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.

Direct observation of ultrafast hydrogen bond strengthening in liquid water

Abstract

Water is one of the most important, yet least understood, liquids in nature. Many anomalous properties of liquid water originate from its well-connected hydrogen bond network1, including unusually efficient vibrational energy redistribution and relaxation2. An accurate description of the ultrafast vibrational motion of water molecules is essential for understanding the nature of hydrogen bonds and many solution-phase chemical reactions. Most existing knowledge of vibrational relaxation in water is built upon ultrafast spectroscopy experiments2,3,4,5,6,7. However, these experiments cannot directly resolve the motion of the atomic positions and require difficult translation of spectral dynamics into hydrogen bond dynamics. Here, we measure the ultrafast structural response to the excitation of the OH stretching vibration in liquid water with femtosecond temporal and atomic spatial resolution using liquid ultrafast electron scattering. We observed a transient hydrogen bond contraction of roughly 0.04 Å on a timescale of 80 femtoseconds, followed by a thermalization on a timescale of approximately 1 picosecond. Molecular dynamics simulations reveal the need to treat the distribution of the shared proton in the hydrogen bond quantum mechanically to capture the structural dynamics on femtosecond timescales. Our experiment and simulations unveil the intermolecular character of the water vibration preceding the relaxation of the OH stretch.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Experiment overview.
Fig. 2: Transient hydrogen bond strengthening.
Fig. 3: First shell hydrogen atom dynamics.
Fig. 4: Thermalization.

Data availability

Experimental data were generated at the MeV-UED facility at the SLAC National Accelerator Laboratory. Data behind each figure are available in Zenodo with the identifier https://doi.org/10.5281/zenodo.4678299. Raw datasets are available from the corresponding authors on reasonable request. Source data are provided with this paper.

Code availability

The non-commercial codes used for the simulation and analysis here are available from the corresponding authors on reasonable request.

References

  1. 1.

    Stillinger, F. H. Water revisited. Science 209, 451–457 (1980).

    CAS  PubMed  Article  ADS  Google Scholar 

  2. 2.

    Perakis, F. et al. Vibrational spectroscopy and dynamics of water. Chem. Rev. 116, 7590–7607 (2016).

    CAS  PubMed  Article  Google Scholar 

  3. 3.

    Lindner, J. et al. Vibrational relaxation of pure liquid water. Chem. Phys. Lett. 421, 329–333 (2006).

    CAS  Article  ADS  Google Scholar 

  4. 4.

    Ramasesha, K., De Marco, L., Mandal, A. & Tokmakoff, A. Water vibrations have strongly mixed intra- and intermolecular character. Nat. Chem. 5, 935–940 (2013).

    CAS  PubMed  Article  Google Scholar 

  5. 5.

    Bakker, H. J. et al. Transient absorption of vibrationally excited water. J. Chem. Phys. 116, 2592–2598 (2002).

    CAS  Article  ADS  Google Scholar 

  6. 6.

    Fecko, C. J., Eaves, J. D., Loparo, J. J., Tokmakoff, A. & Geissler, P. L. Ultrafast hydrogen-bond dynamics in the infrared spectroscopy of water. Science 301, 1698–1702 (2003).

    CAS  PubMed  Article  ADS  Google Scholar 

  7. 7.

    Ashihara, S., Huse, N., Espagne, A., Nibbering, E. T. J. & Elsaesser, T. Ultrafast structural dynamics of water induced by dissipation of vibrational energy. J. Phys. Chem. A 111, 743–746 (2007).

    CAS  PubMed  Article  Google Scholar 

  8. 8.

    Auer, B. M. & Skinner, J. L. IR and Raman spectra of liquid water: theory and interpretation. J. Chem. Phys. 128, 224511 (2008).

    CAS  PubMed  Article  ADS  Google Scholar 

  9. 9.

    Amann-Winkel, K. et al. X-ray and neutron scattering of water. Chem. Rev. 116, 7570–7589 (2016).

    CAS  PubMed  Article  Google Scholar 

  10. 10.

    Sellberg, J. A. et al. Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature. Nature 510, 381–384 (2014).

    CAS  PubMed  Article  ADS  Google Scholar 

  11. 11.

    Beyerlein, K. R. et al. Ultrafast nonthermal heating of water initiated by an X-ray free-electron laser. Proc. Natl Acad. Sci. USA 115, 5652–5657 (2018).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  12. 12.

