Skip to main content

Thank you for visiting nature.com. 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.

  • Review Article
  • Published:

Electronic-structure methods for materials design

Nature Materials volume 20, pages 736–749 (2021)Cite this article

Subjects

Abstract

The accuracy and efficiency of electronic-structure methods to understand, predict and design the properties of materials has driven a new paradigm in research. Simulations can greatly accelerate the identification, characterization and optimization of materials, with this acceleration driven by continuous progress in theory, algorithms and hardware, and by adaptation of concepts and tools from computer science. Nevertheless, the capability to identify and characterize materials relies on the predictive accuracy of the underlying physical descriptions, and on the ability to capture the complexity of realistic systems. We provide here an overview of electronic-structure methods, of their application to the prediction of materials properties, and of the different strategies employed towards the broader goals of materials design and discovery.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: An overview of some key first-principles approaches to predict materials properties.

panels reproduced with permission from: a, ref. 166, APS; b, ref. 182, Springer Nature Ltd; c, ref. 129, APS; e, ref. 91, APS. Panel d adapted with permission from ref. 79, APS

Fig. 2: An overview of some key first-principles approaches to predict materials properties and spectroscopies.

panels reproduced with permission from: a, ref. 183, APS; c, ref. 168, APS; e, ref. 117, Springer Nature Ltd; f, ref. 60, Springer Nature Ltd. Panels adapted with permission from: b, ref. 172, APS; d, ref. 32, AIP

Fig. 3: An illustration of the high-throughput screening approach.

figure reproduced with permission from ref. 148, under a Creative Commons License CC BY 4.0

Similar content being viewed by others

References

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

    Article  CAS  Google Scholar 

  2. Bartók, A. P. et al. Machine learning unifies the modeling of materials and molecules. Sci. Adv. 3, e1701816 (2017).

    Article  Google Scholar 

  3. Tshitoyan, V. et al. Unsupervised word embeddings capture latent knowledge from materials science literature. Nature 571, 95–98 (2019).

    Article  CAS  Google Scholar 

  4. Di Ventra, M. & Traversa, F. L. Perspective: memcomputing: leveraging memory and physics to compute efficiently. J. Appl. Phys. 123, 180901 (2018).

    Article  CAS  Google Scholar 

  5. Barkoutsos, P. K. et al. Quantum algorithms for electronic structure calculations: particle–hole Hamiltonian and optimized wave-function expansions. Phys. Rev. A 98, 022322 (2018).

    Article  CAS  Google Scholar 

  6. Pribram-Jones, A., Gross, D. A. & Burke, K. DFT: a theory full of holes? Rev. Phys. Chem. 66, 283–304 (2015).

    Article  CAS  Google Scholar 

  7. Hohenberg, P. & Kohn, W. Inhomogeneus electron gas. Phys. Rev. 136, B864–B871 (1964).

    Article  Google Scholar 

  8. van Noorden, R., Maher, B. & Nuzzo, R. The top 100 papers. Nature 514, 550–553 (2014).

    Article  CAS  Google Scholar 

  9. van Setten, M. J. et al. GW100: benchmarking G0W0 for molecular systems. J. Chem. Theory Comput. 11, 5665–5687 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  11. Rangel, T. et al. Reproducibility in G0W0 calculations for solids. Comput. Phys. Commun. 255, 107242 (2020).

    Article  CAS  Google Scholar 

  12. de Jong, M. et al. Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data 2, 150009 (2015).

    Article  CAS  Google Scholar 

  13. Isaacs, E. B. & Wolverton, C. Performance of the strongly constrained and appropriately normed density functional for solid-state materials. Phys. Rev. Mater. 2, 063801 (2018).

    Article  CAS  Google Scholar 

  14. Borlido, P. et al. Large-scale benchmark of exchange-correlation functionals for the determination of electronic band gaps of solids. J. Chem. Theory Comput. 15, 5069–5079 (2019).

    Article  CAS  Google Scholar 

  15. Marzari, N. Materials modelling: the frontiers and the challenges. Nat. Mater. 15, 381–382 (2016).

    Article  CAS  Google Scholar 

  16. Parr, R. G. & Yang, W. Density-Functional Theory of Atoms and Molecules (Oxford Science Publications, 1989).

  17. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    Article  Google Scholar 

  18. Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).

    Article  CAS  Google Scholar 

  19. Giustino, F. Electron–phonon interactions from first principles. Rev. Mod. Phys. 89, 015003 (2017).

    Article  Google Scholar 

  20. Errea, I. et al. Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride. Nature 578, 66–69 (2020).

    Article  CAS  Google Scholar 

  21. Perdew, J. P. & Levy, M. Physical content of the exact Kohn–Sham orbital energies: band gap and derivative discontinuities. Phys. Rev. Lett. 51, 1884–1887 (1983).

    Article  CAS  Google Scholar 

  22. Godby, R. W., Schlüter, M. & Sham, L. J. Trends in self-energy operators and their corresponding exchange-correlation potentials. Phys. Rev. B 36, 6497–6500 (1987).

