{
  "abstract": "Quantum tunnelling plays a central role in the structure and spectroscopy of hydrogen-bonded systems, and its sensitivity to isotopic substitution provides a stringent probe of the underlying potential-energy landscape. Despite extensive numerical studies, many high-level approaches tend to obscure the simple physical relationships linking effective mass, barrier geometry, and tunnelling amplitudes. Here, we develop a Cornell-type analytical--numerical framework to describe proton and deuteron tunnelling, combining a semi-analytical localized wavefunction ansatz with numerical solutions of the one-dimensional Schrödinger equation. The resulting tunnelling splittings exhibit an exponential dependence on the square root of the effective isotope mass,$\\ln(ΔE)\\propto -\\sqrt{μ_{\\mathrm{eff}}}$, in agreement with semiclassical Wentzel--Kramers--Brillouin (WKB) theory. Comparison with multidimensional reaction-space calculations for the formic acid dimer shows that this scaling persists in fully coupled 3D and 5D quantum models, yielding an empirical relation $\\ln(ΔE)= -1.75\\sqrt{μ_{\\mathrm{eff}}}+2.60$. The present framework provides a transparent and computationally efficient approach for quantifying mass-scaling and tunnelling dynamics in hydrogen-bonded and other double-well systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Chemical Physics 607 (2026) 113203",
  "arxiv": "2609.25074",
  "author_total": 1,
  "authors": [
    {
      "name": "Krishna Kingkar Pathak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1504by5zqfp91.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25074",
  "fulltext_url": null,
  "id": "1504by5zqfp91",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25074",
  "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",
      "hep-ph"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25074",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1504by5zqfp91.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25074",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25074"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Mass-Scaling of Quantum Tunnelling in Hydrogen Bonds: Analytical Model and Comparison with Multidimensional Potentials",
  "title_text": "Mass-Scaling of Quantum Tunnelling in Hydrogen Bonds: Analytical Model and Comparison with Multidimensional Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/1504by5zqfp91",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.chemphys.2026.113203",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}