Google Scholar 

  19. 19.

    Ceriotti, M., Tribello, G. A. & Parrinello, M. Demonstrating the transferability and the descriptive power of sketch-map. J. Chem. Theory Comput. 9, 1521–1532 (2013).

    CAS  Google Scholar 

  20. 20.

    Pettifor, D. A chemical scale for crystal-structure maps. Solid State Commun. 51, 31–34 (1984).

    CAS  Google Scholar 

  21. 21.

    Villars, P. A. A three-dimensional structural stability diagram for 1011 binary AB2 intermetallic compounds: II. J. Alloys Compd. 99, 33 (1984).

    CAS  Google Scholar 

  22. 22.

    Isayev, O. et al. Materials cartography: representing and mining materials space using structural and electronic fingerprints. Chem. Mater. 27, 735–743 (2015).

    CAS  Google Scholar 

  23. 23.

    Kitaigorodsky, A. I. The close-packing of molecules in crystals of organic compounds. J. Phys. 9, 351–352 (1945).

    Google Scholar 

  24. 24.

    Nowacki, W. Symmetrie und physikalisch-chemische Eigenschaften krystallisierter Verbindungen. I. Die Verteilung der Kristallstrukturen über die 219 Raumgruppen. Helv. Chim. Acta 25, 863–878 (1942).

    CAS  Google Scholar 

  25. 25.

    Baur, W. & Kassner, D. The perils of Cc: comparing the frequencies of falsely assigned space groups with their general population. Acta Cryst. B 48, 356–369 (1992).

    Google Scholar 

  26. 26.

    Urusov, V. S. & Nadezhina, T. N. Frequency distribution and selection of space groups in inorganic crystal chemistry. J. Struct. Chem. 50, 22–37 (2009).

    Google Scholar 

  27. 27.

    Pauling, L. The principles determining the structure of complex ionic crystals. J. Am. Chem. Soc. 51, 1010–1026 (1929).

    CAS  Google Scholar 

  28. 28.

    Villars, P. & Iwata, S. Binary, ternary and quaternary compound former/nonformer prediction via Mendeleev number. Chem. Met. Alloys 6, 81–108 (2013).

    Google Scholar 

  29. 29.

    Sun, W. et al. The thermodynamic scale of inorganic crystalline metastability. Sci. Adv. 2, e1600225 (2016).

    Google Scholar 

  30. 30.

    Zhang, W. et al. Unexpected stable stoichiometries of sodium chlorides. Science 342, 1502–1505 (2013).

    CAS  Google Scholar 

  31. 31.

    Dong, X. et al. A stable compound of helium and sodium at high pressure. Nat. Chem. 9, 440–445 (2017).

    CAS  Google Scholar 

  32. 32.

    Niu, H., Oganov, A. R., Chen, X.-Q. & Li, D. Prediction of novel stable compounds in the Mg-Si-O system under exoplanet pressures. Sci. Rep. 5, 18347 (2015).

    CAS  Google Scholar 

  33. 33.

    Oganov, A. R. & Glass, C. W. Crystal structure prediction using ab initio evolutionary techniques: principles and applications. J. Chem. Phys. 124, 244704 (2006).

    Google Scholar 

  34. 34.

    Valle, M. & Oganov, A. R. Crystal fingerprint space – a novel paradigm for studying crystal-structure sets. Acta Cryst. A 66, 507–517 (2010).

    CAS  Google Scholar 

  35. 35.

    Stillinger, F. H. Exponential multiplicity of inherent structures. Phys. Rev. E 59, 48 (1999).

    CAS  Google Scholar 

  36. 36.

    Freeman, C., Newsam, J., Levine, S. & Catlow, C. R. A. Inorganic crystal structure prediction using simplified potentials and experimental unit cells: application to the polymorphs of titanium dioxide. J. Mater. Chem. 3, 531–535 (1993).

    CAS  Google Scholar 

  37. 37.

    Schmidt, M. U. & Englert, U. Prediction of crystal structures. J. Chem. Soc. 1996, 2077–2082 (1996).

    Google Scholar 

  38. 38.

    Pickard, C. J. & Needs, R. J. High-pressure phases of silane. Phys. Rev. Lett. 97, 045504 (2006).

    Google Scholar 

  39. 39.

    Oganov, A. R., Lyakhov, A. O. & Valle, M. How evolutionary crystal structure prediction works - and why. Acc. Chem. Res. 44, 227–237 (2011).

    CAS  Google Scholar 

  40. 40.

    Deaven, D. M. & Ho, K.-M. Molecular geometry optimization with a genetic algorithm. Phys. Rev. Lett. 75, 288 (1995).

    CAS  Google Scholar 

  41. 41.

    Call, S. T., Zubarev, D. Y. & Boldyrev, A. I. Global minimum structure searches via particle swarm optimization. J. Comput. Chem. 28, 1177–1186 (2007).

    CAS  Google Scholar 

  42. 42.

    Wang, Y., Lv, J., Zhu, L. & Ma, Y. Crystal structure prediction via particle-swarm optimization. Phys. Rev. B 82, 094116 (2010).

    Google Scholar 

  43. 43.

    Lonie, D. C. & Zurek, E. Xtalopt: an open-source evolutionary algorithm for crystal structure prediction. Comp. Phys. Comm. 182, 372–387 (2011).

    CAS  Google Scholar 

  44. 44.

    Tipton, W. W. & Hennig, R. G. A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials. J. Phys. Condens. Matter 25, 495401 (2013).

    Google Scholar 

  45. 45.

    Martonak, R., Laio, A. & Parrinello, M. Predicting crystal structures: the Parrinello-Rahman method revisited. Phys. Rev. Lett. 90, 075503 (2003).

    CAS  Google Scholar 

  46. 46.

    Goedecker, S. Minima hopping: an efficient search method for the global minimum of the potential energy surface of complex molecular systems. J. Chem. Phys. 120, 9911 (2004).

    CAS  Google Scholar 

  47. 47.

    Amsler, M. & Goedecker, S. Crystal structure prediction using the minima hopping method. J. Chem. Phys. 133, 224104 (2010).

    Google Scholar 

  48. 48.

