Integrating density functional theory with machine learning for enhanced band gap prediction in metal oxides

Abstract

In this study, we used a combination of density functional theory with Hubbard U correction (DFT+U) and machine learning (ML) to accurately predict the band gaps and lattice parameters of metal oxides: TiO₂ (rutile and anatase), cubic ZnO, cubic ZnO₂, cubic CeO₂, and cubic ZrO₂. Our results show that including U_p values for oxygen 2p orbitals alongside U_d/f for metal 3d or 4f orbitals significantly enhances the accuracy of these predictions. Through extensive DFT+U calculations, we identify optimal (U_p, U_d/f) integer pairs that closely reproduce experimentally measured band gaps and lattice parameters for each oxide: (8 eV, 8 eV) for rutile TiO₂; (3 eV, 6 eV) for anatase TiO₂; (6 eV, 12 eV) for c-ZnO; (10 eV, 10 eV) for c-ZnO₂; (9 eV, 5 eV) for c-ZrO₂; and (7 eV, 12 eV) for c-CeO₂. Our ML analysis showed that simple supervised ML models can closely reproduce these DFT+U results at a fraction of the computational cost and generalize well to related polymorphs. Our approach builds on existing high-throughput DFT+U frameworks by providing fast pre-DFT estimates of structural properties and band gaps. Since this work does not aim to improve the underlying DFT+U method, the ML model shares its limitations. We also note that the reported values of U_p strongly depend on the choice of correlated orbitals, and caution is recommended with a different choice of correlated orbitals.