{
  "abstract": "Several ad hoc dispersion models for density-functional theory are based on the use of Hirshfeld (or \"stockholder\") partition of a molecular charge density, which provides an in situ definition of atomic size. We show that a recently introduced \"optimized\" quantum Drude oscillator model for dispersion admits a closed-form solution in terms of the Lambert $W$ function, whose branches identify the compact and diffuse oscillator solutions. The compact solution determines the $C_8$ (dipole-quadrupole) dispersion coefficient analytically from the free-atom polarizability, $C_6$ coefficient, and van der Waals radius, without any reference $C_8$ data. Next, we provide a formal basis for a relativistic version of the atoms-in-molecule Hirshfeld partition. Using four-component Dirac-Hartree-Fock densities for isolated atoms defines a strictly positive deformation field that carries the relativistic changes in atomic density into the Hirshfeld partition. A uniqueness theorem for the non-relativistic case is extended to relativistic Hirshfeld atoms and admits an asymptotic expansion through quadratic order in the fine-structure constant. Normalization requires the relativistic density correction to reshape the reference atom while preserving its population. Finally, four-component polarizabilities and C6 coefficients are reported for closed-shell atoms and ions, which supply the reference data required to extend atoms-in-molecules dispersion models into the heavy-element regime. Periodic trends are observable in a scalar contraction factor that measures relativistic effects.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01624",
  "author_total": 2,
  "authors": [
    {
      "name": "Keegan Paice"
    },
    {
      "name": "John M. Herbert"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7ca7dn4jbjknv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01624",
  "fulltext_url": null,
  "id": "7ca7dn4jbjknv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01624",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7215875252",
  "pdf_url": "https://arxiv.org/pdf/2610.01624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7ca7dn4jbjknv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.01624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01624"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Relativistic Hirshfeld atoms in a molecule: An information-theoretic view, with application to Drude oscillator dispersion models",
  "title_text": "Relativistic Hirshfeld atoms in a molecule: An information-theoretic view, with application to Drude oscillator dispersion models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/7ca7dn4jbjknv",
  "venue": "arXiv",
  "versions": []
}