{
  "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 $\\varepsilon_k$ to the higher VIEs $I_k$. Chong, Gritsenko and Baerends (CGB) established empirically that $I_k + \\varepsilon_k\\propto\\sqrt{\\varepsilon_{\\mathrm{HOMO}}-\\varepsilon_k}$. 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$_2$O, 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 $c(0)=1.185\\pm0.017$ eV$^{1/2}$ and $s=1.987\\pm0.041$ eV$^{1/2}$, with $R^{2}\\ge0.9996$ for H$_2$O, 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 $α^{*}=0.597\\pm0.008$. At $α^{*}$ the HOMO-referenced GKS occupied levels satisfy $\\varepsilon_k\\approx-I_k$ 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 $α=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22024",
  "author_total": 5,
  "authors": [
    {
      "name": "Vishal Subramanian"
    },
    {
      "name": "Bikash Kanungo"
    },
    {
      "name": "John P. Perdew"
    },
    {
      "name": "Vikram Gavini"
    },
    {
      "name": "Gabor I. Csonka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atjvhc8wg5hvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22024",
  "fulltext_url": null,
  "id": "atjvhc8wg5hvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22024",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7222749673",
  "pdf_url": "https://arxiv.org/pdf/2610.22024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atjvhc8wg5hvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.22024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22024"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Vertical ionization energies from inverse generalized Kohn-Sham calculations at fixed electron density",
  "title_text": "Vertical ionization energies from inverse generalized Kohn-Sham calculations at fixed electron density",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/atjvhc8wg5hvs",
  "venue": "arXiv",
  "versions": []
}