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Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange

Nature Chemistry volume 16, pages 1838–1844 (2024)Cite this article

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Abstract

The transport of excess protons in water is central to acid–base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

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Fig. 1: Diffusion constant and vibrational spectra.
Fig. 2: Proton transfer mechanism.
Fig. 3: Vibrational fingerprints of H-bond configurations.
Fig. 4: Proton transport.

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Data availability

Molecular configurations, energies and forces used for NNP training and the relative displacement of the Wannier centroids for DWNN are publicly available on Zenodo at https://doi.org/10.5281/zenodo.11965260 (ref. 55). Source data are provided with this paper.

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Acknowledgements

This work was supported through a PhD fellowship to A.G. from the French Ministry of Higher Education and Research and an HPC allocation from GENCI-IDRIS (D.L., grant A0110707156). W.H.T. acknowledges support from the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the US Department of Energy, through grant no. DE-SC0021114.

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Authors and Affiliations

  1. PASTEUR, Department of Chemistry, École normale supérieure, PSL University, Sorbonne Université, CNRS, Paris, France

    Axel Gomez & Damien Laage

  2. Department of Chemistry, University of Kansas, Lawrence, KS, USA

    Ward H. Thompson

Authors
  1. Axel Gomez
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  2. Ward H. Thompson
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  3. Damien Laage
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Contributions

W.H.T. and D.L. conceptualized the project. A.G. performed the simulations. A.G., W.H.T. and D.L. analysed the data and wrote the manuscript.

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Correspondence to Damien Laage.

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Extended data

Extended Data Fig. 1 Hydrogen-bond coordinate.

Schematic representation of the atoms involved in the calculation of the H-bond coordinate around Ob.

Extended Data Fig. 2 Proton transfer free energy profiles in H2O and in D2O at 300 K.

One-dimensional free energy profile along the reaction coordinate determined from the two-dimensional surface in Fig. 2b and Supplementary Fig. 2 (A) with the revPBE0-D3 NNP and (B) with the B3LYP-D3 NNP, respectively for H2O with nuclear quantum effects (solid orange lines), D2O with nuclear quantum effects (solid purple lines) and H2O with classical nuclei (orange dashes). Shaded regions show the 95% confidence interval derived from 20 independent trajectories.

Source data

Extended Data Fig. 3 Proton transfer free energy profiles normalized by the thermal energy.

One-dimensional free energy profile along the reaction coordinate calculated with the revPBE0-D3 NNP in simulations of H2O with nuclear quantum effects at 300 K (orange), 250 K (green) and 350 K (blue). The very small temperature dependence of the central barrier in kBT units suggests that it is mostly of entropic origin. Shaded regions show the 95% confidence interval derived from 20 independent trajectories.

Source data

Extended Data Fig. 4 Random walk modeling of the diffusion coefficient.

(A) Stable proton hopping time-correlation function \(1-C{ij}(t)=1-\langle pi(0)pj(t)\rangle\) (see definition in ref. 59) from our revPBE0-D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories. (B) Distribution of Oa-Ob distances in Eigen-like (3a,4b) (green) and Zundel-like (3a,3b) (purple) H-bond arrangements from our revPBE0-D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories. (C) Distribution of (Oa-Ob)2 squared distances in our revPBE0- D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories.

Source data

Extended Data Fig. 5 Proton transfer enthalpy surface.

Enthalpic contribution to the proton transfer free energy surface in Fig. 2b computed at the revPBE0-D3 level from TRPMD simulations of H2O at 300 K using fluctuation theory60.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–9, discussion and Tables 1–6.

Source data

Source Data Fig. 1

Source data for Fig. 1a–c.

Source Data Fig. 2

Source data for Fig. 2b,c.

Source Data Fig. 3

Source data for Fig. 3a–d.

Source Data Fig. 4

Source data for Fig. 4a–c.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2a,b.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3.

Source Data Extended Data Fig. 4

Source data for Extended Data Fig. 4a–c.

Source Data Extended Data Fig. 5

Source data for Extended Data Fig. 5.

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Gomez, A., Thompson, W.H. & Laage, D. Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange. Nat. Chem. 16, 1838–1844 (2024). https://doi.org/10.1038/s41557-024-01593-y

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