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Machine learning accelerated finite-field simulations for electrochemical interfaces

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Two neural networks trained on DFT data replace ab initio molecular dynamics for the Au(100)/NaCl(aq) interface, enabling nanosecond trajectories and extrapolation to cell potentials beyond the training range.

desk verdict A credible ML finite-field workflow with real validation, but its headline capacitance and high-voltage turnover need stronger extrapolation checks. read the letter →

arxiv 2506.10548 v1 pith:HXSS5CDO submitted 2025-06-12 physics.chem-ph cond-mat.mtrl-sci

Chaoqiang Feng , Bin Jiang This is my paper · ORCID
classification physics.chem-phcond-mat.mtrl-sci
keywords electrochemistryelectricdoublelayerfinite-fieldsimulationmachinelearningpotentialneuralnetworkforcefieldelectrondensityresponseHelmholtzcapacitanceAu(100)/NaCl(aq)interface
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Electrochemical interfaces are hard to simulate because the electrolyte needs nanoseconds to equilibrate, while finite-field ab initio molecular dynamics is limited to tens of picoseconds. This paper argues that two neural networks trained on first-principles data remove that bottleneck: a field-dependent machine learning potential predicts atomic forces under an applied electric field, and a machine-learned electron density response model predicts how charge rearranges at the electrode. Tested on a Au(100)/NaCl(aq) full cell, the models produce multi-nanosecond trajectories, a Helmholtz capacitance of about $20.8\ \mu\mathrm{F}/\mathrm{cm}^2$ at 0 V, and electrolyte polarization that tracks cell potentials from -4 V to 4 V even though training used only 0, 1, and 2 V. The longer trajectories also reveal a structural turnover: near the anode, interfacial water reorients above about 2.5 V as the positively charged electrode begins to outcompete adsorbed chloride ions for water molecules.

What carries the argument

The argument rides on two paired neural network models plus a specific cell geometry. The FIREANN potential uses the field-induced embedded atom density (FI-EAD) descriptor, whose field-dependent orbital makes the network explicitly aware of the applied field's direction and magnitude, with message-passing iterations adding nonlocal electrostatic information; this model supplies forces at every configuration. The MLEDR model places ghost atoms at electron-density grid points and learns the difference between the electron density with and without the applied field, giving the charge response used for capacitance. The finite-field cell setup (reference [39]) imposes a voltage across a complete cell without a vacuum gap, so electroneutrality and constant-potential conditions emerge naturally from the metal's free-electron response.

What would settle it

Run fresh DFT reference calculations at cell potentials inside the extrapolated region, for example 3.5 V and -3.5 V, and in the 2880-atom cell, then compare atomic forces and field-induced electron densities with FIREANN and MLEDR predictions; if the force error grows far beyond the reported 43 meV/Å or the charge response shifts the Helmholtz capacitance by more than a few microfarads per square centimeter, the extrapolation claim would be overturned.

Watch

Extended reading notes

Core claim

On the authors' terms, the central discovery is that fully first-principles finite-field molecular dynamics can be replaced by a two-model machine learning pipeline with no classical approximation for either electrode or electrolyte. The field-dependent potential learns the potential energy surface from DFT forces, while the electron density response model learns the field-induced density difference, so the surface charge response and differential Helmholtz capacitance follow from machine learning predictions rather than additional DFT post-processing. The specific physical finding is a potential-driven turnover in anodic water orientation: at low potentials, adsorbed chloride ions orient water with an O-H bond toward the electrode, but above about 2.5 V the concentrated positive charge on the anode attracts the oxygen end of water more strongly, shifting the dominant angular population from roughly 135 degrees to smaller angles. The authors attribute this discovery to nanosecond-scale sampling, which removes relaxation artifacts that make short AIMD concentration profiles unreliable.

Load-bearing premise

The load-bearing assumption is that a force field and a charge-response model trained on 12,139 configurations at just 0, 1, and 2 V stay accurate from -4 V to 4 V and in a 2880-atom cell that was never part of the training set.

