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.

  • Perspective
  • Published:

Guidelines for robust and reproducible point defect simulations in crystals

Nature Reviews Materials (2026)Cite this article

Subjects

Abstract

Many physical properties of functional materials are governed by their impurities rather than their bulk characteristics. Defects in crystals can activate electronic and ionic conductivity, create active centres for catalysis or store information through localized spin configurations. Accurate modelling of defect behaviour is therefore essential for predicting material performance and optimizing functionality across a vast application space. However, defect simulations are sensitive to choices made during setup, execution and analysis. In this Perspective, we highlight best practices for calculating and reporting point defect properties through computational methods, with a focus on the widely adopted supercell approach. Key considerations include accurate representation of the structural and electronic properties of the host material, appropriate choice of charge states, sufficient optimization of defect geometries and reproducible calculation of defect formation energies. Adhering to these practices will facilitate robust comparisons between studies and improve the integration of computational predictions with experimental results. We emphasize the importance of reporting computational parameters and correction schemes. Ultimately, an open approach to point defect simulations will strengthen the impact of computational studies and accelerate materials engineering.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Fig. 1: Considerations for accurate defect modelling.
Fig. 2: Enumerating defects and their charge states.
Fig. 3: Defect modelling in periodic supercells.
Fig. 4: Workflow for determining defect and carrier concentrations under quasiequilibrium conditions.

Similar content being viewed by others

References

  1. Catlow, C., Corish, J., Jacobs, P. & Lidiard, A. The thermodynamics of characteristic defect parameters. J. Phys. C Solid State Phys. 14, L121 (1981).

    Article  CAS  Google Scholar 

  2. Nicolson, A., Kavanagh, S. R., Savory, C. N., Watson, G. W. & Scanlon, D. O. Cu2SiSe3 as a promising solar absorber: harnessing cation dissimilarity to avoid killer antisites. J. Mater. Chem. A 11, 14833–14839 (2023).

    Article  CAS  Google Scholar 

  3. Wang, X., Kavanagh, S. R., Scanlon, D. O. & Walsh, A. Upper efficiency limit of Sb2Se3 solar cells. Joule 8, 2105–2122 (2024).

    Article  CAS  Google Scholar 

  4. Yuan, Z. et al. Discovery of the zintl-phosphide BaCd2P2 as a long carrier lifetime and stable solar absorber. Joule 8, 1412–1429 (2024).

    Article  CAS  Google Scholar 

  5. Whalley, L. D. et al. Giant Huang–Rhys factor for electron capture by the iodine intersitial in perovskite solar cells. J. Am. Chem. Soc. 143, 9123–9128 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Kavanagh, S. R. et al. Intrinsic point defect tolerance in selenium for indoor and tandem photovoltaics. Energy Environ. Sci. 18, 4431–4446 (2025).

    Article  CAS  Google Scholar 

  7. Squires, A. G., Ganeshkumar, L., Savory, C. N., Kavanagh, S. R. & Scanlon, D. O. Oxygen dimerization as a defect-driven process in bulk LiNiO2. ACS Energy Letters https://doi.org/10.1021/acsenergylett.4c01307 (2024).

  8. Murdock, B. E. et al. Li-site defects induce formation of Li-rich impurity phases: implications for charge distribution and performance of LiNi0.5−xMxMn1.5O4 cathodes (M = Fe and Mg; x = 0.05–0.2). Adv. Mater. https://doi.org/10.1002/adma.202400343 (2024).

  9. Gorai, P., Famprikis, T., Singh, B., Stevanović, V. & Canepa, P. Devil is in the defects: electronic conductivity in solid electrolytes. Chem. Mater. 33, 7484–7498 (2021).

    Article  CAS  Google Scholar 

  10. Hoang, K. & Johannes, M. D. Defect chemistry in layered transition-metal oxides from screened hybrid density functional calculations. J. Mater. Chem. A 2, 5224–5235 (2014).

    Article  CAS  Google Scholar 

  11. Eggestad, K., Selbach, S. M. & Williamson, B. A. D. Doping implications of Li solid state electrolyte Li7La3Zr2O12. J. Mater. Chem. A 12, 15666–15675 (2024).

    Article  CAS  Google Scholar 

  12. Squires, A. G. et al. Low electronic conductivity of Li7La3Zr2O12 solid electrolytes from first principles. Phys. Rev. Mater. https://doi.org/10.1103/PhysRevMaterials.6.085401 (2022).

  13. Hu, J. et al. Enabling ionic transport in Li3AlP2: the roles of defects and disorder. J. Mater. Chem. A 13, 6427–6439 (2025).

    Article  CAS  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Turiansky, M. E. & Van de Walle, C. G. Dielectric loss due to charged-defect acoustic phonon emission. APL Quantum https://doi.org/10.1063/5.0205532 (2024).

  16. Jackson, A. J. et al. Computational prediction and experimental realization of earth-abundant transparent conducting oxide Ga-doped ZnSb2O6. ACS Energy Lett. 7, 3807–3816 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Willis, J. et al. Limits to hole mobility and doping in copper iodide. Chem. Mater. 35, 8995–9006 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Li, K., Willis, J., Kavanagh, S. R. & Scanlon, D. O. Computational prediction of an antimony-based n-type transparent conducting oxide: F-doped Sb2O5. Chem. Mater. 36, 2907–2916 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Varley, J. B., Peelaers, H., Janotti, A. & Van De Walle, C. G. Hydrogenated cation vacancies in semiconducting oxides. J. Phys. Condens. Matter 23, 334212 (2011).

