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/ϵ_M] that is dominant in wide-gap materials and the Thomas-Fermi metallic screening [exp(-ζ r) ] 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.