{"id":"d93a05e5-47bb-4740-994d-3d060f045124","arxiv_id":"2608.04806","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A GGA-cost exchange-correlation functional combining C09 exchange with PBE correlation accurately models lattice constants and polarization of PbTiO3 and BaTiO3, and a MACE potential trained on it reproduces the PbTiO3 ferroelectric transition temperature.","lead":"The paper introduces C09x-PBEc, a density functional that pairs C09 exchange with PBE correlation, and tests it on lead titanate and barium titanate. It reports that this combination matches the accuracy of more expensive van der Waals functionals for ferroelectric properties at a lower cost, and that a machine learning potential trained on it reproduces the ferroelectric transition temperature of PbTiO3.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The MLIP proof-of-concept may rest on a training-set coverage gap: MD sampling used MACE-MPA-0-D3 at 300–900 K, yet that generator has Tc = 1082 K, while C09x-PBEc has Tc = 738 K, so the paraelectric basin of the target functional is likely undersampled.","rationale":"The reader's weakest assumption is that the MACE-MPA-0-D3-generated training set adequately covers the C09x-PBEc potential energy surface, and I agree. The concern becomes sharper when the generator's own Tc (1082 K) is compared with the target functional's Tc (738 K): the sampling temperature range 300–900 K does not include a single temperature at which the generator is in the paraelectric phase, while for C09x-PBEc the two highest sampling temperatures are paraelectric. Thus the training set is likely biased toward ferroelectric configurations precisely where the two functionals differ, and the trained MLIP's 738 K transition could be an artifact of sparse or missing data rather than a property of C09x-PBEc. This concern targets only the MLIP demonstration, not the DFT-level benchmark results, which directly show that C09x-PBEc gives lattice parameters and polarizations close to the vdW-DF-C09 values and to experiment. Because the central functional claim has independent support and the MLIP claim can be tested by retraining on appropriately sampled data, the appropriate verdict remains conditional rather than accept or reject. The reader already reached CONDITIONAL; my analysis strengthens the reason for that condition without moving the verdict.","tokens_in":11812,"tokens_out":6843,"duration_ms":514235,"concrete_test":"Compute the phase/order-parameter distribution of the 551 training structures: for each snapshot from the 800 K and 900 K runs, record c/a and the soft-mode displacement, and count how many lie in the paraelectric basin (c/a < ~1.05, near-zero polarization). Then generate 100–200 fresh NPT configurations at 800 and 900 K by running MD directly with C09x-PBEc on a 3×3×3 supercell, label them with C09x-PBEc, and retrain the MACE model. If the MLIP's force/energy error on these on-distribution paraelectric configurations is large, or if the retrained model's Tc shifts by more than ~50 K, the published 738 K value is not robust evidence for C09x-PBEc.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The proof-of-concept MLIP result (Tc = 738 K, Table IV) is the only direct evidence that C09x-PBEc is usable for MLIP training, and it rests on the unstated assumption that 551 single-point C09x-PBEc labels assigned to MACE-MPA-0-D3 MD snapshots cover the C09x-PBEc potential energy surface. That assumption is insecure: the data were generated at 300–900 K (Section IV), but the generator MACE-MPA-0-D3 has Tc = 1082 K (Table IV), so over the whole sampling window it remains biased toward the tetragonal ferroelectric basin. C09x-PBEc, by contrast, has Tc = 738 K; its equilibrium at 800 and 900 K is the cubic/paraelectric phase. Unless the cubic-seeded MD runs happened to explore the paraelectric basin despite the generator's higher Tc, the training set will be sparse exactly in the region where the two functionals differ most, and the 738 K crossover observed in the trained MLIP would be an extrapolation of the model rather than a learned property of C09x-PBEc. The manuscript does not report the phase distribution, c/a histogram, or order-parameter coverage of the 551 structures, nor any validation against C09x-PBEc MD at 800–900 K. This makes the central MLIP demonstration vulnerable: the generator's phase bias may predetermine the apparent transition temperature, so agreement with experiment could arise for the wrong reason.