{"id":"ab0663f3-57ac-45b0-84c2-52eea460dc13","arxiv_id":"2509.08497","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Low-energy phonon modes localized at the edges of MoS2 nanoparticles increase atomic vibrations up to about a nanometer from the edge, explaining the HR-TEM contrast decay reported by Chen et al.","lead":"The paper uses molecular dynamics with a machine-learned potential to show that atoms near the edges of molybdenum disulphide nanoparticles vibrate more strongly than bulk atoms, because of low-energy phonon modes trapped at the edges. This explains a puzzling electron microscopy observation and argues that full MD, not independent-atom models, is needed to interpret HR-TEM images.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The edge-state explanation rests on an ENNP with no reported phonon validation: no test-set errors or DFT comparison of low-frequency modes is given, so the central mechanism could be a potential artifact.","rationale":"The reader identified the unquantified ML potential as the weakest assumption, and my reading agrees. The paper's own text supports this concern: the final potential is trained on about 400 DFT configurations, no test-set errors are reported, and the same potential is used for MD, exit-wave simulation, and phonon analysis. The ensemble-of-five error estimate is used only for active learning and to flag extrapolation, not to validate the Hessian. This is not an accusation of error; it is a request for evidence that the low-frequency edge modes are physical. The free-standing strip proxy and the qualitative experimental match are additional limitations, but they are secondary because the potential question undermines the mechanism itself. The paper does contain independent support worth crediting: the active-learning loop caught an unphysical trajectory and fixed it by adding configurations to the training set, which shows genuine care in the workflow. However, that does not address phonon accuracy. Given that the claimed mechanism is directly tied to low-energy force constants, the correct verdict remains conditional acceptance pending quantitative validation of the ENNP phonons against DFT. I therefore keep the reader's CONDITIONAL verdict unchanged.","tokens_in":8572,"tokens_out":4468,"duration_ms":379921,"concrete_test":"Compute DFT (PBE-D3, GPAW) finite-displacement phonons for the same 20-unit-cell MoS2 strip used in Fig. 3, at least at the Gamma and X points, and compare the ENNP Hessian eigenmodes with DFT: mode energies below 25 meV and squared edge weights. Also report RMSE(force) and RMSE(energy) on the held-out 50-configuration test set. If the ENNP reproduces the localized low-energy modes (e.g., frequency differences below 2-3 meV and edge-weight overlap above 0.8), the central mechanism survives; if not, the edge-state explanation is an artifact of the potential.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that enhanced vibrational amplitude near MoS2 edges is caused by low-energy phonon edge states, identified using the same equivariant neural network potential (ENNP) that drives the MD simulations. For that claim to hold, the ENNP must reproduce the low-frequency Hessian and eigenmodes of edge and near-edge configurations quantitatively. The paper never reports this. It describes an active-learning workflow (generations 0-6), a held-out test set of 50 DFT configurations, and ensemble force disagreement as an error monitor, but it gives no force/energy RMSEs and no comparison of ENNP phonon DOS, band structure, or force constants against DFT. The final potential was fitted to roughly 400 PBE-D3 configurations, mostly relaxation endpoints with residual forces below 0.2 eV/A, a regime that does not specifically constrain low-frequency modes; finite-displacement phonon calculations amplify small force errors at low frequencies. Since the same potential is used for the MD vibrational amplitudes (Fig. 1), the exit-wave comparison (Fig. 2), and the phonon analysis (Fig. 3), any bias in its low-energy force constants propagates directly into the central mechanism. The paper's 'built-in error estimation' is ensemble variance among five fits, which detects extrapolation but is not an accuracy certificate for phonons. This is the load-bearing weakness: if the edge-localized modes below about 25 meV are not present in DFT Hessians, the attribution in the abstract and the conclusion fails.