Pith Number

pith:IRKHHXQU

pith:2026:IRKHHXQUCZBS4QXMNDJG3S3MLZ

not attested not anchored not stored refs resolved

Phase Space Bottlenecks in an Adiabatic Marcus Hamiltonian: Cusp Geometry, NHIMs, and Mixed Valence Electron Transfer

Stephen Wiggins

A cusp condition in asymmetry and coupling parameters determines when the lower adiabatic Marcus surface supports a phase-space transition state.

arxiv:2605.17385 v1 · 2026-05-17 · physics.chem-ph · math.DS

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. I, 1956

[2] Adiabatic theory of outer sphere electron-transfer reactions in solution, 1961

[3] Mixed valence chemistry — A survey and classification, 1968

[4] Electron-transfer reactions in condensed phases, 1984

[5] Electron transfers in chemistry and biology, 1985

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:55.914124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

445473de1416432e42ec68d26dcb6c5e4108d821906867f3eee6e7204ab3b71a

Aliases

arxiv: 2605.17385 · arxiv_version: 2605.17385v1 · doi: 10.48550/arxiv.2605.17385 · pith_short_12: IRKHHXQUCZBS · pith_short_16: IRKHHXQUCZBS4QXM · pith_short_8: IRKHHXQU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IRKHHXQUCZBS4QXMNDJG3S3MLZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 445473de1416432e42ec68d26dcb6c5e4108d821906867f3eee6e7204ab3b71a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44eaa376cb6dd0cd5e9ad955228ab7dffa044d439d79872e036272352e0be154",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2026-05-17T11:03:38Z",
    "title_canon_sha256": "86bfba200da3be53022283d28b056db11cb2d28a8f4071fec763f705916cc558"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17385",
    "kind": "arxiv",
    "version": 1
  }
}