    Article  CAS  PubMed  Google Scholar 

  20. Sabino, F. P., Chatratin, I., Janotti, A. & Dalpian, G. M. Hole conductivity through a defect band in ZnGa2O6. Phys. Rev. Mater. https://doi.org/10.1103/PhysRevMaterials.6.064602 (2022).

  21. Hachmioune, S., Ganose, A. M., Sullivan, M. B. & Scanlon, D. O. Exploring the thermoelectric potential of MgB4: electronic band structure, transport properties, and defect chemistry. Chem. Mater. 36, 6062–6073 (2024).

    Article  CAS  Google Scholar 

  22. Xiong, Y. et al. High-throughput identification of spin-photon interfaces in silicon. Sci. Adv. https://doi.org/10.1126/sciadv.adh8617 (2023).

  23. Yan, Q., Kar, S., Chowdhury, S. & Bansil, A. The case for a defect genome initiative. Adv. Mater. https://doi.org/10.1002/adma.202303098 (2024).

  24. Shen, J.-X., Voss, L. F. & Varley, J. B. Simulating charged defects at database scale. J. Appl. Phys. https://doi.org/10.1063/5.0203124 (2024).

  25. Kumagai, Y., Tsunoda, N., Takahashi, A. & Oba, F. Insights into oxygen vacancies from high-throughput first-principles calculations. Phys. Rev. Mater. 5, 123803 (2021).

    Article  CAS  Google Scholar 

  26. Mosquera-Lois, I., Kavanagh, S. R., Ganose, A. M. & Walsh, A. Machine-learning structural reconstructions for accelerated point defect calculations. npj Comput. Mater. 10, 121 (2024).

    Article  Google Scholar 

  27. Mannodi-Kanakkithodi, A. et al. Machine-learned impurity level prediction for semiconductors: the example of Cd-based chalcogenides. npj Comput. Mater. https://doi.org/10.1038/s41524-020-0296-7 (2020).

  28. Kavanagh, S. R. Identifying split vacancy defects with machine-learned foundation models and electrostatics. J. Phys. Energy 7, 045002 (2025).

    Article  Google Scholar 

  29. Coletti, G. et al. Impact of metal contamination in silicon solar cells. Adv. Funct. Mater. 21, 879–890 (2011).

    Article  CAS  Google Scholar 

  30. Luo, T. et al. Creation of nitrogen-vacancy centers in chemical vapor deposition diamond for sensing applications. New J. Phys. 24, 033030 (2022).

    Article  CAS  Google Scholar 

  31. Mosquera-Lois, I., Kavanagh, S. R., Klarbring, J., Tolborg, K. & Walsh, A. Imperfections are not 0 K: free energy of point defects in crystals. Chem. Soc. Rev. 52, 5812–5826 (2023).

    Article  CAS  PubMed  Google Scholar 

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

    Article  Google Scholar 

  33. Kim, S., Hood, S. N., Park, J.-S., Whalley, L. D. & Walsh, A. Quick-start guide for first-principles modelling of point defects in crystalline materials. J. Phys. Energy 2, 036001 (2020).

    Article  CAS  Google Scholar 

  34. Kröger, F. A. & Vink, H. J. in Solid State Physics (eds Seitz, F. & Turnbull, D.) Vol. 3, 307–435 (Academic Press, 1956).

  35. Zhang, S. & Northrup, J. Chemical potential dependence of defect formation energies in GaAs: application to Ga self-diffusion. Phys. Rev. Lett. 67, 2339–2342 (1991).

    Article  CAS  PubMed  Google Scholar 

  36. Mosquera-Lois, I., Kavanagh, S. R., Walsh, A. & Scanlon, D. O. Identifying the ground state structures of point defects in solids. npj Comput. Mater. https://doi.org/10.1038/s41524-023-00973-1 (2023).

  37. Wilkinson, M. D. et al. The FAIR Guiding Principles for scientific data management and stewardship. Sci. Data 3, 160018 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  38. Drabold, D. A. & Estreicher, S. (eds) Theory of Defects in Semiconductors 2007 edn (Springer, 2006).

  39. Lidiard, A. B. The Mott–Littleton method: an introductory survey. J. Chem. Soc. Faraday Trans. 2 85, 341–349 (1989).

    Article  CAS  Google Scholar 

  40. Zhu, L. et al. Formation of intrinsic point defects in AlN: a study of donor and acceptor characteristics using hybrid QM/MM techniques. J. Mater. Chem. A 12, 25449–25464 (2024).

    Article  CAS  Google Scholar 

  41. Zhang, X. et al. Toward a consistent prediction of defect chemistry in CeO2. Chem. Mater. 35, 207–227 (2023).

    Article  CAS  PubMed  Google Scholar 

  42. De Souza, R. & Harrington, G. Revisiting point defects in ionic solids and semiconductors. Nat. Mater. 22, 794–797 (2023).

    Article  PubMed  Google Scholar 

  43. Mosquera-Lois, I. & Kavanagh, S. R. In search of hidden defects. Matter 4, 2602–2605 (2021).

    Article  Google Scholar 

  44. Gao, W. & Tkatchenko, A. Electronic structure and van der Waals interactions in the stability and mobility of point defects in semiconductors. Phys. Rev. Lett. https://doi.org/10.1103/PhysRevLett.111.045501 (2013).

  45. Zhang, X. & Wei, S.-H. Origin of efficiency enhancement by lattice expansion in hybrid-perovskite solar cells. Phys. Rev. Lett. 128, 136401 (2022).

