Origin of the Difference between Kohn-Sham and ∆SCF Band gaps for Delocalized Electron–Hole Excitations in Hybrid-Functional Supercell Calculations
Abstract
We examine the relationship between ground-state generalized Kohn–Sham (GKS) band gaps and self-consistent ∆SCF excitation energies for delocalized electron–hole excitations in finite periodic supercells. For a vertical excitation at the undistorted ground-state geometry, these two quantities are expected to coincide when the promoted electron and hole remain Bloch-like. This is mostly true with semilocal functionals, but not with hybrid functionals for which the difference increases linearly with the fraction of exact exchange. The origin of this difference is derived from two equivalent viewpoints: the total-energy change associated with the ∆SCF excitation and the occupation-dependent orbital gap shift arising from the self-consistent potential response. The residual energy arises from the orbital-dependent exact-exchange selfenergy associated with the electron-hole pair and decreases approximately as 1/N
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BibTeX
@misc{fu2026origin,
title = {{Origin of the Difference between Kohn-Sham and ∆SCF Band gaps for Delocalized Electron–Hole Excitations in Hybrid-Functional Supercell Calculations}},
author = {Mingxue Fu and Arghya Bhowmik and Juan Maŕıa Garćıa-Lastra},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010150/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010150/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Origin of the Difference between Kohn-Sham and ∆SCF Band gaps for Delocalized Electron–Hole Excitations in Hybrid-Functional Supercell Calculations
AU - Mingxue Fu
AU - Arghya Bhowmik
AU - Juan Maŕıa Garćıa-Lastra
PY - 2026
DA - 2026/10/09
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010150/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010150/v1
AB - We examine the relationship between ground-state generalized Kohn–Sham (GKS) band gaps and self-consistent ∆SCF excitation energies for delocalized electron–hole excitations in finite periodic supercells. For a vertical excitation at the undistorted ground-state geometry, these two quantities are expected to coincide when the promoted electron and hole remain Bloch-like. This is mostly true with semilocal functionals, but not with hybrid functionals for which the difference increases linearly with the fraction of exact exchange. The origin of this difference is derived from two equivalent viewpoints: the total-energy change associated with the ∆SCF excitation and the occupation-dependent orbital gap shift arising from the self-consistent potential response. The residual energy arises from the orbital-dependent exact-exchange selfenergy associated with the electron-hole pair and decreases approximately as 1/N
ER -