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents a combined molecular dynamics (MD) and phonon study of carbon-supported MoS2 nanoparticles, using an equivariant neural network potential (ENNP) trained on a limited set of DFT (PBE-D3) calculations via an active-learning workflow. The authors report enhanced vibrational amplitudes near the nanoparticle edges, both for Mo and S atoms, and show that this enhancement extends roughly a nanometer from the edge. They attribute this behavior to low-energy phonon modes localized at the edges, identified by projecting the phonon density of states (DOS) onto the edge formula units of a 20-unit-cell-wide strip. They further simulate HR-TEM exit waves using the frozen-phonon method with MD snapshots and observe a decay of the imaginary-part peak values near the edges, consistent with the experimental findings of Chen et al. The paper also emphasizes the value of correlated MD over independent-atom models for quantitative image interpretation and presents the active-learning workflow as a way to obtain accurate machine-learning potentials with built-in error estimation.","tokens_in":8908,"tokens_out":5840,"duration_ms":56524,"significance":"If the central claim holds, the paper makes a useful contribution by explaining the experimentally observed edge-induced contrast decay through phonon edge states, and by demonstrating the necessity of correlated atomic motion in HR-TEM simulations. The active-learning framework for training an ENNP with a few hundred DFT configurations is a practical step toward simulating realistic nanostructures beyond DFT. The manuscript is clearly written and the workflow is described in sufficient detail to be reproduced. However, the central explanation rests on the reliability of the ENNP for low-frequency phonons, a point that is not quantitatively validated. The paper therefore has clear potential but requires strengthening of the evidence before its main claims can be considered fully supported.","major_comments":[{"comment":"The central claim that low-energy phonon edge states cause the enhanced vibrational amplitudes is not supported by any quantitative validation of the ENNP for phonon properties. The manuscript reports neither force/energy test-set errors nor a comparison of the ENNP phonon DOS, band structure, or force constants against DFT results. Because the same potential is used for the MD simulations, the exit-wave simulations, and the phonon analysis, any inaccuracy in the low-frequency force constants propagates directly into the edge-state conclusion. Please provide test-set error metrics and a direct DFT comparison of the low-energy phonon modes (for example, a DFT phonon calculation on a small strip or cluster) to demonstrate that the edge states are not an artifact of the machine-learning potential.","section":"Generation of the machine learning potentials and Phonon band structure simulations"},{"comment":"The phonon calculations are performed on a free-standing 2D sheet, which possesses a quadratic transverse acoustic mode (the bending mode) that the authors acknowledge may distort the lowest parts of the DOS. This is a serious concern because the edge-induced DOS increase appears precisely at low energies. Without a correction, a constraining of the out-of-plane motion, or a comparison to a supported strip, it remains possible that the low-energy enhancement is dominated by the free-standing bending mode rather than by localized edge states. The authors should quantify the effect of this artifact on the edge-projected DOS, for instance by repeating the calculation with the out-of-plane directions constrained or by applying a weak restoring force.","section":"Phonon band structure simulations (Appendix)"},{"comment":"The vibrational amplitudes underlying the comparison with experiment are computed from a single 5 ps production trajectory per condition, following 5 ps of thermalization. This sampling may be insufficient to converge the variance of atomic positions, especially for the low-frequency edge modes whose periods are on the order of several picoseconds. The manuscript does not report block averaging, independent trajectories, or any convergence analysis with respect to simulation length. Given that the exit-wave comparison and the central interpretation rest on these amplitudes, the quantitative conclusions are not yet statistically supported. Additional analysis of statistical convergence is needed.","section":"Molecular Dynamics and Nanoparticle simulations"},{"comment":"The claim of a 'built-in error estimation' is stronger than what is actually demonstrated. The ensemble of five potentials is used during active learning and for validation of shorter sequences, but the production MD and the phonon calculations use a single potential trained on the full generation-5 dataset. No uncertainty estimates or error bars are provided for the central results (vibrational amplitude profiles, exit-wave peak values, or phonon DOS). Please clarify the role of the ensemble in the final