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REVIEW 3 major objections 5 minor 104 references

Identifying Split Vacancy Defects with Machine-Learned Foundation Models and Electrostatics

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A tiered screen combining geometric enumeration, formal-charge electrostatics, and a pretrained machine-learned potential can identify split-vacancy defects across essentially all known inorganic solids, and such defects are common…

desk verdict A smart screening pipeline that makes a strong case that split vacancies are common, but the headline prevalence number rides on ML extrapolation that the paper hasn't yet validated in the chemistries where it matters most. read the letter →

arxiv 2412.19330 v3 pith:PKTOS3OX submitted 2024-12-26 cond-mat.mtrl-sci physics.chem-phphysics.comp-ph

Seán R. Kavanagh This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.chem-phphysics.comp-ph PACS 61.72.jj71.55.-i
keywords splitvacanciespointdefectsdefectmetastabilitymachine-learnedinteratomicpotentialselectrostaticscreeninghigh-throughputcationfoundationmodels
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

Split vacancies are defects in which removing one atom triggers a nearby atom to move into an interstitial position, leaving two vacancies flanking one interstitial. This paper argues that these reconstructions are common rather than exotic: in a large high-throughput test, roughly 10% of cation vacancies relax to a split vacancy that is lower in energy than the simple vacancy, with energy lowerings averaging about 0.8 eV and exceeding 2 eV in some cases. Because standard defect simulations usually relax from the unperturbed vacancy geometry, they systematically miss these lower-energy states. The paper shows that a cheap pre-screen based on formal-charge electrostatics, followed by relaxation with a general machine-learned interatomic potential, can find split vacancies across essentially all known inorganic solids, yielding thousands of predicted low-energy split-vacancy configurations.

What carries the argument

The load-bearing object is the split vacancy itself, defined as the stoichiometry-conserving complex $[V_X + X_i + V_X]$ in which one host atom leaves its lattice site to sit between two empty sites. The workflow that carries the argument is a tiered screening algorithm: geometric enumeration of candidate complexes (with vacancy-interstitial distances under 5 Å), an electrostatic pre-screen using Ewald sums with formal ionic charges and a 110% energy cutoff relative to the simple vacancy, a relaxation pass with a foundation machine-learned interatomic potential (retaining geometries that stay split and lie within 0.35 eV of the simple vacancy), and final density functional theory evaluation. The paper's key empirical claim is that the formal-charge electrostatic energy, despite ignoring screening, strain, and covalency, ranks the candidate geometries well enough that the true low-energy split vacancies sit in the low-energy tail of the electrostatic distribution.

What would settle it

Take a set of compounds with strongly covalent or low-symmetry bonding (e.g., small-gap semiconductors, transition-metal oxides with partially filled d shells, or layered van der Waals solids), enumerate all candidate split vacancies for a sample of cation vacancies, relax every candidate with DFT (no electrostatic pre-screen), and count how many low-energy split vacancies (ΔE < −0.025 eV) have initial electrostatic energies above the 110% cut-off; if a material-dependent fraction falls above the cut-off, the pre-screen's recall is not universal.

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Extended reading notes

Core claim

The central claim is that low-energy split vacancies—stoichiometry-conserving complexes of the form $[V_X + X_i + V_X]$—are a widespread feature of cation vacancies in inorganic compounds, and that they can be identified systematically by a tiered workflow: enumerate all symmetry-inequivalent vacancy-interstitial-vacancy combinations within 5 Å, compute their formal-charge Ewald energies, keep only those within 110% of the simple vacancy's electrostatic energy, relax the survivors with a pretrained machine-learned interatomic potential, and finally confirm with density functional theory. Applied to a set of stable insulating metal oxides, the workflow finds 93 cation vacancies whose split (or split-like) geometry lies 0.05–3 eV below the best simple vacancy; extrapolated to a database of roughly 150,000 known and predicted compounds, the ML stage predicts about 29,000 cation vacancies classified as split vacancies, with density functional theory spot checks on oxides and nitrides confirming 40–60% of the predictions. If these numbers hold, the standard practice of relaxing defects from the ideal vacancy geometry is missing the true ground state for a substantial fraction of all cation vacancies.

Load-bearing premise

The screen assumes that a formal-charge Ewald energy within 110% of the simple vacancy's electrostatic energy is a necessary condition for a split vacancy to be low in energy; if a material's bonding is dominated by covalency, strain, or charge localization, low-energy split vacancies may sit above that cut-off and never reach the machine-learning or DFT stages.

Editorial extensions

If this is right

  • Standard defect relaxations that start from the ideal vacancy and relax locally will miss the true ground state for roughly 10% of cation vacancies, so defect concentrations and properties computed from simple vacancies are systematically wrong for those materials.
  • The mean energy lowering of about 0.8 eV changes equilibrium defect populations by orders of magnitude: roughly a factor of 10^3 at 1000 K and 10^10 at 300 K for a single defect.
  • The ML-accelerated screen achieves a discovery acceleration factor of about 120 relative to random candidate selection, making whole-database defect structure searches feasible in about a GPU-day.
  • The predicted split-vacancy database is integrated into the defect-generation toolkit, so researchers are automatically alerted when their host compound has a likely split vacancy and at what confidence.
  • The method's success is specific to fully ionized (formal-charge) defects; it does not address metastabilities driven by charge localization, which require different handling.