    Article  CAS  PubMed  Google Scholar 

  46. Meesala, S. et al. Strain engineering of the silicon-vacancy center in diamond. Phys. Rev. B https://doi.org/10.1103/PhysRevB.97.205444 (2018).

  47. Santra, P. et al. Strain-modulated defect engineering of two-dimensional materials. npj 2D Mater. Appl. https://doi.org/10.1038/s41699-024-00472-x (2024).

  48. Gouveia, J. D. & Coutinho, J. Can we rely on hybrid-DFT energies of solid-state problems with local-DFT geometries? Electron. Struct. 1, 015008 (2019).

    Article  CAS  Google Scholar 

  49. Mosquera-Lois, I., Kavanagh, S. R., Walsh, A. & Scanlon, D. O. ShakeNBreak: navigating the defect configurational landscape. J. Open Source Softw. 7, 4817 (2022).

    Article  Google Scholar 

  50. Neilson, W. D., Rizk, J., Cooper, M. W. D. & Andersson, D. A. Oxygen potential, uranium diffusion, and defect chemistry in UO2±x: a density functional theory study. J. Phys. Chem. C 128, 21559–21571 (2024).

    Article  CAS  Google Scholar 

  51. Zhao, X.-G., Dalpian, G. M., Wang, Z. & Zunger, A. Polymorphous nature of cubic halide perovskites. Phys. Rev. B https://doi.org/10.1103/PhysRevB.101.155137 (2020).

  52. Ogawa, K., Kavanagh, S. R., Oba, F. & Walsh, A. Defect tolerance via external passivation in the photocatalyst SrTiO3:Al. J. Am. Chem. Soc. 147, 23180–23191 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Kayastha, P., Fransson, E., Erhart, P. & Whalley, L. Octahedral tilt-driven phase transitions in BaZrS3 chalcogenide perovskite. J. Phys. Chem. Lett. 16, 2064–2071 (2025).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Choi, M., Oba, F., Kumagai, Y. & Tanaka, I. Anti-ferrodistortive-like oxygen-octahedron rotation induced by the oxygen vacancy in cubic SrTiO3. Adv. Mater. 25, 86–90 (2013).

    Article  CAS  PubMed  Google Scholar 

  55. Mosquera-Lois, I., Klarbring, J. & Walsh, A. Point defect formation at finite temperatures with machine learning force fields. Chem. Sci. https://pubs.rsc.org/en/content/articlelanding/2025/sc/d4sc08582e (2025).

  56. Zhong, X., Höfling, F. & John, T. Hydrogen diffusion in garnet: insights from atomistic simulations. Geochem. Geophys. Geosyst. 26, e2024GC011951 (2025).

    Article  CAS  Google Scholar 

  57. Mosquera-Lois, I. & Walsh, A. Dynamic vacancy levels in CsPbCl3 obey equilibrium defect thermodynamics. PRX Energy https://doi.org/10.1103/dxmb-8s96 (2025).

  58. Deák, P., Gali, A., Aradi, B. & Frauenheim, T. Accurate gap levels and their role in the reliability of other calculated defect properties. Phys. Stat. Sol. B 248, 790–798 (2011).

    Article  Google Scholar 

  59. Lyons, J. L. & Van de Walle, C. G. Computationally predicted energies and properties of defects in GaN. npj Comput. Mater. https://doi.org/10.1038/s41524-017-0014-2 (2017).

  60. Gorai, P. & Stevanović, V. Comment on ‘Understanding the intrinsic p-type behavior and phase stability of thermoelectric α-Mg3Sb2’. ACS Appl. Energy Mater. 3, 106–108 (2020).

    Article  CAS  Google Scholar 

  61. Alkauskas, A., Dreyer, C. E., Lyons, J. L. & Van de Walle, C. G. Role of excited states in Shockley–Read–Hall recombination in wide-band-gap semiconductors. Phys. Rev. B 93, 201304 (2016).

    Article  Google Scholar 

  62. Kavanagh, S. R. Accurately Modelling Point Defects in Semiconductors: The Case of CdTe. Doctoral thesis, Univ. College London (2024).

  63. Yang, J.-H., Yin, W.-J., Park, J.-S., Ma, J. & Wei, S.-H. Review on first-principles study of defect properties of CdTe as a solar cell absorber. Semicond. Sci. Technol. 31, 083002 (2016).

    Article  Google Scholar 

  64. Pan, J., Metzger, W. K. & Lany, S. Spin–orbit coupling effects on predicting defect properties with hybrid functionals: a case study in CdTe. Phys. Rev. B 98, 054108 (2018).

    Article  CAS  Google Scholar 

  65. Chatratin, I., Dou, B., Wei, S.-H. & Janotti, A. Doping limits of phosphorus, arsenic, and antimony in CdTe. J. Phys. Chem. Lett. 14, 273–278 (2023).

    Article  CAS  PubMed  Google Scholar 

  66. Dabo, I. et al. Koopmans’ condition for density-functional theory. Phys. Rev. B https://doi.org/10.1103/PhysRevB.82.115121 (2010).

  67. Demchenko, D. O. et al. Koopmans-tuned Heyd-Scuseria-Ernzerhof hybrid functional calculations of acceptors in GaN. Phys. Rev. B https://doi.org/10.1103/PhysRevB.110.035203 (2024).

