{"id":"ef2196e6-fb09-4ece-97b2-a0ef9ce6d463","arxiv_id":"2506.15652","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A GNN Monte Carlo framework predicts that surface termination disorder in MXenes creates a peak in electrical conductivity near the order-disorder transition, while optical conductivity stays composition-controlled.","lead":"This paper builds a machine-learning plus Monte Carlo pipeline that predicts how random surface atom arrangements change the electrical and optical behavior of MXene materials. It finds that electrical conductivity spikes near the order-disorder transition, while optical properties mostly track the average chemical composition.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The conductivity peak near T_c may be an artifact of the harmonic-mean ensemble average with fixed tau, since MC configurations are not series conductors and disorder scattering is not microscopically computed.","rationale":"The paper presents a coherent framework and reports good GNN accuracy on held-out configurations, with R2 of 0.99 (energy), 0.87-0.89 (optical conductivity), and 0.96-0.98 (electrical conductivity), and the MC machinery is standard. I do not see an internal inconsistency in the GNN training or in the DFT/Wannier pipeline taken on its own. The weakest link is not the GNN accuracy but the physical interpretation of the ensemble-averaged electrical conductivity. The reader's weakest assumption correctly flags the fixed tau = 10 fs as a concern, but I think the harmonic-mean averaging rule in Eq. (5) is at least as load-bearing. The paper explicitly justifies the harmonic mean by treating the ensemble as a stack of configurations in series, but a Metropolis trajectory samples alternative configurations of one periodic supercell, not spatially connected domains. The conductivity of a disordered 2D sheet is not generally the harmonic mean of conductivities of independent configurations; it depends on the actual spatial distribution of terminations and the transport regime. Consequently, the temperature-dependent peak near the order-disorder transition could be a consequence of the series mixing rule and the fixed relaxation time rather than a genuine disorder-driven transport signature. This does not invalidate the framework's usefulness as a computational tool, but it does mean the central physical claim should be treated as conditional until the averaging rule and relaxation-time sensitivity are tested. I therefore keep the reader's CONDITIONAL verdict unchanged, while emphasizing a somewhat different and more fundamental concern.","tokens_in":13573,"tokens_out":3933,"duration_ms":50396,"concrete_test":"Recompute Figure 3(b) with the trained GNN and the same Metropolis trajectories using three averaging prescriptions: (i) the harmonic mean of Eq. (5), (ii) the arithmetic mean of per-configuration conductivities, and (iii) a direct Boltzmann transport calculation on a larger equilibrated 10x10 supercell (or several representative equilibrated configurations) at temperatures across T_c, each repeated with tau = 2, 10, and 20 fs. If the peak near T_c appears only for the harmonic mean or only for one tau value, the claimed competition between scattering and electron filling is likely an artifact of the averaging and relaxation-time assumptions; if it persists for all averaging schemes and tau values, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the temperature dependence of the ensemble-averaged electrical conductivity, including a peak near the order-disorder transition, reflects a real competition between scattering and electron filling. Two modeling choices jointly support this claim, and both are unvalidated. First, Eqs. (2)-(3) use a single constant relaxation time tau = 10 fs for every configuration and temperature; no disorder-induced scattering enters except through the ad hoc configurational averaging. Second, Eq. (5) defines the ensemble conductivity as the harmonic mean of per-configuration conductivities, justified only by a 'series conductors' picture. But configurations visited by Metropolis MC are not spatial domains in series; they are alternative realizations of the same 2D sheet. Under a fixed applied field, the physically natural configurational average of the conductivity is an arithmetic or proper effective-medium average, not the harmonic mean. The harmonic mean is dominated by rare low-conductivity configurations and can produce a peak or downturn near T_c that is an artifact of the mixing rule rather than a transport signature. The text's 'scattering effects' are thus not actually computed microscopically; they are put in by the harmonic average plus a fixed tau. This is load-bearing because the abstract's central claim is precisely about the temperature dependence of electrical conductivity and its physical origin.