An Accurate Alternative to Hybrid Functionals for Germanium: DFT+α

High Resolution Image Download MS PowerPoint Slide The accuracy of bulk-property predictions in density functional theory (DFT) calculations depends on the choice of the exchange-correlation functional. While the Perdew–Burke–Ernzerhof (PBE) functional systematically overestimates lattice parameters and strongly underestimates electronic band gaps, hybrid functionals such as Heyd–Scuseria–Ernzerhof (HSE) offer better overall agreement across a broad range of materials. Using germanium as a critical test case, we challenge the ability of both functionals to capture the semiconductor properties. Although HSE improves PBE’s gap error, it fails to reproduce germanium’s correct Γ–L indirect and Γ–Γ band gaps simultaneously. Noting that the PBE-underestimated energy separation between the 4p valence-band maximum and 4s conduction-band minimum causes unphysical sp mixing, we propose DFT+α, a semiempirical correction scheme applied selectively to 4s-like orbitals. For germanium, DFT+α restores the proper ordering and orbital character of the band edges and yields accurate lattice constants, bulk modulus, elastic constants, and phonon frequencies at a fraction of hybrid-functional computational cost.