{
  "abstract": "Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30022",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuhao Chen"
    },
    {
      "name": "Donald G. Truhlar"
    },
    {
      "name": "Xiao He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49p8ras2skg29.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30022",
  "fulltext_url": null,
  "id": "49p8ras2skg29",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30022",
  "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",
      "cs.AI"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7223200219",
  "pdf_url": "https://arxiv.org/pdf/2610.30022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49p8ras2skg29.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.30022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30022"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals",
  "title_text": "Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/49p8ras2skg29",
  "venue": "arXiv",
  "versions": []
}