Oxidation states and ionicity


The concepts of oxidation state and atomic charge are entangled in modern materials science. We distinguish between these quantities and consider their fundamental limitations and utility for understanding material properties. We discuss the nature of bonding between atoms and the techniques that have been developed for partitioning electron density. While formal oxidation states help us count electrons (in ions, bonds, lone pairs), variously defined atomic charges are usefully employed in the description of physical processes including dielectric response and electronic spectroscopies. Such partial charges are introduced as quantitative measures in simple mechanistic models of a more complex reality, and therefore may not be comparable or transferable. In contrast, oxidation states are defined to be universal, with deviations constituting exciting challenges as evidenced in mixed-valence compounds, electrides and highly correlated systems. This Perspective covers how these concepts have evolved in recent years, our current understanding and their significance.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Charge distribution in TiO2.
Fig. 2: Illustration of five approaches for partitioning electron density between atomic centres in chemical systems.


  1. 1.

    Karen, P. Oxidation state, a long-standing issue! Angew. Chem. Int. Ed. 54, 4716–4726 (2015).

    CAS  Article  Google Scholar 

  2. 2.

    IUPAC Compendium of Chemical Terminology 2nd edn (eds McNaught, A. D. & Wilkinson, A.) (Blackwell Scientific, Oxford, 1997); https://doi.org/10.1351/goldbook.O04365

  3. 3.

    Goodman, C. H. L. Ionic-covalent bonding in crystals. Nature 187, 590–591 (1960).

    CAS  Article  Google Scholar 

  4. 4.

    MooserE.. & PearsonW. B.. The ionic character of chemical bonds. Nature 406–408, 1961 (1920).

    Google Scholar 

  5. 5.

    Cochran, W. ‘Effective’ ionic charge in crystals. Nature 191, 60–61 (1961).

    CAS  Article  Google Scholar 

  6. 6.

    Catlow, C. R. A. & Stoneham, A. M. Ionicity in solids. J. Phys. C Solid State 16, 4321–4338 (1983).

    CAS  Article  Google Scholar 

  7. 7.

    Raebiger, H., Lany, S. & Zunger, A. Charge self-regulation upon changing the oxidation state of transition metals in insulators. Nature 453, 763–766 (2008).

    CAS  Article  Google Scholar 

  8. 8.

    Jansen, M. & Wedig, U. A piece of the picture - misunderstanding of chemical concepts. Angew. Chemie Int. Ed. 47, 10026–10029 (2008).

    CAS  Article  Google Scholar 

  9. 9.

    Koch, D. & Manzhos, S. On the charge state of titanium in titanium dioxide. J. Phys. Chem. Lett. 8, 1593–1598 (2017).

    CAS  Article  Google Scholar 

  10. 10.

    Walsh, A., Sokol, A. A., Buckeridge, J., Scanlon, D. O. & Catlow, R. A. Electron counting in solids: oxidation states, partial charges, and ionicity. J. Phys. Chem. Lett. 8, 2074–2075 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    Pauling, L. The modern theory of valency. J. Chem. Soc. 0, 1461–1467 (1948).

    CAS  Article  Google Scholar 

  12. 12.

    Massidda, S., Yu, J., Freeman, A. J. & Koelling, D. D. Electronic structure and properties of YBa2Cu3O7-δ, a low dimensional, low density of states superconductor. Phys. Lett. A 122, 198–202 (1987).

    CAS  Article  Google Scholar 

  13. 13.

    Kageyama, H. et al. Expanding frontiers in materials chemistry and physics with multiple anions. Nat. Commun. 9, 772 (2018).

    Article  CAS  Google Scholar 

  14. 14.

    Zhang, J. et al. Designing high-performance layered thermoelectric materials through orbital engineering. Nat. Commun. 7, 10892 (2016).

    CAS  Article  Google Scholar 

  15. 15.

    Zeier, W. G. et al. Engineering half-heusler thermoelectric materials using Zintl chemistry. Nat. Rev. Mater. 1, 16032 (2016).

    CAS  Article  Google Scholar 

  16. 16.

    Gillespie, R. J. The valence-shell electron-pair repulsion (VSEPR) theory of directed valency. J. Chem. Educ. 40, 295–301 (1963).

    CAS  Article  Google Scholar 

  17. 17.

    Griffith, J. & Orgel, L. Ligand-field theory. Q. Rev. 11, 381–393 (1957).

    CAS  Article  Google Scholar 

  18. 18.

    Cockayne, E., Levin, I., Wu, H. & Llobet, A. Magnetic structure of bixbyite α-Mn2O3: a combined DFT+U and neutron diffraction study. Phys. Rev. B 87, 184413 (2013).