    Article  CAS  Google Scholar 

  23. Casida, M. E. Generalization of the optimized-effective-potential model to include electron correlation: a variational derivation of the Sham–Schlüter equation for the exact exchange-correlation potential. Phys. Rev. A 51, 2005–2013 (1995).

    Article  CAS  Google Scholar 

  24. Perdew, J. P. et al. Understanding band gaps of solids in generalized Kohn–Sham theory. Proc. Natl Acad. Sci. USA 114, 2801–2806 (2017).

    Article  CAS  Google Scholar 

  25. Nguyen, N. L., Colonna, N., Ferretti, A. & Marzari, N. Koopmans-compliant spectral functionals for extended systems. Phys. Rev. X 8, 021051 (2018).

    Google Scholar 

  26. Sun, J., Ruzsinszky, A. & Perdew, J. P. Strongly constrained and appropriately normed semilocal density functional. Phys. Rev. Lett. 115, 036402 (2015).

    Article  CAS  Google Scholar 

  27. Anisimov, V. I., Zaanen, J. & Andersen, O. K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44, 943–954 (1991).

    Article  CAS  Google Scholar 

  28. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).

    Article  CAS  Google Scholar 

  29. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A. & Joannopoulos, J. D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045–1097 (1992).

    Article  CAS  Google Scholar 

  30. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  Google Scholar 

  31. Ghiringhelli, L. M. et al. Towards efficient data exchange and sharing for big-data driven materials science: metadata and data formats. npj Comput. Mater. 3, 46 (2017).

    Article  CAS  Google Scholar 

  32. Skylaris, C.-K., Haynes, P. D., Mostofi, A. A. & Payne, M. C. Introducing ONETEP: linear-scaling density functional simulations on parallel computers. J. Chem. Phys. 122, 084119 (2005).

    Article  CAS  Google Scholar 

  33. Wang, Y. A. & Carter, E. A. in Theoretical Methods in Condensed Phase Chemistry (ed. Schwartz, S. D.) 117–184 (Springer, 2002).

  34. Baer, R., Neuhauser, D. & Rabani, E. Self-averaging stochastic Kohn–Sham density-functional theory. Phys. Rev. Lett. 111, 106402 (2013).

    Article  CAS  Google Scholar 

  35. Gunnarsson, O. & Lundqvist, B. I. Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 13, 4274–4298 (1976).

    Article  CAS  Google Scholar 

  36. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  37. Fu, Y. & Singh, D. J. Applicability of the strongly constrained and appropriately normed density functional to transition-metal magnetism. Phys. Rev. Lett. 121, 207201 (2018).

    Article  CAS  Google Scholar 

  38. Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).

    Article  CAS  Google Scholar 

  39. Peverati, R. & Truhlar, D. G. Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Phil. Trans. R. Soc. A 372, 20120476 (2014).

    Article  CAS  Google Scholar 

  40. Tran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. Phys. Rev. Lett. 102, 226401 (2009).

    Article  CAS  Google Scholar 

  41. Gritsenko, O., van Leeuwen, R., van Lenthe, E. & Baerends, E. J. Self-consistent approximation to the Kohn–Sham exchange potential. Phys. Rev. A 51, 1944–1954 (1995).

    Article  CAS  Google Scholar 

  42. Görling, A. Hierarchies of methods towards the exact Kohn–Sham correlation energy based on the adiabatic-connection fluctuation-dissipation theorem. Phys. Rev. B 99, 235120 (2019).

    Article  Google Scholar 

  43. Cohen, A. J., Mori-Sanchez, P. & Yang, W. Insights into current limitations of density functional theory. Science 321, 792–794 (2008).

    Article  CAS  Google Scholar 

  44. Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981).

    Article  CAS  Google Scholar 

  45. Pederson, M. R., Ruzsinszky, A. & Perdew, J. P. Communication: self-interaction correction with unitary invariance in density functional theory. J. Chem. Phys. 140, 121103 (2014).

    Article  CAS  Google Scholar 

  46. Cococcioni, M. & Gironcoli, S. D. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B 71, 035105 (2005).

    Article  CAS  Google Scholar 

  47. Kronik, L. & Kümmel, S. Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional. Phys. Chem. Chem. Phys. 22, 16467–16481 (2020).

    Article  CAS  Google Scholar 

  48. Dabo, I. et al. Koopmans’ condition for density-functional theory. Phys. Rev. B 82, 115121 (2010).

    Article  CAS  Google Scholar 

  49. Refaely-Abramson, S., Jain, M., Sharifzadeh, S., Neaton, J. B. & Kronik, L. Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory. Phys. Rev. B 92, 081204 (2015).

    Article  CAS  Google Scholar 

  50. Perdew, J. P., Ernzerhof, M. & Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 105, 9982–9985 (1996).

    Article  CAS  Google Scholar 

  51. Brawand, N. P., Vörös, M., Govoni, M. & Galli, G. Generalization of dielectric-dependent hybrid functionals to finite systems. Phys. Rev. X 6, 041002 (2016).