Reading between the lines

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

  • If the 10% prevalence holds, experimental probes that assume simple monovacancy pictures—positron annihilation, EPR, deep-level spectroscopy—may need re-analysis across broader materials classes.
  • The same geometry+electrostatics+ML pipeline could be applied to other stoichiometry-conserving defect complexes (divacancies, antisite pairs, DX-like off-centre substitutions) and to colour-centre discovery for quantum technologies.
  • Given the reported 40–60% DFT validation accuracy, the ML screen over-predicts; the true number of split vacancies in the full database is likely in the thousands rather than 29,000, though still a large fraction of the initial estimate.
  • A testable extension is to benchmark the 110% electrostatic cut-off against a chemically diverse set of compounds to measure its recall, and to use a tighter cut-off where covalent bonding dominates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents a multi-stage screening workflow for identifying split-vacancy defects: enumeration of candidate V_X–X_i–V_X complexes, an Ewald-based formal-charge electrostatic prescreen with a 110% energy cutoff, relaxation of survivors with the MACE-mp foundation model, and final DFT confirmation of selected candidates. The workflow is first validated on known split-vacancy cases and on a 444-oxide DFT screen, which finds 93 lower-energy cation vacancies. The method is then applied to the full Materials Project database, yielding ML predictions of roughly 55,000 lower-energy cation vacancies and 29,000 ML-classified split vacancies. The paper argues that split vacancies are common (around 10% of cation vacancies) and that foundation ML potentials can accelerate such defect searches, with explicit caveats about their limited domain of validity.

Significance. If the central claims hold, the paper is significant: it offers a practical computational pipeline for finding a class of defect reconstructions that local structure-searching methods routinely miss, provides a concrete DFT-validated set of 93 lower-energy cation vacancies in oxides, and demonstrates that a foundation ML potential, combined with electrostatic screening, can search the full Materials Project space. The known-case benchmark (PBEsol vs PBE0 relative energies with R2=0.998) is a strong piece of evidence that semi-local DFT is adequate for these fully-ionized defects, and the open code and database (modulo the placeholder DOI) are valuable community resources. The main weakness is that the quantitative census results are ML predictions with only partial validation, and the manuscript's own precision-correction is not carried through to its headline prevalence statement.

major comments (3)
  1. [Discussion & Conclusions] The headline prevalence statement is inconsistent with the paper's own precision correction. The Results report that the ML model predicts 29,000 (10%) of cation vacancies in the Materials Project to be split vacancies, and the Discussion repeats 'around 10% of cation vacancies in all inorganic solids'. However, the preceding text states that applying the ~40% precision from the oxide and nitride validations yields ~12,000 true split vacancies, which is approximately 4% of cation vacancies, not 10%. Please revise the Discussion to quote the precision-corrected figure or to label the 10% explicitly as an uncorrected ML prediction (an upper bound). As written, the conclusion overstates the established prevalence.
  2. [Machine Learning Acceleration (Fig. 7)] The census numbers (55,000 and 29,000) are based entirely on MACE-mp relaxations, with DFT confirmation only for an oxide subset (44% precision for lower-energy split vacancies) and a nitride subset (39% precision for split-classified relaxations). Both validation sets are compositionally limited, and Fig. 7c,d show the highest predicted prevalences in halides, carbon, chalcogenides, mercury, and coinage-metal compounds - precisely the chemistries where formal-charge electrostatics and the PBE-trained MACE-mp model are least tested. The ~40% precision is applied as a uniform correction factor, but no evidence is given that it transfers to these untested chemistry classes. Please provide a stratified DFT check across the chemistries that dominate the predicted census, or explicitly state that the 29,000 and 10% figures remain unconfirmed predictions.
  3. [Algorithm 1 and 'Screening Split Cation Vacancies in Oxides'] The recall of the electrostatic prescreen is not quantified. The 110% cutoff is an ad hoc tuning parameter, and the paper shows only that the known split-vacancy cases fall below it; no DFT calculations are performed on candidates that fail the cutoff. Since the abstract claims the approach 'allows the screening of all solid-state compounds', the possibility of false negatives - especially in chemistries where strain, pair repulsion, or covalent effects dominate - should be addressed. I recommend relaxing a random sample of excluded candidates for a few diverse host compounds to estimate the prescreen's sensitivity, or clearly stating that the true recall is unknown and that the pipeline is a heuristic search rather than a complete enumeration.
minor comments (5)
  1. [Data availability] The database and code DOI is given as a placeholder ('https://doi.org/10.5281/zenodo.XXXX'); please provide the actual DOI before publication.
  2. [Fig. 4b caption] The caption refers to 'the full DFT calculated dataset (~1000 compounds)', while the oxide screen described in the text covers the first 444 compounds; please clarify what structures are included in this figure.
  3. [Table 2] The metric definitions are crowded into the caption; consider moving the definitions of TPR/FPR/TNR/FNR and the prevalence note into the main text or a separate methods paragraph for readability.
  4. [Introduction] The statement that ShakeNBreak fails to identify the split-vacancy ground state for V_Ga in Ga2O3 is attributed to unpublished work; please add a citation or a public preprint if available.
  5. [Algorithm 1] The '+0.35 eV' energy window in the 'exhaustive' ML criterion and the 10% electrostatic cutoff are both presented without sensitivity analysis; a brief justification of these numerical choices would help readers gauge how robust the screening is to their variation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the screening is a cascade of independent energy evaluations with external DFT validation.

full rationale

The paper does not define its target result into existence. Split vacancies are identified by a geometric site-matching definition (Section S1.1) and by relative energies from DFT or MACE-mp, neither of which is constructed from the screening thresholds. The electrostatic cutoff (110% of the simple-vacancy Ewald energy) and the ML energy window (0.35 eV) are calibrated on known/validation cases, but they only prune the candidate set; they do not determine which relaxed geometries are split vacancies or whether those are lower in energy. The full-Materials-Project prevalence counts are ML predictions, and the paper applies a ~40% precision correction to derive lower bounds (Results, Fig. 7), even though the Discussion later states ~10% without that correction. That is an extrapolation/overclaim risk, not a circular reduction. Self-citations to doped, ShakeNBreak, and the author's prior ML-defect work are present but not load-bearing: the central validation uses independent DFT (PBEsol/PBE0 and MP-setup PBE) on oxides and nitrides, and MACE-mp is an external foundation model. No equation or fitted parameter is reused as its own output, so the derivation chain is not circular.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

