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.

  • Letter
  • Published:

The nature of the hydrated excess proton in water

Abstract

Explanations for the anomalously high mobility of protons in liquid water began with Grotthuss's idea1, 2 of ‘structural diffusion’ nearly two centuries ago. Subsequent explanations have refined this concept by invoking thermal hopping3, 4, proton tunnelling5, 6 or solvation effects7. More recently, two main structural models have emerged for the hydrated proton. Eigen8, 9 proposed the formation of an H9O4+ complex in which an H3O+ core is strongly hydrogen-bonded to three H2O molecules. Zundel10, 11, meanwhile, supported the notion of an H5O2+ complex in which the proton isshared between two H2O molecules. Here we use ab initio path integral12,13,14 simulations to address this question. These simulations include time-independent equilibrium thermal and quantum fluctuations of all nuclei, and determine interatomic interactions from the electronic structure. We find that the hydrated proton forms a fluxional defect in the hydrogen-bonded network, with both H9O4+ and H5O2+ occurring only in thesense of ‘limiting’ or ‘ideal’ structures. The defect can become delocalized over several hydrogen bonds owing to quantum fluctuations. Solvent polarization induces a small barrier to proton transfer, which is washed out by zero-point motion. The proton can consequently be considered part of a ‘low-barrier hydrogen bond’15, 16, in which tunnelling is negligible and the simplest concepts of transition-state theory do not apply. The rate of proton diffusion is determined by thermally induced hydrogen-bond breaking in the second solvation shell.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Examples of simulation configurations.
Figure 2: Representation of relative proton positions.
Figure 3: Particle density of a representative delocalized quantum configuration.

Similar content being viewed by others

References

  1. de Grotthuss, C. J. T. Sur la décomposition de l'eau et des corps qu'elle tient en dissolution à l'aide de l'électricité galvanique. Ann. Chim. LVIII, 54–74 (1806).

    Google Scholar 

  2. Atkins, P. W. Physical Chemistry 6th edn, Ch. 24.8, 741 (Oxford Univ. Press, (1998)).

    Google Scholar 

  3. Hückel, E. Theorie der Beweglichkeiten des Wasserstoff- und Hydroxylions in wässriger Lösung. Z. Elektrochem. 34, 546–562 (1928).

    Google Scholar 

  4. Stearn, A. E. & Eyring, J. The deduction of reaction mechanisms from the theory of absolute rates. J.Chem. Phys. 5, 113–124 (1937).

    Article  ADS  CAS  Google Scholar 

  5. Bernal, J. D. & Fowler, R. H. Atheory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions. J. Chem. Phys. 1, 515–548 (1933).

    Article  ADS  CAS  Google Scholar 

  6. Wannier, G. Die Beweglichkeit des Wasserstoff- und Hydroxylions in wäßriger Lösung. Ann. Phys. (Leipz.) 24, 545–590 (1935).

    Article  ADS  CAS  Google Scholar 

  7. Huggins, M. L. Hydrogen bridges in ice and liquid water. J. Phys. Chem. 40, 723–731 (1936).

    Article  CAS  Google Scholar 

  8. Wicke, E., Eigen, M. & Ackermann, Th. Über den Zustand des Protons (Hydroniumions) in wäßriger Lösung. Z. Phys. Chem. (N.F.) 1, 340–364 (1954).

    Article  Google Scholar 

  9. Eigen, M. Proton transfer, acid–base catalysis and enzymatic hydrolysis. Angew. Chem. Int. Edn Engl. 3, 1–19 (1964).

    Article  Google Scholar 

  10. Zundel, G. & Metzger, H. Energiebänder der tunnelnden Überschuß-Protenon in flüssigen Säuren. Eine IR-spektroskopische Untersuchung der Natur der Gruppierungen H5O+2. Z. Physik. Chem. (N.F.) 58, 225–245 (1968).

    Article  CAS  Google Scholar 

  11. Zundel, G. in The Hydrogen Bond—Recent Developments in Theory and Experiments. II. Structure and Spectroscopy (eds Schuster, P., Zundel, G. & Sandorfy, C.) 683–766 (North-Holland, Amsterdam, (1976)).

    Google Scholar 

  12. Marx, D. & Parrinello, M. Ab initio path-integral molecular dynamics. Z. Phys. B (Rapid Note) 95, 143–144 (1994).

    Article  ADS  CAS  Google Scholar 

  13. Marx, D. & Parrinello, M. Ab initio path integral molecular dynamics: basic ideas. J. Chem. Phys. 104, 4077–4082 (1996).

    Article  ADS  CAS  Google Scholar 

  14. Tuckerman, M. E., Marx, D., Klein, M. L. & Parrinello, M. Efficient and general algorithms for path integral Car–Parrinello molecular dynamics. J. Chem. Phys. 104, 5579–5588 (1996).

    Article  ADS  CAS  Google Scholar 

  15. Cleland, W. W. & Kreevoy, M. M. Low-barrier hydrogen bonds and enzymic catalysis. Science 264, 1887–1890 (1994).

    Article  ADS  CAS  Google Scholar 

  16. Tuckerman, M. E., Marx, D., Klein, M. L. & Parrinello, M. On the quantum nature of the shared proton in hydrogen bonds. Science 275, 817–820 (1997).