    Wen, H., Huse, N., Schoenlein, R. W. & Lindenberg, A. M. Ultrafast conversions between hydrogen bonded structures in liquid water observed by femtosecond x-ray spectroscopy. J. Chem. Phys. 131, 234505 (2009).

    PubMed  Article  ADS  CAS  Google Scholar 

  13. 13.

    Perakis, F. et al. Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics. Nat. Commun. 9, 1917 (2018).

    PubMed  PubMed Central  Article  ADS  CAS  Google Scholar 

  14. 14.

    Kim, K. H. et al. Direct observation of bond formation in solution with femtosecond X-ray scattering. Nature 518, 385–389 (2015).

    CAS  PubMed  Article  ADS  Google Scholar 

  15. 15.

    van Driel, T. B. et al. Atomistic characterization of the active-site solvation dynamics of a model photocatalyst. Nat. Commun. 7, 13678 (2016).

    PubMed  PubMed Central  Article  ADS  CAS  Google Scholar 

  16. 16.

    Nunes, J. P. F. et al. Liquid-phase mega-electron-volt ultrafast electron diffraction. Struct. Dyn. 7, 024301 (2020).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  17. 17.

    Koralek, J. D. et al. Generation and characterization of ultrathin free-flowing liquid sheets. Nat. Commun. 9, 1353 (2018).

    PubMed  PubMed Central  Article  ADS  CAS  Google Scholar 

  18. 18.

    Ihee, H. Visualizing solution-phase reaction dynamics with time-resolved X-ray liquidography. Acc. Chem. Res. 42, 356–366 (2009).

    CAS  PubMed  Article  Google Scholar 

  19. 19.

    Skinner, L. B., Benmore, C. J., Neuefeind, J. C. & Parise, J. B. The structure of water around the compressibility minimum. J. Chem. Phys. 141, 214507 (2014).

    CAS  PubMed  Article  ADS  Google Scholar 

  20. 20.

    Haldrup, K. et al. Observing solvation dynamics with simultaneous femtosecond X-ray emission spectroscopy and X-ray scattering. J. Phys. Chem. B 120, 1158–1168 (2016).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  21. 21.

    Morawietz, T., Singraber, A., Dellago, C. & Behler, J. How van der Waals interactions determine the unique properties of water. Proc. Natl Acad. Sci. USA 113, 8368–8373 (2016).

    CAS  PubMed  PubMed Central  Article  ADS  Google Scholar 

  22. 22.

    Dettori, R. et al. Simulating energy relaxation in pump–probe vibrational spectroscopy of hydrogen-bonded liquids. J. Chem. Theory Comput. 13, 1284–1292 (2017).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  23. 23.

    Dettori, R., Ceriotti, M., Hunger, J., Colombo, L. & Donadio, D. Energy relaxation and thermal diffusion in infrared pump–probe spectroscopy of hydrogen-bonded liquids. J. Phys. Chem. Lett. 10, 3447–3452 (2019).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  24. 24.

    Gilli, P., Bertolasi, V., Ferretti, V. & Gilli, G. Evidence for resonance-assisted hydrogen bonding. 4. Covalent nature of the strong homonuclear hydrogen bond. Study of the O-H-O system by crystal structure correlation methods. J. Am. Chem. Soc. 116, 909–915 (1994).

    CAS  Article  Google Scholar 

  25. 25.

    Lippincott, E. R. & Schroeder, R. One‐dimensional model of the hydrogen bond. J. Chem. Phys. 23, 1099–1106(1955).

    CAS  Article  ADS  Google Scholar 

  26. 26.

    Staib, A. & Hynes, J. T. Vibrational predissociation in hydrogen-bonded OH…O complexes via OH stretch-OO stretch energy transfer. Chem. Phys. Lett. 204, 197–205 (1993).

    CAS  Article  ADS  Google Scholar 

  27. 27.

    McKenzie, R. H., Bekker, C., Athokpam, B. & Ramesh, S. G. Effect of quantum nuclear motion on hydrogen bonding. J. Chem. Phys. 140, 174508 (2014).

    PubMed  Article  ADS  CAS  PubMed Central  Google Scholar 

  28. 28.

    Grabowski, S. J. What is the covalency of hydrogen bonding? Chem. Rev. 111, 2597–2625 (2011).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  29. 29.

    Shibata, S. & Bartell, L. S. Electron‐diffraction study of water and heavy water. J. Chem. Phys. 42, 1147–1151 (1965).

    CAS  Article  ADS  Google Scholar 

  30. 30.