    Zhou, X.-F., Oganov, A. R., Qian, G.-R. & Zhu, Q. First-principles determination of the structure of magnesium borohydride. Phys. Rev. Lett. 109, 245503 (2012).

    Google Scholar 

  49. 49.

    Meredig, B. & Wolverton, C. A hybrid computational–experimental approach for automated crystal structure solution. Nat. Mater. 12, 123–127 (2013).

    CAS  Google Scholar 

  50. 50.

    Fortes, A. D., Suard, E., Lemee-Cailleau, M.-H., Pickard, C. J. & Needs, R. J. Crystal structure of ammonia monohydrate phase II. J. Am. Chem. Soc. 131, 13508 (2009).

    CAS  Google Scholar 

  51. 51.

    Naslain, R. & Kasper, J. S. The crystal structure of the phi phase in the boron-sodium system. J. Solid State Chem. 1, 150–151 (1970).

    CAS  Google Scholar 

  52. 52.

    Albert, B. A new old: sodium boride: Linked pentagonal bipyramids and octahedra in Na3B20. Angew. Chem. Int. Ed. 37, 1117–1118 (1998).

    CAS  Google Scholar 

  53. 53.

    He, X.-L. et al. Predicting the ground-state structure of sodium boride. Phys. Rev. B 97, 100102 (2018).

    CAS  Google Scholar 

  54. 54.

    Li, Y.-F. & Selloni, A. Mosaic texture and double c-axis periodicity of β-NiOOH: insights from first-principles and genetic algorithm calculations. J. Chem. Phys. Lett. 5, 3981–3985 (2014).

    CAS  Google Scholar 

  55. 55.

    Zakaryan, H. A., Kvashnin, A. G. & Oganov, A. R. Stable reconstruction of the (110) surface and its role in pseudocapacitance of rutile-like RuO2. Sci. Rep. 7, 10357 (2017).

    Google Scholar 

  56. 56.

    Morris, A. J., Grey, C. & Pickard, C. J. Thermodynamically stable lithium silicides and germanides from density functional theory calculations. Phys. Rev. B 90, 054111 (2014).

    Google Scholar 

  57. 57.

    Jung, H. et al. Elucidation of the local and long-range structural changes that occur in germanium anodes in lithium-ion batteries. Chem. Mater. 27, 1031–1041 (2015).

    CAS  Google Scholar 

  58. 58.

    Filinchuk, Y. et al. Porous and dense magnesium boro-hydride frameworks: synthesis, stability, and reversible absorption of guest species. Angew. Chem. Int. Ed. 50, 11162–11166 (2011).

    CAS  Google Scholar 

  59. 59.

    Zeng, Z. et al. A novel phase of Li15Si4 synthesized under pressure. Adv. Eng. Mater. 5, 1500214 (2015).

    Google Scholar 

  60. 60.

    Akahama, Y., Mizuki, Y., Nakano, S., Hirao, N. & Ohishi, Y. Raman scattering and X-ray diffraction studies on phase III of solid hydrogen. J. Phys. Conf. Ser. 950, 042060 (2017).

    Google Scholar 

  61. 61.

    Howie, R. T., Dalladay-Simpson, P. & Gregoryanz, E. Raman spectroscopy of hot hydrogen above 200 GPa. Nat. Mater. 14, 495–499 (2015).

    CAS  Google Scholar 

  62. 62.

    Akahama, Y. et al. Evidence from X-ray diffraction of orientational ordering in phase III of solid hydrogen at pressures up to 183 GPa. Phys. Rev. B 82, 060101 (2010).

    Google Scholar 

  63. 63.

    Dalladay-Simpson, P., Howie, R. T. & Gregoryanz, E. Evidence for a new phase of dense hydrogen above 325 Gigapascals. Nature 529, 63–67 (2016).

    CAS  Google Scholar 

  64. 64.

    Pickard, C. J. & Needs, R. J. Structure of phase III of solid hydrogen. Nat. Phys. 3, 473–476 (2007).

    CAS  Google Scholar 

  65. 65.

    Monserrat, B., Needs, R. J., Gregoryanz, E. & Pickard, C. J. Hexagonal structure of phase III of solid hydrogen. Phys. Rev. B 94, 134101 (2016).

    Google Scholar 

  66. 66.

    Monserrat, B. et al. Structure and metallicity of phase V of hydrogen. Phys. Rev. Lett. 120, 255701 (2018).

    CAS  Google Scholar 

  67. 67.

    Bartels-Rausch, T. et al. Ice structures, patterns, and processes: a view across the icefields. Rev. Mod. Phys. 84, 885 (2012).

    CAS  Google Scholar 

  68. 68.

    Falenty, A., Hansen, T. C. & Kuhs, W. F. Formation and properties of ice XVI obtained by emptying a type sII clathrate hydrate. Nature 516, 231–233 (2014).

    CAS  Google Scholar 

  69. 69.

    Pickard, C. J. & Needs, R. J. Highly compressed ammonia forms an ionic crystal. Nat. Mater. 7, 775–779 (2008).

    CAS  Google Scholar 

  70. 70.

    Ninet, S. et al. Experimental and theoretical evidence for an ionic crystal of ammonia at high pressure. Phys. Rev. B 89, 174103 (2014).

    Google Scholar 

  71. 71.

    Nakahata, I., Matsui, N., Akahama, Y. & Kawamura, H. Structural studies of solid methane at high pressures. Chem. Phys. Lett. 302, 359–362 (1999).

    CAS  Google Scholar 

  72. 72.

    Zhu, Q., Oganov, A. R., Glass, C. W. & Stokes, H. T. Constrained evolutionary algorithm for structure prediction of molecular crystals: methodology and applications. Acta Cryst. B 68, 215–226 (2012).

    Google Scholar 

  73. 73.

    Maynard-Casely, H. et al. The distorted close-packed crystal structure of methane A. J. Chem. Phys. 133, 064504 (2010).

    CAS  Google Scholar 

  74. 74.

    Zhou, Z. F. & Harris, K. D. M. Design of a molecular quasicrystal. ChemPhysChem 7, 1649–1653 (2006).

    CAS  Google Scholar 

  75. 75.