  68. Chen, W., Griffin, S. M., Rignanese, G.-M. & Hautier, G. Nonunique fraction of Fock exchange for defects in two-dimensional materials. Phys. Rev. B 106, L161107 (2022).

    Article  CAS  Google Scholar 

  69. Skone, J. H., Govoni, M. & Galli, G. Self-consistent hybrid functional for condensed systems. Phys. Rev. B https://doi.org/10.1103/PhysRevB.89.195112 (2014).

  70. Gerosa, M. et al. Defect calculations in semiconductors through a dielectric-dependent hybrid DFT functional: the case of oxygen vacancies in metal oxides. J. Chem. Phys. https://doi.org/10.1063/1.4931805 (2015).

  71. Deák, P., Frauenheim, T. & Gali, A. Limits of the scaled shift correction to levels of interstitial defects in semiconductors. Phys. Rev. B https://doi.org/10.1103/PhysRevB.75.153204 (2007).

  72. Lany, S. & Zunger, A. Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: case studies for ZnO and GaAs. Phys. Rev. B 78, 235104 (2008).

    Article  Google Scholar 

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

    Article  Google Scholar 

  74. Wang, Z., Brock, C., Matt, A. & Bevan, K. H. Implications of the DFT+U method on polaron properties in energy materials. Phys. Rev. B 96, 125150 (2017).

    Article  Google Scholar 

  75. Uhrin, M., Zadoks, A., Binci, L., Marzari, N. & Timrov, I. Machine learning Hubbard parameters with equivariant neural networks. npj Comput. Mater. https://doi.org/10.1038/s41524-024-01501-5 (2025).

  76. Timrov, I., Aquilante, F., Cococcioni, M. & Marzari, N. Accurate electronic properties and intercalation voltages of olivine-type Li-ion cathode materials from extended Hubbard functionals. PRX Energy https://doi.org/10.1103/PRXEnergy.1.033003 (2022).

  77. Freysoldt, C., Neugebauer, J. & Van de Walle, C. G. Fully ab initio finite-size corrections for charged-defect supercell calculations. Phys. Rev. Lett. 102, 016402 (2009).

    Article  PubMed  Google Scholar 

  78. Kumagai, Y. & Oba, F. Electrostatics-based finite-size corrections for first-principles point defect calculations. Phys. Rev. B 89, 195205 (2014).

    Article  Google Scholar 

  79. Gake, T., Kumagai, Y., Freysoldt, C. & Oba, F. Finite-size corrections for defect-involving vertical transitions in supercell calculations. Phys. Rev. B 101, 020102 (2020).

    Article  CAS  Google Scholar 

  80. Kavanagh, S. R. Vaspup2.0. Zenodo (2023).

  81. Buckeridge, J., Scanlon, D. O., Walsh, A. & Catlow, C. R. A. Automated procedure to determine the thermodynamic stability of a material and the range of chemical potentials necessary for its formation relative to competing phases and compounds. Comput. Phys. Commun. 185, 330–338 (2014).

    Article  CAS  Google Scholar 

  82. Stevanović, V., Lany, S., Zhang, X. & Zunger, A. Correcting density functional theory for accurate predictions of compound enthalpies of formation: fitted elemental-phase reference energies. Phys. Rev. B 85, 115104 (2012).

    Article  Google Scholar 

  83. Jain, A. et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Materials https://doi.org/10.1063/1.4812323 (2013).

  84. 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 

  85. Kavanagh, S. R. et al. doped: Python toolkit for robust and repeatable charged defect supercell calculations. J. Open Source Softw. 9, 6433 (2024).

    Article  Google Scholar 

  86. Zagorac, D., Müller, H., Ruehl, S., Zagorac, J. & Rehme, S. Recent developments in the inorganic crystal structure database: theoretical crystal structure data and related features. J. Appl. Crystallogr. 52, 918–925 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Cen, J., Zhu, B. & Scanlon, D. O. Exploring battery cathode materials in the Li–Ni–O phase diagrams using structure prediction. J. Phys. Energy 5, 035005 (2023).

    Article  CAS  Google Scholar 

  88. Toriyama, M. Y., Lee, C.-W., Snyder, G. J. & Gorai, P. Defect chemistry and doping of lead phosphate oxo apatite Pb10(PO4)6O. ACS Energy Lett. 9, 428–431 (2024).

    Article  CAS  Google Scholar 

  89. Morgan, B. J. & Watson, G. W. Intrinsic n-type defect formation in TiO2: a comparison of rutile and anatase from GGA+U calculations. J. Phys. Chem. C 114, 2321–2328 (2010).

    Article  CAS  Google Scholar 

  90. Swallow, J. E. N. et al. Self-compensation in transparent conducting F-doped SnO2. Adv. Funct. Mater. https://doi.org/10.1002/adfm.201701900 (2017).

  91. Jackson, A. J., Tiana, D. & Walsh, A. A universal chemical potential for sulfur vapours. Chem. Sci. 7, 1082–1092 (2016).

    Article  CAS  PubMed  Google Scholar 

  92. Kayastha, P., Longo, G. & Whalley, L. D. A first-principles thermodynamic model for the Ba–Zr–S system in equilibrium with sulfur vapor. ACS Appl. Energy Mater. 7, 11326–11333 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  93. Comparotto, C. et al. Thermodynamic insights into the Ba–S system for the formation of BaZrS3 perovskites and other Ba sulfides. J. Mater. Chem. A 13, 9983–9991 (2025).