    Ceriotti, M. et al. Nuclear quantum effects in water and aqueous systems: experiment, theory, and current challenges. Chem. Rev. 116, 7529–7550 (2016).

    CAS  PubMed  Article  Google Scholar 

  31. 31.

    Weathersby, S. P. et al. Mega-electron-volt ultrafast electron diffraction at SLAC National Accelerator Laboratory. Rev. Sci. Instrum. 86, 073702 (2015).

    CAS  PubMed  Article  ADS  Google Scholar 

  32. 32.

    Bertie, J. E. & Lan, Z. Infrared intensities of liquids XX: the intensity of the OH stretching band of liquid water revisited, and the best current values of the optical constants of H2O(l) at 25 °C between 15,000 and 1 cm-1. Appl. Spectrosc. 50, 1047–1057 (1996).

    CAS  Article  ADS  Google Scholar 

  33. 33.

    Sorenson, J. M., Hura, G., Glaeser, R. M. & Head-Gordon, T. What can x-ray scattering tell us about the radial distribution functions of water? J. Chem. Phys. 113, 9149–9161 (2000).

    CAS  Article  ADS  Google Scholar 

  34. 34.

    Brockway, L. O. Electron diffraction by gas molecules. Rev. Mod. Phys. 8, 0231–0266 (1936).

    CAS  Article  ADS  Google Scholar 

  35. 35.

    Hubbell, J. H. et al. Atomic form factors, incoherent scattering functions, and photon scattering cross sections. J. Phys. Chem. Ref. Data 4, 471–538 (1975).

    CAS  Article  ADS  Google Scholar 

  36. 36.

    Yang, J. et al. Structure retrieval in liquid-phase electron scattering. Phys. Chem. Chem. Phys. 23, 1308–1316 (2021).

  37. 37.

    Horn, H. W. et al. Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. J. Chem. Phys. 120, 9665–9678 (2004).

    CAS  PubMed  Article  ADS  Google Scholar 

  38. 38.

    Levine, B. G., Stone, J. E. & Kohlmeyer, A. Fast analysis of molecular dynamics trajectories with graphics processing units—radial distribution function histogramming. J. Comput. Phys. 230, 3556–3569 (2011).

    CAS  PubMed  PubMed Central  MATH  Article  ADS  Google Scholar 

  39. 39.

    Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph. 14, 33–38 (1996).

    CAS  PubMed  Article  Google Scholar 

  40. 40.

    Dohn, A. O. et al. On the calculation of X-ray scattering signals from pairwise radial distribution functions. J. Phys. B 48, 244010 (2015).

    Article  ADS  CAS  Google Scholar 

  41. 41.

    Bartell, L. S. & Gavin, R. M. Effects of electron correlation in x-ray and electron diffraction. J. Am. Chem. Soc. 86, 3493–3498 (1964).

    CAS  Article  Google Scholar 

  42. 42.

    Wang, J. H., Tripathi, A. N. & Smith, V. H. Chemical-binding and electron orrelation-effects in x-ray and high-energy electron-scattering. J. Chem. Phys. 101, 4842–4854 (1994).

    CAS  Article  ADS  Google Scholar 

  43. 43.

    Hammer, B., Hansen, L. B. & Nørskov, J. K. Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals. Phys. Rev. B 59, 7413–7421 (1999).

    Article  ADS  Google Scholar 

  44. 44.

    Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

    PubMed  Article  ADS  CAS  Google Scholar 

  45. 45.

    Bussi, G., Donadio, D. & Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 126, 014101 (2007).

    PubMed  Article  ADS  CAS  Google Scholar 

  46. 46.

    Zwanzig, R. in Non-equilibrium Statistical Mechanics, 1st edn, ch. 1, 18–21 (Oxford Univ. Press, 2001).

  47. 47.

    Ceriotti, M. & Parrinello, M. The δ-thermostat: selective normal-modes excitation by colored-noise Langevin dynamics. Procedia Comput. Sci. 1, 1607–1614 (2010).

    Article  Google Scholar 

  48. 48.

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

    CAS  Article  ADS  Google Scholar 

  49. 49.

    Cao, J. & Voth, G. A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. III. Phase space formalism and analysis of centroid molecular dynamics. J. Chem. Phys. 101, 6157–6167 (1994).

    CAS  Article  ADS  Google Scholar 

  50. 50.

    Markland, T. E. & Ceriotti, M. Nuclear quantum effects enter the mainstream. Nature Reviews Chemistry 2, 0109, https://doi.org/10.1038/s41570-017-0109 (2018).