    Google Scholar 

  52. Stöhr, M., Van Voorhis, T. & Tkatchenko, A. Theory and practice of modeling van der Waals interactions in electronic-structure calculations. Chem. Soc. Rev. 48, 4118–4154 (2019).

    Article  Google Scholar 

  53. Cococcioni, M. & Marzari, N. Energetics and cathode voltages of LiMPO4 olivines (M=Fe,Mn) from extended Hubbard functionals. Phys. Rev. Mater. 3, 033801 (2019).

    Article  Google Scholar 

  54. Blügel, S., Weinert, M. & Dederichs, P. H. Ferromagnetism and antiferromagnetism of 3d-metal overlayers on metals. Phys. Rev. Lett. 60, 1077–1080 (1988).

    Article  Google Scholar 

  55. Niu, Q. & Kleinman, L. Spin-wave dynamics in real crystals. Phys. Rev. Lett. 80, 2205–2208 (1998).

    Article  CAS  Google Scholar 

  56. Heinze, S. et al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011).

    Article  CAS  Google Scholar 

  57. Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996).

    Article  CAS  Google Scholar 

  58. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).

    Article  CAS  Google Scholar 

  59. Biermann, S., Aryasetiawan, F. & Georges, A. First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory. Phys. Rev. Lett. 90, 086402 (2003).

    Article  CAS  Google Scholar 

  60. Werner, P. et al. Satellites and large doping and temperature dependence of electronic properties in hole-doped BaFe2As2. Nat. Phys. 8, 331–337 (2012).

    Article  CAS  Google Scholar 

  61. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).

    Article  CAS  Google Scholar 

  62. Falke, S. M. et al. Coherent ultrafast charge transfer in an organic photovoltaic blend. Science 344, 1001–1005 (2014).

    Article  CAS  Google Scholar 

  63. Sangalli, D., Dal Conte, S., Manzoni, C., Cerullo, G. & Marini, A. Nonequilibrium optical properties in semiconductors from first principles: a combined theoretical and experimental study of bulk silicon. Phys. Rev. B 93, 195205 (2016).

    Article  CAS  Google Scholar 

  64. Ullrich, C. A. Time-Dependent Density-Functional Theory: Concepts and Applications (Oxford Univ. Press, 2012).

  65. Stefanucci, G. & van Leeuwen, R. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge Univ. Press, 2013).

  66. Martin, R. M., Reining, L. & Ceperley, D. Interacting Electrons Theory and Computational Approaches (Cambridge Univ. Press, 2016).

  67. de Melo, P. M. M. C. & Marini, A. Unified theory of quantized electrons, phonons, and photons out of equilibrium: a simplified ab initio approach based on the generalized Baym–Kadanoff ansatz. Phys. Rev. B 93, 155102 (2016).

    Article  CAS  Google Scholar 

  68. Giustino, F. Materials Modelling Using Density Functional Theory (Oxford Univ. Press, 2014).

  69. Alfè, D., Gillan, M. J. & Price, G. D. The melting curve of iron at the pressures of the Earth’s core from ab initio calculations. Nature 401, 462–464 (1999).

    Article  Google Scholar 

  70. Cavazzoni, C. et al. Superionic and metallic states of water and ammonia at giant planet conditions. Science 283, 44–46 (1999).

    Article  CAS  Google Scholar 

  71. Car, R. & Parrinello, M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985).

    Article  CAS  Google Scholar 

  72. Parrinello, M. & Rahman, A. Crystal structure and pair potentials: a molecular-dynamics study. Phys. Rev. Lett. 45, 1196–1199 (1980).

    Article  CAS  Google Scholar 

  73. Teter, M. P., Payne, M. C. & Allan, D. C. Solution of Schrödinger’s equation for large systems. Phys. Rev. B 40, 12255–12263 (1989).

    Article  CAS  Google Scholar 

  74. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  CAS  Google Scholar 

  75. Marzari, N., Vanderbilt, D. & Payne, M. C. Ensemble density-functional theory for ab initio molecular dynamics of metals and finite-temperature insulators. Phys. Rev. Lett. 79, 1337–1340 (1997).

    Article  CAS  Google Scholar 

  76. Frenkel, D. & Smit, B. Understanding Molecular Simulation: From Algorithms to Applications (Academic-Press, 2001).

  77. Marx, D. & Parrinello, M. Structural quantum effects and three-centre two-electron bonding in CH\({}_{5}^{+}\). Nature 375, 216–218 (1995).

    Article  CAS  Google Scholar 

  78. Ceriotti, M., Bussi, G. & Parrinello, M. Langevin equation with colored noise for constant-temperature molecular dynamics simulations. Phys. Rev. Lett. 102, 020601 (2009).

    Article  CAS  Google Scholar 

  79. Giannozzi, P., de Gironcoli, S., Pavone, P. & Baroni, S. Ab initio calculation of phonon dispersions in semiconductors. Phys. Rev. B 43, 7231–7242 (1991).

