Pith. sign in

REVIEW 3 major objections 5 minor 54 references

Correlated reaction coordinate motion produces non-additive rate enhancement for electron and energy transfer in multi-acceptor structures

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Multi-acceptor electron and energy transfer can beat the additive factor-of-two limit when acceptor–acceptor coupling is strong, temperature is low, and acceptor vibrations move anti-correlated.

desk verdict A genuinely new mechanism—acceptor–acceptor reorganization energy from correlated reaction-coordinate motion—is buried under an oversold comparison to experiment that rests on hand-picked correlation parameters. read the letter →

arxiv 2506.21504 v1 pith:CDDJME2I submitted 2025-06-26 physics.chem-ph physics.atm-clusphysics.comp-phquant-ph

Hanggai Nuomin , Feng-Feng Song , Peng Zhang , David N. Beratan This is my paper · ORCID
classification physics.chem-phphysics.atm-clusphysics.comp-phquant-ph
keywords electrontransferenergymulti-acceptorsystemsvibroniccouplingreaction-coordinatecorrelationacceptor-acceptorreorganizationnon-additiverateenhancementquantuminterference
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper explains a puzzling experimental observation: adding a second, chemically identical acceptor to a donor–acceptor molecule speeds up electron transfer 4–5 fold, although the simplest classical and coherent-quantum counting arguments predict only a factor of two. The authors analyze a donor–two-acceptor model and find three coupled effects of acceptor–acceptor interaction — a shift in reaction free energy, new higher-order coupling pathways, and correlated motion of the two reaction coordinates — with the last effect decisive when the motion is anti-correlated. In that regime the acceptor–acceptor reorganization energy reaches $3\lambda$, and low temperature preserves the quantum vibronic pathways that carry the non-additive contribution, yielding a predicted rate ratio of $k_{D\to A_1A_2}/k_{D\to A}=5.82$ for $V_{A_1A_2}=400\,\mathrm{cm}^{-1}$ at $10\,\mathrm{K}$, close to the measured 4-fold enhancement. If the picture is right, multiple acceptors are not just parallel channels for charge or energy flow; the correlation of their nuclear motion is a tunable design variable for transfer kinetics.

What carries the argument

The machinery is a three-electronic-state vibronic Hamiltonian ($|D\rangle$, $|A_1\rangle$, $|A_2\rangle$) in which two sets of harmonic modes are shared between the two acceptor states with weights $\alpha$ and $\beta$ obeying $\alpha^2+\beta^2=1$, so the angle between the two reaction coordinates is tunable from fully correlated ($\alpha=\beta$) through uncorrelated ($\alpha=1$, $\beta=0$) to anti-correlated ($\beta<0$). The derived quantity that carries the argument is the acceptor–acceptor reorganization energy $\lambda^{\mathrm{reorg}}_{A_1,A_2} = \sum_n [(\alpha s_n-\beta s_n)^2 + (\beta s_n-\alpha s_n)^2]/\omega_n$, which is zero for fully correlated motion, $2\lambda$ for uncorrelated motion, and $3\lambda$ in the anti-correlated case used for the strong-enhancement predictions. Rates are computed by a partial summation of vibronic propagation pathways, a diagrammatic expansion of the donor survival amplitude kept to second order in the donor–acceptor coupling but summed to arbitrary order in the acceptor–acceptor coupling, with Monte Carlo evaluation of the thermal averages; the method is validated against the exact two-state Fermi golden rule in the fully correlated limit.

What would settle it

Compute the acceptor–acceptor reorganization energy (equivalently the correlation parameters $\alpha$ and $\beta$) for the experimental anthracene–1,4-benzoquinone molecule from its vibrational normal modes and solvent response. If it comes out at $2\lambda$ or less rather than the assumed $3\lambda$, the predicted $k_{D\to A_1A_2}/k_{D\to A}$ at $V_{A_1A_2}=400\,\mathrm{cm}^{-1}$ and $T=10\,\mathrm{K}$ falls toward 4 or below, weakening the claimed explanation. A complementary experiment would measure the two-acceptor/single-acceptor rate ratio as a function of temperature down to 10 K: the model predicts a steep rise below about 100 K because the non-additive pathways carry $\coth(\omega/k_BT)$ factors, whereas a purely coupling-based explanation would be nearly flat.