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper introduces a computational framework that combines graph neural networks (GNNs) with Monte Carlo (MC) simulations to predict ensemble-averaged spectral properties of atomically disordered materials. The authors train an equivariant GNN to predict total energy, optical conductivity, and electrical conductivity spectra for 3,000 configurations of surface-termination-disordered MXene monolayers (Ti3C2O2−x−yFx), using DFT plus Wannier-interpolated Kubo-Greenwood/Boltzmann transport calculations as ground truth. The trained GNN is then used as the energy and property evaluator inside Metropolis MC simulations (canonical and semi-grand canonical ensembles) to compute heat capacities and ensemble-averaged conductivities as functions of temperature. The central physical claim is that the ensemble-averaged electrical conductivity exhibits a peak near the order-disorder transition temperature for F-rich stoichiometries, attributed to a competition between scattering and electron-filling effects, whereas the optical conductivity is robust to local disorder and reflects only the global chemical composition.","tokens_in":13857,"tokens_out":6950,"duration_ms":75817,"significance":"The framework addresses a real computational bottleneck: direct DFT sampling of configurational disorder for transport properties is prohibitive, and the GNN appears to achieve high accuracy on the reduced targets (R² of 0.99 for energy, 0.89–0.87 for optical, 0.96–0.98 for electrical conductivity; MAPE below 4% for the fully terminated set). The MC protocol is standard, and the use of persistent homology features for vacancy identification is a useful technical contribution. If the averaging prescription and transport approximations are validated, the framework could enable statistically meaningful ensemble predictions that are inaccessible to direct DFT. However, the novelty lies mainly in the combination of existing methods; the physical conclusions about the conductivity peak are conditional on the modeling choices discussed below.","major_comments":[{"comment":"The harmonic-mean prescription for the ensemble-averaged conductivity is not physically justified for a two-dimensional monolayer, and this choice is load-bearing for the central claim. The Metropolis MC samples alternative configurations of the same 2D sheet; these are not a stack of conductors in series. For an in-plane electric field, the configurational average of the conductivity should be an arithmetic mean (or an effective-medium average appropriate to the 2D geometry), not a harmonic mean, which is dominated by the least-conductive configurations. Because the ordered and disordered phases have very different conductivity distributions, the harmonic mean can produce a peak near the transition temperature even if the per-configuration conductivities are monotonic in temperature. The authors should test the robustness of the peak to the averaging rule (e.g., arithmetic mean or Bruggeman effective-medium approximation) and provide a more concrete justification for the series picture.","section":"Computational Methods, Eq. (5)"},{"comment":"The electrical conductivity of each configuration is computed with a constant relaxation time tau = 10 fs, independent of configuration, temperature, and energy. As a result, the temperature dependence of sigma_ele within a single configuration is controlled only by the Fermi-Dirac derivative and the configuration-dependent transport distribution function; no microscopic disorder-scattering mechanism is included. The 'scattering effects' invoked in the interpretation of the conductivity peak therefore enter only through the configurational averaging in Eq. (5). Since Eq. (5) is itself in question (see previous comment), the attribution of the peak to a competition between scattering and electron filling is not supported by the calculations as presented. The authors should either demonstrate that the peak and its position are robust to tau within a reasonable range (e.g., 1-100 fs), adopt an energy- and/or configuration-dependent relaxation-time model, or soften the claim to refer to the configurational average of the transport distribution function rather than to scattering.","section":"Computational Methods, Eqs. (2)-(3)"},{"comment":"The Monte Carlo averages are reported without error bars or convergence diagnostics. The paper states that each temperature uses 2e5 steps with a 20% burn-in, but no autocorrelation analysis, block averaging, or multiple independent runs are provided. The conductivity peak in Fig. 3(b) is a relatively small feature, and it is essential to demonstrate that it is not a Monte Carlo fluctuation. Please report error bars on the heat capacity and averaged conductivities (e.g., from jackknife over blocks or independent runs) and the autocorrelation times of the energy and conductivity time series.","section":"MC Simulation"}],"minor_comments":[{"comment":"The caption of Figure 3 states 'under grand canonical ensemble' for results that are canonical; the grand canonical results appear in Figure 4. Please correct the captions to avoid confusion.","section":"Figure 3 caption"},{"comment":"References [22] and [39] are duplicates of the same Graph Attention Networks paper; please consolidate.","section":"References"},{"comment":"The phrase 'the recent development of machine learning techniques' is nearly repeated in the first two paragraphs; please streamline the wording.","section":"Introduction"},{"comment":"The sentence 'we employed the DFT+U method, with a U value of 3 eV is added to the 3d orbitals of Ti atoms' is grammatically