    Hautier, G., Fischer, C., Ehrlacher, V., Jain, A. & Ceder, G. Data mined ionic substitutions for the discovery of new compounds. Inorg. Chem. 50, 656–663 (2010).

    Google Scholar 

  76. 76.

    Davies, D. W. et al. Computer-aided design of metal chalcohalide semiconductors: from chemical composition to crystal structure. Chem. Sci. 9, 1022–1030 (2018).

    CAS  Google Scholar 

  77. 77.

    Allahyari, Z. & Oganov, A. R. Coevolutionary search for optimal materials in the space of all possible compounds. Preprint at arXiv (2018).

  78. 78.

    Lyakhov, A. O., Oganov, A. R., Stokes, H. T. & Zhu, Q. New developments in evolutionary structure prediction algorithm USPEX. Comput. Phys. Commun. 184, 1172–1182 (2013).

    CAS  Google Scholar 

  79. 79.

    Lyakhov, A. O. & Oganov, A. R. Evolutionary search for superhard materials: methodology and applications to forms of carbon and TiO2. Phys. Rev. B 84, 092103 (2011).

    Google Scholar 

  80. 80.

    Zhang, X. et al. First-principles structural design of superhard materials. J. Chem. Phys. 138, 114101 (2013).

    Google Scholar 

  81. 81.

    Zhu, Q., Oganov, A. R., Salvado, M. A., Pertierra, P. & Lyakhov, A. O. Denser than diamond: ab initio search for superdense carbon allotropes. Phys. Rev. B 83, 193410 (2011).

    Google Scholar 

  82. 82.

    Xiang, H., Huang, B., Kan, E., Wei, S.-H. & Gong, X. Towards direct-gap silicon phases by the inverse band structure design approach. Phys. Rev. Lett. 110, 118702 (2013).

    CAS  Google Scholar 

  83. 83.

    Nunez-Valdez, M., Allahyari, Z., Fan, T. & Oganov, A. R. Efficient technique for computational design of thermoelectric materials. Comput. Phys. Comm. 222, 152–157 (2018).

    CAS  Google Scholar 

  84. 84.

    Kvashnin, A. G., Oganov, A. R., Samtsevich, A. I. & Allahyari, Z. Computational search for novel hard chromium-based materials. J. Phys. Chem. Lett. 8, 755–764 (2017).

    CAS  Google Scholar 

  85. 85.

    Zhang, Y.-Y., Gao, W., Chen, S., Xiang, H. & Gong, X.-G. Inverse design of materials by multi-objective differential evolution. Comput. Mater. Sci. 98, 51–55 (2015).

    CAS  Google Scholar 

  86. 86.

    Yu, X.-H., Oganov, A. R., Zhu, Q., Qi, F. & Qian, G.-R. The stability and unexpected chemistry of oxide clusters. Phys. Chem. Chem. Phys. 20, 30437–30444 (2018).

    CAS  Google Scholar 

  87. 87.

    Lepeshkin, S. et al. Super-oxidation of silicon nanoclusters: magnetism and reactive oxygen species at the surface. Nanoscale 8, 1816–1820 (2016).

    CAS  Google Scholar 

  88. 88.

    Fubini, B. & Hubbard, A. Reactive oxygen species (ROS) and reactive nitrogen species (RNS) generation by silica in inflammation and fibrosis. Free Radic. Biol. Med. 34, 1507–1516 (2003).

    CAS  Google Scholar 

  89. 89.

    Lepeshkin, S. V., Baturin, V. S., Yu. Uspenskii, A. & Oganov, A. R. Method for simultaneous prediction of atomic structure and stability of nanoclusters in a wide area of compositions. J. Phys. Chem. Lett. 10, 102–106 (2019).

    CAS  Google Scholar 

  90. 90.

    Piazza, Z. A. et al. Planar hexagonal B36 as a potential basis for extended single-atom layer boron sheets. Nat. Commun. 5, 3113 (2014).

    Google Scholar 

  91. 91.

    Zhai, H.-J. et al. Observation of an all-boron fullerene. Nat. Chem. 6, 727–731 (2014).

    CAS  Google Scholar 

  92. 92.

    Ashton, M., Paul, J., Sinnott, S. B. & Hennig, R. G. Topology-scaling identification of layered solids and stable exfoliated 2D materials. Phys. Rev. Lett. 118, 106101 (2017).

    Google Scholar 

  93. 93.

    Revard, B. C., Tipton, W. W., Yesypenko, A. & Hennig, R. G. Grand-canonical evolutionary algorithm for the prediction of two-dimensional materials. Phys. Rev. B 93, 054117 (2016).

    Google Scholar 

  94. 94.

    Zhou, X.-F. et al. Semimetallic two-dimensional boron allotrope with massless Dirac fermions. Phys. Rev. Lett. 112, 085502 (2014).

    Google Scholar 

  95. 95.

    Mannix, A. J. et al. Synthesis of borophenes: Anisotropic, two-dimensional boron polymorphs. Science 350, 1513–1516 (2015).

    CAS  Google Scholar 

  96. 96.

    Zhu, Z. et al. Multivalency-driven formation of Te-based monolayer materials: a combined first-principles and experimental study. Phys. Rev. Lett. 119, 106101 (2017).

    Google Scholar 

  97. 97.

    Chen, J., Schusteritsch, G., Pickard, C. J., Salzmann, C. G. & Michaelides, A. Two dimensional ice from first principles: Structures and phase transitions. Phys. Rev. Lett. 116, 025501 (2016).

    Google Scholar 

  98. 98.

    Chen, J., Schusteritsch, G., Pickard, C. J., Salzmann, C. G. & Michaelides, A. Double-layer ice from first principles. Phys. Rev. B 95, 094121 (2017).

    Google Scholar 

  99. 99.

    Corsetti, F., Zubeltzu, J. & Artacho, E. Enhanced configurational entropy in high-density nanoconfined bilayer ice. Phys. Rev. Lett. 116, 085901 (2016).

    Google Scholar 

  100. 100.

    Binnig, G., Rohrer, H., Gerber, C. & Weibel, E. 7×7 reconstruction on Si (111) resolved in real space. Phys. Rev. Lett. 50, 120 (1983).

    CAS  Google Scholar 

  101. 101.