No invented physical entities are introduced. The screening depends on the free parameters and domain assumptions listed above; the most consequential are the 110 percent electrostatic cutoff and the transferability of MACE-mp to defect supercells.

free parameters (8)
  • Electrostatic screening cutoff factor = 1.10 times the simple vacancy electrostatic energy
    Chosen so known lower-energy split vacancies are mostly captured (Fig. 4a); directly controls how many candidates reach ML/DFT.
  • Vacancy-interstitial distance cutoff = 5 Å for each V_X-X_i pair
    Defines the enumerated complex space; split vacancies with longer V_X-X_i distances would be missed.
  • Exhaustive ML energy window = +0.35 eV
    Set to raise true positive rate of MACE-mp to 81 percent at the price of false positives (Table 2).
  • Lower-energy classification threshold = -0.025 eV
    Used to count a vacancy as lower energy than the simple vacancy; changes reported prevalence numbers.
  • Metastable-state energy separation = 25 meV
    Used to declare distinct metastable states; affects the count of 210 metastable states.
  • Split-vacancy site-matching tolerance = 50 percent of bulk bond length
    Distance tolerance in doped classification; determines whether a relaxed geometry is labeled split or non-trivial.
  • Minimum interstitial-host distance = 1.0 Å
    Filters out unphysically close interstitial sites during Voronoi generation.
  • Interstitial clustering tolerance = 0.55 Å
    Merges Voronoi interstitial sites closer than this; affects candidate geometry list.
assumptions (6)
  • domain assumption Formal oxidation-state assignments (bond-valence analysis or ICSD statistics) are reliable enough for electrostatic screening across all Materials Project compounds.
    Used to assign charges for Ewald energies; Section S1.2 acknowledges integer oxidation states are only determined for about 110,000 of 150,000 compounds, so a large fraction of the database is screened without reliable formal charges.
  • domain assumption Split-vacancy formation is dominated by electrostatics and strain, making a formal-charge Ewald model a sufficient first filter.
    Stated as the main physical insight and used to justify the 110 percent cutoff in Algorithm 1; covalent and charge-localization effects are assumed to be rare for fully-ionized states.
  • domain assumption Semi-local DFT (PBEsol/PBE) accurately ranks split vs simple vacancy energies for fully-ionized defects.
    The paper tests this on known cases (R2 = 0.998 between PBEsol and PBE0) and invokes it for all oxide and nitride DFT screening, but assumes transfer to every new compound.
  • ad hoc to paper The MACE-mp foundation model, trained on bulk crystal relaxations in the Materials Project, transfers to charged defect supercells and split-vacancy candidate geometries.
    No defect-specific retraining is performed; the model is used as a universal surrogate. The paper's own validation shows 39-53 percent true positive rates on split-vacancy subsets, so this transferability is imperfect.
  • domain assumption Supercells with minimum image distance 10 Å and at least 50 atoms are large enough that finite-size corrections do not change relative point/split vacancy energies.
    The SI shows corrections up to 0.1-0.3 eV for metastable split vacancies with large V_X-X_i distances, so for the full database this assumption can fail in borderline cases.
  • standard math Pymatgen EwaldSummation with a compensating background charge is an acceptable electrostatic model for charged supercells.
    Ewald summation is a standard method; the specific treatment of charged defects with a jellium background is conventional.

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Pith. "Pith review of Identifying Split Vacancy Defects with Machine-Learned Foundation Models and Electrostatics." pith.science (2026). https://pith.science/paper/PKTOS3OX

@misc{pith2026241219330,
  author       = {Pith},
  title        = {Pith review of: Identifying Split Vacancy Defects with Machine-Learned Foundation Models and Electrostatics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKTOS3OX}},
  note         = {Machine review of arXiv:2412.19330}
}
abstract

Point defects are ubiquitous in solid-state compounds, dictating many functional properties such as conductivity, catalytic activity and carrier recombination. Over the past decade, the prevalence of metastable defect geometries and their importance to relevant properties has been increasingly recognised. A striking example is split vacancies, where an isolated atomic vacancy transforms to a stoichiometry-conserving complex of two vacancies and an interstitial ($V_X \rightarrow [V_X + X_i + V_X]$), which can be accompanied by a dramatic energy lowering and change in behaviour. These species are particularly challenging to identify from computation, due to the `non-local' nature of this reconstruction. Here, I present an approach for the efficient identification of these defects, through tiered screening which combines geometric analysis, electrostatic energies and foundation machine learning (ML) models. This approach allows the screening of all solid-state compounds in the Materials Project database (including all entries in the ICSD, along with several thousand predicted metastable materials), identifying thousands of low energy split vacancy configurations, hitherto unknown. This study highlights both the potential utility of (foundation) machine-learning potentials, with important caveats, the significant prevalence of split vacancy defects in inorganic solids, and the importance of global optimisation approaches for defect modelling.

Figures

Figures reproduced from arXiv: 2412.19330 by the authors.