incorrect; please revise.","section":"Computational Methods, First-Principles Calculations"},{"comment":"The parity plots in Figure 2(b-d) report R² and MAPE for the reduced (mean) quantities; please also report the mean absolute error on the full spectra, or at least for the temperatures/photon energies shown in Figure 2(e-f), so the reader can judge spectral accuracy.","section":"Figure 2"},{"comment":"The text refers to the 'grand canonical ensemble' while stating that the total number of surface termination groups remains fixed; this is a semi-grand canonical ensemble. Please define the ensemble more precisely or use standard terminology.","section":"MC Simulation"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for a general physics/materials journal. The main uncertainty is whether the harmonic-mean ensemble averaging is physically meaningful for the in-plane conductivity of a 2D monolayer; this is fixable if the authors provide additional validation with alternative averaging rules and tau sensitivity. I do not see any citation or novelty concerns beyond those noted in the main report."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You asked for my take on the Fang, Hsu, and Yan paper. Short version: the framework is a legitimate step forward, but the central claim about a conductivity peak near the order-disorder transition is not something I'd trust as presented. The problem is not the GNN (which looks solid) but the way they average over configurations.\n\nWhat's genuinely new here: training an equivariant GNN to predict full optical and electrical conductivity spectra from Wannier Hamiltonians, then embedding it in Metropolis Monte Carlo to get ensemble-averaged spectral properties. That's a sensible way to make disorder-averaged transport accessible, and the GNN accuracy is good—R2 between 0.87 and 0.99 on held-out configurations, with small MAPEs. The optical conductivity story is physically plausible and likely robust: the 1.5 eV interband peak is composition-controlled, and disorder does not seem to wash it out. The persistent-homology/virtual-node extension for vacancies is also a useful addition.\n\nThe soft spot is load-bearing. Equation (5) defines the ensemble conductivity as the harmonic mean of per-configuration conductivities, with the justification that the configurations are like conductors in series. But they aren't. Each MC configuration is an alternative realization of the same 2D sheet, not a spatial segment of a larger sample. The natural configurational average of the conductivity is arithmetic (or an effective-medium average). The harmonic mean is dominated by rare low-conductivity configurations, and as the temperature crosses T_c and the configurational weights shift, that alone can produce a peak in the average. The fixed tau=10 fs in Eq. (2) compounds the problem: no disorder-induced scattering is computed microscopically, so the 'scattering' in the abstract is effectively imported through the averaging rule. The authors never test whether the peak survives an arithmetic average, and they give no error bars or convergence checks on the MC averages. That makes the headline result conditional at best. There is also a figure caption mismatch (Figure 3 labeled grand canonical when the text says canonical) and no code or data released.\n\nWho should read this? Anyone working on ML for disordered materials will find the framework useful, and the optical conductivity results are worth attention. But don't build on the conductivity peak without redoing the averaging yourself.\n\nMy recommendation: send it to a serious referee. It's not desk-rejectable; the framework and the optical part are solid enough to warrant discussion. But the authors need to justify—or replace—the harmonic mean, and test sensitivity to tau, before the peak can be taken as a real transport signature. I'd accept it only with major revision.","headline":"A solid ML-MC framework for ensemble spectral properties, but the headline conductivity peak may be an artifact of the harmonic-mean averaging.","tokens_in":14347,"tokens_out":3776,"would_cite":false,"duration_ms":44180,"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":"A GNN-plus-Monte-Carlo pipeline computes ensemble-averaged electrical and optical conductivity of disordered MXenes.","keywords":["graph neural networks","Monte Carlo simulation","configurational disorder","MXene surface terminations","electrical conductivity","optical conductivity","ensemble averaging","persistent homology"],"falsifier":"Recompute the ensemble-averaged electrical conductivity with configuration-dependent scattering times obtained, for example, from first-principles electron-phonon or disorder scattering, or measure temperature-dependent conductivity of MXene films with controlled F:O ratios; if the peak near the order-disorder transition disappears in either test, the fixed-tau approximation is responsible for the central effect.","tokens_in":13383,"feed_emoji":"⚡","tokens_out":5731,"duration_ms":62736,"temperature":0.7,"pith_summary":"This paper introduces a computational pipeline that combines graph neural networks (GNNs) with Monte Carlo simulations to compute thermodynamic and ensemble-averaged functional properties of