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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 Up values for oxygen 2p orbitals alongside Ud/f for metal 3d or 4f orbitals significantly enhances the accuracy of these predictions. Through extensive DFT+U calculations, we identify optimal (Up, Ud/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 Up strongly depend on the choice of correlated orbitals, and caution is recommended with a different choice of correlated orbitals. 

Density functional theory (DFT) calculations are performed to compute the lattice constants, formation energies and vacancy formation energies of transition metal nitrides (TMNs) for transition metals (TM) ranging from 3d–5d series. The results obtained using six different DFT exchange and correlation potentials (LDA, AM05, BLYP, PBE, rPBE, and PBEsol) show that the experimental lattice constants are best predicted by rPBE, while the values obtained using AM05, PBE, rPBE and PBEsol lie between the LDA and BLYP calculated values. A linear relationship is observed between the lattice constants and formation energies with the mean radii of TM and the difference in the electronegativity of TM and N in TMNs, respectively. Our calculated vacancy formation energies, in general, show that N-vacancies are more favorable than TM-vacancies in most TMNs. We observe that N-vacancy formation energies are linearly correlated with the calculated bulk formation energies indicating that TMNs with large negative formation energies are less susceptible to the formation of N-vacancies. Thus, our results from this extensive DFT study not only provide a systematic comparison of various DFT functionals in calculating the properties of TMNs but also serve as reference data for the computation-driven experimental design of materials. 

Pt and Pd monolayer on transition metal nitrides as efficient and low-cost catalysts for hydrogen evolution reaction.