Editorial extensions

If this is right

  • Constant-potential machine learning molecular dynamics can run for nanoseconds on metal/electrolyte cells, so ion concentration profiles and potentials of mean force can be statistically converged instead of being read from 10-100 ps ab initio runs.
  • Differential Helmholtz capacitance can be obtained directly from the learned charge response, without extra DFT single-point calculations for every sampled configuration.
  • Cell potentials can be varied continuously beyond the training window, making it possible to map potential-driven structural transitions such as the water-orientation turnover near 2.5 V without retraining.
  • The same trained models transfer to cells larger than the training cell: the 2880-atom Au(100)/NaCl(aq) system reproduces the small-cell ion and water distributions, supporting size scalability.
  • AIMD concentration profiles contain artificial oscillations from incomplete relaxation, so the longer MLMD trajectories give more reliable interfacial structure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If this sparse-training recipe generalizes, active learning at a few cell potentials could become a standard protocol for mapping the full potential window of other metal/electrolyte interfaces, making finite-field machine learning molecular dynamics a screening tool for electrode materials.
  • The predicted anodic water reorientation near 2.5 V is a testable signature: in situ vibrational sum-frequency or surface-enhanced infrared spectroscopy of interfacial water should show the dominant water orientation shifting as the applied potential crosses that threshold.
  • Because the potential energy surface is trained on forces only, total energies are not directly available, so computing free energies and reaction barriers would require an additional energy model or thermodynamic integration.
  • The electron density response model predicts a density difference, not the total density; properties such as absolute work functions or site-resolved charge transfer would need a supplementary model for the field-free electron density.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript proposes a machine-learning-accelerated finite-field method for electrochemical interfaces. It combines two neural-network models: FIREANN, a field-dependent machine-learned potential trained on DFT forces, and MLEDR, a machine-learned electron-density-response model trained on DFT charge densities. The method is demonstrated on the Au(100)/NaCl(aq) interface, with training data from active-learning AIMD at 0, 1, and 2 V cell potentials. The authors report nanosecond-scale MLMD trajectories, a Helmholtz capacitance of about 20.8 uF/cm2 at 0 V, and a potential-dependent reorientation of interfacial water at the anode starting near 2.5 V, which they attribute to competition between the charged anode and adsorbed chloride ions. They further claim successful extrapolation of the ML models to cell potentials in the [-4, 4] V range and scalability to an 8x8 supercell with 2880 atoms.

Significance. If the central claims hold, this is a valuable methodological contribution: it replaces classical electrode/electrolyte descriptions in finite-field simulations with fully ML-learned DFT-level components, enables nanosecond sampling at first-principles accuracy, and provides a route to potential-dependent interfacial structure and capacitance. The paper's strengths include the use of active learning for dataset construction, the release of the FIREANN code and the PES dataset, and the explicit recognition that AIMD timescales are insufficient for electrolyte relaxation. The method's headline quantitative outputs (the capacitance and the high-potential water-orientation turnover), however, rest on two models whose accuracy outside the training window is not directly established, so the current evidence is suggestive rather than conclusive.

major comments (3)
  1. [Sec. 3.1, Fig. 2] The claimed extrapolation to the full [-4, 4] V range is supported only by the model's own smooth response, not by comparison with DFT at potentials outside the 0-2 V training window. The ramp test in Fig. 2 shows that the FIREANN-generated electrolyte polarization follows the applied potential and returns on reversal, but because the trajectory is generated by the very potential being tested, this demonstrates internal consistency rather than accuracy. Furthermore, the AIMD comparison in Fig. 2c, limited to 30 ps, cannot serve as a stringent reference for the slow ionic polarization that dominates the response at this concentration, as the paper itself notes that 10-100 ps AIMD is insufficient for electrolyte relaxation. I recommend adding direct DFT checks, e.g., forces, energies, or charge densities computed for configurations sampled at 3 V and 4 V, or alternatively reframing the high-potential results as unvalidated predictions rather than validated extrapolations.
  2. [Sec. 3.2, Eq. (7)] The MLEDR model that provides the surface charge density sigma_m used in the Helmholtz capacitance calculation has no reported accuracy metric in the main text or the SI. The only error reported is the FIREANN force RMSE of about 43 meV/A (Table S1); there is no RMSE or other validation for the predicted electron density response. Since the capacitance value of about 20.8 uF/cm2 and the charge-transfer/charge-inversion analysis in Fig. 3 depend entirely on MLEDR, the absence of any error metric prevents independent audit of these headline results. Please report MLEDR training and validation errors, include a direct comparison of predicted versus DFT charge-density differences for representative configurations, and make the electron-response dataset publicly available rather than 'available upon request.'
  3. [Sec. 3.3, Fig. S3 and Fig. S5] The anodic water-reorientation turnover starting at about 2.5 V lies entirely outside the 0-2 V training range, so its reliability depends on the unvalidated extrapolation discussed above. In addition, the large-cell (8x8, 2880-atom) simulations in Fig. S5 are claimed to 'compare well' with the smaller training cell, but the comparison appears to be only visual and no quantitative error metric is provided for the large-cell results. To support the structural conclusions, please provide a quantitative comparison of ion concentration and water orientation profiles between the 4x4 and 8x8 cells, and include a DFT spot-check of forces and/or charge response at high cell potentials and in the larger cell.
minor comments (5)
  1. [Sec. 2.1] The text says 'the charge response defined in Eq. 5' but Eq. (5) is the message-passing iteration; the MLEDR target is defined in Eq. (6). Please correct the cross-reference.
  2. [Sec. 2.1] The sentence 'which can be used to generate new FI-EAD features via Eq. (3)' appears to refer to Eq. (4), which is the squared linear combination that forms the FI-EAD feature. Please check the equation numbering and the intended reference.
  3. [Fig. 3 caption] The caption states 'The grey area in all panel indicates the Au electrode'; 'all panel' should be 'all panels'.
  4. [Table of Contents entry] The Table of Contents entry contains the typo 'finite-filed simulations'; it should be 'finite-field simulations'.
  5. [References] Reference [49] is listed as '2025' with no journal, volume, or DOI; please provide complete citation information.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: DFT-trained models are checked against AIMD; self-citations are methodological, and the extrapolation test is self-consistent rather than definitionally forced.