    Article  CAS  Google Scholar 

  19. 19.

    Shen, X.-F. et al. A magnetic route to measure the average oxidation state of mixed-valent manganese in manganese oxide octahedral molecular sieves (OMS). J. Am. Chem. Soc. 127, 6166–6167 (2005).

    CAS  Article  Google Scholar 

  20. 20.

    Dirac, P. A. M. Quantum mechanics of many-electron systems. Proc. R. Soc. London A Math. Phys. Eng. Sci. 123, 714–733 (1929).

    CAS  Article  Google Scholar 

  21. 21.

    Szabo, A. & Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover, Mineola, 1996).

  22. 22.

    Mcweeny, R. The density matrix in many-electron quantum mechanics. I. Generalized product functions. factorization and physical interpretation of the density matrices. Proc. R. Soc. Lond. A. Math. Phys. Sci. 253, 242–259 (1959).

    CAS  Article  Google Scholar 

  23. 23.

    Kantorovich, L. N. & Zapol, B. P. A diagram technique for nonorthogonal electron group functions. I. Right coset decomposition of symmetric group. J. Chem. Phys. 96, 8420–8426 (1992).

    CAS  Article  Google Scholar 

  24. 24.

    Bader, R. F. W. & Nguyen-Dang, T. T. Quantum theory of atoms in molecules—Dalton revisited. Adv. Quantum Chem. 14, 63–124 (1981).

    CAS  Article  Google Scholar 

  25. 25.

    Kohn, W. Analytic properties of Bloch waves and Wannier functions. Phys. Rev. 115, 809–821 (1959).

    Article  Google Scholar 

  26. 26.

    Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).

    CAS  Article  Google Scholar 

  27. 27.

    Mulliken, R. S. Electronic population analysis on LCAO–MO molecular wave functions. I. J. Chem. Phys. 23, 1833–1840 (1955).

    CAS  Article  Google Scholar 

  28. 28.

    Christoffersen, R. E. & Baker, K. A. Electron population analysis. gross atomic charges in molecules. Chem. Phys. Lett. 8, 4–9 (1971).

    CAS  Article  Google Scholar 

  29. 29.

    Hirshfeld, F. L. Bonded-atom fragments for describing molecular charge densities. Theor. Chim. Acta 44, 129–138 (1977).

    CAS  Article  Google Scholar 

  30. 30.

    Becke, A. D. & Edgecombe, K. E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 92, 5397–5403 (1990).

    CAS  Article  Google Scholar 

  31. 31.

    Savin, A. et al. Electron localization in solid‐state structures of the elements: the diamond structure. Angew. Chem. Int. Ed. English 31, 187–188 (1992).

    Article  Google Scholar 

  32. 32.

    Dick, B. G. & Overhauser, A. W. Theory of the dielectric constants of alkali halide crystals. Phys. Rev. 112, 90–103 (1958).

    CAS  Article  Google Scholar 

  33. 33.

    Spaldin, N. A. A beginner’s guide to the modern theory of polarization. J. Solid State Chem. 195, 2–10 (2012).

    CAS  Article  Google Scholar 

  34. 34.

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

    CAS  Article  Google Scholar 

  35. 35.

    Jiang, L., Levchenko, S. V. & Rappe, A. M. Rigorous definition of oxidation states of ions in solids. Phys. Rev. Lett. 108, 166403 (2012).

    Article  CAS  Google Scholar 

  36. 36.

    Day, P., Hush, N. S. & Clark, R. J. H. Mixed valence: origins and developments. Philos. Trans. A. Math. Phys. Eng. Sci. 366, 5–14 (2008).

    CAS  Article  Google Scholar 

  37. 37.

    Robin, M. B. & Day, P. Mixed valence chemistry—a survey and classification. Adv. Inorg. Chem. Radiochem. 10, 247–422 (1968).

    Article  Google Scholar 

  38. 38.

    Allen, J. P., Scanlon, D. O. & Watson, G. W. Electronic structure of mixed-valence silver oxide AgO from hybrid density-functional theory. Phys. Rev. B 81, 161103 (2010).

    Article  CAS  Google Scholar 

  39. 39.

    Conejeros, S., Moreira, I., de, P. R., Alemany, P. & Canadell, E. Nature of holes, oxidation states, and hypervalency in covellite (CuS). Inorg. Chem. 53, 12402–12406 (2014).

    CAS  Article  Google Scholar 

  40. 40.

    Senn, M. S., Wright, J. P. & Attfield, J. P. Charge order and three-site distortions in the Verwey structure of magnetite. Nature 481, 173–176 (2012).

    CAS  Article  Google Scholar 

  41. 41.

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

    CAS  Article  Google Scholar 

  42. 42.