atomically disordered materials, where direct density-functional sampling is too expensive. Applying it to the MXene monolayer Ti3C2O2−xFx with mixed F/O terminations and vacancies, the authors claim that surface-termination disorder changes the temperature dependence of electrical conductivity, producing a peak near the order-disorder phase-transition temperature. They explain the peak as a competition between F groups acting as scattering centers in the ordered phase and as electron donors that raise the Fermi level and restore metallicity in the disordered phase. By contrast, they find that optical conductivity stays nearly unchanged across the transition and is controlled mainly by the global F:O composition. The payoff would be a practical route to disorder-aware predictions for materials such as high-entropy alloys and disordered magnets.","feed_headline":"Disorder creates a conductivity peak in MXenes","feed_subtitle":"A GNN-Monte Carlo pipeline computes disorder-averaged transport that direct DFT cannot; optics stay composition-controlled.","key_machinery":"The central machinery is an equivariant graph neural network that takes a crystal structure as a graph and simultaneously predicts total energy, optical conductivity spectrum, and electrical conductivity spectrum, trained on thousands of configurations whose spectra are precomputed from maximally localized Wannier Hamiltonians. This surrogate is embedded in Metropolis Monte Carlo simulations, where the ensemble average of conductivities is taken as the harmonic mean across sampled configurations, treating the stack of configurational supercells as conductors in series. For partially terminated structures, the graph is augmented with virtual nodes for known vacancy sites and with persistent homology features that encode vacancy positions, since standard GNN message passing dilutes defect information.","core_discovery":"The authors claim that the ensemble average of spectral transport properties, not just energies, can be computed for disordered materials by training an equivariant GNN on density-functional/Wannier data and running it inside Metropolis Monte Carlo at each temperature. On Ti3C2O2−xFx, this produces the paper's central finding: the configurational heat capacity has a peak marking an order-disorder transition at a temperature that rises with F and vacancy content, and the ensemble-averaged electrical conductivity shows a peak near that transition for F-rich stoichiometries, while staying monotonic for low F content. The microscopic story is that in the ordered phase isolated F groups act as scattering defects, while above the transition the average translational symmetry is restored and F doping raises the Fermi level, switching the transport from semimetal-like to metal-like. The same calculation shows that optical conductivity is essentially unaffected by local disorder and is governed by chemical composition, with the 1.5 eV peak intensity decreasing as F content increases. The paper frames these results as evidence that the framework captures disorder-driven physics that direct first-principles configurational sampling cannot reach.","pith_inferences":["The single-tau approximation likely understates disorder scattering in the ordered phase; a config-dependent tau could strengthen or weaken the predicted peak, so the quantitative shape of the peak should be read as a model prediction rather than a direct observable.","The harmonic-mean ensemble average is physically motivated for series-connected configurational slabs, but arithmetic or effective-medium averages would give different magnitudes; comparing them would test how much the peak depends on the averaging rule.","The framework could be extended to predict scattering times or spectral broadening directly from the GNN, turning the fixed-tau assumption into a learned quantity and making the conductivity prediction falsifiable per configuration.","Since the optical 1.5 eV peak is tied to Fermi-level filling, optical measurements on samples with controlled F content offer a quick experimental check of the composition-governance claim, independent of transport."],"forward_implications":["For F-rich Ti3C2O2−xFx, the ensemble electrical conductivity develops a maximum near the order-disorder transition, whereas low-F compositions show monotonic metallic-like decline.","Optical conductivity is insensitive to configurational disorder and temperature; the 1.5 eV peak amplitude tracks the F fraction, making it a composition probe.","Adding termination vacancies raises the order-disorder transition temperature and suppresses electrical conductivity by disrupting the periodic potential.","Grand-canonical simulations show that even small changes in F content with temperature can move the transition temperature and qualitatively alter transport behavior.","The same GNN-in-MC workflow is proposed as a general route for disorder-driven phenomena in high-entropy alloys and disordered magnetic compounds."],"supporting_citations":[{"why":"Supplies the high-throughput Wannier workflow that produces DFT-level optical and electrical conductivity spectra for the training dataset.","marker":"36"},{"why":"Provides the equivariant GNN architecture for direct prediction