results and provide quantitative uncertainty measures for the main figures.","section":"Abstract and Nanoparticle simulations"}],"minor_comments":[{"comment":"The parenthetical citation 'by Chen et al (Nature Communications 12, 5007 (2021).' is missing a closing parenthesis.","section":"Abstract"},{"comment":"The text refers to 'the 3 nm wide MoS2 nanoparticle in Fig. 1(b)', but Fig. 1 shows a nanoparticle with radius 3 nm; the terminology is ambiguous and should be consistent.","section":"Exit wave simulations"},{"comment":"The description of the trajectory collection could state explicitly that only a single trajectory per condition was used and that no block or ensemble averaging was performed, which would make the sampling limitations transparent.","section":"Molecular Dynamics"},{"comment":"The caption of Figure 3 mentions that bands are 'colored by their weight' but does not define the weight; the definition is given in the text, but adding it to the caption would improve readability.","section":"Figure 3"},{"comment":"The conclusion states that the potential 'shows that the vibrational amplitudes are significantly enhanced in a region near the edge' without acknowledging the potential limitations regarding trajectory length and phono validation; a brief caveat would be appropriate.","section":"Conclusion"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern about the lack of phonon validation is justified and is the key factor behind my recommendation. The paper is otherwise well-written and the workflow is presented in a reproducible manner. I would encourage the editor to request a revision that adds quantitative validation of the ENNP for low-frequency phonons and addresses the sampling and free-standing-sheet artifacts. The paper could become a solid contribution if these points are resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you care about quantitative HR-TEM interpretation or ML potentials for 2D materials. The real news is the explanation: the enhanced vibrational amplitude near MoS2 edges seen by Chen et al. is attributed to low-energy phonon modes localized at the edge, and these modes extend a few lattice constants into the sheet. That attribution is new as far as I know, and it matters because it argues that correlated MD, not an independent-atom Einstein model, is needed for quantitative image interpretation.\n\nWhat the paper does well: the active-learning ENNP workflow is a genuine methodological contribution. Roughly 400 DFT configurations, query-by-committee with ensemble disagreement, and an honest account of the unphysical Mo migration event they caught and fixed. The phonon projected DOS on a strip shows a clear low-energy enhancement at the edges, with modes penetrating a few unit cells, consistent with the MD amplitudes and the simulated exit-wave decay.\n\nThe soft spot is the one the stress-test flags, and it is the load-bearing one: the ENNP's accuracy for low-frequency phonons is never quantified. There are no force/energy RMSEs on the held-out set, and no comparison of the ML phonon DOS or force constants against DFT. The training data are mostly relaxation endpoints with forces below 0.2 eV/A, which does not specifically constrain low-frequency modes. Finite-displacement phonon calculations amplify small force errors at low energies. Since the same potential drives the MD, the exit-wave simulation, and the phonon analysis, any bias in its low-energy force constants propagates directly into the edge-state claim. This is addressable: report test-set errors, and compute at least bulk and strip phonons at the DFT level for a few configurations, or compare against the experimental phonon DOS.\n\nSmaller issues: the MD statistics are thin—one 5 ps collection window per condition—and the phonon analysis uses a free-standing strip while the MD includes the graphite support, a mismatch the authors acknowledge. The comparison to the Chen et al. data is qualitative; they do not overlay the experimental decay curve. None of these are fatal, but they should be asked about in review.