{"id":"2ee98455-c4f1-4cac-ae58-9fc85640b952","arxiv_id":"2411.14732","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A machine-learned force field that takes electric potential as an input predicts that Cu atoms on 1T'-MoS2 assemble into small clusters at potentials below -0.1 V vs SHE.","lead":"The authors add an electric potential input to a machine-learned force field, which lets molecular dynamics simulations run at a fixed voltage. Simulating copper atoms on a MoS2 surface, they find the atoms gather into small clusters when the potential drops below -0.1 V vs SHE.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Training-set U labels come from fixed-charge VASPsol runs, not constant-potential sampling; the -0.1 V aggregation threshold is an untested extrapolation.","rationale":"Good-faith reading: the authors propose a useful engineering shortcut - include U as a global input to a neural-network potential - and they validate the model on in-distribution energies, forces, and VDOS. That part is credible: RMSEs of 8 meV/atom and 0.08 eV/A are consistent with well-trained MLFFs, and the VDOS comparison provides an independent check. The problematic step is the leap from 'we label fixed-charge structures by their VASPsol potential' to 'MD at a chosen U is a constant-potential simulation.' In a true grand-canonical calculation, the electron number is adjusted on the fly so that the potential equals the target; here U is only an input feature and the training data are fixed-charge. The paper's own statement that charge fluctuations are 'fully suppressed' acknowledges an approximation, but it does not establish that the learned E(R,U) matches the constant-potential surface, especially at negative potentials where no charged training data exist for the 96-Cu system (the only charged sets are Cu4/+0.5e and Cu5/-0.5e). Without any same-configuration charge series, the NN cannot know how a given configuration responds to a change in potential; it can only interpolate between configurations that happen to have different U labels. If the U labels are not transferable (e.g., because the PZC or the charge-potential relation shifts with coverage and cell size), the -0.1 V threshold is not a prediction but a label artifact. This is not an attack on the authors' integrity; it is a call for one decisive reference calculation. The proposed CP-AIMD benchmark on Cu4/MoS2 at -0.1 V is small enough to be practical and directly tests whether the MLFF's negative-potential aggregation behavior is real. The reader's weakest assumption points in the same direction, but I have sharpened it to the fixed-charge versus constant-potential training mismatch and the absence of same-configuration charge series; hence 'partial' agreement.","tokens_in":11402,"tokens_out":8757,"duration_ms":90519,"concrete_test":"Run a reference constant-potential AIMD (e.g., the constant-potential method in VASP or CP2K) for 10-20 ps on a Cu4/MoS2 slab at U = -0.1 V, starting from a dispersed Cu4 configuration comparable to the MLFF training structures, and collect both the trajectory and forces. On a common set of configurations, compare (i) the MLFF forces against the CP-AIMD forces and (ii) the Cu-Cu RDF from the CP-AIMD trajectory against the MLFF trajectory at the same U. If the force RMSE exceeds the 0.08 eV/A training error, or if the CP-AIMD trajectory does not develop the 2.4 A Cu-Cu peak that the MLFF predicts at -0.1 V, then the aggregation threshold is an artifact of the fixed-charge-to-U labeling and is not a constant-potential outcome.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that E_tot(R,U) in Eq. (1) is the potential-energy surface at a fixed electrode potential, i.e., the grand-canonical Legendre transform of fixed-charge DFT. The training set does not establish this. It contains 2,999 neutral, 900 Cu4 with +0.5e, and 420 Cu5 with -0.5e structures; U is not imposed as an independent control but is assigned after the fact from the VASPsol potential of each fixed-charge calculation. For most atomic environments, only a single charge state is present, so the U-dependence in the neural network is learned by regressing across configurations whose U labels are correlated with coverage, charge, and local geometry. There are no constant-potential training trajectories and no same-configuration charge series. The CP-MLMD on the 96-Cu slab at -0.1 V and -0.3 V is therefore an extrapolation outside the sampled (charge, coverage, U) manifold. The reported validations (energy/force RMSE, VDOS, the +0.685 V dispersed-trajectory check) test interpolation within that manifold, not the ability to predict forces under a genuinely held potential at negative bias or at 96-Cu coverage. Because the aggregation threshold is the central claim and the U-label transferability is deferred entirely to the SI, the load-bearing assumption is that the fixed-charge labels define the same U variable that the MD is supposed to fix.