full rationale

The central derivation chain is empirical rather than algebraic. FIREANN forces are trained on DFT forces (Section 2.2; Table S1 RMSE ~43 meV/A), and MLEDR is trained on DFT charge responses defined by Eq. (6); the differential capacitance (Eq. 7) is then a post-processing use of the learned charge response, not a quantity that enters the training labels by construction. Validation against AIMD (Fig. 2c) uses DFT forces on MLMD-equilibrated configurations, and the paper itself notes that AIMD timescales are too short for full electrolyte relaxation, which weakens but does not invert the comparison. The extrapolation claim to +/-4 V (Section 3.1) is demonstrated by ramping the cell potential in MLMD trajectories generated by the same FIREANN model; this shows self-consistency and smooth response, not independent DFT accuracy outside 0-2 V, so it is a validation gap rather than a circular reduction. Citations [36], [37], and [41] are self-citations of the group's architectures and active-learning workflow, but the present paper's accuracy claims rest on its own RMSE and AIMD comparisons, not on those citations as external proof. The unreleased MLEDR dataset and the missing charge-response error metric raise auditability concerns but do not make the capacitance result equivalent to its input by definition. Overall, no prediction reduces to a fitted parameter or to a self-citation chain; score 2 reflects minor non-load-bearing self-citation and a self-consistency-based extrapolation test.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

All quantitative results come from fitted neural networks and a chosen DFT reference; there is no parameter-free derivation. The main hidden assumptions are transferability of the learned models beyond the training range, the adequacy of the DFT labels, and the correctness of the finite-field setup. The only introduced computational object is the ghost-atom grid used for electron density prediction.

free parameters (3)
  • FIREANN PES neural-network weights = Not disclosed (trained on 12,139 DFT configurations)
    These weights determine all MLMD forces and hence every structural result; they are learned parameters and not derived from theory.
  • MLEDR charge response neural-network weights = Not disclosed (trained on DFT charge density differences for the same configurations)
    The model predicts the electron density shift delta n and therefore the surface charge and Helmholtz capacitance; no validation error is reported in the main text.
  • FI-EAD descriptor hyperparameters = Not reported
    GTO widths, angular momentum cutoffs, and the number of message-passing iterations are hand-chosen and affect the accuracy of both the PES and the charge response model.
assumptions (5)
  • domain assumption PBE-D3 with GTH pseudopotentials and DZVP basis is an adequate first-principles reference for the Au(100)/NaCl(aq) interface under applied fields.
    All training labels come from this DFT setup (Section 2.2); if this level of theory is wrong for specific adsorption or polarization, the ML models inherit the error.
  • domain assumption The Dufils et al. finite-field constant-potential formulation correctly imposes the cell potential in 3D periodic boundary conditions and produces two physical electric double layers.
    The whole workflow adopts this method (Section 2.2 and reference 39); the simulation results depend on its validity.
  • domain assumption Training on atomic forces alone is sufficient because energies of periodic systems under applied fields are multivalued; force predictions uniquely determine the molecular dynamics statistics.
    Stated in Sections 2.2 and 3.1; this is necessary because no energy targets are used.
  • domain assumption The active learning procedure with 12,139 configurations has converged and covers the configuration space needed for extrapolation to potentials and system sizes outside the training data.
    Underlies the claimed extrapolation in Section 3.1 and the 8x8 supercell test; no convergence criteria or uncertainty estimates are reported.
  • domain assumption The MLEDR ghost-atom local representation captures the long-range electrostatic charge response of the metal and electrolyte.
    Section 2.1: charge response is learned on local environments of grid points; if nonlocal response matters beyond the FI-EAD message passing, the learned delta n may be biased.
invented entities (1)
  • Ghost atoms (electron density grid points in MLEDR)
    purpose: Grid points at which the local atomic environment is encoded to predict the field-induced electron density difference delta n(r).
    Computational construct, not a physical entity; the charge response predictions depend on this representation, and no experimental observable is attached to it.

