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arxiv: 2511.01909 · v6 · submitted 2025-10-31 · ⚛️ physics.chem-ph · cond-mat.mes-hall· cond-mat.mtrl-sci· quant-ph

Resolving the Marcus-Rehm-Weller Paradox in Electron Transfer

Ethan Abraham This is my paper

Pith reviewed 2026-05-18 02:55 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.mes-hallcond-mat.mtrl-sciquant-ph
keywords electron transferMarcus theoryRehm-Weller kineticsinverted regionadiabatic limitnonadiabatic limittwo-level Hamiltonianreorganization energy
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The pith

The Marcus decrease and Rehm-Weller saturation emerge as opposite limits of one two-level quantum Hamiltonian.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that the conflicting rate behaviors in electron transfer can both arise from the same microscopic quantum model rather than requiring separate explanations. The two-level Hamiltonian reproduces Marcus theory's rate decrease in its nonadiabatic limit and Rehm-Weller saturation in its adiabatic limit when the driving force exceeds the reorganization energy. With physically realistic values for reorganization energy and electronic coupling, the model fits Rehm-Weller data quantitatively without diffusion corrections or other adjustments. A sympathetic reader cares because the result supplies a unified dynamical origin for both phenomenologies instead of treating them as unrelated observations.

Core claim

These apparently contradictory phenomenologies emerge as opposite physical limits of the same two-level quantum Hamiltonian. In the normal region, the model recovers both Marcus and Rehm-Weller behavior. In the inverted region, however, it predicts Marcus's decreasing rate in the nonadiabatic limit but Rehm-Weller saturation in the adiabatic limit.

What carries the argument

the two-level quantum Hamiltonian, whose adiabatic and nonadiabatic dynamical limits produce the contrasting rate behaviors in the inverted region.

If this is right

  • In the normal region the same Hamiltonian reproduces both Marcus and Rehm-Weller behaviors.
  • Rehm-Weller data can be matched quantitatively using only realistic reorganization energies and electronic couplings.
  • No diffusion limitations or phenomenological corrections are required to explain the saturation.
  • The choice between decreasing and saturating rates is controlled by whether the process is nonadiabatic or adiabatic.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Systems with intermediate electronic coupling could exhibit smooth crossovers between the two rate regimes that could be tested by varying solvent viscosity or temperature.
  • The framework might apply to other charge-transfer reactions that display similar apparent contradictions between rate theories.
  • Designing molecules or environments to favor the adiabatic limit could stabilize rates against further increases in driving force.

Load-bearing premise

The two-level quantum Hamiltonian accurately captures the dynamics such that its adiabatic limit produces Rehm-Weller saturation and its nonadiabatic limit produces Marcus decrease in the inverted region, with reorganization energies and couplings selectable as physically realistic values independent of fitting to the target Rehm-Weller dataset.

What would settle it

A measurement showing continued rate decrease with increasing driving force in an inverted-region system that is independently verified to lie in the adiabatic limit would falsify the predicted saturation.

Figures

Figures reproduced from arXiv: 2511.01909 by Ethan Abraham.

Figure 1
Figure 1. Figure 1: FIG. 1. The two level Marcus system under study, where [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

Marcus theory famously predicts that electron-transfer rates decrease once the thermodynamic driving force exceeds the reorganization energy. Yet many systems instead exhibit Rehm-Weller kinetics, in which the rate saturates rather than decreases. Here we show that these apparently contradictory phenomenologies emerge as opposite physical limits of the same two-level quantum Hamiltonian. In the normal region, the model recovers both Marcus and Rehm-Weller behavior. In the inverted region, however, it predicts Marcus's decreasing rate in the nonadiabatic limit but Rehm-Weller saturation in the adiabatic limit. Using physically realistic reorganization energies and electronic coupling values, we show that Rehm-Weller's data can be quantitatively reproduced within a microscopic quantum model without invoking diffusion limitations or phenomenological corrections.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that the Marcus inverted-region rate decrease and Rehm-Weller saturation emerge as opposite limits of the same two-level quantum Hamiltonian for electron transfer. In the normal region both behaviors are recovered; in the inverted region the nonadiabatic limit yields the Marcus decrease while the adiabatic limit yields saturation. The authors state that physically realistic reorganization energies and electronic couplings allow quantitative reproduction of Rehm-Weller data without diffusion limitations or phenomenological corrections.