    Zhu, Q., Li, L., Oganov, A. R. & Allen, P. B. Evolutionary method for predicting surface reconstructions with variable stoichiometry. Phys. Rev. B 87, 195317 (2013).

    Google Scholar 

  102. 102.

    Lu, S., Wang, Y., Liu, H., M.-S., Miao & Ma, Y. Self-assembled ultrathin nanotubes on diamond (100) surface. Nat. Commun. 5, 3666 (2014).

    CAS  Google Scholar 

  103. 103.

    Chuang, F., Ciobanu, C. V., Shenoy, V., Wang, C.-Z. & Ho, K.-M. Finding the reconstructions of semiconductor surfaces via a genetic algorithm. Surf. Sci. 573, L375–L381 (2004).

    CAS  Google Scholar 

  104. 104.

    Sierka, M. et al. Oxygen adsorption on Mo(112) surface studied by ab initio genetic algorithm and experiment. J. Chem. Phys. 126, 234710 (2007).

    Google Scholar 

  105. 105.

    Vilhelmsen, L. B. & Hammer, B. A genetic algorithm for first principles global structure optimization of supported nano structures. J. Chem. Phys. 141, 044711 (2014).

    Google Scholar 

  106. 106.

    Wang, Q., Oganov, A. R., Zhu, Q. & Zhou, X.-F. New reconstructions of the (110) surface of rutile TiO2 predicted by an evolutionary method. Phys. Rev. Lett. 113, 266101 (2014).

    Google Scholar 

  107. 107.

    Zhou, R., Qu, B., Li, D., Sun, X. & Zeng, X. C. Anatase (101) reconstructed surface with novel functionalities: Desired bandgap for visible light absorption and high chemical reactivity. Adv. Func. Mater. 28, 1705529 (2018).

    Google Scholar 

  108. 108.

    Chen, P., Xu, Y., Wang, N., Oganov, A. R. & Duan, W. Effects of ferroelectric polarization on surface phase diagram: evolutionary algorithm study of the BaTiO3 (001) surface. Phys. Rev. B 92, 085432 (2015).

    Google Scholar 

  109. 109.

    Harmer, M. P. The phase behavior of interfaces. Science 332, 182–183 (2011).

    CAS  Google Scholar 

  110. 110.

    Von Alfthan, S., Haynes, P., Kaski, K. & Sutton, A. Are the structures of twist grain boundaries in silicon ordered at 0 K? Phys. Rev. Lett. 96, 055505 (2006).

    Google Scholar 

  111. 111.

    Frolov, T., Divinski, S., Asta, M. & Mishin, Y. Effect of interface phase transformations on diffusion and segregation in high-angle grain boundaries. Phys. Rev. Lett. 110, 255502 (2013).

    CAS  Google Scholar 

  112. 112.

    Frolov, T., Olmsted, D. L., Asta, M. & Mishin, Y. Structural phase transformations in metallic grain boundaries. Nat. Commun. 4, 1899 (2013).

    Google Scholar 

  113. 113.

    Schusteritsch, G. & Pickard, C. J. Predicting interface structures: from SrTiO3 to graphene. Phys. Rev. B. 90, 035424 (2014).

    Google Scholar 

  114. 114.

    Zhu, Q., Samanta, A., Li, B., Rudd, R. E. & Frolov, T. Predicting phase behavior of grain boundaries with evolutionary search and machine learning. Nat. Commun. 9, 467 (2018).

    Google Scholar 

  115. 115.

    Frolov, T. et al. Grain boundary phases in bcc metals. Nanoscale 10, 8253–8268 (2018).

    CAS  Google Scholar 

  116. 116.

    Xiang, H., Da Silva, J. L., Branz, H. M. & Wei, S.-H. Understanding the clean interface between covalent Si and ionic Al2O3. Phys. Rev. Lett. 103, 116101 (2009).

    CAS  Google Scholar 

  117. 117.

    Chua, A. L.-S., Benedek, N. A., Chen, L., Finnis, M. W. & Sutton, A. P. A genetic algorithm for predicting the structures of interfaces in multicomponent systems. Nat. Mater. 9, 418 (2010).

    CAS  Google Scholar 

  118. 118.

    Zhao, X. et al. Interface structure prediction from first-principles. J. Phys. Chem. C 118, 9524–9530 (2014).

    CAS  Google Scholar 

  119. 119.

    Caviglia, A. et al. Electric field control of the LaAlO3/SrTiO3 interface ground state. Nature 456, 624–627 (2008).

    CAS  Google Scholar 

  120. 120.

    Weber, J. et al. Quantum computing with defects. Proc. Natl Acad. Sci. USA 107, 8513–8518 (2010).

    CAS  Google Scholar 

  121. 121.

    Coomer, B. J., Goss, J. P., Jones, R., Oberg, S. & Briddon, P. R. Identification of the tetra-interstitial in silicon. J. Phys. Condens. Matter 13, L1–L7 (2001).

    CAS  Google Scholar 

  122. 122.

    Humble, P. The structure and mechanism of formation of platelets in natural type Ia diamond. Proc. R. Soc. A 381, 65–81 (1982).

    CAS  Google Scholar 

  123. 123.

    Morris, A. J., Pickard, C. J. & Needs, R. J. Hydrogen/silicon complexes in silicon from computational searches. Phys. Rev. B 78, 184102 (2008).

    Google Scholar 

  124. 124.

    Morris, A. J., Pickard, C. J. & Needs, R. J. Hydrogen/nitrogen/oxygen defect complexes in silicon from computational searches. Phys. Rev. B 80, 144112 (2009).

    Google Scholar 

  125. 125.

    Mulroue, J., Morris, A. J. & Duffy, D. M. Ab initio study of intrinsic defects in zirconolite. Phys. Rev. B 84, 094118 (2011).

    Google Scholar 

  126. 126.

    Morris, A. J., Grey, C. P., Needs, R. J. & Pickard, C. J. Energetics of hydrogen/lithium complexes in silicon analyzed using the Maxwell construction. Phys. Rev. B 84, 224106 (2011).

    Google Scholar 

  127. 127.