    Article  CAS  Google Scholar 

  94. Crawford, C. M., Ortiz, B. R., Gorai, P., Stevanovic, V. & Toberer, E. S. Experimental and computational phase boundary mapping of Co4Sn6Te6. J. Mater. Chem. A 6, 24175–24185 (2018).

    Article  CAS  Google Scholar 

  95. Ohno, S. et al. Phase boundary mapping to obtain n-type Mg3Sb2-based thermoelectrics. Joule 2, 141–154 (2018).

    Article  CAS  Google Scholar 

  96. Borgsmiller, L., Zavanelli, D. & Snyder, G. J. Phase-boundary mapping to engineer defects in thermoelectric materials. PRX Energy https://doi.org/10.1103/PRXEnergy.1.022001 (2022).

  97. Shimoda, M. et al. Controlling defects to achieve reproducibly high ionic conductivity in Na3SbS4 solid electrolytes. Chem. Mater. 34, 5634–5643 (2022).

    Article  CAS  Google Scholar 

  98. Choi, Y.-S., Costa, S. I. R., Tapia-Ruiz, N. & Scanlon, D. O. Intrinsic defects and their role in the phase transition of Na-ion anode Na2Ti3O7. ACS Appl. Energy Mater. 6, 484–495 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  99. Williamson, B. A. D., Eggestad, K. & Selbach, S. M. Pseudo-lithium vacancies in hydrogen rich Li3OCl. J. Mater. Chem. A https://doi.org/10.1039/d4ta08352k (2025).

  100. Fioretti, A. N. et al. Understanding and control of bipolar self-doping in copper nitride. J. Appl. Phys. https://doi.org/10.1063/1.4948244 (2016).

  101. Goyal, A., Gorai, P., Peng, H., Lany, S. & Stevanović, V. A computational framework for automation of point defect calculations. Comput. Mater. Sci. 130, 1–9 (2017).

    Article  Google Scholar 

  102. Broberg, D. et al. PyCDT: a Python toolkit for modeling point defects in semiconductors and insulators. Comput. Phys. Commun. 226, 165–179 (2018).

    Article  CAS  Google Scholar 

  103. Kononov, A., Lee, C.-W., Shapera, E. P. & Schleife, A. Identifying native point defect configurations in α-alumina. J. Phys. Condens. Matter 35, 334002 (2023).

    Article  CAS  Google Scholar 

  104. Zimmermann, N. E. R., Horton, M. K., Jain, A. & Haranczyk, M. Assessing local structure motifs using order parameters for motif recognition, interstitial identification, and diffusion path characterization. Front. Mater. https://doi.org/10.3389/fmats.2017.00034 (2017).

  105. Shen, J.-X. & Varley, J. pymatgen-analysis-defects: a Python package for analyzing point defects in crystalline materials. J. Open Source Softw. 9, 5941 (2024).

    Article  Google Scholar 

  106. Ong, S. P. et al. Python Materials Genomics (pymatgen): a robust, open-source Python library for materials analysis. Comput. Mater. Sci. 68, 314–319 (2013).

    Article  CAS  Google Scholar 

  107. Gorai, P. Beginner’s guide to interpreting defect and defect level diagrams. PRX Energy 4, 032001 (2025).

    Article  Google Scholar 

  108. Frodason, Y. K., Johansen, K. M., Bjørheim, T. S., Svensson, B. G. & Alkauskas, A. Zn vacancy as a polaronic hole trap in ZnO. Phys. Rev. B 95, 094105 (2017).

    Article  Google Scholar 

  109. Lee, C.-W., Din, N. U., Brennecka, G. L. & Gorai, P. Defects and oxygen impurities in ferroelectric wurtzite Al1-xScxN alloys. Appl. Phys. Lett. https://doi.org/10.1063/5.0211892 (2024).

  110. Wang, X., Kavanagh, S. R., Scanlon, D. O. & Walsh, A. Four-electron negative-U vacancy defects in antimony selenide. Phys. Rev. B https://doi.org/10.1103/PhysRevB.108.134102 (2023).

  111. Morris, A. J., Needs, R. J., Salager, E., Grey, C. P. & Pickard, C. J. Lithiation of silicon via lithium zintl-defect complexes from first principles. Phys. Rev. B https://doi.org/10.1103/physrevb.87.174108 (2013).

  112. Huang, M. et al. Dasp: defect and dopant ab-initio simulation package. J. Semicond. 43, 042101 (2022).

    Article  Google Scholar 

  113. Arrigoni, M. & Madsen, G. K. H. Spinney: post-processing of first-principles calculations of point defects in semiconductors with Python. Comput. Phys. Commun. 264, 107946 (2021).

    Article  CAS  Google Scholar 

  114. Yuan, Z. & Hautier, G. First-principles study of defects and doping limits in CaO. Appl. Phys. Lett. 124, 232101 (2024).

    Article  CAS  Google Scholar 

  115. Sokol, A. A. et al. Point defects in ZnO. Faraday Discuss. 134, 267–282 (2007).

    Article  CAS  PubMed  Google Scholar 

  116. Kavanagh, S. R., Walsh, A. & Scanlon, D. O. Rapid recombination by cadmium vacancies in CdTe. ACS Energy Lett. 6, 1392–1398 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  117. Zhang, X. et al. Toward a consistent prediction of defect chemistry in CeO2. Chem. Mater. 35, 207–227 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  118. Meggiolaro, D. & De Angelis, F. First-principles modeling of defects in lead halide perovskites: best practices and open issues. ACS Energy Lett. 3, 2206–2222 (2018).