    Article  CAS  Google Scholar 

  80. Gonze, X. & Lee, C. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B 55, 10355–10368 (1997).

    Article  CAS  Google Scholar 

  81. Milman, V. et al. Free energy and entropy of diffusion by ab initio molecular dynamics: alkali ions in silicon. Phys. Rev. Lett. 70, 2928–2931 (1993).

    Article  CAS  Google Scholar 

  82. Laio, A. & Parrinello, M. Escaping free-energy minima. Proc. Natl Acad. Sci. USA 99, 12562–12566 (2002).

    Article  CAS  Google Scholar 

  83. Körmann, F., Dick, A., Grabowski, B., Hickel, T. & Neugebauer, J. Atomic forces at finite magnetic temperatures: phonons in paramagnetic iron. Phys. Rev. B 85, 125104 (2012).

    Article  CAS  Google Scholar 

  84. Hammer, B. & Norskov, J. K. Why gold is the noblest of all the metals. Nature 376, 238–240 (1995).

    Article  CAS  Google Scholar 

  85. De Vita, A., Štich, I., Gillan, M. J., Payne, M. C. & Clarke, L. J. Dynamics of dissociative chemisorption: Cl2/Si(111)-(2 × 1). Phys. Rev. Lett. 71, 1276–1279 (1993).

    Article  Google Scholar 

  86. Nørskov, J. K. et al. Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B 108, 17886–17892 (2004).

    Article  CAS  Google Scholar 

  87. Lazzeri, M., Vittadini, A. & Selloni, A. Structure and energetics of stoichiometric TiO2 anatase surfaces. Phys. Rev. B 63, 155409 (2001).

    Article  CAS  Google Scholar 

  88. Reuter, K., Frenkel, D. & Scheffler, M. The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics. Phys. Rev. Lett. 93, 116105 (2004).

    Article  CAS  Google Scholar 

  89. Hörmann, N. G., Andreussi, O. & Marzari, N. Grand canonical simulations of electrochemical interfaces in implicit solvation models. J. Chem. Phys. 150, 041730 (2019).

    Article  CAS  Google Scholar 

  90. Persson, K. A., Waldwick, B., Lazic, P. & Ceder, G. Prediction of solid-aqueous equilibria: scheme to combine first-principles calculations of solids with experimental aqueous states. Phys. Rev. B 85, 235438 (2012).

    Article  CAS  Google Scholar 

  91. Jóhannesson, G. H. et al. Combined electronic structure and evolutionary search approach to materials design. Phys. Rev. Lett. 88, 255506 (2002).

    Article  CAS  Google Scholar 

  92. Zhong, W., Vanderbilt, D. & Rabe, K. M. First-principles theory of ferroelectric phase transitions for perovskites: the case of BaTiO3. Phys. Rev. B 52, 6301–6312 (1995).

    Article  CAS  Google Scholar 

  93. Naumov, I. I., Bellaiche, L. & Fu, H. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737–740 (2004).

    Article  CAS  Google Scholar 

  94. Csányi, G., Albaret, T., Payne, M. C. & De Vita, A. ‘Learn on the fly’: a hybrid classical and quantum-mechanical molecular dynamics simulation. Phys. Rev. Lett. 93, 175503 (2004).

    Article  CAS  Google Scholar 

  95. Li, Z., Kermode, J. R. & De Vita, A. Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. Phys. Rev. Lett. 114, 096405 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  98. Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012).

    Article  CAS  Google Scholar 

  99. Son, Y.-W., Cohen, M. L. & Louie, S. G. Half-metallic graphene nanoribbons. Nature 444, 347–349 (2006).

    Article  CAS  Google Scholar 

  100. Prezzi, D., Varsano, D., Ruini, A. & Molinari, E. Quantum dot states and optical excitations of edge-modulated graphene nanoribbons. Phys. Rev. B 84, 041401 (2011).

    Article  CAS  Google Scholar 

  101. Ruffieux, P. et al. On-surface synthesis of graphene nanoribbons with zigzag edge topology. Nature 531, 489–492 (2016).

    Article  CAS  Google Scholar 

  102. Pham, T. A., Ping, Y. & Galli, G. Modelling heterogeneous interfaces for solar water splitting. Nat. Mater. 16, 401–408 (2017).

    Article  CAS  Google Scholar 

  103. Poncé, S., Li, W., Reichardt, S. & Giustino, F. First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials. Rep. Prog. Phys. 83, 036501 (2020).

    Article  CAS  Google Scholar 

  104. Cepellotti, A. & Marzari, N. Thermal transport in crystals as a kinetic theory of relaxons. Phys. Rev. X 6, 041013 (2016).

    Google Scholar 

  105. Simoncelli, M., Marzari, N. & Mauri, F. Unified theory of thermal transport in crystals and glasses. Nat. Phys. 15, 809–813 (2019).