    CAS  Article  Google Scholar 

  51. 51.

    Hockney, R. W. & Eastwood, J. W. Computer simulation using particles, 1st edn, ch. 1 (Taylor & Francis, 1988).

  52. 52.

    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    CAS  MATH  Article  ADS  Google Scholar 

  53. 53.

    Dunning, T. H. Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007–1023 (1989).

  54. 54.

    Ufimtsev, I. S. & Martínez, T. J. Quantum chemistry on graphical processing units. 1. Strategies for two-electron integral evaluation. J. Chem. Theory Comput. 4, 222–231 (2008).

    CAS  PubMed  Article  Google Scholar 

  55. 55.

    Ufimtsev, I. S. & Martinez, T. J. Quantum chemistry on graphical processing units. 2. Direct self-consistent-field implementation. J. Chem. Theory Comput. 5, 1004–1015 (2009).

    CAS  PubMed  Article  Google Scholar 

  56. 56.

    Ufimtsev, I. S. & Martinez, T. J. Quantum chemistry on graphical processing units. 3. Analytical energy gradients, geometry optimization, and first principles molecular dynamics. J. Chem. Theory Comput. 5, 2619–2628 (2009).

    CAS  PubMed  Article  Google Scholar 

  57. 57.

    Yang, J. et al. Simultaneous observation of nuclear and electronic dynamics by ultrafast electron diffraction. Science 368, 885–889 (2020).

    CAS  PubMed  Article  ADS  Google Scholar 

  58. 58.

    Shibata, S., Sekiyama, H., Tachikawa, K. & Moribe, M. Chemical bonding effect in electron scattering by gaseous molecules. J. Mol. Struct. 641, 1–6 (2002).

    CAS  Article  ADS  Google Scholar 

  59. 59.

    Jensen, P. Hamiltonians for the internal dynamics of triatomic molecules. J. Chem. Soc. Faraday Trans. 84, 1315–1339 (1988).

    CAS  Article  Google Scholar 

  60. 60.

    Wilson, E. B. J., Decius, J. C. & Cross, P. C. Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra (Dover Publications, 2012).

  61. 61.

    Ceriotti, M., Bussi, G. & Parrinello, M. Colored-noise thermostats à la carte. J. Chem. Theory Comput. 6, 1170–1180 (2010).

    CAS  Article  Google Scholar 

  62. 62.

    Ceriotti, M., Bussi, G. & Parrinello, M. Nuclear quantum effects in solids using a colored-noise thermostat. Phys. Rev. Lett. 103, 030603 (2009).

    PubMed  Article  ADS  CAS  PubMed Central  Google Scholar 

  63. 63.

    Marsalek, O. & Markland, T. E. Ab initio molecular dynamics with nuclear quantum effects at classical cost: ring polymer contraction for density functional theory. J. Chem. Phys. 144, 054112 (2016).

    PubMed  Article  ADS  CAS  PubMed Central  Google Scholar 

  64. 64.

    Habershon, S. & Manolopoulos, D. E. Zero point energy leakage in condensed phase dynamics: an assessment of quantum simulation methods for liquid water. J. Chem. Phys. 131, 244518 (2009).

    PubMed  Article  ADS  CAS  PubMed Central  Google Scholar 

  65. 65.

    Salvat, F., Jablonski, A. & Powell, C. J. ELSEPA - Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules. Comput. Phys. Commun. 165, 157–190 (2005).

    CAS  Article  ADS  Google Scholar 

  66. 66.

    Kim, J. G. et al. Mapping the emergence of molecular vibrations mediating bond formation. Nature 582, 520–524 (2020).

    CAS  PubMed  Article  ADS  PubMed Central  Google Scholar 

  67. 67.

    Császár, A. G. et al. First-principles prediction and partial characterization of the vibrational states of water up to dissociation. J. Quant. Spectrosc. Radiat. Transfer 111, 1043–1064 (2010).

    Article  ADS  CAS  Google Scholar 

  68. 68.

