An Exchange-Correlation Functional for Fast and Accurate Modeling of Ferroelectric Perovskites

Chiara Gattinoni; Owain T. Beynon

REVIEW 4 major objections 6 minor 47 references

An Exchange-Correlation Functional for Fast and Accurate Modeling of Ferroelectric Perovskites

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2608.04806 v1 pith:BMCQUTLX submitted 2026-08-05 cond-mat.mtrl-sci

Owain T. Beynon , Chiara Gattinoni This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords Densityfunctionaltheoryexchange-correlationC09exchangeferroelectricperovskitesspontaneouspolarizationmachinelearninginteratomicpotentialPbTiO3Ba

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the 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.

The 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.

Other 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.

The 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.

Referee Report

4 major / 6 minor

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.

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 (4)

[Section IV] 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 III, Eq. (5) and Fig. 3] 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.
[Table II and Section III text] 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 IV and Table IV] 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.

minor comments (6)

[Section IV] The name 'Bernedsen' should be 'Berendsen', and the abbreviation 'MACE-MP-0-D3' should be 'MACE-MPA-0-D3' for consistency.
[Section IV and Conclusions] 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.
[Figure 4 caption] The caption lists 'tetragonal PbTiO3' and 'cubic PbTiO3' twice; presumably one pair refers to BaTiO3, and the caption should be corrected.
[Section III] The text refers to 'C09-PBEx' where the functional is elsewhere called 'C09x-PBEc'; please correct the notation.
[Section III] The units in 'within 0.05 Cm−1' should be Cm−2, matching the polarization values in Table II.
[Eqs. (4)-(5)] 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.

Circularity Check

1 steps flagged · score 3.0 of 10

Landau Tc estimates are anchored to experimental Tc via Eq. (5), but the MLIP NPT result is independent; no load-bearing self-citation.

fitted input called prediction [Section III, Eq. (5) and Fig. 3]
"From this it is possible to estimate the phase transition temperature, Tc, for each DFT functional via: Tc = γP^2 (5) where γ is a constant derived from the experimental transition temperature and spontaneous polarization, and P is the spontaneous polarization from calculations."

Because γ is defined using the experimental transition temperature and spontaneous polarization, the 'estimated' Tc for each functional is not an independent first-principles prediction. It is Tc_exp scaled by (P_DFT/P_exp)^2, so Fig. 3's comparison of 'predicted' transition temperatures against experiment is anchored to the experimental Tc by construction. The Landau estimate therefore reduces to a test of how well each functional reproduces the experimental polarization. This is a transparent but construction-dependent input, and it is not the paper's central evidence: the MLIP NPT calculation of Tc (738 K) is a direct simulation that does not use Eq. (5).

full rationale

The paper's main derivation chain is self-contained. C09x-PBEc is explicitly defined in Eq. (1)-(3) by combining C09 exchange (with parameters taken from Cooper's published functional) and PBE correlation. The structural, polarization, and Born-effective-charge results are direct DFT outputs benchmarked against experiment, and the MLIP proof-of-concept is an NPT molecular-dynamics simulation trained on 551 C09x-PBEc single-point labels. The only construction-dependent 'prediction' is the Landau-based Tc estimate in Section III: Eq. (5) sets Tc = gamma P^2 with gamma derived from the experimental Tc and P, so the 'estimated Tc' values in Fig. 3 are a rescaling of each functional's P anchored to the experimental Tc by construction. This is a fitted-input estimate rather than an independent prediction, but it is not the central evidence: the MLIP NPT result (738 K vs about 747 K experimental) is generated without that gamma and is therefore independent. No load-bearing self-citations appear; C09 exchange is cited to Cooper (2010), and the MACE model is cited to external prior work. The training-set coverage concern about MACE-MPA-0-D3 sampling is a validation and robustness risk, not a by-construction reduction, so it does not count as circularity under the stated rules.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard DFT practice plus several domain-specific assumptions: transferability of pseudopotentials across functionals, convergence of numerical settings, adequacy of the training set, and reliability of experimental references. The only explicit fitted parameter is gamma in the Landau Tc estimates.