    Article  CAS  Google Scholar 

  119. Swift, M. W., Peelaers, H., Mu, S., Morton, J. J. L. & Van de Walle, C. G. First-principles calculations of hyperfine interaction, binding energy, and quadrupole coupling for shallow donors in silicon. npj Comput. Mater. https://doi.org/10.1038/s41524-020-00448-7 (2020).

  120. Kieczka, D. et al. Defects in WS2 monolayer calculated with a nonlocal functional: any difference from GGA? Electron. Struct. 5, 024001 (2023).

    Article  CAS  Google Scholar 

  121. Whalley, L. D. Steric engineering of point defects in lead halide perovskites. J. Phys. Chem. C 127, 15738–15746 (2023).

    Article  CAS  Google Scholar 

  122. Wang, Z., Wei, S. & Zhang, X. Comment on ‘wide-range-tunable ps-type conductivity of transparent CuI1−xBrx alloy’. Adv. Funct. Mater. https://doi.org/10.1002/adfm.202112765 (2022).

  123. Xu, J. et al. Defect tolerance of mixed b-site organic–inorganic halide perovskites. ACS Energy Lett. 6, 4220–4227 (2021).

    Article  CAS  Google Scholar 

  124. Peng, H. et al. Convergence of density and hybrid functional defect calculations for compound semiconductors. Phys. Rev. B https://doi.org/10.1103/PhysRevB.88.115201 (2013).

  125. Zhang, X., Turiansky, M. E., Shen, J.-X. & Van de Walle, C. G. Defect tolerance in halide perovskites: a first-principles perspective. J. Appl. Phys. https://doi.org/10.1063/5.0083686 (2022).

  126. Shi, B. X. et al. General embedded cluster protocol for accurate modeling of oxygen vacancies in metal-oxides. J. Chem. Phys. https://doi.org/10.1063/5.0087031 (2022).

  127. Johannes, M. D., Hoang, K., Allen, J. L. & Gaskell, K. Hole polaron formation and migration in olivine phosphate materials. Phys. Rev. B https://doi.org/10.1103/PhysRevB.85.115106 (2012).

  128. Hoang, K. & Johannes, M. D. Defect physics in complex energy materials. J. Phys. Condens. Matter 30, 293001 (2018).

    Article  PubMed  Google Scholar 

  129. Woods-Robinson, R. et al. Designing transparent conductors using forbidden optical transitions. Matter 6, 3021–3039 (2023).

    Article  CAS  Google Scholar 

  130. Oba, F. & Kumagai, Y. Design and exploration of semiconductors from first principles: a review of recent advances. Appl. Phys. Express 11, 060101 (2018).

    Article  Google Scholar 

  131. Broberg, D. et al. High-throughput calculations of charged point defect properties with semi-local density functional theory — performance benchmarks for materials screening applications. npj Comput. Mater. https://doi.org/10.1038/s41524-023-01015-6 (2023).

  132. Kumagai, Y. et al. Alkali mono-pnictides: a new class of photovoltaic materials by element mutation. PRX Energy 2, 043002 (2023).

    Article  Google Scholar 

  133. Deák, P., Udvarhelyi, P., Thiering, G. & Gali, A. The kinetics of carbon pair formation in silicon prohibits reaching thermal equilibrium. Nat. Commun. 14, 361 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  134. Razinkovas, L., Maciaszek, M., Reinhard, F., Doherty, M. W. & Alkauskas, A. Photoionization of negatively charged NV centers in diamond: theory and ab initio calculations. Phys. Rev. B 104, 235301 (2021).

    Article  CAS  Google Scholar 

  135. Dhaliah, D., Xiong, Y., Sipahigil, A., Griffin, S. M. & Hautier, G. First-principles study of the t center in silicon. Phys. Rev. Mater. https://doi.org/10.1103/PhysRevMaterials.6.L053201 (2022).

  136. Dou, W., Spooner, K. B., Kavanagh, S. R., Zhou, M. & Scanlon, D. O. Band degeneracy and anisotropy enhances thermoelectric performance from Sb2Si2Te6 to Sc2Si2Te6. J. Am. Chem. Soc. 146, 17679–17690 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  137. Erhart, P., Sadigh, B., Schleife, A. & Åberg, D. First-principles study of codoping in lanthanum bromide. Phys. Rev. B https://doi.org/10.1103/PhysRevB.91.165206 (2015).

  138. Larsen, A. H. et al. The atomic simulation environment — a Python library for working with atoms. J. Phys. Condens. Matter 29, 273002 (2017).

    Article  Google Scholar 

  139. Kumagai, Y. Corrections on formation energies and eigenvalues of point defect calculations in two-dimensional materials. Phys. Rev. B 109, 054106 (2024).

    Article  CAS  Google Scholar 

  140. Makov, G. & Payne, M. C. Periodic boundary conditions in ab initio calculations. Phys. Rev. B 51, 4014–4022 (1995).

    Article  CAS  Google Scholar 

  141. Leslie, M. & Gillan, N. J. The energy and elastic dipole tensor of defects in ionic crystals calculated by the supercell method. J. Phys. C Solid State Phys. 18, 973–982 (1985).

    Article  CAS  Google Scholar 

  142. Murphy, S. T. & Hine, N. D. M. Anisotropic charge screening and supercell size convergence of defect formation energies. Phys. Rev. B 87, 094111 (2013).

    Article  Google Scholar 

  143. Chagas da Silva, M. et al. Self-consistent potential correction for charged periodic systems. Phys. Rev. Lett. 126, 076401 (2021).