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a new exchange-correlation functional, C09x-PBEc, defined as C09 exchange (Cooper's exchange enhancement factor) combined with PBE correlation. It benchmarks this functional against PBE, PBEsol, revPBE, vdW-DF, vdW-DF2, and their C09 variants for lattice parameters, spontaneous polarization, Born effective charges, and computational cost in PbTiO3 and BaTiO3. The authors find that C09x-PBEc reproduces the experimental lattice constants and polarizations much better than standard GGA functionals while retaining roughly GGA-level cost. They further train a MACE machine-learning interatomic potential (MLIP) on 551 single-point C09x-PBEc labels obtained from MACE-MPA-0-D3 MD snapshots, and report that this MLIP yields a ferroelectric-to-paraelectric transition temperature for PbTiO3 of 738 K, close to the experimental 747 K and far better than the tested MACE foundation models. The paper concludes that C09 exchange, rather than non-local correlation, is the essential ingredient for accurate ferroelectric properties, and that C09x-PBEc is a suitable functional for MLIP training.","tokens_in":12186,"tokens_out":8050,"duration_ms":87342,"significance":"If the static DFT benchmarking and the MLIP training-set coverage are confirmed, the paper makes a useful practical contribution: it isolates C09 exchange as the key ingredient, provides a semilocal functional with GGA-level cost, and demonstrates that an MLIP trained with it can reproduce the PbTiO3 phase transition. The functional construction itself introduces no fitted parameters, the static tables are internally consistent, and the direct NPT MLIP transition temperature is a strong independent result that does not rely on the Landau calibration. However, the quantitative accuracy claims for BaTiO3 are overstated, the Landau-based Tc estimates are calibrated to experimental input, and the MLIP proof-of-concept lacks evidence of phase-space coverage. These issues weaken the current presentation but do not destroy the central idea, which is defensible after revision.","major_comments":[{"comment":"The MLIP training-set coverage is a load-bearing concern. The 551 training structures were generated by MD with MACE-MPA-0-D3 at 300-900 K, but Table IV shows that this generator has Tc = 1082 K, whereas the C09x-PBEc-trained MLIP has Tc = 738 K. Over most of the sampling window the generator is therefore biased toward the tetragonal ferroelectric basin, while C09x-PBEc is already paraelectric at 800-900 K. The manuscript reports no c/a histogram, order-parameter distribution, or phase decomposition of the 551 structures, and it does not validate the trained MLIP against direct C09x-PBEc MD at 800-900 K. Without such evidence, the 738 K crossover could be an extrapolation of the MLIP rather than a learned property of C09x-PBEc. Please add this analysis or explicitly reframe the MLIP claim as a demonstration pending phase-space validation.","section":"Section IV"},{"comment":"The Landau-based Tc estimates are calibrated, not predicted. Equation (5) uses gamma 'derived from the experimental transition temperature and spontaneous polarization.' If gamma is material-specific, then Tc_DFT = gamma P_DFT^2 is merely a rescaling of the polarization error and adds no independent information; if gamma is global, the text does not say how a single constant can match both PbTiO3 and BaTiO3. In either case, the Tc values in Fig. 3 should be presented as a fitted comparison, not as ab initio predictions, and no uncertainty or sensitivity to gamma is reported. Please state this explicitly and, if possible, supplement with direct MD estimates.","section":"Section III, Eq. (5) and Fig. 3"},{"comment":"The polarization accuracy claim for BaTiO3 is overstated. The text says C09x-PBEc is 'within 0.05 Cm−1 of the experimental value,' but Table II shows 0.33 Cm−2 versus the experimental 0.27 Cm−2, a 22% error; vdW-DF-C09 gives 0.34 Cm−2, a 26% error. This is inconsistent with the introduction's statement that C09-coupled functionals predict BaTiO3 polarization within 11% of experiment [8]. Please correct the text and the abstract, or clarify that the 11% refers to a different experimental reference used in Ref. [8].","section":"Table II and Section III text"},{"comment":"The MLIP comparison is not a matched control. A custom 551-structure C09x-PBEc-trained MACE model is compared with pretrained MACE-MPA-0 and MACE-MPA-0-D3 foundation models trained on PBE+U data; no MLIP trained on PBE data with the same architecture, training-set size, and protocol is included. The claim of 'a marked improvement on MLIPs trained using GGA' is therefore not directly supported by a controlled experiment. Please either train a matched PBE-trained baseline or soften the claim to a comparison against the specific pretrained foundation models used here.","section":"Section IV and Table IV"}],"minor_comments":[{"comment":"The name 'Bernedsen' should be 'Berendsen', and the abbreviation 'MACE-MP-0-D3' should be 'MACE-MPA-0-D3' for consistency.","section":"Section IV"},{"comment":"The transition temperature is quoted as 738 K in Table IV and Section IV but as 737 K in the Conclusions; please reconcile these values.","section":"Section IV and Conclusions"},{"comment":"The caption lists 'tetragonal PbTiO3' and 'cubic PbTiO3' twice; presumably one pair refers to BaTiO3, and the