Band gap predictions of double perovskite oxides using machine learning

The study addresses the challenge of accurately and efficiently predicting band gaps in oxide perovskites across a vast chemical space. Band gap is central to applications in electronics, optoelectronics, and energy technologies, yet standard DFT with local or semi-local functionals systematically underestimates band gaps and high-fidelity methods are too costly for large-scale screening. The authors propose a hierarchical machine learning framework that first classifies materials as wide-gap (Eg ≥ 0.5 eV) versus narrow/metallic, then performs regression to predict Eg for the wide-gap class, enabling rapid down-selection of promising double perovskite oxide candidates that are also predicted to be formable and thermodynamically stable. The purpose is to efficiently explore millions of compositions, derive physical insight via feature importance and partial dependence, and deliver a prioritized list of novel, stable, wide-gap double perovskites for further investigation.

Prior works have used a variety of ML methods (SVR, ANN, OLSR, LASSO) to predict band gaps in inorganic and organic materials, often with elemental descriptors. Early efforts (Gu et al.) used small experimental datasets; later studies expanded to computational datasets and explored ensemble learning and multi-fidelity approaches (e.g., Pilania et al. with co-Kriging and general band gap frameworks; GNN-based multi-fidelity models by Na et al. and Li et al.; graph learning for diverse perovskites by Omprakash et al.). Some studies prioritized interpretability (ACE) or combined disparate datasets (ensemble learning). In perovskites, many efforts focused on single perovskites or limited double perovskite sets, constraining generalizability. Use of features like formation energy can improve accuracy but is costly for large-scale predictions. The present work extends prior efforts by covering a much larger and chemically diverse oxide perovskite space, linking formability, stability, insulator classification, and quantitative band-gap prediction, and delivering concrete, novel candidate lists.

• Chemical space and datasets: Considered 68 elements for A- and B-sites and oxygen as anion, enumerating all charge-balanced ABO3, A2BB′O6, AA′B2O6, and AA′BB′O6 perovskites. After accounting for duplicates and valence combinations, 946,292 unique compositions were generated. The training set Dp comprises 5,152 cubic oxide perovskites whose structures were DFT-relaxed (cubic constraint) and band gaps computed. Of these, 1,575 with Eg ≥ 0.5 eV formed the regression training set DBG.
• Candidate sets: Removing the 5,152 training entries yields Dc = 941,140 chemically compatible candidates. Previously developed ML models (Talapatra et al., 2021) for formability and thermodynamic stability were applied to obtain DFS = 462,248 predicted formable and stable cubic candidates (probability cutoff 0.5).
• Labels: Using Eg threshold 0.5 eV, training compounds were labeled as wide-gap (insulator) or narrow-gap (metal/very small gap).
• Descriptors: Started from 68 elemental/structural features; after screening (Pearson correlation) and Recursive Feature Elimination (RFE), retained 28 descriptors: 24 atom-specific compound descriptors (for A and B sites, symmetric and anti-symmetric combinations of elemental HOMO, LUMO, ionization energy, electronegativity, Zunger pseudopotential radius, electron affinity) plus 4 perovskite geometric descriptors (Goldschmidt tolerance factor t, octahedral factor u, and mismatch factors μA, μB based on Shannon ionic radii). For classification, all 28 were important; for regression, 21 atom-specific plus all 4 geometric were used.
• ML models: Random Forest (Scikit-learn). Classification model Mc trained on Dp to separate wide vs narrow (five-fold CV; typical 90/10 train/test). Regression model MR trained on DBG to predict Eg for wide-gap materials (five-fold CV; typical 90/10). Hyperparameters: Mc: n_estimators=200, max_depth=25; MR: n_estimators=200, max_depth=50. Stratified splits for classification.
• DFT details: VASP with PBE-GGA; spin-polarized; plane-wave cutoff 533 eV; Monkhorst-Pack k-point grid with ≥5000 k-points per reciprocal atom; Methfessel-Paxton smearing (order 1); structural relaxations to 1e-6 eV energy change and <0.01 eV/Å forces; final static calculations for band gaps. Atomic HOMO/LUMO levels computed for isolated atoms (non-spin-polarized) in large vacuum cells.
• Uncertainty quantification: Confidence intervals for MR via bias-corrected infinitesimal jackknife / jackknife-after-bootstrap approaches; also examined prediction confidence trends.
• Workflow application: Sequentially applied Mc to DFS to identify wide-gap candidates (probability ≥0.5), yielding DW = 13,589. Applied MR to predict Eg for DW, then down-selected high-confidence candidates with ≥0.9 probability for formability, stability, and wide-gap classification, yielding DS = 310. Performed validating DFT PBE calculations for the 310 to confirm predictions. Generated design maps and partial dependence plots for feature interpretation.