    Article  CAS  PubMed  Google Scholar 

  144. Suo, Z.-J., Luo, J.-W., Li, S.-S. & Wang, L.-W. Image charge interaction correction in charged-defect calculations. Phys. Rev. B 102, 174110 (2020).

    Article  CAS  Google Scholar 

  145. Xiao, J. et al. Realistic dimension-independent approach for charged-defect calculations in semiconductors. Phys. Rev. B 101, 165306 (2020).

    Article  CAS  Google Scholar 

  146. Freysoldt, C. & Neugebauer, J. First-principles calculations for charged defects at surfaces, interfaces, and two-dimensional materials in the presence of electric fields. Phys. Rev. B 97, 205425 (2018).

    Article  CAS  Google Scholar 

  147. Falletta, S., Wiktor, J. & Pasquarello, A. Finite-size corrections of defect energy levels involving ionic polarization. Phys. Rev. B 102, 041115 (2020).

    Article  CAS  Google Scholar 

  148. Kumagai, Y. Finite-size corrections to defect energetics along one-dimensional configuration coordinate. Phys. Rev. B 107, L220101 (2023).

    Article  CAS  Google Scholar 

  149. Freysoldt, C., Neugebauer, J., Tan, A. M. Z. & Hennig, R. G. Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials. Phys. Rev. B https://doi.org/10.1103/PhysRevB.105.014103 (2022).

  150. Kokott, S. et al. Efficient all-electron hybrid density functionals for atomistic simulations beyond 10-000 atoms. J. Chem. Phys. https://doi.org/10.1063/5.0208103 (2024).

  151. Hayes, W. & Stoneham, A. M. Defects and Defect Processes in Nonmetallic Solids (Wiley, 1985).

  152. Kasamatsu, S., Tada, T. & Watanabe, S. Theoretical analysis of space charge layer formation at metal/ionic conductor interfaces. Solid State Ionics 183, 20–25 (2011).

    Article  CAS  Google Scholar 

  153. Neilson, W. D. & Murphy, S. T. DefAP: a Python code for the analysis of point defects in crystalline solids. Comput. Mater. Sci. 210, 111434 (2022).

    Article  CAS  Google Scholar 

  154. Hagemark, K. Frozen-in native defects in semiconductor compounds. J. Phys. Chem. Solids 37, 461–464 (1976).

    Article  CAS  Google Scholar 

  155. Sasaki, K. & Maier, J. Low temperature defect chemistry of oxides. J. Eur. Ceram. Soc. 19, 741–745 (1999).

    Article  CAS  Google Scholar 

  156. Buckeridge, J. Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy. Comput. Phys. Commun. 244, 329–342 (2019).

    Article  CAS  Google Scholar 

  157. Squires, A. G., Scanlon, D. O. & Morgan, B. J. Native defects and their doping response in the lithium solid electrolyte Li7La3Zr2O12. Chem. Mater. 32, 1876–1886 (2019).

    Article  Google Scholar 

  158. Kubicek, M. et al. Oxygen vacancies in fast lithium-ion conducting garnets. Chem. Mater. 29, 7189–7196 (2017).

    Article  CAS  Google Scholar 

  159. Fallon, M. J. et al. Exploring the anion site disorder kinetics in lithium argyrodites. J. Am. Chem. Soc. 147, 10151–10159 (2025).

    Article  CAS  PubMed  Google Scholar 

  160. Eames, C. et al. Ionic transport in hybrid lead iodide perovskite solar cells. Nat. Commun. https://doi.org/10.1038/ncomms8497 (2015).

  161. Karmakar, A. et al. Influence of hidden halogen mobility on local structure of CsSn(Cl1-xBrx)3 mixed-halide perovskites by solid-state NMR. Chem. Sci. 12, 3253–3263 (2021).

    Article  CAS  Google Scholar 

  162. Chatratin, I., Evangelista, I., McCandless, B., Shafarman, W. & Janotti, A. Defect stability in CdTe based on formation energies and migration barriers. J. Phys. Chem. C 129, 1398–1407 (2025).

    Article  CAS  Google Scholar 

  163. Ma, J., Yang, J., Wei, S.-H. & Da Silva, J. L. F. Correlation between the electronic structures and diffusion paths of interstitial defects in semiconductors: the case of CdTe. Phys. Rev. B 90, 155208 (2014).

    Article  Google Scholar 

  164. Krasikov, D. & Sankin, I. Defect interactions and the role of complexes in the CdTe solar cell absorber. J. Mater. Chem. A 5, 3503–3513 (2017).

    Article  CAS  Google Scholar 

  165. Squires, A. G., Scanlon, D. O. & Morgan, B. J. Py-sc-fermi: self-consistent Fermi energies and defect concentrations from electronic structure calculations. J. Open Source Softw. 8, 4962 (2023).

    Article  Google Scholar 

  166. Arnab, K. A. et al. Quantitative modeling of point defects in β-Ga2O3 combining hybrid functional energetics with semiconductor and processes thermodynamics. Phys. Chem. Chem. Phys. 27, 11129–11143 (2025).

    Article  CAS  PubMed  Google Scholar 

  167. Kavanagh, S. R., Scanlon, D. O., Walsh, A. & Freysoldt, C. Impact of metastable defect structures on carrier recombination in solar cells. Faraday Discuss. 239, 339–356 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  168. Toriyama, M. Y. et al. How to analyse a density of states. Mater. Today Electron. 1, 100002 (2022).

