{
  "abstract": "A method for solving the two-center Dirac equation using a Gaussian-product basis set tailored to the axial symmetry of diatomic systems is presented. For the ground state of H$_2^+$ at an internuclear distance $R=2.0~a_0$, we obtain a relativistic energy with relative precision at the $10^{-18}$ level. The properties of the basis set allow for an analytic Fourier transform of the wave function. As a first application we evaluate, for the first time, the zero-potential contribution to the one-loop self-energy for H$_2^+$ in Feynman and Coulomb gauges. Although this contribution is not separately gauge invariant, its calculation provides a proof of principle for the use of the present framework in prospective QED calculations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03217",
  "author_total": 1,
  "authors": [
    {
      "name": "Dávid Ferenc"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmnabpkjtz537.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03217",
  "fulltext_url": null,
  "id": "cmnabpkjtz537",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03217",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Atomic and Molecular Physics"
    ]
  ],
  "openalex": "W7220414686",
  "pdf_url": "https://arxiv.org/pdf/2610.03217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmnabpkjtz537.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03217"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Two-center Dirac equation in a Gaussian basis set",
  "title_text": "Two-center Dirac equation in a Gaussian basis set",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/cmnabpkjtz537",
  "venue": "arXiv",
  "versions": []
}