Figure 1
Figure 1. Split vacancy configurations in solids. (a) Schematic illustration of the transformation from a single atomic vacancy (top) to a split vacancy geometry (bottom) using V Ga in R¯3c α￾Ga2O3 as an example. Vacancy positions are indicated by the hollow circles, curved arrows depict the movement of the neighbouring cation in transforming from the single vacancy to the split vacancy, and dashed grey circles depict the 10t… view at source ↗
Figure 2
Figure 2. Generation of interstitial and split vacancy geometries via doped (a) Interstitial generation workflow, using MgTiO3 as an example. Mg cations are in orange, Ti in blue and O in red. Candidate interstitial sites are shown as grey spheres. The point symmetries and minimum distances to host atoms of the final symmetry-inequivalent interstitial sites are given underneath. (b) Split vacancy generation workflow, using th… view at source ↗
Figure 3
Figure 3. Geometric and DFT energy analysis of split vacancies. (a) Geometric analysis of the split vacancy for V Ga in R¯3c α-Ga2O3, indicating short and long cation-anion bond lengths. The interstitial cation within the split vacancy ([V X + Xi + V X]) is highlighted in lighter blue as in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Electrostatic and DFT energy distributions of investigated vacancy structures. (a) Violin distribution plots of the relative electrostatic energies of candidate V X-Xi-V X complexes, with V X-Xi distances less than 5 ˚A and interstitial sites determined by Voronoi tess…
Figure 5
Figure 5. Figure 5: Low energy vacancy configurations in Sb2O5, before and after DFT relaxation. The relative energies according to DFT (PBEsol) and an electrostatic model (assuming formal ionic charges, inflating magnitudes) are shown alongside, with the simple point vacancy set to 0 eV …
Figure 6
Figure 6. Figure 6: Screening split cation vacancies in metal oxides. (a) Schematic diagram of the initial screening workflow employed to identify split cation vacancies in stable metal oxide compounds. 93 lower energy cation vacancies are identified, corresponding to ∼10 % of all possibl…
Figure 7
Figure 7. Figure 7: ML-accelerated screening of split vacancies. (a) ML-accelerated screening workflow employed to predict the formation of split cation vacancies in all compounds in the Materials Project 55 (MP) database. (b) Normalised prevalence of distinct low-energy split vacancies w…

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Works this paper leans on

104 extracted references · 77 canonical work pages

  1. [1]

    Freysoldt, B

    C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti and C. G. Van de Walle, First-principles calculations for point defects in solids, Reviews of Modern Physics, 2014, 86, 253–305

    2014

  2. [2]

    Mosquera-Lois, S

    I. Mosquera-Lois, S. R. Kavanagh, J. Klarbring, K. Tolborg and A. Walsh, Imperfections are not 0 K: free energy of point defects in crystals, Chemical Society Reviews, 2023, 52, 5812–5826

    2023

  3. [3]

    Oba and Y

    F. Oba and Y. Kumagai, Design and exploration of semiconductors from first principles: A review of recent advances, Applied Physics Express , 2018, 11, 060101

    2018

  4. [4]

    D. C. Asebiah, E. M. Mozur, A. A. Koegel, A. Nicolson, S. R. Kavanagh, D. O. Scanlon, O. G. Reid and J. R. Neilson, Defect-Limited Mobility and Defect Thermochemistry in Mixed A-Cation Tin Perovskites: (CH $ 3$NH$ 3$)$ {1–x}$Cs$ x$SnBr$ 3$, ACS Applied Energy Materials , 2024, 7, 7992–8003

    2024

  5. [5]

    M. E. Turiansky, A. Alkauskas, M. Engel, G. Kresse, D. Wickramaratne, J.-X. Shen, C. E. Dreyer and C. G. Van de Walle, Nonrad: Computing nonradiative capture coefficients from first principles, Computer Physics Communications, 2021, 267, 108056

    2021

  6. [6]

    S. R. Kavanagh, R. S. Nielsen, J. L. Hansen, R. S. Davidsen, O. Hansen, A. E. Samli, P. C. K. Vesborg, D. O. Scanlon and A. Walsh, Intrinsic point defect tolerance in selenium for indoor and tandem photovoltaics, Energy & Environmental Science , 2025, 18, 4431–4446

    2025

  7. [7]

    Zhang and S.-H

    X. Zhang and S.-H. Wei, Origin of Efficiency Enhancement by Lattice Expansion in Hybrid-Perovskite Solar Cells, Physical Review Letters, 2022, 128, 136401

    2022

  8. [8]

    Kumagai, S

    Y. Kumagai, S. R. Kavanagh, I. Suzuki, T. Omata, A. Walsh, D. O. Scanlon and H. Morito, Alkali Mono-Pnictides: A New Class of Photovoltaic Materials by Element Mutation, PRX Energy, 2023, 2, 043002

    2023

Show all 104 references
  1. [9]

    Mosquera-Lois and S

    I. Mosquera-Lois and S. R. Kavanagh, In search of hidden defects, Matter, 2021, 4, 2602–2605

    2021

  2. [10]

    Kononov, C.-W

    A. Kononov, C.-W. Lee, E. P. Shapera and A. Schleife, Identifying native point defect configurations in α-alumina, Journal of Physics: Condensed Matter , 2023, 35, 334002

    2023

  3. [11]

    Mosquera-Lois, S

    I. Mosquera-Lois, S. R. Kavanagh, A. Walsh and D. O. Scanlon, Identifying the ground state structures of point defects in solids, npj Computational Materials , 2023, 9, 1–11. REFERENCES 20

    2023

  4. [12]

    D. V. Lang and R. A. Logan, Large-Lattice-Relaxation Model for Persistent Photoconductivity in Compound Semiconductors, Physical Review Letters , 1977, 39, 635–639

    1977

  5. [13]

    D. J. Chadi and K. J. Chang, Energetics of DX-center formation in GaAs and {{\ensuremath{Al\ xGa\ {1-x}As}}} alloys, Physical Review B, 1989, 39, 10063–10074

    1989

  6. [14]

    Alkauskas, C

    A. Alkauskas, C. E. Dreyer, J. L. Lyons and C. G. Van de Walle, Role of excited states in Shockley-Read-Hall recombination in wide-band-gap semiconductors, Physical Review B, 2016, 93, 201304

    2016

  7. [15]

    S. R. Kavanagh, D. O. Scanlon, A. Walsh and C. Freysoldt, Impact of metastable defect structures on carrier recombination in solar cells, Faraday Discussions, 2022, 239, 339– 356

    2022

  8. [16]

    B. Dou, S. Falletta, J. Neugebauer, C. Freysoldt, X. Zhang and S.-H. Wei, Chemical Trend of Nonradiative Recombination in Cu ( In , Ga ) Se 2 Alloys, Physical Review Applied, 2023, 19, 054054

    2023

  9. [17]

