{
  "abstract": "Marcus--Hush theory describes electron transfer through reorganization energies, driving forces, and electronic coupling, but it does not by itself determine when an adiabatic model possesses a local Hamiltonian bottleneck. We study a minimal asymmetric two-degree-of-freedom lower-sheet Hamiltonian with an exactly separable harmonic transverse mode. For this conservative model, we establish a necessary-and-sufficient root count for the stationary points and recover the known cusp boundary for disappearance of the lower-sheet double well. We then interpret that boundary in Hamiltonian phase space: inside the cusp, the lower sheet has an index-one saddle and the associated local transition-state structures --- an unstable periodic-orbit NHIM, its stable and unstable manifolds, and an attached dividing surface --- exist; outside the cusp, this local saddle-mediated structure is absent. The result applies to this conservative adiabatic potential-energy Hamiltonian. It does not describe solvent free-energy dynamics, bath-induced mode coupling, or nonadiabatic transfer, and it does not predict Marcus rates for realistic condensed-phase electron-transfer systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Chemical Physics 613 (2027) 113517",
  "arxiv": "2605.17385",
  "author_total": 1,
  "authors": [
    {
      "name": "Stephen Wiggins"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47ymctaxza8f1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.17385",
  "fulltext_url": null,
  "id": "47ymctaxza8f1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.17385",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.17385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47ymctaxza8f1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2605.17385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.17385"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A cusp criterion for a local phase-space bottleneck in a minimal adiabatic Marcus Hamiltonian",
  "title_text": "A cusp criterion for a local phase-space bottleneck in a minimal adiabatic Marcus Hamiltonian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/47ymctaxza8f1",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.chemphys.2026.113517",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}