{
  "annotation_id": "e1a29789-106a-44fe-9453-30fa491e69c3",
  "date_created": "2026-03-02T18:00:39.832000Z",
  "date_modified": "2026-03-02T18:00:39.832000Z",
  "file_hash": "4c0cbdc6cd9e560171d1f5b2c8288d27d9bf76f89953bda61cc5d485a77335c7",
  "private": false,
  "record": {
    "abstract": "Precise solutions of the Hartree-Fock equations for the ground state of the\nhydrogen molecule are obtained for a wide range of internuclear distances R by\nmeans of a two-dimensional fully numerical mesh computational method. The\nspatial parts of the single-electron wave functions are found to be coinciding\nfor R\u003c2.30a.u. At larger distances they become different and as R-\u003e\\infty each\nof them takes the form corresponding to a separate atom. This quantum phase\ntransition occurring at R=2.30a.u. gives a natural boundary between a\ndelocalized behavior of electrons in the molecule and their distribution over\nseparate atoms. This phenomenon can be also considered as an analog of the\nWigner crystallization or the Mott transition on the level of a single\nmolecule.",
    "arxiv_id": "physics/0206036",
    "authors": [
      "Mikhail V. Ivanov"
    ],
    "categories": [
      "physics.atom-ph",
      "physics.chem-ph"
    ],
    "title": "Quantum phase transition in the Hartree-Fock wave function of the   hydrogen molecule",
    "url": "https://arxiv.org/abs/physics/0206036"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "826ed8f8-62a2-4fa2-ad45-7125f7cc7018",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}