    Huang, S

    M. Huang, S. Wang and S. Chen, Metastability and anharmonicity enhance defect- assisted nonradiative recombination in low-symmetry semiconductors , 2023, http:// arxiv.org/abs/2312.01733, arXiv:2312.01733 [cond-mat]

    2023 arXiv

  10. [18]

    A. G. Squires, L. Ganeshkumar, C. N. Savory, S. R. Kavanagh and D. O. Scanlon, Oxygen Dimerization as a Defect-Driven Process in Bulk LiNiO $ 2$, ACS Energy Letters, 2024, 9, 4180–4187

    2024

  11. [19]

    J. Cen, B. Zhu, S. R. Kavanagh, A. G. Squires and D. O. Scanlon, Cation disorder dominates the defect chemistry of high-voltage LiMn 1.5 Ni 0.5 O 4 (LMNO) spinel cathodes, Journal of Materials Chemistry A , 2023, 11, 13353–13370

    2023

  12. [20]

    A. B. Kehoe, D. O. Scanlon and G. W. Watson, Role of Lattice Distortions in the Oxygen Storage Capacity of Divalently Doped CeO2, Chemistry of Materials , 2011, 23, 4464–4468

    2011

  13. [21]

    X. Wang, S. R. Kavanagh, D. O. Scanlon and A. Walsh, Four-electron negative- $U$ vacancy defects in antimony selenide, Physical Review B , 2023, 108, 134102

    2023

  14. [22]

    Lany and A

    S. Lany and A. Zunger, Metal-Dimer Atomic Reconstruction Leading to Deep Donor States of the Anion Vacancy in II-VI and Chalcopyrite Semiconductors, Physical Review Letters, 2004, 93, 156404

    2004

  15. [23]

    Y. K. Frodason, C. Zimmermann, E. F. Verhoeven, P. M. Weiser, L. Vines and J. B. Varley, Multistability of isolated and hydrogenated Ga–O divacancies in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}} {2}{\mathrm{O}} {3}$, Physi- cal Review Materials , 2021, 5, 025402

    2021

  16. [24]

    Portoff, M

    A. Portoff, M. Stavola, W. B. Fowler, S. J. Pearton and E. R. Glaser, Hydrogen centers as a probe of VGa(2) defects in β-Ga2O3, Applied Physics Letters , 2023, 122, 062101

    2023

  17. [25]

    J. B. Varley, H. Peelaers, A. Janotti and C. G. Van De Walle, Hydrogenated cation vacancies in semiconducting oxides, Journal of Physics: Condensed Matter , 2011, 23, 334212

    2011

  18. [26]

    W. B. Fowler, M. Stavola, A. Venzie and A. Portoff, Metastable structures of cation vacancies in semiconducting oxides, Journal of Applied Physics , 2024, 135, 170901

    2024

  19. [27]

    Lei and G

    Y. Lei and G. Wang, Linking diffusion kinetics to defect electronic structure in metal oxides: Charge-dependent vacancy diffusion in alumina, Scripta Materialia , 2015, 101, 20–23

    2015

  20. [28]

    Mazzolini, J

    P. Mazzolini, J. B. Varley, A. Parisini, A. Sacchi, M. Pavesi, A. Bosio, M. Bosi, L. Seravalli, B. M. Janzen, M. N. Marggraf, N. Bernhardt, M. R. Wagner, A. Ardenghi, O. Bierwagen, A. Falkenstein, J. Kler, R. A. De Souza, M. Martin, F. Mezzadri, C. Borelli and R. Fornari, Engi...

    2024

  21. [29]

    Okumura and J

    H. Okumura and J. B. Varley, MOCVD growth of Si-doped α-(AlGa)2O3 on m-plane α-Al2O3 substrates, Japanese Journal of Applied Physics , 2024, 63, 075502

    2024

  22. [30]

    Y. K. Frodason, J. B. Varley, K. M. H. Johansen, L. Vines and C. G. Van de Walle, Migration of Ga vacancies and interstitials in$\ensuremath{\beta}\text{\ensuremath{- }}{\mathrm{Ga}} {2}{\mathrm{O}} {3}$, Physical Review B , 2023, 107, 024109

    2023

  23. [31]

    Karjalainen, V

    A. Karjalainen, V. Prozheeva, K. Simula, I. Makkonen, V. Callewaert, J. B. Var- ley and F. Tuomisto, Split Ga vacancies and the unusually strong anisotropy of positron annihilation spectra in $\ensuremath{\beta}\text{\ensuremath{- }}{\mathrm{Ga}} {2}{\mathrm{O}} {3}$, Physical...

    2020

  24. [32]

    Karjalainen, I

    A. Karjalainen, I. Makkonen, J. Etula, K. Goto, H. Murakami, Y. Kumagai and F. Tuomisto, Split Ga vacancies in n-type and semi-insulating β-Ga2O3 single crystals, Applied Physics Letters , 2021, 118, 072104

    2021

  25. [33]

    Skachkov, W

    D. Skachkov, W. R. L. Lambrecht, H. J. von Bardeleben, U. Gerstmann, Q. D. Ho and P. De´ ak, Computational identification of Ga-vacancy related electron paramagnetic resonance centers in β-Ga2O3, Journal of Applied Physics , 2019, 125, 185701

    2019

  26. [34]

    H. J. von Bardeleben, S. Zhou, U. Gerstmann, D. Skachkov, W. R. L. Lambrecht, Q. D. Ho and P. De´ ak, Proton irradiation induced defects inβ-Ga2O3: A combined EPR and theory study, APL Materials , 2019, 7, 022521

    2019

  27. [35]

    J. M. Johnson, Z. Chen, J. B. Varley, C. M. Jackson, E. Farzana, Z. Zhang, A. R. Arehart, H.-L. Huang, A. Genc, S. A. Ringel, C. G. Van de Walle, D. A. Muller and J. Hwang, Unusual Formation of Point-Defect Complexes in the Ultrawide-Band-Gap Semiconductor $\ensuremath{\beta}\...