Watch

Extended reading notes

Core claim

The paper's central claim is that the non-additive rate enhancement in donor–two-acceptor systems arises from acceptor–acceptor interactions acting through three channels: a free-energy shift created by the acceptor–acceptor electronic coupling $V_{A_1A_2}$; coherently summed donor–acceptor coupling pathways of third and higher order (e.g., D→A1→A2→D and its repetitions); and, most importantly, the reorganization energy for A1→A2 transfer, which is set by the correlation between the two donor-to-acceptor reaction coordinates. When the two coordinates move out of phase with weights $\alpha\approx 0.97$ and $\beta\approx -0.26$, that reorganization energy is $3\lambda$, and the higher-order vibronic pathways — whose contributions carry factors like $\coth(\omega/k_BT)$ — survive at low temperature and amplify the rate well beyond the additive factor of two. The model obtains $k_{D\to A_1A_2}/k_{D\to A}=5.82$ for $V_{A_1A_2}=400\,\mathrm{cm}^{-1}$ at $10\,\mathrm{K}$, which the authors take to explain the measured 4-fold enhancement in the anthracene–dibenzoquinone system, and it predicts that systems with nearly parallel charge-transfer dipoles, for which the acceptor–acceptor reorganization energy is small, should show only the additive enhancement.

Load-bearing premise

The load-bearing premise is that, in the actual experimental molecule, the two acceptors' reaction-coordinate motions are strongly anti-correlated, giving an acceptor–acceptor reorganization energy near $3\lambda$ (three times the donor–acceptor reorganization energy); the paper supports this assignment with only a qualitative dipole-moment argument and never computes that quantity for the molecule.

Editorial extensions

If this is right

  • The model attributes the measured 4- to 5-fold enhancement of the anthracene–dibenzoquinone system mainly to acceptor–acceptor reorganization energy created by anti-correlated reaction-coordinate motion, amplified at low temperature; the earlier $\sqrt{2}\times\sqrt{2}=4$-fold coupling argument is recovered as the fully correlated limit.
  • When the two charge-transfer dipole moments are nearly parallel, as in the zinc porphyrin–NDI two-acceptor structures, the acceptor–acceptor reorganization energy is small and the predicted enhancement collapses to the additive factor of about two, matching the reported two-fold acceleration.
  • At high temperature the vibrational bath is classical and a factor $\coth(\omega/k_BT)$ suppresses every non-additive pathway, so the two-acceptor rate cannot exceed twice the one-acceptor rate; strong enhancement requires low temperature or, equivalently, high-frequency vibrations.
  • A donor with three anti-correlated acceptors sustains a 4-fold enhancement at 10 K even with acceptor–acceptor coupling as small as $80\,\mathrm{cm}^{-1}$, indicating that each added acceptor adds constructively interfering pathways.
  • The analysis yields a concrete design strategy: maximize the A1-to-A2 reorganization energy by arranging acceptors so their charge-separation dipole changes differ strongly, keep acceptor–acceptor electronic coupling strong, and operate at low temperature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The quantitative match with experiment rests on an assumed parameter: the paper sets the anti-correlated weights ($\alpha\approx0.97$, $\beta\approx-0.26$) and hence $\lambda_{A_1A_2}=3\lambda$ from a qualitative dipole-moment argument. Computing $\alpha$ and $\beta$ for the actual molecule from its normal modes would either confirm the assignment or show that the real system sits in a milder regi
  • A tunable design knob follows: the enhancement should vary continuously with the angle between the two charge-transfer dipole moments, from roughly the additive factor near 0 degrees (parallel) up to 5- to 6-fold near 120 degrees (anti-correlated); a homologous series of linkers that rotates the two acceptors relative to each other would map out this curve and test the mechanism directly.
  • The pathway-interference mechanism should carry over to energy transfer in multi-chromophore light-harvesting assemblies, where correlated pigment vibrations are common; the analysis implies that engineering anti-correlated motion among acceptor chromophores could push energy-transfer rates beyond the sum of pairwise channels at cryogenic temperatures.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper develops a partial-summation vibronic pathway theory for electron/energy transfer (ET/EnT) in one-donor, multi-acceptor systems. The model includes donor-acceptor and acceptor-acceptor electronic couplings, two (or three) correlated reaction-coordinate mode sets, and a Lorentzian spectral density. The authors analyze four correlation regimes and show that, for anti-correlated acceptor vibrations with a large acceptor-acceptor reorganization energy, the two-acceptor/single-acceptor rate ratio can reach 5.82 at 10 K for V_A1A2 = 400 cm^-1, which they compare with the 4- to 5-fold enhancement measured in Ref. 5. The fully correlated limit is benchmarked against an exact two-state Fermi golden rule calculation and agrees.