    Article  CAS  Google Scholar 

  106. Bernardi, M., Vigil-Fowler, D., Lischner, J., Neaton, J. B. & Louie, S. G. Ab initio study of hot carriers in the first picosecond after sunlight absorption in silicon. Phys. Rev. Lett. 112, 257402 (2014).

    Article  CAS  Google Scholar 

  107. Gonze, X. & Vigneron, J.-P. Density-functional approach to nonlinear-response coefficients of solids. Phys. Rev. B 39, 13120–13128 (1989).

    Article  CAS  Google Scholar 

  108. Marcolongo, A., Umari, P. & Baroni, S. Microscopic theory and quantum simulation of atomic heat transport. Nat. Phys. 12, 80–84 (2016).

    Article  CAS  Google Scholar 

  109. Song, J. & Curtin, W. A. Atomic mechanism and prediction of hydrogen embrittlement in iron. Nat. Mater. 12, 145–151 (2013).

    Article  CAS  Google Scholar 

  110. Arsenlis, A. et al. Enabling strain hardening simulations with dislocation dynamics. Model. Simul. Mater. Sci. Eng. 15, 553–595 (2007).

    Article  Google Scholar 

  111. Pasquarello, A. & Car, R. Identification of Raman defect lines as signatures of ring structures in vitreous silica. Phys. Rev. Lett. 80, 5145–5147 (1998).

    Article  CAS  Google Scholar 

  112. Puzder, A., Williamson, A. J., Grossman, J. C. & Galli, G. Surface chemistry of silicon nanoclusters. Phys. Rev. Lett. 88, 097401 (2002).

    Article  CAS  Google Scholar 

  113. Pickard, C. J. & Mauri, F. All-electron magnetic response with pseudopotentials: NMR chemical shifts. Phys. Rev. B 63, 245101 (2001).

    Article  CAS  Google Scholar 

  114. Golze, D., Dvorak, M. & Rinke, P. The GW compendium: a practical guide to theoretical photoemission spectroscopy. Front. Chem. 7, 377 (2019).

    Article  CAS  Google Scholar 

  115. Neaton, J. B., Hybertsen, M. S. & Louie, S. G. Renormalization of molecular electronic levels at metal-molecule interfaces. Phys. Rev. Lett. 97, 216405 (2006).

    Article  CAS  Google Scholar 

  116. Thygesen, K. S. & Rubio, A. Renormalization of molecular quasiparticle levels at metal–molecule interfaces: trends across binding regimes. Phys. Rev. Lett. 102, 046802 (2009).

    Article  CAS  Google Scholar 

  117. Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat. Phys. 5, 438–442 (2009).

    Article  CAS  Google Scholar 

  118. Vanderbilt, D. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge Univ. Press, 2018).

  119. Resta, R. & Vanderbilt, D. Theory of Polarization: A Modern Approach 31–68 (Springer, 2007).

  120. Resta, R. Theory of the electric polarization in crystals. Ferroelectrics 136, 51–55 (1992).

    Article  CAS  Google Scholar 

  121. King-Smith, R. D. & Vanderbilt, D. Theory of polarization of crystalline solids. Phys. Rev. B 47, 1651–1654 (1993).

    Article  CAS  Google Scholar 

  122. Xiao, D., Shi, J. & Niu, Q. Berry phase correction to electron density of states in solids. Phys. Rev. Lett. 95, 137204 (2005).

    Article  CAS  Google Scholar 

  123. Thonhauser, T., Ceresoli, D., Vanderbilt, D. & Resta, R. Orbital magnetization in periodic insulators. Phys. Rev. Lett. 95, 137205 (2005).

    Article  CAS  Google Scholar 

  124. Gonze, X., Ghosez, P. & Godby, R. W. Density-polarization functional theory of the response of a periodic insulating solid to an electric field. Phys. Rev. Lett. 74, 4035–4038 (1995).

    Article  CAS  Google Scholar 

  125. Gresch, D. et al. Z2Pack: numerical implementation of hybrid Wannier centers for identifying topological materials. Phys. Rev. B 95, 075146 (2017).

    Article  Google Scholar 

  126. Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

    Article  CAS  Google Scholar 

  127. Sanchez, J., Ducastelle, F. & Gratias, D. Generalized cluster description of multicomponent systems. Physica A 128, 334–350 (1984).

    Article  Google Scholar 

  128. Zunger, A., Wei, S.-H., Ferreira, L. G. & Bernard, J. E. Special quasirandom structures. Phys. Rev. Lett. 65, 353–356 (1990).

    Article  CAS  Google Scholar 

  129. Ferreira, L. G., Wei, S.-H. & Zunger, A. First-principles calculation of alloy phase diagrams: the renormalized-interaction approach. Phys. Rev. B 40, 3197–3231 (1989).

    Article  CAS  Google Scholar 

  130. de Fontaine, D. Cluster approach to order-disorder transformations in alloys. Solid State Phys. 47, 33–176 (1994).