caption should be corrected.","section":"Figure 4 caption"},{"comment":"The text refers to 'C09-PBEx' where the functional is elsewhere called 'C09x-PBEc'; please correct the notation.","section":"Section III"},{"comment":"The units in 'within 0.05 Cm−1' should be Cm−2, matching the polarization values in Table II.","section":"Section III"},{"comment":"The derivation connecting the Landau expansion coefficients a and b in Eq. (4) to the relation Tc = gamma P^2 in Eq. (5) is not given; please add a short derivation or an explicit reference.","section":"Eqs. (4)-(5)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a condensed-matter/materials-science journal. The direct combination of C09 exchange with PBE correlation is a modest novelty, but the systematic benchmarking and the MLIP demonstration make it a useful contribution. The main risks are the MLIP training-set coverage gap, the calibrated Landau analysis, and the overstated BaTiO3 accuracy; all are addressable in revision. I do not see grounds for rejection, but the central MLIP claim needs additional validation before the paper can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the functional itself is a straightforward and useful contribution—C09 exchange plus PBE correlation gives near-GGA cost and vdW-DF-class accuracy for the ferroelectric properties they test. The benchmark tables are self-consistent and the cost comparison is clear. That part is solid and worth building on.\n\nThe weak spot is the MLIP section. The 738 K transition temperature for PbTiO3 is the headline 'direct' evidence that C09x-PBEc is MLIP-ready, but the training set was generated by running MACE-MPA-0-D3 MD at 300–900 K. That foundation model has its own transition near 1082 K, so over the whole sampling window it is biased toward the tetragonal basin. C09x-PBEc, by contrast, transitions near 738 K; its equilibrium at 800 and 900 K should be cubic/paraelectric. Unless the MD runs explicitly seeded cubic structures and happened to explore the paraelectric basin, the 551 labels will be sparse exactly in the region where C09x-PBEc differs from the generator, and the trained model's 738 K crossover is likely an extrapolation rather than a learned property. The paper doesn't report the phase distribution, c/a histogram, or any validation against C09x-PBEc MD at high temperature. That needs to be fixed before the claim is credible.\n\nOther soft spots: the BaTiO3 polarization is 0.33 C/m2 vs 0.27 experimental—a 22% error—while the abstract says 'within 11%'; the 11% figure comes from the earlier vdW-DF-C09 study, not from this paper. The Landau Tc estimates use a gamma fitted to experiment, so those numbers are circular and carry no error bars. And the MLIP baseline is not a matched PBE-trained model, just the foundation models, so 'marked improvement over GGA-trained MLIPs' is not an apples-to-apples comparison.\n\nThe functional claim itself isn't undermined by any of this. If you need a cheap functional for ferroelectric perovskites, C09x-PBEc looks like a credible choice, and the deposited structures on NOMAD are a plus. This deserves a serious referee, but with major revisions: check the training-set coverage, add a matched PBE baseline, fix the abstract, and make the inputs/code available.","headline":"C09x-PBEc is a useful, simple functional for ferroelectric perovskites, but the MLIP transition-temperature result is undermined by an unchecked training-set coverage gap.","tokens_in":12681,"tokens_out":3440,"would_cite":true,"duration_ms":34274,"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":"The paper shows that combining C09 exchange with PBE correlation yields a functional, C09x-PBEc, that matches non-local functionals for ferroelectric perovskites at GGA cost and produces a machine-learned potential with the right PbTiO3…","keywords":["Density functional theory","exchange-correlation functional","C09 exchange","ferroelectric perovskites","spontaneous polarization","machine learning interatomic potential","PbTiO3","BaTiO3"],"falsifier":"Take the C09x-PBEc-trained potential and compare its forces, energies, and stresses against freshly computed C09x-PBEc DFT on a held-out set of structures generated by C09x-PBEc molecular dynamics, including high-temperature and distorted configurations; if the errors are comparable to a PBE-trained potential's errors, the functional is not driving the accuracy. A second decisive test is to train an MLIP on C09x-PBEc for BaTiO3: the paper's reasoning predicts a transition temperature near the experimental 393 K, while a PBE-trained potential would overshoot by hundreds of kelvin.","tokens_in":11647,"feed_emoji":"⚛️","tokens_out":8117,"duration_ms":82083,"temperature":0.7,"pith_summary":"The paper argues that one ingredient of the exchange-correlation functional, the C09 exchange term, is what makes density functional theory accurate for the ferroelectric perovskites PbTiO3 and BaTiO3, and that