Significance. If the central mechanism is correct, the paper offers a concrete physical explanation for non-additive rate enhancement in multi-acceptor systems: acceptor-acceptor reorganization energy, generated by anti-correlated reaction-coordinate motion, amplifies higher-order vibronic pathway contributions at low temperature. The framework also yields qualitative design rules (large V_AA, low temperature, large lambda_AA) and extends naturally to three acceptors. The authors provide a reproducible code repository and transparent parameter tables (Tables S1–S3), and the fully correlated case is validated against an exact golden-rule benchmark, which lends credibility to the pathway-summation method in that limit. However, the quantitative comparison with the Phelan experiment rests on assumed, not computed, correlation parameters for the actual molecular structure, so the significance of the experimental claim is currently conditional.

major comments (3)
  1. [Sec. 2.2, Eq. (5), Table S3] The central experimental comparison is grounded in an assumed parameter point rather than a calculation for the molecule of Ref. 5. The anti-correlated simulation uses alpha = sqrt(2+sqrt(3))/2 ≈ 0.97 and beta = -sqrt(2-sqrt(3))/2 ≈ -0.26, chosen specifically so that Eq. (5) gives lambda_AA = 3 lambda = 15,736 cm^-1. Table S3 shows that the headline ratio k_D->A1A2/k_D->A = 5.79 at V_AA = 400 cm^-1 and T = 10 K drops to 4.23 for uncorrelated coordinates, 2.93 for partially correlated coordinates, and 2.88 for fully correlated coordinates. Sec. 3.1 supports the assignment to the anti-correlated regime only with the qualitative statement that the A1->A2 dipole-moment change 'can be substantial.' No calculation of alpha, beta, or lambda_AA for the Phelan molecule is provided. As written, the claim of 'good agreement' with the measured 4- to 5-fold enhancement is therefore an illustration at an assumed parameter point, not a test of the model for the actual molecule. The manuscript should either compute these correlation parameters (e.g., from the DFT charge/displacement data already used in Sec. 2.4) or explicitly reframe the experimental comparison as a conditional prediction that requires verification.
  2. [Sec. 2.4 vs. Sec. 3.1, Fig. 4] The electronic parameters used in the main simulations do not match the values computed for the molecule of Ref. 5. Sec. 2.4 reports DFT-based diabatic couplings V_DA1 = -144.8 cm^-1, V_DA2 = -68.0 cm^-1, and V_AA = 575.8 cm^-1, but the simulations in Fig. 4 and Tables S1–S3 use symmetric V_DA1 = V_DA2 = 109.7 cm^-1 and V_AA up to only 400 cm^-1. The paper does not explain why 109.7 cm^-1 is used instead of the computed values, nor why the computed V_AA = 575.8 cm^-1 is not used in the comparison. This parameter mismatch further weakens the direct quantitative link to the experiment; the predicted ratio of 5.82 is not the ratio for the DFT-characterized molecule.
  3. [Sec. 2.3 and SI Sec. S6] For the general (anti-correlated) case, the rate is computed with a finite-order resummation of acceptor-acceptor pathway terms, as detailed in SI Table S5, and the main text states that pathways with more than two donor-state visits are neglected. The manuscript does not state the truncation order used in the numerical simulations or provide a convergence check. This is load-bearing because the 5.82-fold enhancement is attributed precisely to higher-order AA pathways, and at V_AA = 400 cm^-1 with T = 10 K the AA coupling is not perturbatively small relative to the relevant vibronic energy scales. A convergence test (e.g., increasing the AA pathway order until the rate ratio stabilizes) is needed to demonstrate that the predicted non-additive enhancement is not an artifact of the truncation.
minor comments (5)
  1. [Eqs. (7)–(9)] The equations contain stray '⇐' symbols after the integrals, which appear to be LaTeX artifacts; these should be removed.
  2. [Sec. 3.1] The text says anti-correlated reaction coordinates form 'an angle θ > π'; this should read θ > π/2 (i.e., greater than 90°), consistent with Fig. 2(d).
  3. [Ref. 17] Reference 17 is incomplete: 'J. Am. Chem. Soc. 2024, (17)' lacks the article number or page range.
  4. [Fig. 4 caption] The caption refers to 'First:' and 'Second:' but the figure does not label its two panels; adding (a) and (b) labels would improve clarity.
  5. [Supporting Information] The SI contains several OCR-style artifacts (e.g., 'Vibrnoic Hamiltonian', garbled equation cross-references) that should be cleaned up before publication.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the rate enhancement is a numerical output of the stated Hamiltonian, though the experimental explanation rests on an uncomputed correlation parameter.