• Classification performance: Five-fold CV with 90/10 split achieved training accuracy ≈0.94 and test accuracy ≈0.95; training precision ≈0.95 and test precision ≈0.93. ROC AUC ≈0.98; precision-recall AUC ≈0.96 at threshold 0.5. Most important features: B-site symmetric HOMO, electronegativity, ionization energy; followed by A-site electronegativity and LUMO.
• Regression performance: With 90/10 split over 100 runs, training R^2 ≈0.97 and MAE ≈0.07 eV; test R^2 ≈0.86 and MAE ≈0.18 eV. Learning curves indicate low bias and moderate variance. Feature importance favors B-site descriptors (electronegativity, HOMO/LUMO, Zunger radius) and octahedral factor; geometric t, u have low importance overall.
• Screening outcomes: From 462,248 formable/stable candidates (DFS), 13,589 (≈2.94%) predicted wide-gap (Eg ≥0.5 eV) by Mc at ≥0.5 probability. High-confidence intersection (≥0.9 for formability, stability, wide-gap) yields 310 candidates.
• Validation: DFT PBE calculations confirm all 310 are wide-gap (Eg > 0.5 eV). Predicted vs calculated for the 310: MAE 0.21 eV, MSE 0.07 eV, R^2 0.84, maximum absolute error 0.48 eV.
• Design insights: Design maps (e.g., Ba2BB′O6) show that B-site choices like Ta, Sb, In, La generally increase Eg, with Ta–In combinations reaching up to ~3.9 eV predicted; Bi on B-site tends to lower Eg. Partial dependence analyses identify ranges of A-/B-site electronegativities associated with larger gaps.

The hierarchical ML strategy effectively addresses large-scale band-gap screening by first excluding metallic or very small-gap perovskites, thereby preventing bias in the regression model and enabling accurate Eg predictions within the insulating domain. The strong test metrics for both classification (AUC ~0.98) and regression (MAE ~0.18 eV on held-out data) validate the approach across a chemically diverse space spanning 68 elements. The sequential application to a vast candidate pool yielded 13,589 predicted wide-gap materials, and stringent high-confidence filtering produced 310 novel, predicted formable and stable double perovskites with Eg > 0.5 eV, all validated by DFT. Feature importance and partial dependence analyses illuminate chemistry–property relationships, particularly the dominant role of B-site descriptors, consistent with the oxygen p–transition metal d character of VBM/CBM in oxides. The resulting design maps and trends provide practical guidance for band-gap and band-edge engineering. Despite absolute underestimation by PBE, relative trends are reliably captured, and additional HSE checks (for a subset) confirm systematic PBE underestimation, supporting the use of PBE-trained models for trend-driven discovery.

The work introduces a unique, large-scale hierarchical ML framework that unifies predictions of perovskite formability, thermodynamic stability, insulating nature, and quantitative band gap across a vast oxide double perovskite chemical space. Using low-cost descriptors and robust Random Forest models trained on 5,152 DFT-labeled perovskites (with 1,575 insulators for regression), the study identified 13,589 wide-gap candidates among 462,248 formable/stable compositions and down-selected 310 high-confidence, novel, wide-gap double perovskites. All 310 were validated by DFT to be insulating, with close agreement between predicted and calculated gaps (MAE ~0.21 eV). The approach produces interpretable insights (feature importances, PDPs) and practical design maps, and is readily generalizable to other materials classes. Future work could incorporate higher-fidelity targets (e.g., hybrid-DFT, GW) via multi-fidelity learning, extend to lower-symmetry phases, integrate uncertainty-aware active learning to target underexplored regions of feature space, and drive experimental synthesis and characterization of the proposed candidates.

• Structural constraint: Training and screening are restricted to cubic perovskite symmetry to maintain computational feasibility. Some compounds that are insulating in lower-symmetry phases may be missed if their cubic-phase gaps fall below 0.5 eV.
• DFT fidelity: PBE-GGA underestimates absolute band gaps; while trends are reliable, quantitative gaps may require hybrid/GW or experiment for final validation.
• Descriptor scope: To keep inputs low-cost, the models exclude higher-cost features (e.g., formation energies, charge densities), which could marginally improve accuracy but reduce scalability.
• Data coverage: The vast chemical space inevitably has sparsely sampled regions; PDP-derived optimal feature ranges may be underrepresented in the training data, limiting extrapolative confidence.
• Threshold choice: The 0.5 eV wide/narrow cutoff is illustrative; application-specific thresholds may shift candidate sets and performance metrics.