{
  "abstract": "Directly solving the full electron-nuclear Schrödinger equation remains one of the grand challenges in quantum mechanics. Here, we propose a quantum-chemically motivated orbital-based neural network wavefunction ansatz with explicit many-body electron-electron correlation terms, with parameters depending on the entire electron-nuclear configuration, enabling an accurate description of strongly correlated and/or multi-reference electronic structures by a single Slater-determinant across a broad nuclear configuration space. To train this wavefunction, we further develop an efficient hybrid optimization strategy that combines the variational Monte Carlo technique with local-energy constraints, mitigating the intrinsic sampling bias of the former and considerably reducing the statistical error. These advances are embedded in a unified neural network framework, Schrödinger, enabling the determination of globally accurate potential energy surfaces with a single training for systems ranging from strongly correlated diatomic molecules, triatomic reactions containing conical intersections, to polyatomic multi-reference molecules. This work offers a practical machine-learning tool for solving the electron-nuclear Schrödinger equation and capturing full quantum effects beyond the Born-Oppenheimer approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40112",
  "author_total": 3,
  "authors": [
    {
      "name": "Yaolong Zhang"
    },
    {
      "name": "Bin Jiang"
    },
    {
      "name": "Hua Guo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bjvenpv3tr4w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40112",
  "fulltext_url": null,
  "id": "9bjvenpv3tr4w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40112",
  "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",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7215088685",
  "pdf_url": "https://arxiv.org/pdf/2609.40112",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bjvenpv3tr4w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40112",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40112"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz",
  "title_text": "Smart Machine Learning for Solving the Full Electron-Nuclear Schrödinger Equation with a Quantum-Chemically Inspired Wavefunction Ansatz",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/9bjvenpv3tr4w",
  "venue": "arXiv",
  "versions": []
}