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes EEP-MLFF, an atomic neural-network force field that takes the electrode potential U as an explicit input in addition to atom-centered structural descriptors. The model is trained on DFT data for Cu/1T'-MoS2 systems under implicit solvation (VASPsol), with charge introduced to mimic varying potentials. The authors report MLFF energy/force RMSEs of 8 meV/atom and 0.08 eV/A, a VDOS comparison against DFT, and a CP-MLMD trajectory at +0.685 V that preserves dispersed Cu atoms. The central application is constant-potential molecular dynamics on a 96-Cu slab at several potentials, which shows Cu aggregation into small steric clusters at potentials below -0.1 V vs SHE. The mechanism is interpreted through pCOHP analyses showing potential-dependent Cu-Cu and Cu-S bonding.","tokens_in":11659,"tokens_out":3268,"duration_ms":80059,"significance":"If the central claim is correct, the paper offers a computationally efficient route to nanosecond-scale constant-potential molecular dynamics for electrochemical interfaces, and it makes a falsifiable prediction of a voltage threshold for Cu cluster formation on 1T'-MoS2. The reported accuracy metrics, the VDOS validation, the use of an independent DFT-based pCOHP analysis to rationalize the aggregation, and the explicit potential-dependent architecture are all strengths that make the work potentially useful to the electrocatalysis and ML force-field communities. However, the significance is conditional: the constant-potential interpretation hinges on whether the U labels derived from fixed-charge calculations are transferable to the large, negatively biased, high-coverage systems used in the production simulations.","major_comments":[{"comment":"The central claim that Eq. (1) represents a constant-potential potential-energy surface is not established by the training set. The text states that 'different amounts of charge are introduced into the systems to simulate varying electric potential conditions,' and that the data comprise only neutral, +0.5e, and -0.5e fixed-charge structures. The potential U is evidently assigned after the fact from the VASPsol potential of each fixed-charge calculation, rather than imposed as an independent control. No same-geometry charge series and no constant-potential training trajectories are provided. Consequently, the U-dependence of the neural network is learned by regressing across configurations where U is correlated with coverage, charge, and local geometry, and the production runs at -0.1 V and -0.3 V on the 96-Cu slab are extrapolations outside the sampled (charge, coverage, U) manifold. I ask the authors to provide explicit evidence that the learned U-dependence is transferable: for example, compare EEP-MLFF energies and forces against constant-potential DFT/AIMD for representative configurations at negative potentials, or train with the total charge as an additional input and demonstrate equivalence to a grand-canonical description.","section":"Validation of the Machine-Learning Force Field; Eq. (1)"},{"comment":"The -0.1 V threshold is the main quantitative prediction, but it rests on single CP-MLMD trajectories per potential without uncertainty estimates. Figure 3 reports deterministic time evolutions of N_SA and N_SC from one trajectory at each potential, and the discussion of the 'turning point potential between +0.1 V and -0.1 V' is based on those singles runs. I request multiple independent trajectories (different initial velocities or seeds) per potential, with error bars on the cluster populations, to establish that the aggregation transition is statistically robust rather than a fluctuation of one trajectory.","section":"Evolution From Single Atoms to Single Clusters"},{"comment":"The cluster definition depends on the hand-chosen Cu-Cu distance threshold of 3.2 A. The text and Figure S6 justify this threshold by showing that 2.4 A fails to identify flat-oriented Cu arrays, but they do not test the sensitivity of the central -0.1 V threshold to the cluster criterion. For example, a threshold of 3.0 A or 3.5 A could shift the potential at which SC-Cu species are counted, or change the relative populations of Cu2 and Cu3. Please report the cluster populations as a function of the distance threshold, or provide a physical justification that the reported threshold is the uniquely appropriate one for the 'single cluster' definition.","section":"Evolution From Single Atoms to Single Clusters; Figure S6"},{"comment":"The sentence stating that 'the constant-potential treatment is established on the presumption that system charge fluctuations can be fully suppressed within each time step of MD simulation' is unclear and potentially misleading. In constant-potential AIMD the electron