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Pith. "Pith review of Machine learning accelerated finite-field simulations for electrochemical interfaces." pith.science (2026). https://pith.science/paper/HXSS5CDO

@misc{pith2026250610548,
  author       = {Pith},
  title        = {Pith review of: Machine learning accelerated finite-field simulations for electrochemical interfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HXSS5CDO}},
  note         = {Machine review of arXiv:2506.10548}
}
abstract

Electrochemical interfaces are of fundamental importance in electrocatalysis, batteries, and metal corrosion. Finite-field methods are one of most reliable approaches for modeling electrochemical interfaces in complete cells under realistic constant-potential conditions. However, previous finite-field studies have been limited to either expensive ab initio molecular dynamics or less accurate classical descriptions of electrodes and electrolytes. To overcome these limitations, we present a machine learning-based finite-field approach that combines two neural network models: one predicts atomic forces under applied electric fields, while the other describes the corresponding charge response. Both models are trained entirely on first-principles data without employing any classical approximations. As a proof-of-concept demonstration in a prototypical Au(100)/NaCl(aq) system, this approach not only dramatically accelerates fully first-principles finite-field simulations but also successfully extrapolates to cell potentials beyond the training range while accurately predicting key electrochemical properties. Interestingly, we reveal a turnover of both density and orientation distributions of interfacial water molecules at the anode, arising from competing interactions between the positively charged anode and adsorbed Cl$^-$ ions with water molecules as the applied potential increases. This novel computational scheme shows great promise in efficient first-principles modelling of large-scale electrochemical interfaces under potential control.

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Reference graph

Works this paper leans on

59 extracted references · 59 canonical work pages · cited by 1 Pith paper

  1. [1]

    Sakong, A

    S. Sakong, A. Groß, J. Chem. Phys. 2018, 149

    work page 2018

  2. [2]

    J. Le, A. Cuesta, J. Cheng, J. Electroanal. Chem. 2018, 819, 87-94

    work page 2018

  3. [3]

    J.-B. Le, A. Chen, L. Li, J. -F. Xiong, J. Lan, Y .-P. Liu, M. Iannuzzi, J. Cheng, JACS Au 2021, 1, 569-577

    work page 2021

  4. [4]

    Jeanmairet, B

    G. Jeanmairet, B. Rotenberg, M. Salanne, Chem. Rev. 2022, 122, 10860-10898

    work page 2022

  5. [5]

    L. Zeng, J. Peng, J. Zhang, X. Tan, X. Ji, S. Li, G. Feng, J. Chem. Phys. 2023, 159. 23

    work page 2023

  6. [6]

    X. Wang, Y . Kuang, J.-B. Le, Curr. Opin. Electrochem. 2023, 40, 101341

    work page 2023

  7. [7]

    Andersson, C

    L. Andersson, C. Zhang, Curr. Opin. Electrochem. 2023, 42, 101407

    work page 2023

  8. [8]

    D. Luan, J. Xiao, J. Phys. Chem. Lett. 2023, 14, 685-693

    work page 2023

Show all 59 references
  1. [9]

    Bonnet, T

    N. Bonnet, T. Morishita, O. Sugino, M. Otani, Phys. Rev. Lett. 2012, 109, 266101

    2012

  2. [10]

    M. M. Melander, T. Wu, T. Weckman, K. Honkala, npj Comput. Mater. 2024, 10, 5

    2024

  3. [11]

