Vertical ionization energies from inverse generalized Kohn-Sham calculations at fixed electron density
Abstract
The exact Kohn--Sham (KS) system must have its highest occupied orbital energy equal to the negative of the lowest vertical ionization energy (VIE). No comparable theorem connects the deeper occupied levels εk to the higher VIEs Ik. Chong, Gritsenko and Baerends (CGB) established empirically that Ik + εk∝√(εHOMO−εk). We ask whether a similar relation holds for the exact generalized Kohn-Sham (GKS) system, which incorporates a fraction α of Hartree-Fock exchange. We invert near-exact CCSD/aug-cc-pVQZ ground-state densities of LiH, LiF, H2O, HF, CO, N2 and F2 at α= 0, 0.25, 0.5, 0.75, 1.0 and obtain the exact GKS systems at each admixture. As the density is held fixed and only the operator is varied, the resulting occupied spectra separate the effect of exact-exchange admixture on orbital energies from its effect on the density, two contributions inseparable in a self-consistent hybrid calculation. The CGB relation holds broadly across the family, with a proportionality coefficient linear in α, c(α)=c(0)−sα, where c(0)=1.185±0.017 eV1/2 and s=1.987±0.041 eV1/2, with R2≥0.9996 for H2O, CO, HF and N2. Using the response-potential matrix elements tabulated by Gritsenko, Braïda and Baerends, we decompose the CGB coefficient into response and spectroscopic parts, and find s to agree with the homogeneous-electron-gas step-height coefficient Kg = 1.9932 eV1/2, which we conjecture is its origin. The coefficient vanishes at α*=0.597±0.008. At α* the HOMO-referenced GKS occupied levels satisfy εk≈−Ik across the whole occupied range. The zero crossing is fixed by the core orbitals; in the outer valence the CGB coefficient is already indistinguishable from zero at α=0.
Related
- Ionization Energies, Electron Affinities, Bandgaps, Exciton Binding Energies, and Polarization Energies of Orientation-Controlled Picene, [6]-Phenacene, and [7]-Phenacene Thin Films
- Exchange-Correlation Potentials and Energies from Inverse Generalized Kohn-Sham Calculations
- Fast and Accurate Excitation Energies from Density Matrix Renormalization Group Calculations Improved by Machine Learning
- Mechanism-grounded fragmentation trees enable explicit chemical reasoning for electron ionization mass spectrum prediction
- Fragment-Grounded Neural Simulation of Electron Ionization Mass Spectra at Library Scale
BibTeX
@misc{subramanian2026vertical,
title = {{Vertical ionization energies from inverse generalized Kohn-Sham calculations at fixed electron density}},
author = {Vishal Subramanian and Bikash Kanungo and John P. Perdew and Vikram Gavini and Gabor I. Csonka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22024},
eprint = {2610.22024},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22024},
}
RIS
TY - UNPB
TI - Vertical ionization energies from inverse generalized Kohn-Sham calculations at fixed electron density
AU - Vishal Subramanian
AU - Bikash Kanungo
AU - John P. Perdew
AU - Vikram Gavini
AU - Gabor I. Csonka
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.22024
UR - https://arxiv.org/abs/2610.22024
AB - The exact Kohn--Sham (KS) system must have its highest occupied orbital energy equal to the negative of the lowest vertical ionization energy (VIE). No comparable theorem connects the deeper occupied levels ε_k to the higher VIEs I_k. Chong, Gritsenko and Baerends (CGB) established empirically that I_k + ε_k∝√(ε_HOMO−ε_k). We ask whether a similar relation holds for the exact generalized Kohn-Sham (GKS) system, which incorporates a fraction α of Hartree-Fock exchange. We invert near-exact CCSD/aug-cc-pVQZ ground-state densities of LiH, LiF, H_2O, HF, CO, N_2 and F_2 at α= 0, 0.25, 0.5, 0.75, 1.0 and obtain the exact GKS systems at each admixture. As the density is held fixed and only the operator is varied, the resulting occupied spectra separate the effect of exact-exchange admixture on orbital energies from its effect on the density, two contributions inseparable in a self-consistent hybrid calculation. The CGB relation holds broadly across the family, with a proportionality coefficient linear in α, c(α)=c(0)−sα, where c(0)=1.185±0.017 eV^1/2 and s=1.987±0.041 eV^1/2, with R^2≥0.9996 for H_2O, CO, HF and N_2. Using the response-potential matrix elements tabulated by Gritsenko, Braïda and Baerends, we decompose the CGB coefficient into response and spectroscopic parts, and find s to agree with the homogeneous-electron-gas step-height coefficient K_g = 1.9932 eV^1/2, which we conjecture is its origin. The coefficient vanishes at α^*=0.597±0.008. At α^* the HOMO-referenced GKS occupied levels satisfy ε_k≈−I_k across the whole occupied range. The zero crossing is fixed by the core orbitals; in the outer valence the CGB coefficient is already indistinguishable from zero at α=0.
ER -