    Article  CAS  Google Scholar 

  17. Guissani, Y., Guillot, B. & Bratos, S. The statistical mechanics of the ionic equilibrium of water: a computer simulation study. J. Chem. Phys. 88, 5850–5856 (1988).

    Article  ADS  CAS  Google Scholar 

  18. Halley, J. W., Rustad, J. R. & Rahman, A. Apolarizable, dissociating molecular dynamics model for liquid water. J. Chem. Phys. 98, 4110–4119 (1993).

    Article  ADS  CAS  Google Scholar 

  19. Tuñón, I., Silla, E. & Bertrán, J. Proton solvation in liquid water. An ab initio study using the continuum model. J. Phys. Chem. 97, 5547–5552 (1993).

    Article  Google Scholar 

  20. Laria, D., Ciccotti, G., Ferrario, M. & Kapral, R. Activation free energy for proton transfer in solution. Chem. Phys. 180, 181–189 (1994).

    Article  CAS  Google Scholar 

  21. Komatsuzaki, T. & Ohmine, I. Energetics of proton transfer in liquid water. I. Ab initio study for origin of many-body interaction and potential energy surfaces. Chem. Phys. 180, 239–269 (1994).

    Article  CAS  Google Scholar 

  22. Wei, D. & Salahub, D. R. Hydrated proton clusters and solvent effects on the proton transfer barrier: adensity functional study. J. Chem. Phys. 101, 7633–7643 (1994).

    Article  ADS  CAS  Google Scholar 

  23. Tuckerman, M., Laasonen, K., Sprik, M. & Parrinello, M. Ab initio molecular dynamics simulation of the solvation and transport of H3O+ and OH ions in water. J. Phys. Chem. 99, 5749–5752 (1995); Abinitio molecular dynamics simulation of the solvation and transport of hydronium and hydroxyl ions in water. J. Chem. Phys. 103, 150–161 (1995).

    Article  CAS  Google Scholar 

  24. Lobaugh, J. & Voth, G. A. The quantum dynamics of an excess proton in water. J. Chem. Phys. 104, 2056–2069 (1996).

    Article  ADS  CAS  Google Scholar 

  25. Ando, K. & Hynes, J. T. Molecular mechanism of HCl acid ionization in water: ab initio potential energy surfaces and Monte Carlo simulations. J. Phys. Chem. B 101, 10464–10478 (1997).

    Article  CAS  Google Scholar 

  26. Schmidt, R. G. & Brickmann, J. Molecular dynamics simulation of the proton transport in water. Ber. Bunsenges. Phys. Chem. 101, 1816–1827 (1997).

    Article  CAS  Google Scholar 

  27. Sagnella, D. E. & Tuckerman, M. E. An empirical valence bond model for proton transfer in water. J.Chem. Phys. 108, 2073–2083 (1998).

    Article  ADS  CAS  Google Scholar 

  28. Vuilleumier, R. & Borgis, D. Quantum dynamics of an excess proton in water using an extended empirical valence-bond hamiltonian. J. Phys. Chem. B 102, 4261–4264 (1998).

    Article  CAS  Google Scholar 

  29. Schmitt, U. W. & Voth, G. A. Multistate empirical valence bond model for proton transport in water. J.Phys. Chem. B 102, 5547–5551 (1998).

    Article  CAS  Google Scholar 

  30. Billeter, S. R. & van Gunsteren, W. F. Protonizable water model for quantum dynamical simulations. J.Phys. Chem. A 102, 4669–4678 (1998).

    Article  CAS  Google Scholar 

  31. Kochanski, E., Kelterbaum, R., Klein, S., Rohmer, M. M. & Rahmouni, A. Decades of theoretical work on protonated hydrates. Adv. Quantum Chem. 28, 273–291 (1997).

    Article  ADS  CAS  Google Scholar 

  32. Benoit, M., Marx, D. & Parrinello, M. Tunnelling and zero-point motion in high-pressure ice. Nature 392, 258–261 (1998).

    Article  ADS  CAS  Google Scholar 

  33. Agmon, N. The Grotthuss mechanism. Chem. Phys. Lett. 244, 456–462 (1995); Hydrogen bonds, water rotation and proton mobility. J. Chim. Phys. Phys.-Chim. Biol. 93, 1714–1736 (1996).

    Article  ADS  CAS  Google Scholar 

  34. Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098–3100 (1988).

    Article  ADS  CAS  Google Scholar 

  35. Lee, C., Wang, W. & Parr, R. G. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988).

    Article  ADS  CAS  Google Scholar 

  36. Troullier, N. & Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).

    Article  ADS  CAS  Google Scholar 

  37. Sprik, M., Hutter, J. & Parrinello, M. Ab initio molecular dynamics simulation of liquid water: comparison of three gradient-corrected density functionals. J. Chem. Phys. 105, 1142–1152 (1996).

    Article  ADS  CAS  Google Scholar 

  38. Ojamäe, L., Shavitt, I. & Singer, S. J. Potential models for simulations of the solvated proton in water. J. Chem. Phys. 109, 5547–5564 (1998).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank K.-D. Kreuer for discussions. The calculations were performed on the Cray-T3E/816 of the Max-Planck-Gesellschaft.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dominik Marx.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marx, D., Tuckerman, M., Hutter, J. et al. The nature of the hydrated excess proton in water. Nature 397, 601–604 (1999). https://doi.org/10.1038/17579

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/17579

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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