Skip to main content

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

  • Article
  • Published:

Broadband 2D IR spectroscopy reveals dominant asymmetric H5O2+ proton hydration structures in acid solutions


Given the critical role of the aqueous excess proton in redox chemistry, determining its structure and the mechanism of its transport in water are intense areas of experimental and theoretical research. The ultrafast dynamics of the proton’s hydration structure has made it extremely challenging to study experimentally. Using ultrafast broadband two-dimensional infrared spectroscopy, we show that the vibrational spectrum of the aqueous proton is fully consistent with a protonated water complex broadly defined as a Zundel-like H5O2+ motif. Analysis of the inhomogeneously broadened proton stretch two-dimensional lineshape indicates an intrinsically asymmetric, low-barrier O–H+–O potential that exhibits surprisingly persistent distributions in both its asymmetry and O–O distance. This structural characterization has direct implications for the extent of delocalization exhibited by a proton’s excess charge and for the possible mechanisms of proton transport in water.

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

Access options

Buy this article

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

Fig. 1: Infrared spectrum of the aqueous proton.
Fig. 2: 2D IR difference spectra for 2 M HCl and neat water.
Fig. 3: 2D IR spectrum and lineshape analysis of the proton stretching mode.
Fig. 4: Polarization dependence of cross-peak intensity.
Fig. 5: Model of the aqueous proton structure and vibrational assignments consistent with our measurements.

Similar content being viewed by others


  1. Agmon, N. The Grotthuss mechanism. Chem. Phys. Lett. 244, 456–462 (1995).

    Article  CAS  Google Scholar 

  2. Marx, D. Proton transfer 200 years after von Grotthuss: insights from ab initio simulations. ChemPhysChem 7, 1848–1870 (2006).

    Article  PubMed  Google Scholar 

  3. Cukierman, S. Et tu, Grotthuss! And other unfinished stories. Biochim. Biophys. Acta Bioenerg. 1757, 876–885 (2006).

    Article  CAS  Google Scholar 

  4. Agmon, N. et al. Protons and hydroxide ions in aqueous systems. Chem. Rev. 116, 7642–7672 (2016).

    Article  CAS  PubMed  Google Scholar 

  5. Zundel, G. & Metzger, H. Energiebänder der tunnelnden Überschuß-Protenon in flüssigen Säuren. Eine IR-spektroskopische Untersuchung der Natur der Gruppierungen H5O2 +. Z. Phys. Chem. 58, 225–245 (1968).

    Article  CAS  Google Scholar 

  6. Janoschek, R., Weidemann, E. G., Pfeiffer, H. & Zundel, G. Extremely high polarizability of hydrogen bonds. J. Am. Chem. Soc. 94, 2387–2396 (1972).

    Article  CAS  Google Scholar 

  7. Janosche., R., Weidemen, E. G. & Zundel, G. Calculated frequencies and intensities associated with coupling of proton motion with hydrogen-bond stretching vibration in a double minimum potential surface. J. Chem. Soc. Faraday Trans. II 69, 505–520 (1973).

    Article  Google Scholar 

  8. Wicke, E., Eigen, M. & Ackerman, T. Über den zustand des protons (hydroniumions) in wäßriger lösung. Z. Phys. Chem. 1, 340–364 (1954).

  9. Eigen, M. & Maeyer, L. D. Self-dissociation and protonic charge transport in water and ice. Proc. R. Soc. Lond. 247, 505–533 (1958).

    Article  CAS  Google Scholar 

  10. Thämer, M., De Marco, L., Ramasesha, K., Mandal, A. & Tokmakoff, A. Ultrafast 2D IR spectroscopy of the excess proton in liquid water. Science 350, 78–82 (2015).

    Article  CAS  PubMed  Google Scholar 

  11. Dahms, F. et al. The hydrated excess proton in the Zundel cation H5O2 +: the role of ultrafast solvent fluctuations. Angew. Chem. Int. Ed. 55, 10600–10605 (2016).

    Article  CAS  Google Scholar 

  12. Dahms, F., Fingerhut, B. P., Nibbering, E. T. J., Pines, E. & Elsaesser, T. Large-amplitude transfer motion of hydrated excess protons mapped by ultrafast 2D IR spectroscopy. Science 357, 491–495 (2017).

    Article  CAS  PubMed  Google Scholar 

  13. Daly, C. A. et al. Decomposition of the experimental Raman and infrared spectra of acidic water into proton, special pair, and counter-ion contributions. J. Phys. Chem. Lett. 8, 5246–5252 (2017).

    Article  CAS  PubMed  Google Scholar 

  14. Carpenter, W. B., Fournier, J. A., Lewis, N. H. C. & Tokmakoff, A. Picosecond proton transfer kinetics in water revealed with ultrafast IR spectroscopy. J. Phys. Chem. B 122, 2792–2802 (2018).

    Article  CAS  PubMed  Google Scholar 

  15. Biswas, R., Carpenter, W., Fournier, J. A., Voth, G. A. & Tokmakoff, A. IR spectral assignments for the hydrated excess proton in liquid water. J. Chem. Phys. 146, 11 (2017).

    Article  CAS  Google Scholar 

  16. Berkelbach, T. C., Lee, H. S. & Tuckerman, M. E. Concerted hydrogen-bond dynamics in the transport mechanism of the hydrated proton: a first-principles molecular dynamics study. Phys. Rev. Lett. 103, 238302 (2009).

    Article  CAS  PubMed  Google Scholar 

  17. Marx, D., Tuckerman, M. E., Hutter, J. & Parrinello, M. The nature of the hydrated excess proton in water. Nature 397, 601–604 (1999).