    Soper, A. K. Joint structure refinement of X-ray and neutron diffraction data on disordered materials: application to liquid water. J. Phys. Condens. Matter 19, 335206 (2007).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

Download references

Acknowledgements

We thank T. E. Markland for helpful discussions, and G. M. Stewart for help in producing Fig. 1a. The experiment was performed at the SLAC MeV-UED facility, which is supported in part by the US DOE BES SUF division Accelerator and Detector R&D program, the LCLS Facility, and SLAC under contract nos. DE-AC02-05-CH11231 and DE-AC02-76SF00515. J.P.F.N. and M.C. are supported by the US DOE Office of Science, Basic Energy Sciences under award no. DE-SC0014170. K.L. is supported by a Melvin and Joan Lane Stanford Graduate Fellowship and a Stanford Physics Department fellowship. J.Y., T.F.H., A.A.C., T. J. A.W., E.B., N.H.L., T.J.M. and K.J.G. were supported by the US DOE Office BES, Chemical Sciences, Geosciences, and Biosciences division. A.M.L. acknowledges support from the DOE BES Materials Science and Engineering division under contract DE-AC02-76SF00515. Z.C. and M.M. are supported by the DOE Fusion Energy Sciences under fieldwork proposal no. 100182.

Author information

Affiliations

Authors

Contributions

J.Y., K.J.G., A.M.L. and X.W. proposed the study. J.P.F.N., K.L., E.B., M.C., D.P.D., M.F.-L., M.M., X.S., T.J.A.W., J.Y., A.A.C. and X.W. developed the experimental setup. M.E.K. developed the pump laser setup. J.Y., J.P.F.N., E.B., Z.C., A.A.C., T.F.H., K.L., M.F.-L., M.M., X.S., T.J.A.W and X.W. performed the experiment. J.Y. analysed the experimental data and performed the χ2 fitting. J.Y., A.N., T.J.M. and K.J.G. interpreted the experimental data. R.D. and D.D. performed the pump-probe molecular dynamics simulation. J.P.F.N. performed the equilibrium water simulation. N.H.L. and T.J.M. performed the 1D and 2D quantum simulations and the ab initio electron scattering simulation. J.Y., R.D., N.H.L., D.D., T.J.M., K.J.G. and X.W. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to Jie Yang, Davide Donadio, Kelly J. Gaffney, Todd J. Martinez or Xijie Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Michele Ceriotti, Dmitry Khakhulin 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.

Extended data figures and tables

Extended Data Fig. 1 Extra information for data interpretation.

a, Ab initio simulation of the inelastic and elastic scattering signal change for vOH = 1 in comparison to vOH = 0. The simulation is performed on a single water molecule with OH bond lengths adjusted to the equilibrium length for each vibrational state as predicted in ref. 5 (for more details, see Methods). b, Spectrum of the second and the third harmonics of the pump laser. c, Experimental g2 and temperature evolution up to 100 ps. d, Damped QΔS from experimental data. This is related to Fig. 1c by the damping term \({e}^{-0.03{Q}^{2}}\); equation (3) in Methods

Source data.

Extended Data Fig. 2 Wigner sampling.

a, The three lowest eigenstates (coloured lines) and eigenvalues (horizontal grey lines) of the Lippincott–Schroeder model potential (black line). Inset, the probability distribution of the vOH = 0 and vOH = 1 states, μ and σ represent mean and standard deviation. bc, Wigner distribution for vOH = 0 (b) and vOH = 1 (c). The region of phase space with negative values of the vOH = 1 distribution (orange shades) was excluded from the sampling. Note the different colour gradient used for negative function values. Lippincott–Schroeder model (ROO = 2.85 Å) is used for sampling of the initial displacements and velocities along the OH bonds of the excited molecules

Source data.

Extended Data Fig. 3 Probability density from classical and Wigner sampling.

a, Wigner sampling. Magenta represents vOH = 0, yellow represents vOH = 1. b, Classical sampling. Magenta and yellow represent unexcited and excited molecules, respectively, calculated by averaging over the final 10 fs window during the excitation phase. Dashed black line represents the equilibrium water before excitation. The vertical dotted lines represent the equilibrium distance for each curve, and μ and σ represent the mean and standard deviation of each curve, respectively

Source data.

Extended Data Fig. 4 Examples of pair distances shift.

a, gOO(r) around the first OO peak for four different ΔR1. b, ΔPDFOO for three different ΔR1. c, ΔPDFOH for three different Δr2. d, ΔPDFOH for three different Δr3

Source data.

Extended Data Fig. 5 CPDF analysis.

a, A comparison of experimental and simulated CPDF. The overall scaling factor is achieved by matching the height of the first OO between experimental and simulated curves. The simulation is a 275 K water box under equilibrium condition. b, The simulated elastic and inelastic components of the CPDF, the inelastic component is concentrated to r < 2.5 Å. Exp., experimental; Sim., simulated. c, CPDF for five delay windows (see the key) in full r range. d, CPDF for five delay windows (see the key) around the second OO shell. The peak height around 4.6 Å is used to extract g2 for Fig. 4a

Source data.