    2019

  28. [36]

    Y. Qin, M. Stavola, W. B. Fowler, P. Weiser and S. J. Pearton, Editors’ Choice—Hydrogen Centers in β-Ga2O3: Infrared Spectroscopy and Density Functional Theory, ECS Journal of Solid State Science and Technology , 2019, 8, Q3103

    2019

  29. [37]

    Stavola, W

    M. Stavola, W. B. Fowler, A. Portoff, A. Venzie, E. R. Glaser and S. J. Pearton, Tutorial: Microscopic properties of O–H centers in β-Ga2O3 revealed by infrared spectroscopy and theory, Journal of Applied Physics , 2024, 135, 101101

    2024

  30. [38]

    Weiser, M

    P. Weiser, M. Stavola, W. B. Fowler, Y. Qin and S. Pearton, Structure and vibrational properties of the dominant O-H center in β-Ga2O3, Applied Physics Letters, 2018, 112, 232104

    2018

  31. [39]

    Mosquera-Lois, S

    I. Mosquera-Lois, S. R. Kavanagh, A. Walsh and D. O. Scanlon, ShakeNBreak: Navigating the defect configurational landscape, Journal of Open Source Software, 2022, 7, 4817

    2022

  32. [40]

    Huang, Z

    M. Huang, Z. Zheng, Z. Dai, X. Guo, S. Wang, L. Jiang, J. Wei and S. Chen, DASP: Defect and Dopant ab-initio Simulation Package, Journal of Semiconductors , 2022, 43, 042101

    2022

  33. [41]

    A. J. Morris, C. J. Pickard and R. J. Needs, Hydrogen/silicon complexes in silicon from computational searches, Physical Review B , 2008, 78, 184102

    2008

  34. [42]

    Arrigoni and G

    M. Arrigoni and G. K. H. Madsen, Evolutionary computing and machine learning for discovering of low-energy defect configurations, npj Computational Materials , 2021, 7, 1–13

    2021

  35. [43]

    Kumagai, N

    Y. Kumagai, N. Tsunoda, A. Takahashi and F. Oba, Insights into oxygen vacancies from high-throughput first-principles calculations, Physical Review Materials , 2021, 5, 123803

    2021

  36. [44]

    K. Li, J. Willis, S. R. Kavanagh and D. O. Scanlon, Computational Prediction of an Antimony-Based n-Type Transparent Conducting Oxide: F-Doped Sb2O5, Chemistry of Materials , 2024, 36, 2907–2916

    2024

  37. [45]

    S. R. Kavanagh, A. G. Squires, A. Nicolson, I. Mosquera-Lois, A. M. Ganose, B. Zhu, K. Brlec, A. Walsh and D. O. Scanlon, doped: Python toolkit for robust and repeatable charged defect supercell calculations, Journal of Open Source Software , 2024, 9, 6433. REFERENCES 22

    2024

  38. [46]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Physical Review B, 1993, 47, 558–561

    1993

  39. [47]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,Computational Materials Science, 1996, 6, 15–50

    1996

  40. [48]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Physical Review B - Condensed Matter and Materials Physics , 1996, 54, 11169–11186

    1996

  41. [49]

    Kresse and J

    G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid- metalamorphous- semiconductor transition in germanium, Physical Review B, 1994, 49, 14251–14269

    1994

  42. [50]

    Kresse and D

    G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented- wave method, Physical Review B , 1999, 59, 1758–1775

    1999

  43. [51]

    Gajdoˇ s, K

    M. Gajdoˇ s, K. Hummer, G. Kresse, J. Furthm¨ uller and F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Physical Review B, 2006, 73, 045112

    2006

  44. [52]

    P. E. Bl¨ ochl, Projector augmented-wave method, Physical Review B , 1994, 50, 17953– 17979

    1994

  45. [53]

    Adamo and V

    C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, The Journal of Chemical Physics , 1999, 110, 6158–6170

    1999

  46. [54]

    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, Physical Review Letters, 2008, 100, 136406

    2008

  47. [55]

    A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder and K. a. Persson, The Materials Project: A materials genome approach to accelerating materials innovation, APL Materials , 2013, 1, 011002

    2013

  48. [56]

    J. P. Perdew, K. Burke and M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters, 1996, 77, 3865–3868

    1996

  49. [57]

    S. P. Ong, W. D. Richards, A. Jain, G. Hautier, M. Kocher, S. Cholia, D. Gunter, V. L. Chevrier, K. A. Persson and G. Ceder, Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis, Computational Materials Science, 2013, 68, 314–319

    2013

  50. [58]

    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, S. M. Blau, V. C˘ arare, J. P. Darby, S. De, F. D. Pia, V. L. Deringer, R. Elijoˇ sius, Z. El-Machachi, F. Fal...

    2024 arXiv

  51. [59]

    Batzner, A

    S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt and B. Kozinsky, E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials, Nature Communications, 2022, 13, 2453

    2022

  52. [60]

    C. W. Tan, M. L. Descoteaux, M. Kotak, G. d. M. Nascimento, S. R. Kavanagh, L. Zichi, M. Wang, A. Saluja, Y. R. Hu, T. Smidt, A. Johansson, W. C. Witt, B. Kozinsky and A. Musaelian, High-performance training and inference for deep equivariant interatomic potentials, 2025, http...

    2025 arXiv

  53. [61]

    C. J. Krajewska, S. R. Kavanagh, L. Zhang, D. J. Kubicki, K. Dey, K. Ga lkowski, C. P. Grey, S. D. Stranks, A. Walsh, D. O. Scanlon and R. G. Palgrave, Enhanced visible light absorption in layered Cs 3Bi2Br9 through mixed-valence Sn((II)/Sn(IV) doping, Chemical Science, 2021, ...