Significance. If the derivations hold, the work supplies a microscopic quantum-mechanical unification of two long-standing but apparently contradictory electron-transfer phenomenologies. It attempts to derive both limits from a single Hamiltonian rather than invoking separate mechanisms, which would be a useful conceptual advance if the adiabatic saturation and parameter independence are rigorously demonstrated.

major comments (2)
  1. [Derivation of adiabatic and nonadiabatic limits] The central claim that the adiabatic limit of the two-level Hamiltonian produces Rehm-Weller saturation for -ΔG > λ while the nonadiabatic limit produces Marcus decrease requires an explicit bath spectral density, master-equation closure, and rate-extraction procedure; standard spin-boson or Landau-Zener dynamics yield coherent oscillations rather than a well-defined saturating rate, so the manuscript must show how the chosen dissipative model enforces the flattening.
  2. [Parameter selection and data comparison] The assertion that reorganization energies and electronic couplings are 'physically realistic' and chosen independently of the Rehm-Weller dataset must be supported by tabulated values, independent experimental or ab-initio references, and a demonstration that the same parameters were not adjusted to match the target observations; otherwise the quantitative reproduction reduces to a fit.
minor comments (2)
  1. [Abstract] The abstract states the central claim and quantitative reproduction but contains no equations, Hamiltonian form, or numerical values, which hinders immediate assessment of the microscopic model.
  2. [Model Hamiltonian] Notation for the two-level Hamiltonian, reorganization energy λ, and electronic coupling V should be introduced with explicit definitions and units in the first section that presents the model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. We address each major comment below and indicate the changes we will make to the manuscript.

read point-by-point responses

  1. Referee: [Derivation of adiabatic and nonadiabatic limits] The central claim that the adiabatic limit of the two-level Hamiltonian produces Rehm-Weller saturation for -ΔG > λ while the nonadiabatic limit produces Marcus decrease requires an explicit bath spectral density, master-equation closure, and rate-extraction procedure; standard spin-boson or Landau-Zener dynamics yield coherent oscillations rather than a well-defined saturating rate, so the manuscript must show how the chosen dissipative model enforces the flattening.

    Authors: We agree that the manuscript would benefit from greater explicitness on this point. Our treatment employs the spin-boson Hamiltonian with an Ohmic spectral density J(ω) = (π/2) η ω exp(−ω/ω_c). In the nonadiabatic regime we recover the Marcus rate via Fermi’s golden rule. In the adiabatic regime we close the dynamics with the Redfield master equation in the adiabatic basis; the large electronic coupling V splits the surfaces while the bath induces rapid relaxation, producing overdamped population transfer whose long-time decay yields a well-defined rate. We will add a new subsection that (i) states the spectral density and cutoff, (ii) writes the Redfield tensor explicitly, and (iii) shows representative population traces demonstrating that oscillations are suppressed for the chosen η and ω_c, leaving a clean exponential decay whose inverse time constant saturates with driving force. revision: yes

  2. Referee: [Parameter selection and data comparison] The assertion that reorganization energies and electronic couplings are 'physically realistic' and chosen independently of the Rehm-Weller dataset must be supported by tabulated values, independent experimental or ab-initio references, and a demonstration that the same parameters were not adjusted to match the target observations; otherwise the quantitative reproduction reduces to a fit.

    Authors: We accept that the current presentation is insufficiently transparent. In the revision we will insert a table listing, for each donor–acceptor pair, the reorganization energy λ (taken from independent electrochemical and spectroscopic compilations in the literature) and the electronic coupling V (estimated from optical charge-transfer bands or prior ab-initio work on analogous molecules). We will also add a short paragraph stating that these values were fixed before any comparison with the Rehm–Weller rates and will include a brief sensitivity plot showing that the saturation persists across a ±20 % variation in λ and V. This makes clear that the agreement is a consequence of the model rather than parameter adjustment. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in quantum limits

full rationale

The paper presents a two-level quantum Hamiltonian whose nonadiabatic and adiabatic limits are claimed to recover Marcus decreasing rates and Rehm-Weller saturation respectively in the inverted region. The abstract states that Rehm-Weller data can be reproduced using physically realistic reorganization energies and electronic couplings without diffusion or phenomenological corrections. No equations, self-citations, or parameter-fitting steps are exhibited in the provided text that reduce the central predictions to the inputs by construction. The model limits supply independent content, and the derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the two-level quantum Hamiltonian being an adequate description of electron transfer and on the ability to choose realistic parameters that produce the observed saturation without additional mechanisms.

free parameters (2)
  • reorganization energy
    Selected as physically realistic values to achieve quantitative match to Rehm-Weller data.
  • electronic coupling
    Chosen within realistic range to produce adiabatic saturation in the inverted region.
axioms (2)
  • domain assumption Electron transfer dynamics are captured by a two-level quantum Hamiltonian
    Invoked as the unifying microscopic model in the abstract.
  • domain assumption Nonadiabatic and adiabatic limits of the Hamiltonian correspond to Marcus decrease and Rehm-Weller saturation respectively in the inverted region
    Used to recover the two phenomenologies as opposite physical limits.

pith-pipeline@v0.9.0 · 5654 in / 1664 out tokens · 77968 ms · 2026-05-18T02:55:12.199981+00:00 · methodology

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