number is an additional dynamical variable that fluctuates to keep the potential fixed, not a quantity that is suppressed. If the EEP-MLFF instead fixes U and computes forces from a U-dependent PES, the authors should clarify how this relates to the grand-canonical Legendre transform and how the lack of explicit charge fluctuation is justified for the Cu/MoS2 system. This clarification is needed to support the use of the word 'constant-potential' throughout the manuscript.","section":"Methodology; Eq. (1) and constant-potential implementation"}],"minor_comments":[{"comment":"There is a typo in the second paragraph of the Methodology section: 'large-scale simulations of electrochemical systhave recently seen' should read 'systems have recently seen.'","section":"Methodology"},{"comment":"The Acknowledgement section contains 'NSF (Grand No. 22073041)'; 'Grand' should be 'Grant.'","section":"Acknowledgement"},{"comment":"The phrase 'the signatures of the vibrational spectrum of Cu4/MoS2 evaluated with the constant-potential molecular dynamics simulation' is grammatically awkward; consider 'vibrational density of states' or 'vibrational signatures' for clarity.","section":"Figure 2 caption"},{"comment":"Several critical technical details are deferred to the SI, including the mapping from fixed charge to U, the neural-network hyperparameters, and the definition of the potential window. Since the main text refers to these details to justify the constant-potential interpretation, the SI should be made available with the manuscript and its contents explicitly cross-referenced in the main text.","section":"Supporting Information"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's load-bearing assumption is the transferability of the U labels from fixed-charge VASPsol calculations to the constant-potential MD regime. The SI is not included in the arXiv version, so I could not verify whether the charge-to-U mapping and the potential-dependent cluster expansion framework are described with sufficient rigor. If the SI does not contain a direct validation of the U-dependence (e.g., same-geometry constant-potential benchmarks), the revision should add such validation. The single-trajectory statistics for the -0.1 V threshold also need strengthening before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe new thing here is simple and worth a look: Zhou et al. add the electric potential U as an explicit global input to an atom-centered neural network (EEP-MLFF), alongside the usual structural descriptors. That is a new combination for ML potentials used in electrochemistry, and it is a natural extension of the potential-dependent cluster expansion work they cite. The authors back the method with energy/force RMSE on test sets (8 meV/atom, 0.08 eV/Å) and a VDOS comparison that matches DFT normal modes, which is reasonable evidence that the force field interpolates well within the sampled manifold.\n\nThe application, however, is where I get cautious. The paper claims Cu atoms on 1T'-MoS2 form small clusters below -0.1 V vs SHE, based on constant-potential MLMD of a 96-Cu slab. That result has three soft spots. First, the U labels are not imposed in the training; they are assigned after the fact from VASPsol potentials of fixed-charge calculations. Most training structures are neutral, with only a few charged (900 at +0.5e, 420 at -0.5e). There is no same-configuration charge series, so the NN has to learn the U-dependence by regressing across configurations where U correlates with coverage, charge, and geometry. That does not establish that E_tot(R,U) is the grand-canonical potential surface. Second, the 96-Cu slab is a large extrapolation from a training set that tops out at 18 Cu, and the migration/aggregation events are not validated against any CP-AIMD at negative potentials or high coverage. Third, the aggregation statistics come from single trajectories per potential, with no uncertainty, and the 3.2 Å cluster threshold is hand-picked, though they do test a stricter 2.4 Å and it fails to capture the array structures.\n\nThese are addressable issues rather than fatal ones, and the method itself could be genuinely useful if the potential-label problem is solved. But as written, the central -0.1 V threshold is not robustly supported. I would send this to peer review: the idea is novel and timely, and a referee can push for the SI details on U labels, a small system tested against CP-AIMD, and at least a repeat-trajectory analysis. I would not cite it yet myself, but I would bring it to a reading group as a good example of how careful one must be when attaching a thermodynamic variable like U to a machine-learned potential.","headline":"A promising but under-validated method: adding U as an NN input is new, but the -0.1 V clustering result relies on extrapolated potential labels and single