Effectively improving the accuracy of PBE functional in calculating the solid band gap via machine learning

Band gap is one of the most important parameters determining the electronic, optoelectronic, and other applications of a wide range of materials including semiconductors and insulators. However, the accurate prediction of the band gap of these materials has been a persistent difficulty in quantum chemistry. Numerous studies have attempted to improve the accuracy of the predicted band gap from standard density functional theory (DFT) calculations with local density approximation (LDA) and generalized gradient approximation (GGA), which are well-known to underestimate the band gap severely. With the rapid development of material databases from both experimental and theoretical studies, herein, we develop a correction model to improve the prediction accuracy for the band gap by combing the widely used Perdew-Burke-Ernzerh (PBE-GGA) functional with machine learning approach. The correction model introduces physically meaningful but computationally efficient descriptors to fit the experimental dataset, and an artificial neural network (ANN) model is established to improve the prediction accuracy of computational results from DFT-PBE functional. The new method brings a highly accurate model for the prediction of the band gaps at high-precision G₀W₀ level without increasing computational cost at DFT-PBE level. Further, the error distribution of the predicted band gaps is more in line with the normal distribution compared with DFT-PBE and G₀W₀ methods. The band gap correction model provides a practical way to obtain GW-like quality results from standard DFT calculations, and should be valuable to perform accurate high-throughput screening of semiconductors and insulators for which GW calculations become unfeasible.