free parameters (1)

gamma (Landau coefficient in Tc = gamma P^2) = not reported; derived from experimental Tc and P
Equation (5) defines Tc = gamma P^2; the text states gamma is 'derived from the experimental transition temperature and spontaneous polarization,' so the DFT-based Tc estimates in Fig. 3 are not independent predictions.

assumptions (4)

domain assumption The same ultrasoft pseudopotentials are transferable across PBE, PBEsol, revPBE, vdW-DF, vdW-DF2 and C09-based functionals.
Section II states ultrasoft pseudopotentials were used but does not specify a pseudopotential library or validation for each functional; functional comparisons assume no functional-specific bias.
domain assumption A 50 Ry cutoff and 4x4x4 Monkhorst-Pack grid are converged for all computed properties.
Section II states calculations were performed with converged settings, but no convergence tests are shown.
domain assumption The MACE-MPA-0-D3 foundational model samples configurations representative of the C09x-PBEc potential energy surface.
Section IV: the 551 training structures were generated via MD with MACE-MPA-0-D3, not with C09x-PBEc; labeling them with C09x-PBEc single points assumes the sampled geometries are relevant.
domain assumption Experimental reference values cited for lattice constants and polarization are reliable and comparable across sources.
Tables I-III compare against experimental values from refs [40-47] without uncertainty estimates.

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Pith. "Pith review of An Exchange-Correlation Functional for Fast and Accurate Modeling of Ferroelectric Perovskites." pith.science (2026). https://pith.science/paper/BMCQUTLX

@misc{pith2026260804806,
  author       = {Pith},
  title        = {Pith review of: An Exchange-Correlation Functional for Fast and Accurate Modeling of Ferroelectric Perovskites},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BMCQUTLX}},
  note         = {Machine review of arXiv:2608.04806}
}

read the original abstract

We present a novel exchange correlation functional, C09x-PBEc, which combines C09 exchange with PBE correlation, to accurately model the ferroelectric properties of perovskites while retaining the computational efficiency of GGA functionals. With a growing interest in developing machine learning interatomic potentials (MLIPs) to model large-scale ferroelectric systems of technological relevance, it is important to scrutinise the density functional theory exchange-correlation functionals which are used to compute the forces, energies and stresses the MLIP is trained on. Using the example of the prototypical ferroelectrics lead titanate, PbTiO3, and barium titanate, BaTiO3 we show that many widely used functionals tend to overestimate their lattice constants and spontaneous polarization. Conversely, non-local van der Waals functionals with C09 exchange accurately capture these properties compared to experiment, but with a larger computational overhead than, for example, GGA. We show that C09x-PBEc combines the accuracy provided by the C09 exchange with the computational affordability of GGA, making it an excellent candidate to be used in the training of MLIPs for ferroelectric perovskites. We also demonstrate that an MLIP trained using C09x-PBEc accurately reproduces the ferroelectric-to-paraelectric phase transition temperature of PbTiO3 with respect to experiment, showing a marked improvement on MLIPs trained using GGA.

Figures

Figures reproduced from arXiv: 2608.04806 by the authors.

**Figure 2.** FIG. 2. A) Charge density plots for PbTiO [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Estimated [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Works this paper leans on

47 extracted references · 40 canonical work pages

[8]

S. F. Yuk, K. C. Pitike, S. M. Nakhmanson, M. Eisen- bach, Y. W. Li, and V. R. Cooper, Towards an accu- rate description of perovskite ferroelectrics: exchange and correlation effects, Sci. Rep.7, 43482 (2017)

work page 2017
[1]

Nuraje and K

N. Nuraje and K. Su, Perovskite ferroelectric nanomate- rials, Nanoscale5, 8752 (2013)

work page 2013
[2]