trajectories.","tokens_in":12221,"tokens_out":4237,"would_cite":false,"duration_ms":42681,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"By feeding the applied electric potential into a machine-learned force field as an explicit input, the paper makes constant-potential molecular dynamics practical and predicts that adsorbed Cu atoms on 1T'-MoS2 aggregate into small steric…","keywords":["electric potential input","machine learning force field","constant-potential molecular dynamics","Cu cluster formation","MoS2 electrode","single-cluster catalysts","atomic neural network","electrochemical interfaces"],"falsifier":"Run constant-potential DFT molecular dynamics for the same Cu/MoS2 system at +0.1 V and -0.1 V for a few tens of picoseconds and compare the Cu-Cu radial distribution and the cluster-size populations with the EEP-MLFF trajectories: a 2.4 Å Cu-Cu peak at -0.1 V in the ML run but not in the DFT run, or vice versa at +0.1 V, would show the potential label or the interpolation is wrong.","tokens_in":11161,"feed_emoji":"⚡","tokens_out":7721,"duration_ms":73545,"temperature":0.7,"pith_summary":"The paper tries to establish that the applied electric potential can be treated as an ordinary input feature of a machine-learned force field, so that one trained network supplies energies and forces at any potential and molecular dynamics can be run at constant potential for nanoseconds. It applies this explicit-electric-potential model to Cu atoms adsorbed on 1T'-MoS2, and the constant-potential trajectories show that below roughly -0.1 V vs the standard hydrogen electrode the Cu atoms migrate and assemble into small steric clusters, while at +0.1 V and above they remain mostly dispersed as single atoms. If the model is right, the expensive constant-potential calibration step of ab initio electrochemistry can be replaced by a single interpolation, and electrode potential becomes a practical dial for preparing single-cluster catalysts.","feed_headline":"Voltage-aware AI force field sees Cu atoms clump below -0.1 V","feed_subtitle":"Machine-learned simulations run at fixed voltage predict when single Cu atoms become tiny clusters on MoS2.","key_machinery":"The central object is the explicit-electric-potential atomic neural network, which appends the global scalar $U$ to the smooth SO(3) power-spectrum descriptors of every atom. The argument rests on the established near-quadratic dependence of the system energy on $U$ over a broad range, which lets one network interpolate between training structures generated at different fixed charges in an implicit electrolyte. The network's output is a sum of atomic energies, so the force on each atom is obtained by differentiating through the descriptors; this is what converts potential-dependent energetics into constant-potential trajectories.","core_discovery":"The central claim is that the total energy of an electrochemical interface can be written as $E_{\\rm tot} = \\sum_i E_i(D_i(R_1,\\dots,R_N), U)$, where $D_i$ are atom-centered structural descriptors and $U$ is the applied electric potential shared by all atoms. Because the descriptors depend smoothly on nuclear coordinates, the potential-dependent forces are exact derivatives of this energy, so the trained network can drive molecular dynamics at fixed $U$ with no additional self-consistency loop. Running this constant-potential MLMD on a 96-Cu/1T'-MoS2 slab, the paper finds a potential-driven crossover: at negative potentials the Cu-S bonds weaken and Cu-Cu bonding in close-contact configurations strengthens, so Cu atoms leave their adsorption sites and form tilted dimers, trimers, and small steric clusters below -0.1 V, whereas at positive potentials they stay as single atoms or flat short-range arrays.","pith_inferences":["The same architecture should transfer to other global electrochemical control variables, such as pH or applied strain, provided the energy depends smoothly on them; the paper does not test this.","The -0.1 V threshold and the dominance of Cu2/Cu3 over larger clusters are likely sensitive to Cu coverage, surface defects, and simulation time; the paper uses one slab at roughly 22% coverage.","A denser potential grid in the training set could reveal whether the quadratic energy assumption degrades outside -0.5 V to +0.6 V, and whether a single network trained on multiple coverages can reproduce coverage-dependent cluster statistics.","The predicted crossover between thermodynamic control at positive potentials and kinetic control at negative potentials could be tested by seeding pre-formed larger clusters at negative potentials and checking whether they shrink to Cu2/Cu3 over time."],"forward_implications":["Constant-potential molecular dynamics becomes affordable for nanosecond-scale, multi-hundred-atom electrochemical interfaces, because adding $U$ as an input costs almost nothing at inference