    Article  Google Scholar 

  131. Ozoliņš, V., Wolverton, C. & Zunger, A. Cu-Au, Ag-Au, Cu-Ag, and Ni-Au intermetallics: first-principles study of temperature-composition phase diagrams and structures. Phys. Rev. B 57, 6427–6443 (1998).

    Article  Google Scholar 

  132. Ceder, G., Kohan, A. F., Aydinol, M. K., Tepesch, P. D. & van der Ven, A. Thermodynamics of oxides with substitutional disorder: a microscopic model and evaluation of important energy contributions. J. Am. Ceram. Soc. 81, 517–525 (1998).

    Article  CAS  Google Scholar 

  133. de Fontaine, D., Ceder, G. & Asta, M. Low-temperature long-range oxygen order in YBa2Cu3Oz. Nature 343, 544–546 (1990).

    Article  Google Scholar 

  134. Wolverton, C. & Zunger, A. First-principles prediction of vacancy order-disorder and intercalation battery voltages in LixCoO2. Phys. Rev. Lett. 81, 606–609 (1998).

    Article  CAS  Google Scholar 

  135. Wolverton, C. First-principles prediction of equilibrium precipitate shapes in Al-Cu alloys. Phil. Mag. Lett. 79, 683–690 (1999).

    Article  CAS  Google Scholar 

  136. Maddox, J. Crystals from first principles. Nature 335, 201 (1988).

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  139. Bligaard, T. et al. Pareto-optimal alloys. Appl. Phys. Lett. 83, 4527–4529 (2003).

    Article  CAS  Google Scholar 

  140. Curtarolo, S., Morgan, D., Persson, K., Rodgers, J. & Ceder, G. Predicting crystal structures with data mining of quantum calculations. Phys. Rev. Lett. 91, 135503 (2003).

    Article  CAS  Google Scholar 

  141. Jain, A. et al. Commentary: The materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  CAS  Google Scholar 

  142. Curtarolo, S. et al. AFLOWLIB.ORG: a distributed materials properties repository from high-throughput ab initio calculations. Comput. Mat. Sci. 58, 227–235 (2012).

    Article  CAS  Google Scholar 

  143. Saal, J. E., Kirklin, S., Aykol, M., Meredig, B. & Wolverton, C. Materials design and discovery with high-throughput density functional theory: the Open Quantum Materials Database (OQMD). JOM 65, 1501–1509 (2013).

    Article  CAS  Google Scholar 

  144. Haastrup, S. et al. The computational 2D materials database: high-throughput modeling and discovery of atomically thin crystals. 2D Mater. 5, 042002 (2018).

    Article  CAS  Google Scholar 

  145. Talirz, L. et al. Materials cloud, a platform for open computational science. Sci. Data 7, 299 (2020).

    Article  Google Scholar 

  146. Choudhary, K. et al. The Joint Automated Repository for Various Integrated Simulations (JARVIS) for data-driven materials design. npj Comput. Mater. 6, 173 (2020).

    Article  Google Scholar 

  147. Draxl, C. & Scheffler, M. The NOMAD laboratory: from data sharing to artificial intelligence. J. Phys. Mat. 2, 036001 (2019).

    Article  CAS  Google Scholar 

  148. Singh, A. K., Montoya, J. H., Gregoire, J. M. & Persson, K. A. Robust and synthesizable photocatalysts for CO2 reduction: a data-driven materials discovery. Nat. Commun. 10, 443 (2019).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  150. Hautier, G. Finding the needle in the haystack: materials discovery and design through computational ab initio high-throughput screening. Comput. Mater. Sci. 163, 108–116 (2019).

    Article  CAS  Google Scholar 

  151. Meredig, B. et al. Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys. Rev. B 89, 094104 (2014).

    Article  CAS  Google Scholar 

  152. Ward, L., Agrawal, A., Choudhary, A. & Wolverton, C. A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput. Mater. 2, 16028 (2016).

    Article  Google Scholar 

  153. Ward, L. et al. Matminer: an open source toolkit for materials data mining. Comput. Mater. Sci. 152, 60–69 (2018).

    Article  Google Scholar 

  154. Ghiringhelli, L. M., Vybiral, J., Levchenko, S. V., Draxl, C. & Scheffler, M. Big data of materials science: Critical role of the descriptor. Phys. Rev. Lett. 114, 105503 (2015).

    Article  CAS  Google Scholar 

  155. Bartók, A. P., Kondor, R. & Csányi, G. On representing chemical environments. Phys. Rev. B 87, 184115 (2013).

    Article  CAS  Google Scholar 

  156. Faber, F. A., Lindmaa, A., von Lilienfeld, O. A. & Armiento, R. Machine learning energies of 2 million elpasolite (ABC2D6) crystals. Phys. Rev. Lett. 117, 135502 (2016).

    Article  CAS  Google Scholar 

  157. Ward, L. et al. Including crystal structure attributes in machine learning models of formation energies via Voronoi tessellations. Phys. Rev. B 96, 024104 (2017).

