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# 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.

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## 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.

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## 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

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.

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

### 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

### 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

### 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

### 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

### 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)

### 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)

### 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

### 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

### 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

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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

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