    Article  Google Scholar 

  169. Oliphant, E., Mantena, V., Brod, M., Jeffrey Snyder, G. & Sun, W. Why does silicon have an indirect band gap? Mater. Horiz. 12, 3073–3083 (2025).

    Article  CAS  PubMed  Google Scholar 

  170. Fecher, G. H., Kübler, J. & Felser, C. Chirality in the solid state: chiral crystal structures in chiral and achiral space groups. Materials 15, 5812 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  171. Mao, J. et al. High thermoelectric cooling performance of n-type Mg3Bi2-based materials. Science 365, 495–498 (2019).

    Article  CAS  PubMed  Google Scholar 

  172. Wang, X., Kavanagh, S. R. & Walsh, A. Sulfur vacancies limit the open-circuit voltage of Sb2S3 solar cells. ACS Energy Lett. 10, 161–167 (2025).

    Article  CAS  PubMed  Google Scholar 

  173. Liga, S. M., Kavanagh, S. R., Walsh, A., Scanlon, D. O. & Konstantatos, G. Mixed-cation vacancy-ordered perovskites (Cs2Ti1–xSnxX6; X = I or Br): low-temperature miscibility, additivity, and tunable stability. J. Phys. Chem. C 127, 21399–21409 (2023).

    Article  CAS  Google Scholar 

  174. Zhang, X., Kang, J. & Wei, S.-H. Defect modeling and control in structurally and compositionally complex materials. Nat. Comput. Sci. 3, 210–220 (2023).

    Article  PubMed  Google Scholar 

  175. Kaewmeechai, C., Strand, J. & Shluger, A. Electronic structure and properties of trapped holes in crystalline and amorphous Ga2O3. Phys. Rev. B https://doi.org/10.1103/PhysRevB.111.035203 (2025).

  176. Chen, W., Dahliah, D., Rignanese, G.-M. & Hautier, G. Origin of the low conversion efficiency in Cu2ZnSnS4 kesterite solar cells: the actual role of cation disorder. Energy Environ. Sci. 14, 3567–3578 (2021).

    Article  CAS  Google Scholar 

  177. Muy, S., Johnston, C. & Marzari, N. AiiDA-defects: an automated and fully reproducible workflow for the complete characterization of defect chemistry in functional materials. Electron. Struct. 5, 024009 (2023).

    Article  CAS  Google Scholar 

  178. Ogawa, T., Taguchi, A. & Kuwabara, A. An extended computational approach for point-defect equilibria in semiconductor materials. npj Comput. Mater. 8, 79 (2022).

    Article  CAS  Google Scholar 

  179. Gorai, P. Beginner’s guide to interpreting defect and defect level diagrams. PRX Energy https://doi.org/10.1103/jtyg-xry3 (2025).

  180. Stevanović, V., Lany, S., Zhang, X. & Zunger, A. Correcting density functional theory for accurate predictions of compound enthalpies of formation: fitted elemental-phase reference energies. Phys. Rev. B https://doi.org/10.1103/PhysRevB.85.115104 (2012).

  181. Slavney, A. H., Hu, T., Lindenberg, A. M. & Karunadasa, H. I. A bismuth-halide double perovskite with long carrier recombination lifetime for photovoltaic applications. J. Am. Chem. Soc. 138, 2138–2141 (2016).

    Article  CAS  PubMed  Google Scholar 

  182. Sebastiá-Luna, P. et al. Tuning the optical absorption of Sn-, Ge-, and Zn-substituted Cs2AgBiBr6 double perovskites: structural and electronic effects. Chem. Mater. 33, 8028–8035 (2021).

    Article  Google Scholar 

  183. Lindquist, K. P. et al. Tuning the bandgap of Cs2AgBiBr6 through dilute tin alloying. Chem. Sci. 10, 10620–10628 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  184. Batnaran, B. Computational Study of the Key Imperfections in Energy Materials. Master’s thesis, Univ. College London (2022).

Download references

Acknowledgements

This work was supported by the PRAETORIAN project, funded by UK Research and Innovation (UKRI) under the UK government’s Horizon Europe funding guarantee (EP/Y019504/1). The authors thank B. Batnaran for preliminary calculations on the functional dependence of defect structure searches.

Author information

Authors and Affiliations

  1. School of Chemistry, University of Birmingham Edgbaston, Birmingham, UK

    Alexander G. Squires & David O. Scanlon

  2. Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK

    Seán R. Kavanagh

  3. Department of Materials, Imperial College London, London, UK

    Aron Walsh

Authors
  1. Alexander G. Squires
    View author publications

    Search author on:PubMed Google Scholar

  2. Seán R. Kavanagh
    View author publications

    Search author on:PubMed Google Scholar

  3. Aron Walsh
    View author publications

    Search author on:PubMed Google Scholar

  4. David O. Scanlon
    View author publications

    Search author on:PubMed Google Scholar

Contributions

S.R.K. researched data for the article, D.O.S. contributed to the discussion of content, A.G.S. wrote the manuscript and all authors reviewed and edited the manuscript before submission.

Corresponding authors

Correspondence to Alexander G. Squires, Seán R. Kavanagh, Aron Walsh or David O. Scanlon.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Materials thanks Richard Catlow, Prashun Gorai and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Squires, A.G., Kavanagh, S.R., Walsh, A. et al. Guidelines for robust and reproducible point defect simulations in crystals. Nat Rev Mater (2026). https://doi.org/10.1038/s41578-025-00879-y

Download citation

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1038/s41578-025-00879-y

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