Lichtensteiger, P

C. Lichtensteiger, P. Zubko, M. Stengel, P. Aguado- Puente, J. Triscone, P. Ghosez, and J. Junquera, Ferro- electricity in ultrathin-film capacitors, inOxide Ultrathin Films, edited by G. Pacchioni and S. Valeri (Wiley, 2011) 1st ed., pp. 265–230

work page 2011
[3]

Y. Wang, Z. Yang, and L. Liu, Perovskite-based cata- lysts for syngas upgrading by intensified steam reforming of biomass tar, ACS Sustainable Chem. Eng.12, 15812 (2024)

work page 2024
[4]

Kakekhani and S

A. Kakekhani and S. Ismail-Beigi, Ferroelectric-based catalysis: Switchable surface chemistry, ACS Catal.5, 4537 (2015)

work page 2015
[5]

P. Xie, F. Yang, R. Li, C. Ai, C. Lin, and S. Lin, Improv- ing hydrogen evolution activity of perovskite BaTiO 3 with Mo doping: Experiments and first-principles analy- sis, Int. J. Hydrogen Energy44, 11695 (2019)

work page 2019
[6]

J. Cui, C. Chen, J. Han, K. Cao, W. Zhang, Y. Shen, and M. Wang, Surface plasmon resonance effect in inverted perovskite solar cells, Adv. Sci.3, 1500312 (2016)

work page 2016
[7]

Cardona-Quintero and R

Y. Cardona-Quintero and R. P´ erez-Moyet, Applicability of van der waals density functionals in the calculation of materials properties applied to ferroelectrics, J. Am. Ceram. Soc.108, 20467 (2025)

work page 2025

Show all 47 references

[9]

D. I. Bilc, R. Orlando, R. Shaltaf, G.-M. Rignanese, J. ´I˜ niguez, and P. Ghosez, Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides, Phys. Rev. B77, 165107 (2008)

2008
[10]

Wu and R

Z. Wu and R. E. Cohen, More accurate generalized gra- dient approximation for solids, Phys, Rev, B73, 235116 (2006)

2006
[11]

Zhang, Y

J. Zhang, Y. Qi, and A. M. Rappe, Developing a force field for the Ba 1−xCaxZrO3 ferroelectric alloy: Predic- tion of a ferroelectric superlattice structure, Phys. Rev. B105, 214204 (2022)

2022
[12]

Y.-H. Shin, V. R. Cooper, I. Grinberg, and A. M. Rappe, Development of a bond-valence molecular-dynamics model for complex oxides, Phys. Rev. B71, 054104 (2005)

2005
[13]

Y. Qi, S. Liu, I. Grinberg, and A. M. Rappe, Atomistic description for temperature-driven phase transitions in BaTiO3, Phys. Rev. B94, 134308 (2016)

2016
[14]

Gigli, M

L. Gigli, M. Veit, M. Kotiuga, G. Pizzi, N. Marzari, and M. Ceriotti, Thermodynamics and dielectric response of BaTiO3 by data-driven modeling, npj Comput. Mater8 (2022)

2022
[15]

Sehrawat, K

A. Sehrawat, K. Albe, and J. Rohrer, Machine-learning interatomic potential for BaTiO3 : phase transitions, do- main walls, and grain boundaries, J. Phys. Condens. Mat- ter38(2026)

2026
[16]

A. M. Elena, P. D. Kamath, T. Jaffrelot Inizan, A. S. Rosen, F. Zanca, and K. A. Persson, Machine learned potential for high-throughput phonon calculations of metal—organic frameworks, npj Comput Mater11, 125 (2025)

2025
[17]

T. W. Ko and S. P. Ong, Recent advances and outstand- ing challenges for machine learning interatomic poten- tials, Nat. Comput. Sci.3, 998 (2023)

2023
[18]

Zhang, J

Y. Zhang, J. Sun, J. P. Perdew, and X. Wu, Comparative first-principles studies of prototypical ferroelectric mate- rials by LDA, GGA, and SCAN meta-GGA, Phys. Rev. B96, 035143 (2017)

2017
[19]