    Article  Google Scholar 

  158. Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).

    Article  CAS  Google Scholar 

  159. Chen, C., Ye, W., Zuo, Y., Zheng, C. & Ong, S. P. Graph networks as a universal machine learning framework for molecules and crystals. Chem. Mater. 31, 3564–3572 (2019).

    Article  CAS  Google Scholar 

  160. Park, C. W. & Wolverton, C. Developing an improved crystal graph convolutional neural network framework for accelerated materials discovery. Phys. Rev. Mater. 4, 063801 (2020).

    Article  CAS  Google Scholar 

  161. Aykol, M. et al. Network analysis of synthesizable materials discovery. Nat. Commun. 10, 2018 (2019).

    Article  CAS  Google Scholar 

  162. Hegde, V. I., Aykol, M., Kirklin, S. & Wolverton, C. The phase stability network of all inorganic materials. Sci. Adv. 6, eaay5606 (2020).

    Article  CAS  Google Scholar 

  163. Lindsay, L., Broido, D. A. & Reinecke, T. L. First-principles determination of ultrahigh thermal conductivity of boron arsenide: a competitor for diamond? Phys. Rev. Lett. 111, 025901 (2013).

    Article  CAS  Google Scholar 

  164. Li, Y., Hao, J., Liu, H., Li, Y. & Ma, Y. The metallization and superconductivity of dense hydrogen sulfide. J. Chem. Phys. 140, 174712 (2014).

    Article  CAS  Google Scholar 

  165. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  CAS  Google Scholar 

  166. Yin, M. T. & Cohen, M. L. Microscopic theory of the phase transformation and lattice dynamics of Si. Phys. Rev. Lett. 45, 1004–1007 (1980).

    Article  CAS  Google Scholar 

  167. Freysoldt, C. et al. First-principles calculations for point defects in solids. Rev. Mod. Phys. 86, 253–305 (2014).

    Article  Google Scholar 

  168. Mauri, F., Zakharov, O., de Gironcoli, S., Louie, S. G. & Cohen, M. L. Phonon softening and superconductivity in tellurium under pressure. Phys. Rev. Lett. 77, 1151–1154 (1996).

    Article  CAS  Google Scholar 

  169. Spaldin, N. A. & Ramesh, R. Advances in magnetoelectric multiferroics. Nat. Mater. 18, 203–212 (2019).

    Article  CAS  Google Scholar 

  170. de Gironcoli, S., Giannozzi, P. & Baroni, S. Structure and thermodynamics of SixGe1−x alloys from ab initio Monte Carlo simulations. Phys. Rev. Lett. 66, 2116–2119 (1991).

    Article  Google Scholar 

  171. Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Phys. Rev. B 31, 805–813 (1985).

    Article  CAS  Google Scholar 

  172. Albrecht, S., Reining, L., Del Sole, R. & Onida, G. Ab initio calculation of excitonic effects in the optical spectra of semiconductors. Phys. Rev. Lett. 80, 4510–4513 (1998).

    Article  CAS  Google Scholar 

  173. Rohlfing, M. & Louie, S. G. Excitonic effects and the optical absorption spectrum of hydrogenated Si clusters. Phys. Rev. Lett. 80, 3320–3323 (1998).

    Article  CAS  Google Scholar 

  174. Prandini, G., Rignanese, G.-M. & Marzari, N. Photorealistic modelling of metals from first principles. npj Comput. Mater. 5, 129 (2019).

    Article  Google Scholar 

  175. Attaccalite, C., Grüning, M. & Marini, A. Real-time approach to the optical properties of solids and nanostructures: time-dependent Bethe–Salpeter equation. Phys. Rev. B 84, 245110 (2011).

    Article  CAS  Google Scholar 

  176. Kioupakis, E., Steiauf, D., Rinke, P., Delaney, K. T. & Van de Walle, C. G. First-principles calculations of indirect Auger recombination in nitride semiconductors. Phys. Rev. B 92, 035207 (2015).

    Article  CAS  Google Scholar 

  177. Gilmore, K. et al. Efficient implementation of core-excitation Bethe–Salpeter equation calculations. Comput. Phys. Commun. 197, 109–117 (2015).

    Article  CAS  Google Scholar 

  178. Calandra, M. et al. K-edge X-ray absorption spectra in transition-metal oxides beyond the single-particle approximation: shake-up many-body effects. Phys. Rev. B 86, 165102 (2012).

    Article  CAS  Google Scholar 

  179. Alonso, J. L. et al. Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory. Phys. Rev. Lett. 101, 096403 (2008).

    Article  CAS  Google Scholar 

  180. Tokatly, I. V. Time-dependent density functional theory for many-electron systems interacting with cavity photons. Phys. Rev. Lett. 110, 233001 (2013).

    Article  CAS  Google Scholar 

  181. Ruggenthaler, M. et al. Quantum-electrodynamical density-functional theory: bridging quantum optics and electronic-structure theory. Phys. Rev. A 90, 012508 (2014).

