High-Throughput hybrid-functional DFT calculations of bandgaps and formation energies and multifidelity learning with uncertainty quantification

Despite the fact that first-principles methods are critical tools in the study and design of materials today, the accuracy of density functional theory (DFT) prediction is fundamentally reliant on the exchange-correlation functional chosen to approximate the interactions between electrons. Although the general improvement in accurately calculating the bandgap with the Heyd-Scuseria-Ernzerhof (HSE) hybrid-functional method over the conventional semilocal DFT is well accepted, other properties such as formation energy have not been systematically studied and have yet to be evaluated thoroughly for different classes of materials. A high-Throughput hybrid-functional DFT investigation on materials bandgaps and formation energies is therefore performed in this work. By evaluating over a thousand materials, including metals, semiconductors, and insulators, we have quantitatively verified that the materials bandgaps obtained through HSE [mean absolute error (MAE) = 0.687 eV] are more accurate than those from the Perdew-Burke-Ernzerhof (PBE) functional (MAE = 1.184 eV) when compared to the experimental values. For formation energies, PBE systematically underestimates the magnitude of the formation enthalpies (MAE = 0.175 eV/atom), whereas formation enthalpies obtained from the HSE method are generally more accurate (MAE = 0.147 eV/atom). We have also found that HSE significantly increases the accuracy of formation energy prediction for insulators and strongly bound compounds. A primary application of this new dataset is achieved by building a cokriging multifidelity machine learning (ML) model to quickly predict the bandgaps with HSE-level accuracy when its PBE bandgap is available from DFT calculations. The preliminary goal of our ML model, benchmarked in this work, is to select the semiconductors and insulators which may have been mislabeled as metals from the DFT-PBE calculations in the existing Open Quantum Materials Database. The performance of the cokriging model in reliably predicting HSE bandgaps with quantified model uncertainty is analyzed by comparing the results against published experimental data from the literature.