{
  "abstract": "We show that, for the unique case of a system of electrons and nuclei in one dimension, the $\\hGamma$ operator in phase space electronic structure theory has a zero non-Abelian curl. Using this fact, we are able to show that a phase space electronic structure framework in Wigner space has a one-to-one mapping to the exact fully quantum vibronic Hamiltonian. In other words, one loses no information by working within the framework of phase space electronic structure theory rather than Born-Huang theory; the only difference is that, whereas Born-Huang theory represents the total vibronic Hamiltonian as a quadratic order expansion in $\\hbar$, the Hamiltonian becomes an infinite order expansion in $\\hbar$ within a phase space electronic structure framework (a so-called \"Generalized Born-Huang\" approach). That being said, numerical results at first or second order demonstrate that, for a limited number of electronic states, phase space electronic structure theory strongly outperforms Born-Huang theory -- a result that justifies a great deal more research into this novel electronic structure approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13120",
  "author_total": 4,
  "authors": [
    {
      "name": "Zain Zaidi"
    },
    {
      "name": "Yotam M. Y. Feldman"
    },
    {
      "name": "Linqing Peng"
    },
    {
      "name": "Joseph E. Subotnik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4wr9vkqcamv9c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13120",
  "fulltext_url": null,
  "id": "4wr9vkqcamv9c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13120",
  "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": "W7213182334",
  "pdf_url": "https://arxiv.org/pdf/2609.13120",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4wr9vkqcamv9c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.13120",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13120"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "An Exact Formulation of Phase-Space Electronic Structure Theory in One Dimension by Exploiting the Zero Curvature Condition",
  "title_text": "An Exact Formulation of Phase-Space Electronic Structure Theory in One Dimension by Exploiting the Zero Curvature Condition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/4wr9vkqcamv9c",
  "venue": "arXiv",
  "versions": []
}