\n\nWho is this for? Electron microscopists modeling images, and anyone building targeted ML potentials for nanosystems. It deserves a serious referee. I would send it to review and ask for potential validation data and a quantitative comparison to experiment before accepting. The core idea is plausible, but I want to see the potential's low-frequency fidelity demonstrated.","headline":"A plausible and well-communicated edge-phonon explanation for enhanced vibrations at MoS2 edges, with a genuinely useful active-learning ENNP workflow, but the central mechanism rests on an unvalidated ML potential for low-frequency phonons.","tokens_in":9416,"tokens_out":3333,"would_cite":true,"duration_ms":30486,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Low-energy phonon modes pinned to the edges of MoS2 nanoparticles explain the enhanced atomic vibrations and the contrast fade seen in high-resolution electron microscopy near the boundary.","keywords":["phonon edge states","molybdenum disulphide","molecular dynamics","equivariant neural network potentials","frozen phonon approximation","high-resolution transmission electron microscopy","vibrational amplitudes","active learning"],"falsifier":"Compute the phonon band structure and edge-projected density of states of the same 20-unit-cell MoS2 strip using direct DFT force constants and compare with the machine-learned potential; if the low-frequency edge modes are not reproduced, the explanation fails. Also, measure the temperature dependence of the HR-TEM contrast decay and check that it follows the occupation of the predicted edge-mode energies.","tokens_in":8409,"feed_emoji":"🔬","tokens_out":6824,"duration_ms":59651,"temperature":0.7,"pith_summary":"The paper argues that the enhanced atomic vibrations seen in high-resolution electron microscopy near MoS2 nanoparticle edges are caused by low-energy phonon modes confined to the edges. Using molecular dynamics driven by a machine-learned potential trained on about 400 density-functional calculations, the authors reproduce the falloff of image contrast toward edges seen experimentally and show that it persists for roughly a nanometer. Phonon calculations on a strip of MoS2 reveal edge-localized modes that shift the vibrational density of states to low frequencies and extend a few lattice constants inward. The work makes the case that correlated molecular dynamics, rather than an independent-atom model, is needed to interpret quantitative HR-TEM images of such particles.","feed_headline":"Edge phonon states localize vibrations in MoS2 nanoparticles","feed_subtitle":"Simulations match HR-TEM contrast decay, showing why correlated MD, not independent-atom models, is needed.","key_machinery":"The central object is the edge-localized phonon mode, identified by projecting the phonon density of states of a finite strip onto the formula units at the edges and coloring band-structure modes by the squared vibration amplitude weight on the edge atoms. The argument is carried by the frozen-phonon imaging model: atomic configurations sampled from molecular dynamics are used to generate and average exit waves, and the same machine-learned potential, an equivariant graph neural network trained on roughly 400 DFT configurations, is used for both the molecular dynamics and the phonon calculations. The mechanism is that low-energy edge modes, with energies below roughly $k_B T$, increase the mean-square vibrational amplitude near the edge, which smears the projected electrostatic potential and lowers the exit-wave peaks.","core_discovery":"On the paper's own terms: the enhanced and correlated vibrational amplitudes near the edges of carbon-supported MoS2 nanoparticles, observed in molecular dynamics and in a recent HR-TEM experiment, are due to low-energy phonon modes localized at the nanoparticle edges. Projecting the phonon density of states onto edge formula units shows a strong shift toward low frequencies relative to the bulk sheet, and the band structure of a 20-unit-cell strip contains bands whose weight is concentrated on the Mo or S edge, some extending a few lattice constants into the interior. These modes suppress the imaginary part of the simulated electron exit wave at atomic columns up to a nanometer from the edge, matching the experimental contrast decay. The paper further claims that a workflow combining active learning with equivariant neural network potentials can deliver an accurate potential for this supported-nanoparticle system from only slightly more than 400 DFT configurations, with an ensemble of five potentials providing a posteriori error estimates.","pith_inferences":["If edge-localized low-energy phonons are generic in finite 2D crystals, HR-TEM and STEM contrast simulations of other 2D materials will need the same correlated-molecular-dynamics treatment.","The ensemble disagreement among the five potentials could be turned into a per-atom uncertainty map during molecular dynamics, giving a practical way to detect when the phonon picture itself is unreliable.","A testable extension is temperature dependence: the edge modes' occupation grows with temperature, so the edge-to-bulk contrast decay should steepen at higher temperatures in a way a static disorder model would not predict."],"forward_implications":["HR-TEM image interpretation for MoS2 nanoparticles must include correlated atomic motion: the independent-atom Einstein model