    Kaczmarowski, A., Yang, S., Szlufarska, I. & Morgan, D. Genetic algorithm optimization of defect clusters in crystalline materials. Comput. Mater. Sci. 98, 234–244 (2015).

    CAS  Google Scholar 

  128. 128.

    Aust, R. & Drickamer, H. Carbon: a new crystalline phase. Science 140, 817–819 (1963).

    CAS  Google Scholar 

  129. 129.

    Utsumi, W. & Yagi, T. Light-transparent phase formed by room-temperature compression of graphite. Science 252, 1542–1544 (1991).

    CAS  Google Scholar 

  130. 130.

    Mao, W. L. et al. Bonding changes in compressed superhard graphite. Science 302, 425–427 (2003).

    CAS  Google Scholar 

  131. 131.

    Li, Q. et al. Superhard monoclinic polymorph of carbon. Phys. Rev. Lett. 102, 175506 (2009).

    Google Scholar 

  132. 132.

    Umemoto, K., Wentzcovitch, R. M., Saito, S. & Miyake, T. Body-centered tetragonal C4: a viable sp3 carbon allotrope. Phys. Rev. Lett. 104, 125504 (2010).

    Google Scholar 

  133. 133.

    Wang, J.-T., Chen, C. & Kawazoe, Y. Low-temperature phase transformation from graphite to sp3 orthorhombic carbon. Phys. Rev. Lett. 106, 075501 (2011).

    Google Scholar 

  134. 134.

    Niu, H. et al. Families of superhard crystalline carbon allotropes constructed via cold compression of graphite and nanotubes. Phys. Rev. Lett. 108, 135501 (2012).

    Google Scholar 

  135. 135.

    Boulfelfel, S. E., Oganov, A. R. & Leoni, S. Understanding the nature of superhard graphite. Sci. Rep. 2, 471 (2012).

    Google Scholar 

  136. 136.

    Wang, Y., Panzik, J. E., Kiefer, B. & Lee, K. K. Crystal structure of graphite under room-temperature compression and decompression. Sci. Rep. 2, 520 (2012).

    Google Scholar 

  137. 137.

    Oganov, A. R. & Solozhenko, V.L. Boron: a hunt for superhard polymorphs. J. Superhard Mater. 31, 285 (2009).

    Google Scholar 

  138. 138.

    Oganov, A. R. et al. Ionic high-pressure form of elemental boron. Nature 457, 863–867 (2009).

    CAS  Google Scholar 

  139. 139.

    Solozhenko, V.L., Kurakevych, O. & Oganov, A. R. On the hardness of a new boron phase, orthorhombic γ-B28. J. Superhard Mater. 30, 428 (2008).

    Google Scholar 

  140. 140.

    Podryabinkin, E. V., Tikhonov, E. V., Shapeev, A. V., Oganov, A. R. Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning. Phys. Rev. B 99, 064114 (2019).

  141. 141.

    Niu, H. et al. Structure, bonding, and possible superhardness of CrB4. Phys. Rev. B 85, 144116 (2012).

    Google Scholar 

  142. 142.

    Kvashnin, A. G. et al. New tungsten borides, their stability and outstanding mechanical properties. J. Phys. Chem. Lett. 9, 3470–3477 (2018).

    CAS  Google Scholar 

  143. 143.

    Kolmogorov, A. et al. New superconducting and semiconducting Fe-B compounds predicted with an ab initio evolutionary search. Phys. Rev. Lett. 105, 217003 (2010).

    CAS  Google Scholar 

  144. 144.

    Gou, H. et al. Discovery of a superhard iron tetraboride superconductor. Phys. Rev. Lett. 111, 157002 (2013).

    Google Scholar 

  145. 145.

    Zhang, M. et al. Hardness of FeB4: density functional theory investigation. J. Chem. Phys. 140, 174505 (2014).

    Google Scholar 

  146. 146.

    Wang, Q. et al. Is orthorhombic iron tetraboride superhard? J. Materiomics 1, 45–51 (2015).

    Google Scholar 

  147. 147.

    Van Der Geest, A. & Kolmogorov, A. Stability of 41 metal–boron systems at 0 GPa and 30 GPa from first principles. Calphad 46, 184–204 (2014).

    Google Scholar 

  148. 148.

    Niu, H. et al. Variable-composition structural optimization and experimental verification of MnB3 and MnB4. Phys. Chem. Chem. Phys. 16, 15866–15873 (2014).

    CAS  Google Scholar 

  149. 149.

    Hu, X. et al. Atomic-scale observation and analysis of chemical ordering in M3B2 and M5B3 borides. Acta Mater. 149, 274–284 (2018).

    CAS  Google Scholar 

  150. 150.

    Yu, S., Zeng, Q., Oganov, A. R., Frapper, G. & Zhang, L. Phase stability, chemical bonding and mechanical properties of titanium nitrides: a first-principles study. Phys. Chem. Chem. Phys. 17, 11763–11769 (2015).

    CAS  Google Scholar 

  151. 151.

    Bhadram, V. S., Kim, D. Y. & Strobel, T. A. High-pressure synthesis and characterization of incompressible titanium per-nitride. Chem. Mater. 28, 1616–1620 (2016).

    CAS  Google Scholar 

  152. 152.

    Schilling, A., Cantoni, M., Guo, J. & Ott, H. Superconductivity above 130 K in the Hg–Ba–Ca–Cu–O system. Nature 363, 56–58 (1993).

    CAS  Google Scholar 

  153. 153.

    Monteverde, M. et al. High-pressure effects in fluorinated HgBa2Ca2Cu3O8+δ. Europhys. Lett. 72, 458–464 (2005).

    CAS  Google Scholar 

  154. 154.

    Ashcroft, N. W. Metallic hydrogen: a high-temperature superconductor? Phys. Rev. Lett. 21, 1748 (1968).

    CAS  Google Scholar 

  155. 155.

    Ashcroft, N. W. Hydrogen dominant metallic alloys: high temperature superconductors? Phys. Rev. Lett. 92, 187002 (2004).

    CAS  Google Scholar 

  156. 156.

    Duan, D. et al. Pressure-induced metallization of dense (H2S)2H2 with high-Tc superconductivity. Sci. Rep. 4, 6968 (2014).

    CAS  Google Scholar 

  157. 157.