    H. Cao, X. Lv, S. Qian, J. Li, Y .-G. Wang, J. Phys. Chem. Lett. 2024, 15, 1314- 1320

    2024

  4. [12]

    M. Sun, B. Jin, X. Yang, S. Xu, Nat. Commun. 2025, 16, 3600

    2025

  5. [13]

    P. Li, Y . Jiang, Y . Hu, Y . Men, Y . Liu, W. Cai, S. Chen, Nat. Catal. 2022, 5, 900- 911

    2022

  6. [14]

    B. Tang, Y . Fang, S. Zhu, Q. Bai, X. Li, L. Wei, Z. Li, C. Zhu, Chem. Sci. 2024, 15, 7111-7120

    2024

  7. [15]

    Li, Y .-L

    P. Li, Y .-L. Jiang, Y . Men, Y .-Z. Jiao, S. Chen, Nat. Commun. 2025, 16, 1844

    2025

  8. [16]

    Andersson, M

    L. Andersson, M. Sprik, J. Hutter, C. Zhang, Angew. Chem. Int. Ed. 2025, 64, e202413614

    2025

  9. [17]

    Ringe, N

    S. Ringe, N. G. Hormann, H. Oberhofer, K. Reuter, Chem. Rev. 2021, 122, 10777-10820

    2021

  10. [18]

    Umari, A

    P. Umari, A. Pasquarello, Phys. Rev. Lett. 2002, 89, 157602

    2002

  11. [19]

    Souza, J

    I. Souza, J. Íniguez, D. Vanderbilt, Phys. Rev. Lett. 2002, 89, 117602

    2002

  12. [20]

    Stengel, N

    M. Stengel, N. A. Spaldin, D. Vanderbilt, Nat. Phys. 2009, 5, 304-308

    2009

  13. [21]

    Zhang, M

    C. Zhang, M. Sprik, Phys. Rev. B 2016, 93, 144201

    2016

  14. [22]

    Zhang, J

    C. Zhang, J. r. Hutter, M. Sprik, J. Phys. Chem. Lett. 2019, 10, 3871-3876

    2019

  15. [23]

    Zhang, T

    C. Zhang, T. Sayer, J. Hutter, M. Sprik, J. Phys.: Energy 2020, 2, 032005

    2020

  16. [24]

    van Hees, C

    A. van Hees, C. Zhang, J. Phys. Chem. Lett. 2024, 15, 12212-12217

    2024

  17. [25]

    Sundararaman, D

    R. Sundararaman, D. Vigil-Fowler, K. Schwarz, Chem. Rev. 2022, 122, 10651- 10674

    2022

  18. [26]

    Coretti, C

    A. Coretti, C. Bacon, R. Berthin, A. Serva, L. Scalfi, I. Chubak, K. Goloviznina, M. Haefele, A. Marin-Laflèche, B. Rotenberg, J. Chem. Phys. 2022, 157

    2022

  19. [27]

    L. J. Ahrens-Iwers, M. Janssen, S. R. Tee, R. H. Meißner, J. Chem. Phys. 2022, 157

    2022

  20. [28]

    Scalfi, D

    L. Scalfi, D. T. Limmer, A. Coretti, S. Bonella, P. A. Madden, M. Salanne, B. Rotenberg, Phys. Chem. Chem. Phys. 2020, 22, 10480-10489

    2020

  21. [29]

    Y . Shao, M. Hellstrom, P. D. Mitev, L. Knijff, C. Zhang, J. Chem. Inf. Model. 2020, 60, 1184-1193

    2020

  22. [30]

    Knijff, C

    L. Knijff, C. Zhang, Mach. Learn.: Sci. Technol. 2021, 2, 03LT03

    2021

  23. [31]

    Y . Shao, L. Andersson, L. Knijff, C. Zhang, Electron. Struct. 2022, 4, 014012

    2022

  24. [32]

    Dufils, L

    T. Dufils, L. Knijff, Y . Shao, C. Zhang, J. Chem. Theory Comput. 2023, 19, 5199-5209

    2023

  25. [33]

    Grisafi, A

    A. Grisafi, A. Bussy, M. Salanne, R. Vuilleumier, Phys. Rev. Mater. 2023, 7, 125403

    2023

  26. [34]

    Grisafi, M

    A. Grisafi, M. Salanne, J. Chem. Phys. 2024, 161

    2024

  27. [35]

    J.-X. Zhu, J. Cheng, arXiv preprint arXiv:2407.17740 2024. 24

    2024 arXiv

  28. [36]

