Doubly Screened Hybrid Functional: An Accurate First-Principles Approach for Both Narrow- and Wide-Gap Semiconductors

First-principles prediction of electronic band structures of materials is crucial for rational material design, especially in solar-energy-related materials science. Hybrid functionals that mix the Hartree–Fock exact exchange with local or semilocal density functional approximations have proven to be accurate and efficient alternatives to more sophisticated Green’s function-based many-body perturbation theory. The optimal fraction of the exact exchange, previously often treated as an empirical parameter, is closely related to the screening strength of the system under study. From a physical point of view, the screening has two extreme forms: the dielectric screening [1/ϵM] that is dominant in wide-gap materials and the Thomas–Fermi metallic screening [exp(−ζr) ] that is important in narrow-gap semiconductors. In this work, we have systematically investigated the performances of a nonempirical doubly screened hybrid (DSH) functional that considers both screening mechanisms and found that it excels all other existing hybrid functionals and describes the band gaps of narrow-, medium-, and wide-gap insulating systems with comparably good performances.