{
  "abstract": "Accurate description of short-range quantum effects between a quantum-mechanical (QM) region and its molecular-mechanical (MM) environment remains a central challenge in electrostatic embedding QM/MM methods. In conventional point-charge embedding, MM atoms polarize the QM wave function through electrostatics but lack an explicit electron density, resulting in an incomplete description of short-range Pauli repulsion and, in unfavorable configurations, electron spill-out and excessive QM-MM attraction. Here we develop EmbR, a physically constrained machine-learning framework that restores this missing short-range quantum response while retaining the simplicity of point-charge embedding. Rather than learning an energy correction alone, EmbR predicts environmentdependent MM-site contributions constrained by the spatial overlap between QM electron density and MM-centered density-like functions. These site contributions are then transformed into explicit atom-centered exponential repulsive potentials and incorporated directly into the QM Hamiltonian. A self-consistent energy-matching procedure further accounts for the density relaxation induced by the added repulsive operator without altering the learned spatial distribution. Across amino-acid–water and amino-acid–water/NaCl model systems, EmbR reduces the interaction-energy errors of conventional electrostatic embedding from 20.21–59.18 kcal/mol to 1.23–2.58 kcal/mol relative to counterpoisecorrected full-QM references, while maintaining strong agreement with the reference interaction energies (𝑅2 = 0.9798–0.9912). Beyond energetic accuracy, EmbR suppresses electron spill-out near positively charged MM sites and reproduces the dominant electrondepletion features associated with interfacial Pauli repulsion. These results demonstrate that physically constrained machine learning can provide an efficient intermediate strategy between conventional point-charge embedding and fully electronic embedding approaches by introducing an environment-dependent short-range quantum operator into QM/MM Hamiltonians.",
  "abstract_shown": true,
  "affiliations": [
    "China Pharmaceutical University",
    "School of Science",
    "School of Basic Medicine and Clinical Pharmacy"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Minghao Cao"
    },
    {
      "affs": [
        1,
        0,
        2
      ],
      "name": "Jinfeng Liu",
      "orcid": "0000-0002-0614-5097"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cb6mrns21877z.bib",
  "cited_by": 0,
  "doi": "10.26434/chemrxiv.15008167/v1",
  "fulltext_url": null,
  "id": "cb6mrns21877z",
  "issns": [],
  "landing_url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008167/v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7204949284",
  "pdf_url": "https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15008167/v1",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "American Chemical Society (ACS)",
  "ris": "https://research.draconitic.com/paper/cb6mrns21877z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "10.26434/chemrxiv.15008167",
      "source": "chemrxiv",
      "url": "https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008167/v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Advanced Chemical Physics Studies",
      "subfield": "amo"
    }
  ],
  "title": "Machine-Learned Short-Range Repulsive Hamiltonians for Electrostatic QM/MM Embedding",
  "title_text": "Machine-Learned Short-Range Repulsive Hamiltonians for Electrostatic QM/MM Embedding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:17Z",
  "url": "https://research.draconitic.com/paper/cb6mrns21877z",
  "venue": "ChemRxiv",
  "versions": []
}