    2021

  54. [62]

    Mosquera-Lois, S

    I. Mosquera-Lois, S. R. Kavanagh, A. M. Ganose and A. Walsh, Machine-learning structural reconstructions for accelerated point defect calculations, npj Computational Materials, 2024, 10, 1–9

    2024

  55. [63]

    Lany and A

    S. Lany and A. Zunger, Anion vacancies as a source of persistent photoconductivity in II-VI and chalcopyrite semiconductors, Physical Review B , 2005, 72, 035215

    2005

  56. [64]

    W. D. Neilson, J. Rizk, M. W. D. Cooper and D. A. Andersson, Oxygen Potential, Uranium Diffusion, and Defect Chemistry in UO2 ±x: A Density Functional Theory Study, The Journal of Physical Chemistry C , 2024, 128, 21559–21571

    2024

  57. [65]

    M. M. Santillan, I. Chatratin, A. Janotti and M. D. McCluskey, Room-temperature persistent photoconductivity of KTa O 3, Physical Review Materials , 2024, 8, L111601

    2024

  58. [66]

    Nicolson, S

    A. Nicolson, S. R. Kavanagh, C. N. Savory, G. W. Watson and D. O. Scanlon, Cu2SiSe3 as a promising solar absorber: harnessing cation dissimilarity to avoid killer antisites, Journal of Materials Chemistry A , 2023, 11, 14833–14839

    2023

  59. [67]

    X. Wang, S. R. Kavanagh, D. O. Scanlon and A. Walsh, Upper efficiency limit of Sb 2 Se 3 solar cells, Joule, 2024, 8, 2105–2122

    2024

  60. [68]

    A. Y. Toukmaji and J. A. Board, Ewald summation techniques in perspective: a survey, Computer Physics Communications , 1996, 95, 73–92

    1996

  61. [69]

    Zhang, H

    A. Zhang, H. Li, H. Xu, B. Dou, G. Zhang and W. Wang, Optimizing the n-type carrier concentration of an ${\mathrm{InVO}} {4}$ photocatalyst by codoping with donors and intrinsic defects, Physical Review Applied, 2024, 22, 044047

    2024

  62. [70]

    Yuan and G

    Z. Yuan and G. Hautier, First-principles study of defects and doping limits in CaO, Applied Physics Letters , 2024, 124, 232101

    2024

  63. [71]

    B. E. Murdock, J. Cen, A. G. Squires, S. R. Kavanagh, D. O. Scanlon, L. Zhang and N. Tapia-Ruiz, Li-Site Defects Induce Formation of Li-Rich Impurity Phases: Implications for Charge Distribution and Performance of LiNi0.5−MMn1.5O4 Cathodes (M = Fe and Mg; x = 0.05–0.2), Advanc...

    2024

  64. [72]

    Hoang and M

    K. Hoang and M. D. Johannes, Defect chemistry in layered transition-metal oxides from screened hybrid density functional calculations, Journal of Materials Chemistry A , 2014, 2, 5224–5235

    2014

  65. [73]

    S. R. Kavanagh, A. Walsh and D. O. Scanlon, Rapid Recombination by Cadmium Vacancies in CdTe, ACS Energy Letters, 2021, 6, 1392–1398

    2021

  66. [74]

    Z. Tan, J. Zhang, Y.-C. Chen, J.-P. Chou and Y.-K. Peng, Unravelling the Role of Structural Geometry and Chemical State of Well-Defined Oxygen Vacancies on Pristine CeO2 for H2O2 Activation, The Journal of Physical Chemistry Letters , 2020, 11, 5390– 5396

    2020

  67. [75]

    Zhang, L

    X. Zhang, L. Zhu, Q. Hou, J. Guan, Y. Lu, T. W. Keal, J. Buckeridge, C. R. A. Catlow and A. A. Sokol, Toward a Consistent Prediction of Defect Chemistry in CeO2, Chemistry of Materials , 2023, 35, 207–227

    2023

  68. [76]

    Grasser, B

    T. Grasser, B. Kaczer, W. Goes, T. Aichinger, P. Hehenberger and M. Nelhiebel, 2009 IEEE International Reliability Physics Symposium, 2009, pp. 33–44

    2009

  69. [77]

    C. Lee, M. A. Scarpulla and E. Ertekin, Investigation of Ga intersti- tial and vacancy diffusion in $\ensuremath{\beta}\text{\ensuremath{- }}{\mathrm{Ga}} {2}{\mathrm{O}} {3}$ via split defects: A direct approach via master diffusion equations, Physical Review Materials , 2024...

    2024

  70. [78]

    Kuganathan, P

    N. Kuganathan, P. Iyngaran, R. Vovk and A. Chroneos, Defects, dopants and Mg diffusion in MgTiO3, Scientific Reports, 2019, 9, 4394. REFERENCES 24

    2019

  71. [79]

    H. S. Magar, A. M. Mansour and A. B. A. Hammad, Advancing energy storage and supercapacitor applications through the development of Li+-doped MgTiO3 perovskite nano-ceramics, Scientific Reports, 2024, 14, 1849

    2024

  72. [80]

    B. G. Mullens, F. P. Marlton, M. Saura-M´ uzquiz, P. A. Chater and B. J. Kennedy, Tetrahedra Rotational and Displacive Disorder in the Scheelite-Type Oxide CsReO4, Inorganic Chemistry, 2024, 63, 10386–10396

    2024

  73. [81]

    Sathasivam, B

    S. Sathasivam, B. A. D. Williamson, A. Kafizas, S. A. Althabaiti, A. Y. Obaid, S. N. Basahel, D. O. Scanlon, C. J. Carmalt and I. P. Parkin, Computational and Experimental Study of Ta2O5 Thin Films, The Journal of Physical Chemistry C , 2017, 121, 202–210

    2017

  74. [82]

    Han and T

    C. Han and T. Wang, Understanding the catalytic performances of metal-doped Ta2O5 catalysts for acidic oxygen evolution reaction with computations, Chemical Science , 2024, 15, 14371–14378

    2024

  75. [83]