of optical spectra from crystal structures, adapted here for spectral targets.","marker":"28"},{"why":"Defines maximally localized Wannier functions used to build tight-binding Hamiltonians for efficient conductivity evaluation.","marker":"37"},{"why":"Gives the Boltzmann transport formalism used for electrical conductivity spectra with constant relaxation time.","marker":"61"},{"why":"Provides the Kubo-Greenwood formula used to compute optical conductivity.","marker":"60"},{"why":"Describes the Wang-Landau algorithm considered as an alternative configurational sampling method for thermodynamic properties.","marker":"13"},{"why":"Shows prior GNN treatment of configurational disorder energetics that this work extends to spectral properties.","marker":"31"},{"why":"Introduces persistent homology node features that the paper uses to capture vacancy information in partially terminated MXenes.","marker":"25"},{"why":"Supplies the E(3)-equivariant GNN architecture that informs the model's treatment of local atomic orderings.","marker":"42"}],"fun_headline_variants":["Disorder-induced conductivity peak captured by ML+Monte Carlo","MXene surface disorder sparks conductivity peak at transition","ML framework reveals order-disorder transition in MXene transport","Optical conductivity robust to MXene disorder, transport sensitive","GNN-MC pipeline computes disorder-averaged properties of MXenes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"All electrical-conductivity spectra are computed with one fixed electron scattering time, tau = 10 fs, for every configuration and every temperature; if the real scattering time changes with the local termination environment or temperature, the predicted conductivity peak near the phase transition could be a numerical artifact rather than a physical transport signature.","fun_headline_variants_meta":{"raw":{"variants":["Disorder-induced conductivity peak captured by ML+Monte Carlo","MXene surface disorder sparks conductivity peak at transition","ML framework reveals order-disorder transition in MXene transport","Optical conductivity robust to MXene disorder, transport sensitive","GNN-MC pipeline computes disorder-averaged properties of MXenes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0003,"raw_usage":{"total_tokens":1779,"prompt_tokens":1039,"completion_tokens":740,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":655,"completion_tokens_details":{"reasoning_tokens":657}},"tokens_in":655,"tokens_out":740,"duration_ms":9445,"temperature":1.0,"reasoning_tokens":657,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T23:51:24.424925+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the ensemble-averaged electrical conductivity with configuration-dependent scattering times obtained, for example, from first-principles electron-phonon or disorder scattering, or measure temperature-dependent conductivity of MXene films with controlled F:O ratios; if the peak near the order-disorder transition disappears in either test, the fixed-tau approximation is responsible for the central effect.","supporting_citations":[{"cited_title":"Database of Tensorial Optical and Transport Properties of Materials From the Wannier Function Method","cited_arxiv_id":"2504.00771","evidence_quote":"Supplies the high-throughput Wannier workflow that produces DFT-level optical and electrical conductivity spectra for the training dataset."},{"cited_title":"T.; Okabe, R.; Chotrattanapituk, A.; Li, M","cited_arxiv_id":null,"evidence_quote":"Provides the equivariant GNN architecture for direct prediction of optical spectra from crystal structures, adapted here for spectral targets."},{"cited_title":"A.; Yates, J","cited_arxiv_id":null,"evidence_quote":"Defines maximally localized Wannier functions used to build tight-binding Hamiltonians for efficient conductivity evaluation."},{"cited_title":"High-throughput prediction of the carrier relaxation time via data-driven descriptor","cited_arxiv_id":null,"evidence_quote":"Gives the Boltzmann transport formalism used for electrical conductivity spectra with constant relaxation time."},{"cited_title":"BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis","cited_arxiv_id":null,"evidence_quote":"Provides the Kubo-Greenwood formula used to compute optical conductivity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes the Wang-Landau algorithm considered as an alternative configurational sampling method for thermodynamic properties."},{"cited_title":"Towards accurate prediction of configurational disorder properties in materials using graph neural networks","cited_arxiv_id":null,"evidence_quote":"Shows prior GNN treatment of configurational disorder energetics that this work extends to spectral properties."},{"cited_title":"Leveraging Persistent Homology Features for Accurate Defect Formation Energy Predictions via Graph Neural Networks","cited_arxiv_id":null,"evidence_quote":"Introduces persistent homology node features that the paper uses to capture vacancy information in partially terminated MXenes."},{"cited_title":"B.; Anasori, B.; Hong, S","cited_arxiv_id":null,"evidence_quote":"Supplies the E(3)-equivariant GNN architecture that informs the model's treatment of local atomic orderings."}],"review_version":1}