{
  "abstract": "Quantifying the magnetic properties of open-shell molecules is a common task in chemistry and is increasingly performed in silico using Kohn-Sham density functional theory (KS-DFT). Previous work demonstrates that the predictive accuracy of a few functionals for one such property - hyperfine coupling constants (HFCCs) - is possible, implying that such approximations must yield accurate spin-densities at the nucleus. However, the ability of such functionals to globally predict accurate spin-densities of comparable quality to rigorous ab initio coupled cluster theory, for example, is dubious, despite this being a fundamental quantity for KS-DFT. This work intends to explore the matter by evaluating moments of the spin-density, $\\langle r^n \\rangle = \\int ρ(r)r^n dτ$, $n=-2,\\cdots,2,3$, for second-, third-, and fourth-row atoms to compare various KS-DFT functionals against CCSD. Our results broadly indicate that the tested functionals experience significant deviations with respect to CCSD spin-densities in regions up to 1 Bohr away from the nuclei, with most errors occurring in the immediate vicinity of the nucleus. We find evidence of extreme errors by some functionals for individual $α$/$β$ spin-densities, although several ultimately end up benefiting from significant error cancellation once the corresponding global spin-density is formed. Nevertheless, a comparison between CAM-B3LYP and the Quantum Theory Project (QTP)-family of DFT functionals based on Correlated Orbital Theory conditions across all error metrics demonstrates that QTP00 more accurately reproduces the global spin-density as well as HFCCs, generally offering results in better agreement with CCSD. In line with previous work, we also corroborate the success of PBE0 and the TPSS-family of functionals for HFCCs, further finding that both approximations generally yield spin-densities that are amongst the best.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17385",
  "author_total": 5,
  "authors": [
    {
      "name": "Rodrigo A. Mendes"
    },
    {
      "name": "Zachary W. Windom"
    },
    {
      "name": "Ajith Perera"
    },
    {
      "name": "Roberto L. A. Haiduke"
    },
    {
      "name": "Rodney J. Bartlett"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tdntxds1b3h9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17385",
  "fulltext_url": null,
  "id": "8tdntxds1b3h9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17385",
  "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": "W7213406233",
  "pdf_url": "https://arxiv.org/pdf/2609.17385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tdntxds1b3h9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.17385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17385"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "A note on the accuracy of spin-densities from Kohn-Sham Density Functional Theory",
  "title_text": "A note on the accuracy of spin-densities from Kohn-Sham Density Functional Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/8tdntxds1b3h9",
  "venue": "arXiv",
  "versions": []
}