An Empirical, yet Practical Way To Predict the Band Gap in Solids by Using Density Functional Band Structure Calculations

Band structure calculations based on density functional theory (DFT) with local or gradient-corrected exchange-correlation potentials are known to severely underestimate the band gap of semiconducting and insulating materials. Alternative approaches have been proposed: from semiempirical setups, such as the so-called DFT+U, to hybrid density functionals using a fraction of nonlocal Fock exchange, to modifications of semilocal density functionals. However, the resulting methods appear to be material dependent and lack theoretical rigor. The rigorous many-body perturbation theory based on GW methods provides accurate results but at a very high computational cost. Hereby, we show that a linear correlation between the electronic band gaps obtained from standard DFT and GW approaches exists for most materials and argue that (1) this is a strong indication that the problem of predicting band gaps from standard DFT calculation arises from the assignment of a physical meaning to the Kohn–Sham energy levels rather than from intrinsic errors of the DFT methods and (2) it provides a practical way to obtain GW-like quality results from standard DFT calculations. The latter will be especially useful for systems where the unit cell involves a large number of atoms as in the case of doped or defect-containing materials for which GW calculations become unfeasible.