S. F. Yuk, I. Sargin, N. Meyer, J. T. Krogel, S. P. Beck- man, and V. R. Cooper, Putting error bars on density functional theory, Sci Rep14, 20219 (2024). 8

2024
[20]

Schr¨ oder, V

E. Schr¨ oder, V. R. Cooper, K. Berland, B. I. Lundqvist, P. Hyldgaard, and T. Thonhauser, The vdW-DF fam- ily of nonlocal exchange-correlation functionals, in Non-Covalent Interactions in Quantum Chemistry and Physics(Elsevier, 2017) pp. 241–274

2017
[21]

Berland, C

K. Berland, C. A. Arter, V. R. Cooper, K. Lee, B. I. Lundqvist, E. Schr¨ oder, T. Thonhauser, and P. Hyldgaard, van der waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions, J. Chem. Phys.140, 18A539 (2014)

2014
[22]

V. R. Cooper, Van der waals density functional: An ap- propriate exchange functional, Phys. Rev. B81, 161104 (2010)

2010
[23]

Giannozzi, S

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ- cioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. ...

2009
[24]

Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys

D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B41, 7892 (1990)

1990
[25]

H. J. Monkhorst and J. D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B13, 5188 (1976)

1976
[26]

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

1996
[27]

J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett.100, 136406 (2008)

2008
[28]

generalized gra- dient approximation made simple

Y. Zhang and W. Yang, Comment on “generalized gra- dient approximation made simple”, Phys. Rev. Lett.80, 890 (1998)

1998
[29]

M. Dion, H. Rydberg, E. Schr¨ oder, D. C. Langreth, and B. I. Lundqvist, Van der waals density functional for gen- eral geometries, Phys. Rev. Lett.92, 246401 (2004)

2004
[30]

K. Lee, E. D. Murray, L. Kong, B. I. Lundqvist, and D. C. Langreth, Higher-accuracy van der waals density functional, Phys. Rev. B82, 081101 (2010)

2010
[31]

N. A. Spaldin, A beginner’s guide to the modern theory of polarization, Journal of Solid State Chemistry195, 2 (2012)

2012
[32]

M. K. Horton, P. Huck, R. X. Yang, J. M. Munro, S. Dwaraknath, A. M. Ganose, R. S. Kingsbury, M. Wen, J. X. Shen, T. S. Mathis, A. D. Kaplan, K. Berket, J. Riebesell, J. George, A. S. Rosen, E. W. C. Spotte- Smith, M. J. McDermott, O. A. Cohen, A. Dunn, M. C. Kuner, G.-M. Rign...

2025
[33]

Hjorth Larsen, J

A. Hjorth Larsen, J. Jørgen Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Du lak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. Bjerre Jensen, J. Kermode, J. R. Kitchin, E. Leonhard Kolsbjerg, J. Kubal, K. Kaasb- jerg, S. Lysgaard...

2017
[34]

C. G. Broyden, The convergence of a class of double-rank minimization algorithms 1. general considerations, IMA J Appl Math6, 76 (1970)

1970
[35]

Fletcher, A new approach to variable metric algo- rithms, Comput

R. Fletcher, A new approach to variable metric algo- rithms, Comput. J.13, 317 (1970)

1970
[36]

Goldfarb, A family of variable-metric methods derived by variational means, Math

D. Goldfarb, A family of variable-metric methods derived by variational means, Math. Comp.24, 23 (1970)

1970
[37]

D. F. Shanno, Conditioning of quasi-newton methods for function minimization, Math. Comp.24, 647 (1970)

1970
[38]

Batatia, D

I. Batatia, D. P. Kovacs, G. Simm, C. Ortner, and G. Csanyi, MACE: Higher order equivariant message passing neural networks for fast and accurate force fields (2022)

2022
[39]

Batatia, P

I. Batatia, P. Benner, Y. Chiang, A. M. Elena, D. P. Kov´ acs, J. Riebesell, X. R. Advincula, M. Asta, M. Avaylon, W. J. Baldwin, F. Berger, N. Bernstein, A. Bhowmik, F. Bigi, S. M. Blau, V. C˘ arare, M. Ceriotti, S. Chong, J. P. Darby, S. De, F. Della Pia, V. L. Deringer, R. ...

