{
  "abstract": "Aromaticity underpins molecular stability in fields ranging from pharmaceuticals to organic semiconductors, yet existing prediction methods are either too computationally costly for large-scale screening or too empirically restricted for broad applicability. This work introduces the molecular sheaf, a cellular sheaf model free of empirical parameters for chemical bonding that generalizes standard molecular graph theory. From this the frontier eigengap Δ_F is derived as a spectral approximation of the HOMO-LUMO gap requiring only molecular topology and electron count. Δ_F correctly classifies the aromaticity and antiaromaticity of the full annulene series, including benzene and cyclobutadiene, exactly recovering Hückel theory for regular hydrocarbon systems. At scale, it accounts for 62.5% of the variance in DFT HOMO-LUMO gaps across 17,523 structurally diverse polycyclic aromatic hydrocarbons and 21.7% across 52,000 heteroaromatic systems, with the reduction reflecting the deliberate cost of parameter freedom. This confirms that aromatic character can be approximated from molecular connectivity and electron count alone, suggesting that cellular sheaves offer a largely unexplored mathematical framework for the modeling of chemical bonding and structure. All calculations run at under 1 ms per molecule, over seven orders of magnitude faster than corresponding DFT calculations. The molecular sheaf thus also enables rapid, parameter-free pre-screening of aromatic character from structural data alone.",
  "abstract_shown": true,
  "affiliations": [
    "Perse School"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Roy Han",
      "orcid": "0009-0000-6469-5065"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgbe1w55x63wp.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15010344/v1",
  "fulltext_url": null,
  "id": "cgbe1w55x63wp",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010344/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1605|Synthesis and Properties of Aromatic Compounds"
    ]
  ],
  "openalex": "W7221587854",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15010344/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/cgbe1w55x63wp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "10.26434/chemrxiv.15010344",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010344/v2"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "openalex:1605|Synthesis and Properties of Aromatic Compounds",
      "subfield": "organic"
    }
  ],
  "title": "A Cellular Sheaf Model for Aromaticity in Discrete Molecular Systems",
  "title_text": "A Cellular Sheaf Model for Aromaticity in Discrete Molecular Systems",
  "type": "preprint",
  "updated_at": "2026-11-04T00:20:58Z",
  "url": "https://research.draconitic.com/paper/cgbe1w55x63wp",
  "venue": "ChemRxiv",
  "versions": []
}