{"paper":{"title":"Phase Space Bottlenecks in an Adiabatic Marcus Hamiltonian: Cusp Geometry, NHIMs, and Mixed Valence Electron Transfer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A cusp condition in asymmetry and coupling parameters determines when the lower adiabatic Marcus surface supports a phase-space transition state.","cross_cats":["math.DS"],"primary_cat":"physics.chem-ph","authors_text":"Stephen Wiggins","submitted_at":"2026-05-17T11:03:38Z","abstract_excerpt":"Marcus--Hush theory explains electron transfer in terms of reorganization energies, driving forces, electronic couplings, and reduced free-energy or energy-gap descriptions. These descriptions do not by themselves determine when the underlying adiabatic dynamics possesses a genuine phase space transition state. We address this question for a minimal asymmetric two-degree-of-freedom adiabatic Marcus Hamiltonian obtained from two coupled diabatic harmonic surfaces. Passing to the lower adiabatic sheet gives a classical Hamiltonian with one electron-transfer coordinate and one transverse mode. We"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive an explicit cusp condition in the plane of dimensionless asymmetry and coupling parameters that is necessary and sufficient for the lower sheet to possess an index-one saddle.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lower adiabatic surface obtained from two coupled diabatic harmonic surfaces can be treated as a classical two-degree-of-freedom Hamiltonian whose local equilibria and manifolds control the electron-transfer dynamics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives a cusp criterion in asymmetry-coupling parameter space determining when an adiabatic Marcus Hamiltonian supports a local Hamiltonian bottleneck with NHIMs on the lower sheet.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A cusp condition in asymmetry and coupling parameters determines when the lower adiabatic Marcus surface supports a phase-space transition state.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a15b3c05a8a7592693677d94785b22b04aaa5f0bd7d6409b8c2711856a1a353f"},"source":{"id":"2605.17385","kind":"arxiv","version":1},"verdict":{"id":"b5e2ac9f-f5b8-4f52-8da3-ac4319b4d0e5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:05:24.553775Z","strongest_claim":"We derive an explicit cusp condition in the plane of dimensionless asymmetry and coupling parameters that is necessary and sufficient for the lower sheet to possess an index-one saddle.","one_line_summary":"Derives a cusp criterion in asymmetry-coupling parameter space determining when an adiabatic Marcus Hamiltonian supports a local Hamiltonian bottleneck with NHIMs on the lower sheet.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lower adiabatic surface obtained from two coupled diabatic harmonic surfaces can be treated as a classical two-degree-of-freedom Hamiltonian whose local equilibria and manifolds control the electron-transfer dynamics.","pith_extraction_headline":"A cusp condition in asymmetry and coupling parameters determines when the lower adiabatic Marcus surface supports a phase-space transition state."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17385/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.029099Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:12:57.319769Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.765780Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.705749Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"22b0f3e7b046330d7cf8c232516e7c80279d0e899bc9e64dc53bda08de5611ff"},"references":{"count":23,"sample":[{"doi":"","year":1956,"title":"On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. 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