    Drozdov, A. P., Eremets, M. I., Troyan, I. A., Ksenofontov, V. & Shylin, S. I. Conventional superconductivity at 203 Kelvin at high pressures in the sulfur hydride system. Nature 525, 73–76 (2015).

    CAS  Google Scholar 

  158. 158.

    Errea, I. et al. Quantum hydrogen-bond symmetrization in the superconducting hydrogen sulfide system. Nature 532, 81–84 (2016).

    CAS  Google Scholar 

  159. 159.

    Errea, I. et al. High-pressure hydrogen sulfide from first principles: a strongly anharmonic phonon-mediated superconductor. Phys. Rev. Lett. 114, 157004 (2015).

    Google Scholar 

  160. 160.

    Einaga, M. et al. Crystal structure of the superconducting phase of sulfur hydride. Nat. Phys. 12, 835–838 (2016).

    CAS  Google Scholar 

  161. 161.

    Goncharov, A. F. et al. Hydrogen sulfide at high pressure: change in stoichiometry. Phys. Rev. B 93, 174105 (2016).

    Google Scholar 

  162. 162.

    Li, Y. et al. Dissociation products and structures of solid H2S at strong compression. Phys. Rev. B 93, 020103 (2016).

    Google Scholar 

  163. 163.

    Kruglov, I., Akashi, R., Yoshikawa, S., Oganov, A. R. & Esfahani Davari, M. M. Refined phase diagram of the H-S system with high-Tc superconductivity. Phys. Rev. B 96, 220101 (2017).

    Google Scholar 

  164. 164.

    Wang, H., Tse, J. S., Tanaka, K., Iitaka, T. & Ma, Y. Superconductive sodalite-like clathrate calcium hydride at high pressures. Proc. Natl Acad. Sci. USA 109, 6463–6466 (2012).

    CAS  Google Scholar 

  165. 165.

    Li, Y. et al. Pressure-stabilized superconductive yttrium hydrides. Sci. Rep. 5, 9948 (2015).

    CAS  Google Scholar 

  166. 166.

    Kvashnin, A. G., Semenok, D. V., Kruglov, I. A., Wrona, I. A. & Oganov, A. R. High-temperature superconductivity in a Th–H system under pressure conditions. ACS Appl. Mater. Interfaces 10, 43809–43816 (2018).

    CAS  Google Scholar 

  167. 167.

    Semenok, D., Kvashnin, A. G., Kruglov, I. A. & Oganov, A. R. Actinium hydrides AcH10, AcH12, and AcH16 as high-temperature conventional superconductors. J. Phys. Chem. Lett. 9, 1920–1926 (2018).

    CAS  Google Scholar 

  168. 168.

    Peng, F. et al. Hydrogen clathrate structures in rare earth hydrides at high pressures: possible route to room-temperature superconductivity. Phys. Rev. Lett. 119, 107001 (2017).

    Google Scholar 

  169. 169.

    Geballe, Z. M. et al. Synthesis and stability of lanthanum superhydrides. Angew. Chem. Int. Ed. 57, 688–692 (2017).

    Google Scholar 

  170. 170.

    Kitano, M. et al. Ammonia synthesis using a stable electride as an electron donor and reversible hydrogen store. Nat. Chem. 4, 934–940 (2012).

    CAS  Google Scholar 

  171. 171.

    Ellaboudy, A., Dye, J. L. & Smith, P. B. Cesium 18-crown-6 compounds. A crystalline ceside and a crystalline electride. J. Am. Chem. Soc. 105, 6490–6491 (1983).

    CAS  Google Scholar 

  172. 172.

    Dye, J. L. Electrides: Ionic salts with electrons as the anions. Science 247, 663–668 (1990).

    CAS  Google Scholar 

  173. 173.

    Matsuishi, S. et al. High-density electron anions in a nanoporous single crystal: [Ca24Al28O64]4+(4e-). Science 301, 626–629 (2003).

    CAS  Google Scholar 

  174. 174.

    Ma, Y. et al. Transparent dense sodium. Nature 458, 182–185 (2009).

    CAS  Google Scholar 

  175. 175.

    Pickard, C. J. & Needs, R. J. Predicted pressure-induced s-band ferromagnetism in alkali metals. Phys. Rev. Lett. 107, 087201 (2011).

    Google Scholar 

  176. 176.

    Pickard, C. J. & Needs, R. J. Aluminium at terapascal pressures. Nat. Mater. 9, 624–627 (2010).

    CAS  Google Scholar 

  177. 177.

    Miao, M.-S. & Hoffmann, R. High pressure electrides: a predictive chemical and physical theory. Acc. Chem. Res. 47, 1311–1317 (2014).

    CAS  Google Scholar 

  178. 178.

    Inoshita, T., Jeong, S., Hamada, N. & Hosono, H. Exploration for two-dimensional electrides via database screening and ab initio calculation. Phys. Rev. X 4, 031023 (2014).

    Google Scholar 

  179. 179.

    Ming, W., Yoon, M., Du, M.-H., Lee, K. & Kim, S. W. First-principles prediction of thermodynamically stable two-dimensional electrides. J. Am. Chem. Soc. 138, 15336–15344 (2016).

    CAS  Google Scholar 

  180. 180.

    Zhang, Y., Wang, H., Wang, Y., Zhang, L. & Ma, Y. Computer-assisted inverse design of inorganic electrides. Phys. Rev. X 7, 011017 (2017).

    Google Scholar 

  181. 181.

    Wang, J. et al. Exploration of stable strontium phosphide-based electrides: theoretical structure prediction and experimental validation. J. Am. Chem. Soc. 139, 15668–15680 (2017).

    CAS  Google Scholar 

  182. 182.

    Price, S. L. Predicting crystal structures of organic compounds. Chem. Soc. Rev. 43, 2098–2111 (2014).

    CAS  Google Scholar 

  183. 183.

    Day, G. M. Current approaches to predicting molecular organic crystal structures. Crystallogr. Rev. 17, 3–52 (2011).

    Google Scholar 

  184. 184.

    Reilly, A. M. et al. Report on the sixth blind test of organic crystal structure prediction methods. Acta Cryst. B 72, 439–459 (2016).