    Article  CAS  Google Scholar 

  182. De Vita, A., Galli, G., Canning, A. & Car, R. A microscopic model for surface-induced diamond-to-graphite transitions. Nature 379, 523–526 (1996).

    Article  CAS  Google Scholar 

  183. Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986).

    Article  CAS  Google Scholar 

  184. Szabo, A. & Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (McGraw-Hill, 1989).

  185. Booth, G. H., Grüneis, A., Kresse, G. & Alavi, A. Towards an exact description of electronic wavefunctions in real solids. Nature 493, 365–370 (2013).

    Article  CAS  Google Scholar 

  186. Ceperley, D. M. & Alder, B. J. Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569 (1980).

    Article  CAS  Google Scholar 

  187. Foulkes, W. M. C., Mitas, L., Needs, R. J. & Rajagopal, G. Quantum Monte Carlo simulations of solids. Rev. Mod. Phys. 73, 33–83 (2001).

    Article  CAS  Google Scholar 

  188. Lathiotakis, N. et al. Density-matrix-power functional: performance for finite systems and the homogeneous electron gas. Phys. Rev. A 79, 040501 (2009).

    Article  CAS  Google Scholar 

  189. Ferretti, A., Dabo, I., Cococcioni, M. & Marzari, N. Bridging density-functional and many-body perturbation theory: orbital-density dependence in electronic-structure functionals. Phys. Rev. B 89, 195134 (2014).

    Article  CAS  Google Scholar 

  190. Gatti, M., Olevano, V., Reining, L. & Tokatly, I. Transforming nonlocality into a frequency dependence: a shortcut to spectroscopy. Phys. Rev. Lett. 99, 057401 (2007).

    Article  CAS  Google Scholar 

  191. Vanzini, M. et al. Design of auxiliary systems for spectroscopy. Faraday Discuss. 224, 424–447 (2020).

    Article  CAS  Google Scholar 

  192. Runge, E. & Gross, E. K. U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52, 997–1000 (1984).

    Article  CAS  Google Scholar 

  193. Petersilka, M., Gossmann, U. J. & Gross, E. K. U. Excitation energies from time-dependent density-functional theory. Phys. Rev. Lett. 76, 1212–1215 (1996).

    Article  CAS  Google Scholar 

  194. Lee, C.-C., Hsueh, H. C. & Ku, W. Dynamical linear response of TDDFT with LDA+U functional: strongly hybridized frenkel excitons in NiO. Phys. Rev. B 82, 081106 (2010).

    Article  CAS  Google Scholar 

  195. Caruso, F., Verdi, C., Poncé, S. & Giustino, F. Electron–plasmon and electron–phonon satellites in the angle-resolved photoelectron spectra of n-doped anatase TiO2. Phys. Rev. B 97, 165113 (2018).

    Article  CAS  Google Scholar 

  196. Hedin, L. New method for calculating the one-particle Green’s function with application to the electron gas problem. Phys. Rev. 139, A796–A823 (1965).

    Article  Google Scholar 

  197. van Schilfgaarde, M., Kotani, T. & Faleev, S. Quasiparticle self-consistent GW theory. Phys. Rev. Lett. 96, 226402 (2006).

    Article  CAS  Google Scholar 

  198. Schindlmayr, A., García-González, P. & Godby, R. W. Diagrammatic self-energy approximations and the total particle number. Phys. Rev. B 64, 235106 (2001).

    Article  CAS  Google Scholar 

  199. Del Sole, R., Reining, L. & Godby, R. W. GWΓ approximation for electron self-energies in semiconductors and insulators. Phys. Rev. B 49, 8024–8028 (1994).

    Article  Google Scholar 

  200. Guzzo, M. et al. Valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites. Phys. Rev. Lett. 107, 166401 (2011).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge all the students, researchers and colleagues that developed the theories, algorithms and codes underpinning the research sketched here and that could not always be explicitly cited, but are indirectly present through the references. We are grateful for support from the Swiss NSF for the National Centre for Competence in Research MARVEL on ‘Computational Design and Discovery of Novel Materials’ (N.M.), from the EU Commission for the MaX Centre of Excellence on ‘Materials Design at the eXascale’ under grant no. 824143 (A.F., N.M.), and from the US Department of Commerce and the National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD) under grant no. 70NANB14H012 (C.W.).

Author information

Authors and Affiliations

  1. Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Nicola Marzari

  2. Centro S3, CNR-Istituto Nanoscienze, Modena, Italy

    Andrea Ferretti

  3. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

    Chris Wolverton

Authors
  1. Nicola Marzari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Ferretti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chris Wolverton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicola Marzari.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks Graeme Watson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marzari, N., Ferretti, A. & Wolverton, C. Electronic-structure methods for materials design. Nat. Mater. 20, 736–749 (2021). https://doi.org/10.1038/s41563-021-01013-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-021-01013-3

This article is cited by

Search

Advanced search

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