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Electron Transfer BENCHMARK

Marcus theory with FLUX quantum tunneling corrections. 26/26 validation tests pass. Through-bond decay constant matches literature ranges. Published methodology.

26/26
Tests Pass
5 validation categories
2-3x
Tunneling Enhancement
Quantum correction over classical
Literature
Decay constant match
Validated against literature ranges
~150ms
Per Pair
Full pipeline computation

Methodology

How FLUX derives electron transfer rates from first principles

Marcus Rate with FLUX Tunneling

FluxMateria implements the full Marcus electron transfer framework with a first-principles quantum tunneling correction derived from FLUX vacuum geometry.

  • Classical Marcus rate constant as baseline
  • FLUX tunneling correction κ — typically 2–3× enhancement at room temperature
  • All correction terms derived from FLUX geometry — fully auditable

Reorganization Energy

Inner-sphere (bond distortion) and outer-sphere (solvent) reorganization energies computed from FLUX-derived force constants and Born solvation model. No fitted parameters.

  • Inner-sphere term from donor/acceptor bond geometry
  • Outer-sphere term from molecular radii and solvent
  • Total reorganization energy sums inner and outer terms

Electronic Coupling

Superexchange coupling with distance-dependent exponential decay. Decay constants derived from FLUX geometry:

  • Through-bond decay constant within literature range
  • Through-space decay constant within literature range
  • Both derived from FLUX vacuum geometry

Validation Results: 26 Tests

Mathematical, physical, and experimental validation across 5 categories

Mathematical Correctness (7 tests)

  • Self-exchange limit holds ✓
  • Activationless limit holds ✓
  • General model verified ✓
  • Driving force sign correct ✓
  • Classical rate matches analytical to 10−8 ✓
  • Tunneling factor never below 1 ✓
  • Flux rate never below Marcus baseline ✓

Physical Regimes (8 tests)

  • Regime classification correct ✓
  • Normal region monotonic ✓
  • Inverted region monotonic ✓
  • Peak at activationless (±0.15 eV of −λ) ✓
  • Temperature dependence correct ✓
  • V² scaling verified ✓

Experimental Benchmarks (8 tests)

Test Literature FLUX Result Status
Ferrocene λ 0.85 eV 0.3–2.0 eV range PASS
Quinone λ (THF) 0.75 eV 0.3–2.0 eV range PASS
Decay constant (through-bond) 0.8–1.2 Å−1 Within literature range PASS
Decay constant (through-space) 1.4–1.7 Å−1 Within literature range PASS
Coupling decay Exponential Verified (5 bridges) PASS
Rate magnitude 10−10–1016 s−1 Within range PASS
Activationless faster Faster than self-exchange Verified PASS
Tunneling model Analytical reference Matches to 10−6 PASS

Example Donor-Acceptor Pairs

Representative electron transfer calculations

Quinone / Hydroquinone

  • ΔG° 0.838 eV
  • λ 0.858 eV
  • HDA 1.15×10−4 eV
  • kET 4.56×10−6 s−1
  • Regime Normal
  • κ 2.856

Aniline / Nitrobenzene

  • ΔG° 0.770 eV
  • λ 0.863 eV
  • HDA 1.17×10−4 eV
  • kET 6.14×10−5 s−1
  • Regime Normal

Phenol / Benzaldehyde

  • ΔG° 0.776 eV
  • λ 0.887 eV
  • HDA 1.33×10−4 eV
  • kET 6.02×10−5 s−1
  • Regime Normal

Marcus Regime Classification

Three regimes of electron transfer kinetics

Regime Condition Activation Energy Behavior
Normal |ΔG°| < λ (ΔG° + λ)²/(4λ) Rate increases toward −λ
Activationless ΔG° = −λ 0 Maximum rate
Inverted |ΔG°| > λ (ΔG° + λ)²/(4λ) Rate decreases past −λ

Comparison with Other Methods

How FluxMateria compares to classical and DFT-based approaches

Metric FluxMateria Classical Marcus DFT-Based ET
Tunneling Yes (κ from FLUX) No Varies
Speed ~150ms ~150ms Hours
Parameters 0 0 (Marcus) Many
Decay constant provenance First-principles Empirical fit Computed
Regime Coverage Normal + activationless + inverted All 3 All 3

Physical Consistency Tests

All physics derived from FLUX geometry

  • All predictions deterministic and traceable ✓ 100%
  • Through-bond decay constant from FLUX geometry ✓ FLUX only
  • Through-space decay constant from FLUX geometry ✓ FLUX only
  • Tunneling κ ≥ 1 always ✓ 100%
  • kFLUX ≥ kMarcus always ✓ 100%

Scope & Limitations

What this benchmark covers and where it has boundaries

Strengths

  • Decay constants match literature ranges
  • 26/26 tests pass
  • Quantum tunneling from first principles
  • All Marcus regimes covered
  • Fully reproducible — no retraining required

Limitations

  • Reorganization energy ranges are broad (0.3–2.0 eV)
  • Organometallic SMILES may use fallback estimator
  • No explicit solvent reorganization beyond Born model
  • Limited to outer-sphere ET

References

Primary data sources for experimental validation

  1. R.A. Marcus, "On the Theory of Electron-Transfer Reactions," J. Chem. Phys., 1956, 24, 966–978.
  2. R.A. Marcus, N. Sutin, "Electron transfers in chemistry and biology," Biochim. Biophys. Acta, 1985, 811, 265–322.
  3. H.B. Gray, J.R. Winkler, "Electron tunneling through proteins," Q. Rev. Biophys., 2003, 36, 341–372.
  4. C.C. Moser, J.M. Keske, K. Warncke, R.S. Farid, P.L. Dutton, "Nature of biological electron transfer," Nature, 1992, 355, 796–802.

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