    Article  CAS  Google Scholar 

  18. Kulig, W. & Agmon, N. A. ‘Clusters-in-liquid’ method for calculating infrared spectra identifies the proton-transfer mode in acidic aqueous solutions. Nat. Chem. 5, 29–35 (2013).

    Article  CAS  PubMed  Google Scholar 

  19. Giberti, F., Hassanali, A. A., Ceriotti, M. & Parrinello, M. The role of quantum effects on structural and electronic fluctuations in neat and charged water. J. Phys. Chem. B 118, 13226–13235 (2014).

    Article  CAS  PubMed  Google Scholar 

  20. Swanson, J. M. J. & Simons, J. Role of charge transfer in the structure and dynamics of the hydrated proton. J. Phys. Chem. B 113, 5149–5161 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Asmis, K. R. et al. Gas-phase infrared spectrum of the protonated water dimer. Science 299, 1375–1377 (2003).

    Article  CAS  PubMed  Google Scholar 

  22. Headrick, J. M. et al. Spectral signatures of hydrated proton vibrations in water clusters. Science 308, 1765–1769 (2005).

    Article  CAS  PubMed  Google Scholar 

  23. Fournier, J. A. et al. Snapshots of proton accommodation at a microscopic water surface: understanding the vibrational spectral signatures of the charge defect in cryogenically cooled H+(H2O)n=2-28 clusters. J. Phys. Chem. A 119, 9425–9440 (2015).

    Article  CAS  PubMed  Google Scholar 

  24. Heine, N. et al. Isomer-selective detection of hydrogen-bond vibrations in the protonated water hexamer. J. Am. Chem. Soc. 135, 8266–8273 (2013).

    Article  CAS  PubMed  Google Scholar 

  25. Kim, J., Schmitt, U. W., Gruetzmacher, J. A., Voth, G. A. & Scherer, N. E. The vibrational spectrum of the hydrated proton: comparison of experiment, simulation, and normal mode analysis. J. Chem. Phys. 116, 737–746 (2002).

    Article  CAS  Google Scholar 

  26. Xu, J. Q., Zhang, Y. & Voth, G. A. Infrared spectrum of the hydrated proton in water. J. Phys. Chem. Lett. 2, 81–86 (2011).

    Article  CAS  PubMed  Google Scholar 

  27. Knight, C. & Voth, G. A. The curious case of the hydrated proton. Acc. Chem. Res. 45, 101–109 (2012).

    Article  CAS  PubMed  Google Scholar 

  28. Vendrell, O., Gatti, F. & Meyer, H.-D. Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics. J. Chem. Phys. 127, 184303 (2007).

    Article  CAS  PubMed  Google Scholar 

  29. Wolke, C. T. et al. Spectroscopic snapshots of the proton-transfer mechanism in water. Science 354, 1131–1135 (2016).

    Article  CAS  PubMed  Google Scholar 

  30. Guasco, T. L., Johnson, M. A. & McCoy, A. B. Unraveling anharmonic effects in the vibrational predissociation spectra of H5O2 + and its deuterated analogues. J. Phys. Chem. A 115, 5847–5858 (2011).

    Article  CAS  PubMed  Google Scholar 

  31. Yu, Q. & Bowman, J. M. Communication: VSCF/VCI vibrational spectroscopy of H7O3 + and H9O4 + using high-level, many-body potential energy surfaces and dipole moment surfaces. J. Chem. Phys. 146, 121102 (2017).

    Article  CAS  PubMed  Google Scholar 

  32. Biswas, R., Carpenter, W., Voth, G. A. & Tokmakoff, A. Molecular modeling and assignment of IR spectra of the hydrated excess proton in isotopically dilute water. J. Chem. Phys. 145, 12 (2016).

    Article  CAS  Google Scholar 

  33. Stoyanov, E. S., Stoyanova, I. V. & Reed, C. A. The unique nature of H+ in water. Chem. Sci. 2, 462–472 (2011).

    Article  CAS  Google Scholar 

  34. Carpenter, W. B., Fournier, J. A., Biswas, R., Voth, G. A. & Tokmakoff, A. Delocalization and stretch–bend mixing of the HOH bend in liquid water. J. Chem. Phys. 147, 084503 (2017).

    Article  CAS  PubMed  Google Scholar 

  35. Petersen, P. B. & Tokmakoff, A. Source for ultrafast continuum infrared and terahertz radiation. Opt. Lett. 35, 1962–1964 (2010).

    Article  PubMed  Google Scholar 

Download references


This work was supported by the Office of Basic Energy Sciences, US Department of Energy under grant DOE DE-SC0014305. J.A.F. thanks the Arnold O. Beckman Foundation for support through a postdoctoral fellowship. N.H.C.L. acknowledges support from the Yen Fellowship programme.

Author information

Authors and Affiliations



J.A.F. and A.T. conceived and designed experiments. J.A.F., W.B.C. and N.H.C.L. performed the experiments. All authors discussed the results, analyses and interpretations. J.A.F. and A.T. wrote the paper with input from all authors.

Corresponding author

Correspondence to Andrei Tokmakoff.

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.

Supplementary information

Supplementary information

Supplementary Data and Analysis, Supplementary Figures 1–14

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fournier, J.A., Carpenter, W.B., Lewis, N.H.C. et al. Broadband 2D IR spectroscopy reveals dominant asymmetric H5O2+ proton hydration structures in acid solutions. Nature Chem 10, 932–937 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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