    Y. Zhao, C. Deng, D. Tang, L. Ding, Y. Zhang, H. Sheng, H. Ji, W. Song, W. Ma, C. Chen and J. Zhao, α-Fe2O3 as a versatile and efficient oxygen atom transfer catalyst in combination with H2O as the oxygen source, Nature Catalysis, 2021, 4, 684–691

    2021

  76. [84]

    Banerjee, E

    A. Banerjee, E. F. Holby, A. A. Kohnert, S. Srivastava, M. Asta and B. P. Uberuaga, Thermokinetics of point defects in α-Fe2O3, Electronic Structure, 2023, 5, 024007

    2023

  77. [85]

    B. D. Boruah, B. Wen and M. De Volder, Light Rechargeable Lithium-Ion Batteries Using V2O5 Cathodes, Nano Letters, 2021, 21, 3527–3532

    2021

  78. [86]

    Sucharitakul, G

    S. Sucharitakul, G. Ye, W. R. L. Lambrecht, C. Bhandari, A. Gross, R. He, H. Poelman and X. P. A. Gao, V2O5: A 2D van der Waals Oxide with Strong In-Plane Electrical and Optical Anisotropy, ACS Applied Materials & Interfaces , 2017, 9, 23949–23956

    2017

  79. [87]

    Vinckeviˇ ci¯ ut˙ e, M

    J. Vinckeviˇ ci¯ ut˙ e, M. D. Radin, N. V. Faenza, G. G. Amatucci and A. V. d. Ven, Fundamental insights about interlayer cation migration in Li-ion electrodes at high states of charge, Journal of Materials Chemistry A , 2019, 7, 11996–12007

    2019

  80. [88]

    A. R. Genreith-Schriever, C. S. Coates, K. M¨ arker, I. D. Seymour, E. N. Bassey and C. P. Grey, Probing Jahn–Teller Distortions and Antisite Defects in LiNiO2 with 7Li NMR Spectroscopy and Density Functional Theory, Chemistry of Materials , 2024, 36, 4226–4239

    2024

  81. [89]

    Riebesell, R

    J. Riebesell, R. E. A. Goodall, P. Benner, Y. Chiang, B. Deng, G. Ceder, M. Asta, A. A. Lee, A. Jain and K. A. Persson, Matbench Discovery – A framework to evaluate machine learning crystal stability predictions , 2024, http://arxiv.org/abs/2308. 14920, arXiv:2308.14920 [cond-mat]

    2024 arXiv

  82. [90]

    B. Deng, P. Zhong, K. Jun, J. Riebesell, K. Han, C. J. Bartel and G. Ceder, CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling, Nature Machine Intelligence , 2023, 5, 1031–1041

    2023

  83. [91]

    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, Advances in Neural Information Processing Systems , 2022, 35, 11423–11436

    2022

  84. [92]

    Andrew-S-Rosen/periodic trends: Python script to plot periodic trends as a heat map over the periodic table of elements , https://github.com/Andrew-S-Rosen/periodic_ trends

  85. [93]

    A. H. Larsen, J. J. 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. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, ...

    2017

  86. [94]

    Batatia, S

    I. Batatia, S. Batzner, D. P. Kov´ acs, A. Musaelian, G. N. C. Simm, R. Drautz, C. Ortner, B. Kozinsky and G. Cs´ anyi, The design space of E(3)-equivariant atom- centred interatomic potentials, Nature Machine Intelligence , 2025, 7, 56–67. REFERENCES 25

    2025

  87. [95]

    X. Wang, S. R. Kavanagh and A. Walsh, Sulfur Vacancies Limit the Open-Circuit Voltage of Sb2S3 Solar Cells, ACS Energy Letters, 2025, 10, 161–167

    2025

  88. [96]

    Krasikov and I

    D. Krasikov and I. Sankin, Defect interactions and the role of complexes in the CdTe solar cell absorber, Journal of Materials Chemistry A , 2017, 5, 3503–3513

    2017

  89. [97]

    Razinkovas, M

    L. Razinkovas, M. Maciaszek, F. Reinhard, M. W. Doherty and A. Alkauskas, Photoionization of negatively charged NV centers in diamond: Theory and ab initio calculations, Physical Review B , 2021, 104, 235301

    2021

  90. [98]

    Xiong, J

    Y. Xiong, J. Zheng, S. McBride, X. Zhang, S. M. Griffin and G. Hautier, Computationally Driven Discovery of T Center-like Quantum Defects in Silicon, Journal of the American Chemical Society , 2024, 146, 30046–30056

    2024

  91. [99]

    Davidsson, W

    J. Davidsson, W. Stenlund, A. S. Parackal, R. Armiento and I. A. Abrikosov, Na in diamond: high spin defects revealed by the ADAQ high-throughput computational database, npj Computational Materials , 2024, 10, 1–9

    2024

  92. [100]

    O’Keefe and N

    M. O’Keefe and N. E. Brese, Atom sizes and bond lengths in molecules and crystals, Journal of the American Chemical Society , 1991, 113, 3226–3229

    1991

  93. [101]

    Freysoldt, J

    C. Freysoldt, J. Neugebauer and C. G. Van de Walle, Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations, Physical Review Letters , 2009, 102, 016402

    2009

  94. [102]

    Kumagai and F

    Y. Kumagai and F. Oba, Electrostatics-based finite-size corrections for first-principles point defect calculations, Physical Review B , 2014, 89, 195205

    2014

  95. [103]

    K. A. Arnab, M. Stephens, I. Maxfield, C. Lee, E. Ertekin, Y. K. Frodason, J. B. Varley and M. A. Scarpulla, Quantitative Modeling of Point Defects in $β$-Ga2O3 Combining Hybrid Functional Energetics with Semiconductor and Processes Thermodynamics, 2025, http://arxiv.org/abs/2...

    2025 arXiv

  96. [104]

    Pedregosa, G

    F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot and E. Duchesnay, Scikit-learn: Machine Learning in Python, Journal of Machine Learning ...

    2011

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