cannot reproduce the observed contrast decay.","The vibrational amplitude enhancement extends roughly a nanometer from the edge, so quantitative image simulation must include atoms that are not under-coordinated.","Edge phonon modes, not just the low coordination of the outermost atoms, are the cause of the enhanced amplitudes.","The active-learning and equivariant-neural-network workflow can produce usable potentials from about 400 DFT configurations and can flag out-of-distribution configurations through ensemble disagreement."],"supporting_citations":[{"why":"Supplies the experimental HR-TEM observation of increased vibrational amplitude near MoS2 nanoparticle edges that the simulations match.","marker":"[3]"},{"why":"Provides the frozen-phonon method for including thermal vibrations in image simulation.","marker":"[5]"},{"why":"Supplies the active-learning ('query by committee') strategy for selecting training configurations.","marker":"[8]"},{"why":"Provides the equivariant neural network architecture that makes potentials trainable from few hundred structures.","marker":"[10]"},{"why":"Provides the multislice simulation code used to compute averaged exit waves from MD snapshots.","marker":"[11]"},{"why":"Supplies the DFT energies and forces used to train the machine-learned potential.","marker":"[17, 18]"},{"why":"The exchange-correlation functional used for the DFT training data.","marker":"[19]"},{"why":"Adds dispersion to the DFT training data, needed for the van der Waals interaction with the graphene support.","marker":"[20]"},{"why":"Provides the molecular dynamics integrator and finite-displacement phonon calculations used in the analysis.","marker":"[21]"}],"fun_headline_variants":["Edge phonon states drive MoS2 nanoparticle vibrations","Phonon modes pinned at MoS2 edges explain enhanced vibrations","Low-energy edge modes localize vibrations in MoS2","Simulations show edge phonon confinement in MoS2 nanoparticles","Why MoS2 edges vibrate more: confined phonon modes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The machine-learned potential, trained on about 400 DFT configurations, reproduces the true low-energy vibrational modes of MoS2 edges even though its phonon accuracy is not separately validated against DFT.","fun_headline_variants_meta":{"raw":{"variants":["Edge phonon states drive MoS2 nanoparticle vibrations","Phonon modes pinned at MoS2 edges explain enhanced vibrations","Low-energy edge modes localize vibrations in MoS2","Simulations show edge phonon confinement in MoS2 nanoparticles","Why MoS2 edges vibrate more: confined phonon modes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001032,"raw_usage":{"total_tokens":4313,"prompt_tokens":881,"completion_tokens":3432,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":497,"completion_tokens_details":{"reasoning_tokens":3347}},"tokens_in":497,"tokens_out":3432,"duration_ms":21541,"temperature":1.0,"reasoning_tokens":3347,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:00:58.647256+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the phonon band structure and edge-projected density of states of the same 20-unit-cell MoS2 strip using direct DFT force constants and compare with the machine-learned potential; if the low-frequency edge modes are not reproduced, the explanation fails. Also, measure the temperature dependence of the HR-TEM contrast decay and check that it follows the occupation of the predicted edge-mode energies.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the experimental HR-TEM observation of increased vibrational amplitude near MoS2 nanoparticle edges that the simulations match."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the frozen-phonon method for including thermal vibrations in image simulation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the active-learning ('query by committee') strategy for selecting training configurations."},{"cited_title":"Batzner, A","cited_arxiv_id":null,"evidence_quote":"Provides the equivariant neural network architecture that makes potentials trainable from few hundred structures."},{"cited_title":"Madsen and T","cited_arxiv_id":null,"evidence_quote":"Provides the multislice simulation code used to compute averaged exit waves from MD snapshots."},{"cited_title":"Grimme, J","cited_arxiv_id":null,"evidence_quote":"Adds dispersion to the DFT training data, needed for the van der Waals interaction with the graphene support."},{"cited_title":"Hjorth Larsenet al., The atomic simulation environ- ment - A Python library for working with atoms, J","cited_arxiv_id":null,"evidence_quote":"Provides the molecular dynamics integrator and finite-displacement phonon calculations used in the analysis."}],"review_version":2}