DFT-PBE band gap correction using machine learning with a reduced set of features

In the density functional theory (DFT), it is well-known that the generalized gradient approximation (GGA) underestimates the energy gap. One of the commonly used GGA functionals is the Perdew–Burke–Ernzerhof (PBE) functional. This paper presents a machine learning approach to correct the energy gap estimated by PBE, using a minimal set of five features, to the accuracy level of the many-body perturbation theory G₀W₀ band gap, which is known for its precision but high computational cost. These features are identified by seeking those which can be obtained directly from PBE-DFT calculations or from the standard atomic tables and directly connected to Coulombic interaction, and by minimizing feature correlations. The utilized features are the PBE band gap and the average atomic distance (obtained directly from PBE-DFT calculations) and the average oxidation states, electronegativity, and the minimum difference of electronegativity between constituents (obtained from the standard atomic tables). These features do not require any further atomistic calculations. The developed models are trained and validated using 265 inorganic semiconductors and insulators with energy gaps ranging from 0.75 to 14.55 eV. Several regression techniques have been applied, all of which have produced highly accurate and comparable results. This suggests that the five features employed in the analysis effectively capture the underlying physics. The most accurate model is based on Gaussian process regression (GPR), achieving a validation accuracy of 0.252 eV root-mean-square error (RMSE) and an R² value of 0.9932. The best bootstrapped model achieves an RMSE of 0.232 eV. The developed GPR model is then applied successfully to completely independent data sets. The developed model should allow calculating gaps with G₀W₀ accuracy using the relatively much faster DFT-PBE. This is especially useful in materials discovery where computational efficiency is crucial. Furthermore, the model should allow empirical investigation of the influences of different compositional and structural characteristics on the gap.