2025
[40]

S. A. Mabud and A. M. Glazer, Lattice parameters and birefringence in PbTiO3 single crystals, J. Appl. Crystal- logr.12, 49 (1979)

1979
[41]

Shirane, R

G. Shirane, R. Pepinsky, and B. C. Frazer, X-ray and neutron diffraction study of ferroelectric PbTiO 3, Phys. Rev.97, 1179 (1955)

1955
[42]

K. H. Hellwege and A. M. Hellwege, eds.,Ferroelectrics and Related Substances(Springer, Berlin, 1969)

1969
[43]

G. H. Kwei, A. C. Lawson, S. J. L. Billinge, and S. W. Cheong, Structures of the ferroelectric phases of barium titanate, J. Phys. Chem.97, 2368 (1993)

1993
[44]

M. J. Haun, E. Furman, S. J. Jang, H. A. McKinstry, and L. E. Cross, Thermodynamic theory of PbTiO 3, J. Appl. Phys.62, 3331 (1987)

1987
[45]

H. H. Wieder, Electrical behavior of barium titanatge single crystals at low temperatures, Phys. Rev.99, 1161 (1955)

1955
[46]

A. V. Turik and A. G. Khasabov, On the origin of ferro- electricity in PbTiO 3, Ferroelectrics237, 65 (2000)

2000
[47]

Ghosez, X

P. Ghosez, X. Gonze, P. Lambin, and J.-P. Michenaud, Born effective charges of barium titanate: Band-by- 9 band decomposition and sensitivity to structural fea- tures, Phys. Rev. B51, 6765 (1995)

1995

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [8]

S. F. Yuk, K. C. Pitike, S. M. Nakhmanson, M. Eisen- bach, Y. W. Li, and V. R. Cooper, Towards an accu- rate description of perovskite ferroelectrics: exchange and correlation effects, Sci. Rep.7, 43482 (2017)

work page 2017

[2] [1]

Nuraje and K

N. Nuraje and K. Su, Perovskite ferroelectric nanomate- rials, Nanoscale5, 8752 (2013)

work page 2013

[3] [2]

Lichtensteiger, P

C. Lichtensteiger, P. Zubko, M. Stengel, P. Aguado- Puente, J. Triscone, P. Ghosez, and J. Junquera, Ferro- electricity in ultrathin-film capacitors, inOxide Ultrathin Films, edited by G. Pacchioni and S. Valeri (Wiley, 2011) 1st ed., pp. 265–230

work page 2011

[4] [3]

Y. Wang, Z. Yang, and L. Liu, Perovskite-based cata- lysts for syngas upgrading by intensified steam reforming of biomass tar, ACS Sustainable Chem. Eng.12, 15812 (2024)

work page 2024

[5] [4]

Kakekhani and S

A. Kakekhani and S. Ismail-Beigi, Ferroelectric-based catalysis: Switchable surface chemistry, ACS Catal.5, 4537 (2015)

work page 2015

[6] [5]

P. Xie, F. Yang, R. Li, C. Ai, C. Lin, and S. Lin, Improv- ing hydrogen evolution activity of perovskite BaTiO 3 with Mo doping: Experiments and first-principles analy- sis, Int. J. Hydrogen Energy44, 11695 (2019)

work page 2019

[7] [6]

J. Cui, C. Chen, J. Han, K. Cao, W. Zhang, Y. Shen, and M. Wang, Surface plasmon resonance effect in inverted perovskite solar cells, Adv. Sci.3, 1500312 (2016)

work page 2016

[8] [7]

Cardona-Quintero and R

Y. Cardona-Quintero and R. P´ erez-Moyet, Applicability of van der waals density functionals in the calculation of materials properties applied to ferroelectrics, J. Am. Ceram. Soc.108, 20467 (2025)

work page 2025