    CAS  Google Scholar 

  185. 185.

    Oganov, A. R. Crystal structure prediction: reflections on present status and challenges. Faraday Discuss. 211, 643–660 (2018).

    CAS  Google Scholar 

  186. 186.

    Bull, C. L. et al. ζ-glycine: insight into the mechanism of a polymorphic phase transition. IUCrJ 4, 569–574 (2017).

    CAS  Google Scholar 

  187. 187.

    Neumann, M., Van De Streek, J., Fabbiani, F., Hidber, P. & Grassmann, O. Combined crystal structure prediction and high-pressure crystallization in rational pharmaceutical polymorph screening. Nat. Commun. 6, 7793 (2015).

    CAS  Google Scholar 

  188. 188.

    Zhu, Q. et al. Resorcinol crystallization from the melt: a new ambient phase and new riddles. J. Am. Chem. Soc. 138, 4881–4889 (2016).

    CAS  Google Scholar 

  189. 189.

    Xu, W., Zhu, Q. & Hu, C. T. The structure of glycine dihydrate: implications for the crystallization of glycine from solution and its structure in outer space. Angew. Chem. 129, 2030–2034 (2017).

    Google Scholar 

  190. 190.

    Shtukenberg, A. G. et al. Powder diffraction and crystal structure prediction identify four new coumarin polymorphs. Chem. Sci. 8, 4926–4940 (2017).

    CAS  Google Scholar 

  191. 191.

    Shtukenberg, A. G. et al. The third ambient aspirin polymorph. Cryst. Growth Des. 17, 3562–3566 (2017).

    CAS  Google Scholar 

  192. 192.

    Yang, J. et al. DDT polymorphism and the lethality of crystal forms. Angew. Chem. Int. Ed. 56, 10165–10169 (2017).

    CAS  Google Scholar 

  193. 193.

    Sokolov, A. N. et al. From computational discovery to experimental characterization of a high hole mobility organic crystal. Nat. Commun. 2, 437 (2011).

    Google Scholar 

  194. 194.

    Campbell, J. E., Yang, J. & Day, G. M. Predicted energy–structure–function maps for the evaluation of small molecule organic semiconductors. J. Mater. Chem. C 5, 7574–7584 (2017).

    CAS  Google Scholar 

  195. 195.

    Yang, J. et al. Large–scale computational screening of molecular organic semiconductors using crystal structure prediction. Chem. Mater. 30, 4361–4371 (2018).

    CAS  Google Scholar 

  196. 196.

    Musil, F. et al. Machine learning for the structure–energy–property landscapes of molecular crystals. Chem. Sci. 9, 1289–1300 (2018).

    CAS  Google Scholar 

  197. 197.

    Berardo, E., Turcani, L., Miklitz, M. & Jelfs, K. E. An evolutionary algorithm for the discovery of porous organic cages. Chem. Sci. 9, 8513–8527 (2018).

    CAS  Google Scholar 

  198. 198.

    Wang, Q. et al. Direct band gap silicon allotropes. Chem. Soc. 136, 9826–9829 (2014).

    CAS  Google Scholar 

  199. 199.

    Mujica, A., Pickard, C. J. & Needs, R. J. Low-energy tetrahedral polymorphs of carbon, silicon, and germanium. Phys. Rev. B 91, 214104 (2015).

    Google Scholar 

  200. 200.

    Amsler, M., Botti, S., Marques, M. A., Lenosky, T. J. & Goedecker, S. Low-density silicon allotropes for photovoltaic applications. Phys. Rev. B 92, 014101 (2015).

    Google Scholar 

  201. 201.

    Kim, D. Y., Stefanoski, S., Kurakevych, O. O. & Strobel, T. A. Synthesis of an open-framework allotrope of silicon. Nat. Mater. 14, 169–173 (2015).

    CAS  Google Scholar 

  202. 202.

    Zhu, Q., Oganov, A. R., Lyakhov, A. O. & Yu, X. Generalized evolutionary metadynamics for sampling the energy landscapes and its applications. Phys. Rev. B 92, 024106 (2015).

    Google Scholar 

  203. 203.

    Rapp, L. et al. Experimental evidence of new tetragonal polymorphs of silicon formed through ultrafast laser-induced confined microexplosion. Nat. Commun. 6, 7555 (2015).

    CAS  Google Scholar 

  204. 204.

    Su, C. et al. Construction of crystal structure prototype database: methods and applications. J. Phys. Condens. Matter 29, 165901 (2017).

    Google Scholar 

  205. 205.

    Bushlanov, P. V., Blatov, V. A. & Oganov, A. R. Topology-based crystal structure generator. Comput. Phys. Commun. 236, 1–7 (2019).

    CAS  Google Scholar 

  206. 206.

    Ahnert, S. E., Grant, W. P. & Pickard, C. J. Revealing and exploiting hierarchical material structure through complex atomic networks. NPJ Comput. Mater. 3, 35 (2017).

    Google Scholar 

  207. 207.

    Moran, R. F. et al. Hunting for hydrogen: random structure searching and prediction of NMR parameters of hydrous wadsleyite. Phys. Chem. Chem. Phys. 18, 10173–10181 (2016).

    CAS  Google Scholar 

  208. 208.

    Monserrat, B., Drummond, N. D. & Needs, R. J. Anharmonic vibrational properties in periodic systems: energy, electron- phonon coupling, and stress. Phys. Rev. B 87, 144302 (2013).

    Google Scholar 

  209. 209.

    Souvatzis, P., Eriksson, O., Katsnelson, M. & Rudin, S. Entropy driven stabilization of energetically unstable crystal structures explained from first principles theory. Phys. Rev. Lett. 100, 095901 (2008).

    CAS  Google Scholar 

  210. 210.

    Allen, M. P. & Tildesley, D. J. Computer Simulation of Liquids (Oxford Univ. Press, 2017).

  211. 211.

    Fontaine, D. D. Configurational thermodynamics of solid solutions. Solid State Phys. 34, 73–274 (1979).

    Google Scholar 

  212. 212.

    Zarkevich, N. A. & Johnson, D. D. Reliable first-principles alloy thermodynamics via truncated cluster expansions. Phys. Rev. Lett. 92, 255702 (2004).

