Predicting band gaps and band-edge positions of oxide perovskites using density functional theory and machine learning

Density functional theory (DFT) within the local or semilocal density approximations, i.e., the local density approximation (LDA) or generalized gradient approximation (GGA), has become a workhorse in the electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. The accurate prediction of band gaps using first-principles methods is time consuming, requiring hybrid functionals, quasiparticle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in this correction is desirable for discovering novel materials in high-throughput calculations. In this direction, we use DFT and machine learning techniques to correct band gaps and band-edge positions of a representative subset of $AB{\mathrm{O}}_{3}$ perovskite oxides. Relying on the results of HSE06 hybrid functional calculations as target values of band gaps, we find a systematic band-gap correction of $\ensuremath{\sim}1.5$ eV for this class of materials, where $\ensuremath{\sim}1$ eV comes from downward shifting the valence band and $\ensuremath{\sim}0.5$ eV from uplifting the conduction band. The main chemical and structural factors determining the band-gap correction are determined through a feature selection procedure.