    Albers, R. C. Condensed-matter physics: an expanding view of plutonium. Nature 410, 759–761 (2001).

    CAS  Article  Google Scholar 

  43. 43.

    Janoschek, M. et al. The valence-fluctuating ground state of plutonium. Sci. Adv. 1, e1500188 (2015).

    Article  CAS  Google Scholar 

  44. 44.

    Watanabe, S. & Miyake, K. Quantum valence criticality as an origin of unconventional critical phenomena. Phys. Rev. Lett. 105, 186403 (2010).

    Article  CAS  Google Scholar 

  45. 45.

    Watanabe, S. & Miyake, K. Roles of critical valence fluctuations in Ce- and Yb-based heavy fermion metals. J. Phys. Condens. Matter 23, 094217 (2011).

    Article  CAS  Google Scholar 

  46. 46.

    Yamaoka, H. et al. Role of valence fluctuations in the superconductivity of Ce122 compounds. Phys. Rev. Lett. 113, 086403 (2014).

    CAS  Article  Google Scholar 

  47. 47.

    Putzke, C. et al. Anomalous critical fields in quantum critical superconductors. Nat. Commun. 5, 5679 (2014).

    CAS  Article  Google Scholar 

  48. 48.

    Mondal, S. et al. Experimental evidence of orbital order in α-B12 and γ-B28 polymorphs of elemental boron. Phys. Rev. B 88, 024118 (2013).

    Article  CAS  Google Scholar 

  49. 49.

    Nilsson Pingel, T., Jørgensen, M., Yankovich, A. B., Grönbeck, H. & Olsson, E. Influence of atomic site-specific strain on catalytic activity of supported nanoparticles. Nat. Commun. 9, 2722 (2018).

    Article  CAS  Google Scholar 

  50. 50.

    Anasori, B., Lukatskaya, M. R. & Gogotsi, Y. 2D metal carbides and nitrides (MXenes) for energy storage. Nat. Rev. Mater. 2, 16098 (2017).

    CAS  Article  Google Scholar 

  51. 51.

    Jiang, B., Zuo, J. M., Jiang, N., O’Keeffe, M. & Spence, J. C. H. Charge density and chemical bonding in rutile, TiO2. Acta Crystallogr. A 59, 341–350 (2003).

    CAS  Article  Google Scholar 

  52. 52.

    Burdett, J. K. Structural–electronic relationships in rutile. Acta Crystallogr. Sect. B 51, 547–558 (1995).

    Article  Google Scholar 

  53. 53.

    Scanlon, D. O. et al. Band alignment of rutile and anatase TiO2. Nat. Mater. 12, 798–801 (2013).

    CAS  Article  Google Scholar 

  54. 54.

    Morgan, B. J. & Watson, G. W. A density functional theory + U study of oxygen vacancy formation at the (110), (100), (101), and (001) surfaces of rutile TiO2. J. Phys. Chem. C 113, 7322–7328 (2009).

    CAS  Article  Google Scholar 

  55. 55.

    Weller, M., Overton, T., Rourke, J. & Armstrong, F. Inorganic Chemistry 6th edn (Oxford Univ. Press, Oxford, 2014).

  56. 56.

    Brown, I. D. The Chemical Bond in Inorganic Chemistry: The Bond Valence Model (Oxford Univ. Press, Oxford, 2002).

    Google Scholar 

  57. 57.

    Kurtz, R. L. & Henrich, V. E. Comparison of Ti 2p core-level peaks from TiO2, Ti2O3, and Ti metal, by XPS. Surf. Sci. Spectra 5, 179–181 (1998).

    CAS  Article  Google Scholar 

Download references


C.R.A.C. is grateful for many discussions with A. M. Stoneham on the topic in this Perspective. A.W. thanks R. G. Egdell and A. Regoutz for discussions on X-ray photomemission. A.A.S. is indebted to L. N. Kantorovich for discussions of the electron groups theory and structural elements. The research was supported by the EPSRC (grant nos EP/K016288/1 and EP/N01572X/1), the Leverhulme Trust, and the Royal Society. D.O.S. acknowledges support from the European Research Council (grant no. 758345). This work was carried out with funding from the Faraday Institution (https://faraday.ac.uk; EP/S003053/1), grant no. FIRG003.

Author information




All authors contributed equally to the design, writing and editing of the manuscript.

Corresponding authors

Correspondence to Aron Walsh or C. Richard A. Catlow.

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Walsh, A., Sokol, A.A., Buckeridge, J. et al. Oxidation states and ionicity. Nature Mater 17, 958–964 (2018). https://doi.org/10.1038/s41563-018-0165-7

Download citation

Further reading


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