the expensive non-local van der Waals correlation paired with it is not needed. To show this it introduces a functional called C09x-PBEc, defined by combining C09 exchange with standard PBE correlation. Across the two materials, C09x-PBEc reproduces lattice constants to within about 2 percent, spontaneous polarizations of 0.79 C m$^{-2}$ and 0.33 C m$^{-2}$, and Born effective charges that are markedly closer to experiment than PBE, at a computational cost close to plain PBE and far below vdW functionals. The same functional was then used to label a training set of 551 structures for a machine-learned interatomic potential for PbTiO3, and that potential gave a ferroelectric-to-paraelectric transition temperature of 738 K, against 747 K from experiment, while PBE-based potentials gave 1429 K and 1082 K. A sympathetic reader would take this as evidence that the choice of exchange functional, not the correlation form, controls ferroelectric accuracy and should be the focus when building MLIP training data.","feed_headline":"C09x-PBEc functional nails ferroelectric properties at GGA cost","feed_subtitle":"A GGA-cost functional with C09 exchange matches experiment and trains an MLIP that gets the PbTiO3 transition right.","key_machinery":"The central object is the C09 exchange enhancement factor, $F_x(s) = 1 + \\mu s^2 e^{-\\alpha s^2} + \\kappa(1 - e^{-\\alpha s^2/2})$ with $\\kappa=1.245$, $\\mu=0.0617$, $\\alpha=0.0483$, which multiplies the LDA exchange energy density and depends on the reduced density gradient $s = |\\nabla \\rho|/[2(3\\pi^2)^{1/3}\\rho^{4/3}]$. The C09x-PBEc functional is $E_{xc} = E_x^{\\mathrm{C09}} + E_c^{\\mathrm{PBE}}$, i.e. this exchange term with the standard PBE correlation. The mechanism it carries is the control of the tetragonal $c$ lattice parameter: compared with PBE, C09's reduced short-range repulsion shortens $c$, restores stronger hybridization between Ti and the axial O atom, lowers the ionic contribution to the spontaneous polarization, and thereby fixes the overestimation seen in GGA. The same machinery explains why vdW-DF and vdW-DF2 without C09 exchange remain inaccurate despite adding non-local correlation.","core_discovery":"The central claim is that the C09 exchange enhancement factor is the decisive ingredient for accurate ferroelectric properties, so that combining C09 exchange with ordinary PBE correlation yields essentially the accuracy of the much more expensive vdW-DF-C09 and vdW-DF2-C09 functionals. The evidence is a systematic comparison on tetragonal and cubic PbTiO3 and BaTiO3: plain PBE overestimates the tetragonal c lattice parameter by 15 percent in PbTiO3 and predicts a polarization of 1.26 C m$^{-2}$ against 0.75 C m$^{-2}$ experiment, whereas C09x-PBEc gives c within 1.7 percent and 0.79 C m$^{-2}$. The paper attributes the improvement to the shape of C09's exchange enhancement factor, which has less short-range repulsion at small reduced density gradients than PBE, allowing a shorter c axis and stronger Ti-O hybridization. It closes by showing the practical payoff: a machine-learned interatomic potential trained on C09x-PBEc labels reproduces the PbTiO3 transition temperature within 9 K of experiment, in contrast to PBE-trained potentials that overestimate it by hundreds of kelvin. In the authors' framing, the functional is not a tweak to dispersion corrections but a replacement for the exchange that MLIP training sets should be built on.","pith_inferences":["Since C09x-PBEc is semi-local, a C09x-PBEc-trained potential could in principle be combined with explicit dispersion corrections at the simulation level, separating exchange-driven accuracy from van der Waals effects; the paper does not test this.","The 551 training structures were sampled with a PBE-based foundation model, so the trained potential's agreement with experiment may owe part of its success to the training coverage; an MLIP retrained on C09x-PBEc-sampled trajectories would be a sharper test.","The paper's logic predicts that other functionals whose exchange enhancement factor lowers short-range repulsion in the same density-gradient window should also improve ferroelectric perovskites; scanning the enhancement-factor shape could reveal new cheap functionals.","If C09 exchange is truly the essential ingredient, then BaTiO3's transition temperature, not just its static polarization, should be reproduced by a C09x-PBEc-trained potential; the paper demonstrates this only for PbTiO3."],"forward_implications":["High-throughput screening of ferroelectric perovskites can rely on C09x-PBEc rather than vdW-C09 functionals, cutting cost while keeping structural and polarization accuracy.","MLIP training sets for ferroelectrics should be generated with C09x-PBEc; potentials trained on it are expected to reproduce phase transitions more faithfully than PBE-trained potentials.","The tetragonal $c$ lattice parameter is the sensitive diagnostic: any functional that