An accurate alternative to hybrid functionals for germanium: DFT+$α$
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| Format: | Preprint |
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2025
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| author | Abdurrazaq, Abdulgaffar Lot, Ruggero Jay, Antoine Herrero-Saboya, Gabriela Richard, Nicolas Martin-Samos, Layla Hémeryck, Anne de Gironcoli, Stefano |
| author_facet | Abdurrazaq, Abdulgaffar Lot, Ruggero Jay, Antoine Herrero-Saboya, Gabriela Richard, Nicolas Martin-Samos, Layla Hémeryck, Anne de Gironcoli, Stefano |
| contents | The accuracy of bulk property predictions in density functional theory (DFT) calculations depends on the choice of 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 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 semi-empirical 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 constant, bulk modulus, elastic constants and phonon frequencies at a fraction of hybrid-functional computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An accurate alternative to hybrid functionals for germanium: DFT+$α$ Abdurrazaq, Abdulgaffar Lot, Ruggero Jay, Antoine Herrero-Saboya, Gabriela Richard, Nicolas Martin-Samos, Layla Hémeryck, Anne de Gironcoli, Stefano Materials Science The accuracy of bulk property predictions in density functional theory (DFT) calculations depends on the choice of 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 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 semi-empirical 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 constant, bulk modulus, elastic constants and phonon frequencies at a fraction of hybrid-functional computational cost. |
| title | An accurate alternative to hybrid functionals for germanium: DFT+$α$ |
| topic | Materials Science |
| url | https://arxiv.org/abs/2512.08857 |