Extended Data Fig. 6 Comparison of equilibrium ΔPDF simulation.

ΔPDF from experiment at 2.2 ps (blue with error bars), simulation using Tip4p-Ew force field (orange) and simulation using machine-learning force field (yellow)

Source data.

Extended Data Fig. 7 ΔPDF simulated using different methods.

a–c, ΔPDF consistency. a, The ΔPDF simulated using the conventional method (that is, by first simulating the electron scattering pattern using equation (7), then transforming to real space using equation (3)). b, The ΔPDF simulated by directly applying equation (4), and smoothed by convolution with a Gaussian kernel with a FWHM of 0.53 Å. The weight of OO, OH and HH pairs are chosen to be 1, 0.4 and 0.16, respectively, obtained by atomic scattering cross section and the relative number of each types of atom pairs. The 0.53 Å FWHM of the Gaussian Kernel is obtained using 2π/Qmax, where Qmax = 11.8Å−1 is the maximum Q range in this experiment. c, The ΔPDF simulated by directly applying equation (4) without Gaussian smoothing. The vertical scales of all subpanels are identical. df, Comparison of the ΔPDF in quantum simulations (d), classical simulations with excitation (e) and classical simulations with 3/2 excitation (f)

Source data.

Extended Data Fig. 8 Simulated instantaneous kinetic temperature evolution.

ab, Classical excitation during the 100 fs excitation phase (a), and during the 3 ps relaxation phase (b). cd, Quantum excitation, with vOH = 1 (c) and vOH = 0 (d). Tstretch and Trot are defined in equation (11) and equation (12). In c, the subscript ‘Stretch1’ and ‘Rot1’ indicate the OH bond corresponding to vOH = 1 Wigner sampling, and ‘Stretch2’ and ‘Rot2’ indicate the OH bond corresponding to vOH = 0 Wigner sampling. The superscript ‘excited’ indicates Wigner sampling. Excited and unexcited molecules are calculated separately. The initial temperature before excitation is 300 K

Source data.

Extended Data Fig. 9 Comparison of NNP-based 2D OH stretching vibrational modes in gas phase and frozen phonon liquid phase.

ah, The lowest vibrational eigenstates \(({n}_{1},{n}_{2})\)for a representative configuration (bond angle of 104.4°) among the 200 2D potential energy surfaces considered (ac, eg; dashed black lines indicate symmetric and antisymmetric displacements); and distribution of vibrational frequencies (defined as \(\varDelta {\nu }_{{n}_{1},{n}_{2}}={\nu }_{{n}_{1},{n}_{2}}-{\nu }_{0,0}\)) for the two lowest OH stretching vibrationally excited states for the 200 configurations (dh). The distribution in the gas phase originates from the variation in the bond angle. The vertical lines indicate the experimental gas-phase stretch frequencies67 and \(\varDelta {\nu }_{1}\) from the 1D Lippincott–Schroeder model, respectively. i, Comparison of 1D OH stretch potentials for gas phase and liquid water as obtained from the NNP (blue and red, respectively) and the Lippincott–Schroeder model (black). The transparent thin lines correspond to the underlying 2 × 200 NNP replicates while the corresponding thick lines indicate the average potentials

Source data.

Extended Data Fig. 10 Zero-point energy leakage time.

ac, Comparison of the OO (a), OH (b) and HH (c) RDFs computed during an equilibrium run for a classical distribution of positions and momenta (NVT), during the coupling with the quantum GLE thermostat, from ab initio PIMD simulations63 and measured from neutron diffraction experiments68. The inset in b is a zoom-in on the OH bond peak where, due to the absence of experimental data to compare with, we reported the comparison with DFT-based PIMD simulations. d, Kinetic energies computed during the coupling with the quantum thermostat. e, Kinetic energies computed during the NVE simulations. The inset in d shows a temporal fitting of the stretching temperature decay. f, Time-resolved RDF computed during the NVE relaxation. The black curve refers to the NVT-computed RDF, obtained at T = 300 K. The inset shows the shift of the R1 distance during the system relaxation

Source data.

Supplementary information

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, J., Dettori, R., Nunes, J.P.F. et al. Direct observation of ultrafast hydrogen bond strengthening in liquid water. Nature 596, 531–535 (2021). https://doi.org/10.1038/s41586-021-03793-9

Download citation

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