cures its overestimation should also cure the polarization overestimation.","Landau-theory estimates of $T_c$ from C09-containing functionals land close to experiment for PbTiO3 and BaTiO3, unlike PBE.","C09x-PBEc's accuracy for both covalent-driven (PbTiO3) and ionic-driven (BaTiO3) polarization suggests it is a general choice for perovskite ferroelectrics."],"supporting_citations":[{"why":"Defines the C09 exchange functional and its enhancement factor parameters that C09x-PBEc uses.","marker":"[22]"},{"why":"Shows that vdW functionals with C09 exchange accurately reproduce perovskite ferroelectric properties, the result this paper extends to PBE correlation.","marker":"[8]"},{"why":"Supplies the PBE correlation functional used in C09x-PBEc and the GGA baseline that overestimates polarization.","marker":"[26]"},{"why":"Documents the systematic overestimation of polarization by LDA, GGA, and SCAN that motivates the new functional.","marker":"[18]"},{"why":"Supplies the foundational model whose molecular dynamics trajectories generated the 551 training structures.","marker":"[39]"},{"why":"Supplies the neural network architecture used to train the interatomic potential for PbTiO3.","marker":"[38]"},{"why":"Provides the earlier study of vdW density functionals for ferroelectrics that this work compares against.","marker":"[7]"},{"why":"Experimental PbTiO3 spontaneous polarization (0.75 C m$^{-2}$) used as the accuracy target.","marker":"[44]"},{"why":"Experimental BaTiO3 spontaneous polarization (0.27 C m$^{-2}$) used as the accuracy target.","marker":"[45]"}],"fun_headline_variants":["C09 exchange with PBE correlation: ferroelectrics at GGA cost","New functional blends C09 exchange and PBE correlation for perovskite accuracy","GGA-cost functional matches costly vdW accuracy for ferroelectrics","C09x-PBEc: accurate ferroelectrics without the vdW overhead","Functional with C09 exchange solves ferroelectric lattice and polarization"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the 551 geometries sampled by molecular dynamics with a PBE-based foundation model cover the parts of the potential energy surface where C09x-PBEc differs from PBE; if those regions are missed, the trained potential's 738 K transition temperature could match experiment for the wrong reason.","fun_headline_variants_meta":{"raw":{"variants":["C09 exchange with PBE correlation: ferroelectrics at GGA cost","New functional blends C09 exchange and PBE correlation for perovskite accuracy","GGA-cost functional matches costly vdW accuracy for ferroelectrics","C09x-PBEc: accurate ferroelectrics without the vdW overhead","Functional with C09 exchange solves ferroelectric lattice and polarization"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000247,"raw_usage":{"total_tokens":1621,"prompt_tokens":1100,"completion_tokens":521,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":716,"completion_tokens_details":{"reasoning_tokens":424}},"tokens_in":716,"tokens_out":521,"duration_ms":5781,"temperature":1.0,"reasoning_tokens":424,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:01:47.109996+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the C09x-PBEc-trained potential and compare its forces, energies, and stresses against freshly computed C09x-PBEc DFT on a held-out set of structures generated by C09x-PBEc molecular dynamics, including high-temperature and distorted configurations; if the errors are comparable to a PBE-trained potential's errors, the functional is not driving the accuracy. A second decisive test is to train an MLIP on C09x-PBEc for BaTiO3: the paper's reasoning predicts a transition temperature near the experimental 393 K, while a PBE-trained potential would overshoot by hundreds of kelvin.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Experimental BaTiO3 spontaneous polarization (0.27 C m$^{-2}$) used as the accuracy target."},{"cited_title":"Cardona-Quintero and R","cited_arxiv_id":null,"evidence_quote":"Provides the earlier study of vdW density functionals for ferroelectrics that this work compares against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the C09 exchange functional and its enhancement factor parameters that C09x-PBEc uses."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that vdW functionals with C09 exchange accurately reproduce perovskite ferroelectric properties, the result this paper extends to PBE correlation."},{"cited_title":"Zhang, J","cited_arxiv_id":null,"evidence_quote":"Documents the systematic overestimation of polarization by LDA, GGA, and SCAN that motivates the new functional."},{"cited_title":"Batatia, P","cited_arxiv_id":null,"evidence_quote":"Supplies the foundational model whose molecular dynamics trajectories generated the 551 training structures."},{"cited_title":"Batatia, D","cited_arxiv_id":null,"evidence_quote":"Supplies the neural network architecture used to train the interatomic potential for PbTiO3."}],"review_version":1}