    Zhang, B

    Y . Zhang, B. Jiang, Nat. Commun. 2023, 14, 6424

    2023

  29. [37]

    C. Feng, Y . Zhang, B. Jiang, J. Chem. Theory Comput. 2025, 21, 691-702

    2025

  30. [38]

    Zhang, M

    C. Zhang, M. Sprik, Phys. Rev. B 2016, 94, 245309

    2016

  31. [39]

    Dufils, G

    T. Dufils, G. Jeanmairet, B. Rotenberg, M. Sprik, M. Salanne, Phys. Rev. Lett. 2019, 123, 195501

    2019

  32. [40]

    Martínez, R

    L. Martínez, R. Andrade, E. G. Birgin, J. M. Martínez, J. Comput. Chem. 2009, 30, 2157-2164

    2009

  33. [41]

    Q. Lin, L. Zhang, Y . Zhang, B. Jiang, J. Chem. Theory Comput. 2021, 17, 2691- 2701

    2021

  34. [42]

    T. D. Kühne, M. Iannuzzi, M. D. Ben, V . V . Rybkin, P. Seewald, F. Stein, T. Laino, R. Z. Khaliullin, O. Schütt, F. Schiffmann, D. Golze, J. Wilhelm, S. Chulkov, M. H. Bani-Hashemian, V . Weber, U. Borštnik, M. Taillefumier, A. S. Jakobovits, A. Lazzaro, H. Pabst, T. Müller, ...

    2020

  35. [43]

    J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865-3868

    1996

  36. [44]

    Goedecker, M

    S. Goedecker, M. Teter, J. Hutter, Phys. Rev. B 1996, 54, 1703-1710

    1996

  37. [45]

    Hartwigsen, S

    C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 1998, 58, 3641-3662

    1998

  38. [46]

    VandeV ondele, J

    J. VandeV ondele, J. Hutter, J. Chem. Phys. 2007, 127, 114105

    2007

  39. [47]

    Goerigk, S

    L. Goerigk, S. Grimme, Phys. Chem. Chem. Phys. 2011, 13, 6670-6688

    2011

  40. [48]

    A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, S. J. Plimpton, Comput. Phys. Commun. 2022, 271

    2022

  41. [49]

    J. Guo, M. C. Andrade, C. Hahn, A. Kulkarni, N. Govindarajan, 2025

    2025

  42. [50]

    H. Yuan, H. Yang, P. Hu, H. Wang, ACS Catal. 2021, 11, 6835-6845

    2021

  43. [51]

    H. Yuan, C. Zhu, Y . Hou, H. G. Yang, H. Wang, JACS Au 2024, 4, 3038-3048

    2024

  44. [52]

    Y . Hu, G. Luo, L. Wang, X. Liu, Y . Qu, Y . Zhou, F. Zhou, Z. Li, Y . Li, T. Yao, Adv. Energy Mater. 2021, 11, 2002816

    2021

  45. [53]

    T. Wang, L. Tao, X. Zhu, C. Chen, W. Chen, S. Du, Y . Zhou, B. Zhou, D. Wang, C. Xie, Nat. Catal. 2022, 5, 66-73

    2022

  46. [54]

    G. Ren, M. Zhou, P. Hu, J.-F. Chen, H. Wang, Nat. Commun. 2024, 15, 2346

    2024

  47. [55]

    G. Ren, M. Zhou, H. Wang, J. Am. Chem. Soc. 2024, 146, 6084-6093

    2024

  48. [56]

    Y . Zhou, R. Zhou, X. Zhu, N. Han, B. Song, T. Liu, G. Hu, Y . Li, J. Lu, Y . Li, Adv. Mater. 2020, 32, 2000992

    2020

  49. [57]

    Z. Wang, C. Wang, Y . Hu, S. Yang, J. Yang, W. Chen, H. Zhou, F. Zhou, L. Wang, J. Du, Nano Res., 1-7

  50. [58]

    Y . Liu, J. Zhang, J. Jin, H. Liu, G. Ren, P. Hu, H. Wang, Phys. Chem. Chem. Phys. 2025, 27, 2536-2544

    2025

  51. [59]

    B. Tran, M. J. Janik, S. T. Milner, J. Phys. Chem. C 2024, 128, 20559-20568. 25 Entry for the Table of Contents: A machine learning framework to accelerate finite -field simulations of electrified interfaces, which integrates a field -dependent machine learned force field and ...

    2024

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