    Google Scholar 

  213. 213.

    National Centre of Competence in Research MARVEL. Download the Quantum Mobile Virtual Machine based on Ubuntu Linux with a collection of quantum simulation codes. MARVEL (2017).

  214. 214.

    Khrapov, N., Roizen, V., Posypkin, M., Samtsevich, A. & Oganov, A. R. Volunteer computing for computational materials design. Lobachevskii J. Math. 38, 926–930 (2017).

    Google Scholar 

  215. 215.

    Cao, Y. et al. Quantum chemistry in the age of quantum computing. Preprint at arXiv (2018).

  216. 216.

    Bitzek, E., Koskinen, P., Gahler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Phys. Rev. Lett. 97, 170201 (2006).

    Google Scholar 

  217. 217.

    Michalewicz, Z. & Fogel, D. B. How to Solve It: Modern Heuristics (Springer, 2013).

  218. 218.

    Pannetier, J., Bassas-Alsina, J., Rodriguez-Carvajal, J. & Caignaert, V. Prediction of crystal structures from crystal chemistry rules by simulated annealing. Nature 346, 343–345 (1990).

    CAS  Google Scholar 

  219. 219.

    Schon, J. C. & Jansen, M. First step towards planning of syntheses in solid-state chemistry: determination of promising structure candidates by global optimization. Angew. Chem. Int. Ed. 35, 1286–1304 (1996).

    Google Scholar 

  220. 220.

    Wales, D. J. & Doye, J. P. 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 (1997).

    CAS  Google Scholar 

  221. 221.

    Judson, R. S., Jaeger, E. P., Treasurywala, A. M. & Peterson, M. L. Conformational searching methods for small molecules. II. Genetic algorithm approach. J. Comput. Chem. 14, 1407–1414 (1993).

    CAS  Google Scholar 

  222. 222.

    Bush, T., Catlow, C. R. A. & Battle, P. Evolutionary programming techniques for predicting inorganic crystal structures. J. Mater. Chem. 5, 1269–1272 (1995).

    CAS  Google Scholar 

  223. 223.

    Curtis, F. et al. GAtor: a first-principles genetic algorithm for molecular crystal structure prediction. J. Chem. Theory Comput. 14, 2246–2264 (2018).

    CAS  Google Scholar 

  224. 224.

    Zhu, Q., Oganov, A. R. & Lyakhov, A. O. Evolutionary metadynamics: a novel method to predict crystal structures. CrystEngComm 14, 3596–3601 (2012).

    CAS  Google Scholar 

  225. 225.

    Lejaeghere, K. et al. Reproducibility in density functional theory calculations of solids. Science 351, aad3000 (2016).

    Google Scholar 

  226. 226.

    Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).

    Google Scholar 

  227. 227.

    Behler, J. Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations. Phys. Chem. Chem. Phys. 13, 17930–17955 (2011).

    CAS  Google Scholar 

  228. 228.

    Bartok, A. P., Payne, M. C., Kondor, R. & Csanyi, G. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).

    Google Scholar 

  229. 229.

    Behler, J., Martonak, R., Donadio, D. & Parrinello, M. Metadynamics simulations of the high-pressure phases of silicon employing a high-dimensional neural network potential. Phys. Rev. Lett. 100, 185501 (2008).

    Google Scholar 

  230. 230.

    Deringer, V. L., J. Pickard, C. & Csanyi, G. Data-driven learning of total and local energies in elemental boron. Phys. Rev. Lett. 120, 156001 (2018).

    CAS  Google Scholar 

  231. 231.

    Isayev, O. et al. Universal fragment descriptors for predicting properties of inorganic crystals. Nat. Commun. 8, 15679 (2017).

    CAS  Google Scholar 

  232. 232.

    Zhao, X. et al. Exploring the structural complexity of intermetallic compounds by an adaptive genetic algorithm. Phys. Rev. Lett. 112, 045502 (2014).

    CAS  Google Scholar 

  233. 233.

    Sharma, V. et al. Rational design of all organic polymer dielectrics. Nat. Commun. 5, 4845 (2014).

    CAS  Google Scholar 

  234. 234.

    Nicholls, R. J. et al. Crystal structure of the ZrO phase at zirconium/zirconium oxide interfaces. Adv. Eng. Mater. 17, 211–215 (2015).

    CAS  Google Scholar 

  235. 235.

    Pickard, C. J., Salamat, A., Bojdys, M. J., Needs, R. J. & McMillan, P. F. Carbon nitride frameworks and dense crystalline polymorphs. Phys. Rev. B 94, 094104 (2016).

    Google Scholar 

  236. 236.

    Kruglov, I. A. et al. Uranium polyhydrides at moderate pressures: prediction, synthesis, and expected superconductivity. Sci. Adv. 4, eaat9776 (2018).

    Google Scholar 

  237. 237.

    Wang, Q., Oganov, A. R., Feya, O. D., Zhu, Q. & Ma, D. The unexpectedly rich reconstructions of rutile TiO2(011)-(2×1) surface and the driving forces behind their formation: an ab initio evolutionary study. Phys. Chem. Chem. Phys. 18, 19549–19556 (2016).

    CAS  Google Scholar 

  238. 238.

    Schusteritsch, G., Hepplestone, S. P. & Pickard, C. J. First-principles structure determination of interface materials: the NixInAs nickelides. Phys. Rev. B 92, 054105 (2015).

    Google Scholar 

Download references


A.R.O. thanks the Russian Science Foundation (grant 19-72-30043) for generous support of his research. Q.Z. is funded by the National Nuclear Security Administration under the Stewardship Science Academic Alliances Program through the Department of Energy Cooperative Agreement DE-NA0001982. C.J.P. is supported by the Royal Society through a Royal Society Wolfson Research Merit Award. R.J.N. is funded by the Engineering and Physical Sciences Research Council under grant EP/P034616/1.

Author information




The authors contributed equally to all aspects of the article.

Corresponding authors

Correspondence to Artem R. Oganov or Chris J. Pickard.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links













Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Oganov, A.R., Pickard, C.J., Zhu, Q. et al. Structure prediction drives materials discovery. Nat Rev Mater 4, 331–348 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing