Dynamic exchange-correlation functional for bandgap optimization

This study explores tuning the parameters in the SCAN exchange-correlation (XC) functional to accurately predict the electron bandgap ($E_g$) of various solids, resulting in the development of a dynamic XC functional (d-SCAN) optimized for bandgap predictions. Key findings reveal that $E_g$ can be improved for most materials, often achieving experimental values. However, some materials cannot attain the experimental bandgap with the current SCAN form. The study underscores the crucial roles of SCAN parameters $\kappa$ and $c_{1x}$ in balancing $E_g$ and lattice parameters. The d-SCAN functional shifts the conduction band upward in band structures and also expands charge density in covalent materials for a more accurate electronic distribution. Additionally, it improves the prediction of optical properties, such as the optical dielectric constant and dielectric function. Machine learning (ML) algorithms are employed to predict the SCAN parameters based on solid-state properties (ML-SCAN), surpassing traditional methods in accuracy and variability. This emphasizes the relationship between XC functional parameters and the physical properties of solids. This work represents the first step toward developing a new dynamic ML-driven XC functional specifically designed for semiconductors and insulators.