time.","The Cu/1T'-MoS2 system is predicted to have a voltage threshold near -0.1 V vs SHE, below which single Cu atoms convert into small steric clusters rather than larger aggregates.","Because cluster size and orientation respond to potential, electrode bias can be used as a synthesis handle for single-cluster catalysts, with more negative potentials favoring Cu2 and Cu3 units.","The electronic-structure analysis implies the aggregation is driven by potential-tuned competition between Cu-S and Cu-Cu bonding, not simply by faster diffusion."],"supporting_citations":[{"why":"defines the constant-potential ab initio MD baseline whose calibration cost the new method avoids","marker":"[3]"},{"why":"supplies the implicit electrolyte model used to generate charged training structures with assigned potentials","marker":"[11]"},{"why":"establishes the near-quadratic energy-potential relationship that justifies putting U directly into the network input","marker":"[18]"},{"why":"provides the smooth SO(3) power-spectrum descriptors used to encode each atom's local environment","marker":"[31]"},{"why":"is the force-field generation package used to build the EEP-MLFF model and connect it to molecular dynamics","marker":"[32]"},{"why":"grounds the constant-potential approximation by arguing charge fluctuations are suppressed within an MD timestep","marker":"[33]"},{"why":"is the experimental EXAFS study showing dispersed Cu on 1T-MoS2 near the potential of zero charge, used to validate the large-scale simulation","marker":"[37]"},{"why":"is the molecular dynamics engine used to run the constant-potential trajectories","marker":"[34]"}],"fun_headline_variants":["Voltage-aware MLMD: Cu clusters form below -0.1 V","EEP-MLFF enables constant-potential MD on MoS2","AI force field tunes Cu aggregation with voltage","Simulated voltage switch: Cu atoms to clusters on MoS2"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The voltage value assigned to each training snapshot really represents the electrode potential, and it remains meaningful when the trained model is used for the much larger copper-on-MoS2 slab.","fun_headline_variants_meta":{"raw":{"variants":["Voltage-aware MLMD: Cu clusters form below -0.1 V","EEP-MLFF enables constant-potential MD on MoS2","AI force field tunes Cu aggregation with voltage","Simulated voltage switch: Cu atoms to clusters on MoS2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000164,"raw_usage":{"total_tokens":1275,"prompt_tokens":1001,"completion_tokens":274,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":617,"completion_tokens_details":{"reasoning_tokens":202}},"tokens_in":617,"tokens_out":274,"duration_ms":3970,"temperature":1.0,"reasoning_tokens":202,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:57:57.622895+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run constant-potential DFT molecular dynamics for the same Cu/MoS2 system at +0.1 V and -0.1 V for a few tens of picoseconds and compare the Cu-Cu radial distribution and the cluster-size populations with the EEP-MLFF trajectories: a 2.4 Å Cu-Cu peak at -0.1 V in the ML run but not in the DFT run, or vice versa at +0.1 V, would show the potential label or the interpolation is wrong.","supporting_citations":[{"cited_title":"First- Principles Molecular Dynamics at a Constant Electrode Potential","cited_arxiv_id":null,"evidence_quote":"defines the constant-potential ab initio MD baseline whose calibration cost the new method avoids"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the implicit electrolyte model used to generate charged training structures with assigned potentials"},{"cited_title":"E.; Dabo, I","cited_arxiv_id":null,"evidence_quote":"establishes the near-quadratic energy-potential relationship that justifies putting U directly into the network input"},{"cited_title":"P.; Kondor, R.; Cs \\'a nyi, G","cited_arxiv_id":null,"evidence_quote":"provides the smooth SO(3) power-spectrum descriptors used to encode each atom's local environment"},{"cited_title":"S.; Zhu, Q","cited_arxiv_id":null,"evidence_quote":"is the force-field generation package used to build the EEP-MLFF model and connect it to molecular dynamics"},{"cited_title":"K.; Calegari Andrade, M","cited_arxiv_id":null,"evidence_quote":"grounds the constant-potential approximation by arguing charge fluctuations are suppressed within an MD timestep"},{"cited_title":"Manipulating Coordination Structures of Mixed-Valence Copper Single Atoms on 1T-MoS 2 for Efficient Hydrogen Evolution","cited_arxiv_id":null,"evidence_quote":"is the experimental EXAFS study showing dispersed Cu on 1T-MoS2 near the potential of zero charge, used to validate the large-scale simulation"},{"cited_title":"P.; Aktulga, H","cited_arxiv_id":null,"evidence_quote":"is the molecular dynamics engine used to run the constant-potential trajectories"}],"review_version":1}