{
  "abstract": "The two-level conical intersection of a molecule with odd electron number in the absence of magnetic field obeys time-reversal symmetry $T^{2}=-1$ (referred to as the $T^{2}=-1$ conical intersection), and has a five-dimensional branching space due to the Kramer degeneracy. Similar to how the conical intersection of a molecule in a magnetic field ($T^{2}=0$) behaves as the Dirac monopole, the $T^{2}=-1$ conical intersection behaves as the Yang monopole, an mathematical generalization of Dirac monopole with SU(2) gauge field and SO(5) symmetry. This implies that we can study topological properties of $T^{2}=-1$ conical intersections in chemistry based on what is known about Yang monopole in high energy physics. In this work, we present a few mathematical tools to study this connection. First, we show that geometric algebra and quaternion numbers together provides a natural way to utilize the $T^{2}=-1$ time reversal symmetry and the SO(5) symmetry in scaled coordinates, making it simple to derive eigenfunctions, Berry connection and Berry curvature of $T^{2}=-1$ conical intersection. In particular, this approach provides a simple proof that when viewed from the upper or lower states, the $T^{2}=-1$ conical intersection behaves as the self-dual or self-antidual Yang monopole with second Chern number $C_{2}=+\\frac{1}{4}$ or $-\\frac{1}{4}$ respectively. In addition, we propose a visualization method for the SU(2) Berry connection of $T^{2}=-1$ conical intersection. This is achieved by showing that the nonzero part of the Berry connection induces Hopf-fibration on the $S^{3}$ longitude space, and is further visualized through stereographic projection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Chem. Phys. 164, 084124 (2026)",
  "arxiv": "2611.00429",
  "author_total": 1,
  "authors": [
    {
      "name": "Chenchen Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vaphjz4bq2n5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00429",
  "fulltext_url": null,
  "id": "7vaphjz4bq2n5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00429",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vaphjz4bq2n5.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00429"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Molecular conical intersections with odd electron number are realizations of the topological Yang monopole",
  "title_text": "Molecular conical intersections with odd electron number are realizations of the topological Yang monopole",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/7vaphjz4bq2n5",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1063/5.0315919",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}