Dielectric-dependent hybrid functional based on meta-GGA

Semilocal density functionals such as the Perdew-Burke-Ernzerhof (PBE) functional substantially underestimate experimental band gaps. Hybrid functionals address this band gap problem by admixing a fraction of Fock exchange to semilocal exchange. The optimal mixing parameter depends on the specific material and can be identified as the inverse dielectric constant (dielectric-dependent hybrid functional, DDH). Here, we show that dielectric constants obtained using the r²SCAN meta-GGA functional are significantly more accurate than dielectric constants obtained using the semilocal PBE functional. We propose the DD-r²SCANH functional, a dielectric-dependent hybrid functional based on r²SCAN. DD-r²SCANH can outperform the standard PBE-based DDH in terms of band gaps and other electronic structure properties. Particularly marked improvements are obtained for narrow-gap semiconductors such as Ge and InAs, where PBE wrongly predicts a metallic phase, but r²SCAN opens a band gap.