full rationale

After walking the derivation chain, I find no circular step. The rate ratio k_D→A1A2/k_D→A is a numerical output of the partial-summation rate theory applied to the Hamiltonian in Eqs. (1)–(4). The anti-correlated parameters α≈0.97, β≈−0.26 set the input reorganization energy λ_AA=3λ through Eq. (5); they do not encode the output ratio. Different correlation cases (Tables S1–S3) give different ratios, so the 5.82 value is not an identity with the chosen λ_AA. The paper does not fit the experimental 4-fold enhancement; it computes ratios at several V_AA values and temperatures, and one point (V_AA=400 cm⁻¹, T=10 K, anti-correlated) is close to the Ref. 5 value. The fully correlated limit is checked against an exact two-state Fermi golden rule, providing independent validation of the machinery. The weakness — that α, β, and λ_AA for the experimental molecule are not computed, only justified qualitatively via dipole-moment arguments — is an unverified-input / correctness risk, not circularity. The pathway-theory citations to the authors' own methodological work are not used to forbid alternatives or to import the central physical conclusion. The derivation is therefore self-contained as a model study, with the experimental attribution depending on an assumption rather than on a circular reduction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The model's central prediction rests on the choice of the correlation parameters (alpha, beta), which set the acceptor-acceptor reorganization energy; on the weak-coupling non-adiabatic assumption; and on coherent summation of vibronic pathways without dephasing. The spectral density and electronic couplings are inputs from prior work or DFT, not derived from first principles in this paper.

free parameters (4)
  • alpha, beta (reaction-coordinate correlation parameters) = anti-correlated: alpha = 0.97, beta = -0.26; partially correlated: alpha = 0.866, beta = 0.5
    Chosen by hand to represent correlation regimes; these directly set the acceptor-acceptor reorganization energy via Eq. (5), and thus control the magnitude of the non-additive enhancement.
  • V_DA (donor-acceptor electronic coupling) = 109.7 cm^-1
    Set equal for both acceptors by symmetry; the value is an average of the magnitudes of DFT-computed couplings VDA1 = -144.84, VDA2 = -67.97 cm^-1 (Sec 2.4), not an independent measurement.
  • V_A1A2 (acceptor-acceptor electronic coupling) = 100, 200, 400 cm^-1 (scan)
    Varied to explore the effect; the experimental molecule's DFT value is 575.79 cm^-1, which is not used in the main rate plots.
  • Spectral density parameters lambda, eta, Omega = lambda = 5245.4 cm^-1, eta = 263.4 cm^-1, Omega = 76.8 cm^-1
    Model bath inputs from prior literature (Refs 30,39), not derived for the specific molecule; they set absolute rates but are not the origin of non-additivity.
assumptions (6)
  • domain assumption Condon approximation: electronic couplings V are independent of nuclear coordinates.
    Sec 2.1 states 'We assume that the electronic interaction (V) between the donor and acceptor diabatic electronic states are independent of nuclear degrees of freedom.'
  • domain assumption Non-adiabatic weak-coupling limit: perturbative expansion in DA coupling to second order.
    Sec 2.1 cites coupling values of about 0.01 eV to justify weak coupling; the rate theory uses second-order DA perturbation theory.
  • ad hoc to paper No vibrational pathway dephasing: all vibronic pathways are summed coherently.
    Sec 2.1 states 'All vibronic pathways are summed coherently (i.e., no vibronic pathway dephasing is included)'; the conclusions state the theory operates 'without explicitly including environmental decoherence'.
  • domain assumption Initial thermal equilibrium on the donor potential surface.
    Sec 2.3 states the initial vibrational distribution is 'in thermal equilibrium, as in the Marcus formulation'.
  • ad hoc to paper Neglect of pathways with more than two donor-state visits.
    Sec 2.3 states paths with more than two DA interactions are weak and 'higher-order pathways that originate from back-scattering between the acceptor sites and D ... are typically small and are not considered here'.
  • ad hoc to paper Truncation of the AA coupling pathway series at finite order for the general (anti-correlated) case.
    SI S6: infinite-order resummation is derived only when the two acceptor Hamiltonians are identical; for general cases only the first few orders are tabulated, and the paper does not state the truncation order used in the rate calculations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Correlated reaction coordinate motion produces non-additive rate enhancement for electron and energy transfer in multi-acceptor structures." pith.science (2026). https://pith.science/paper/CDDJME2I

@misc{pith2026250621504,
  author       = {Pith},
  title        = {Pith review of: Correlated reaction coordinate motion produces non-additive rate enhancement for electron and energy transfer in multi-acceptor structures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CDDJME2I}},
  note         = {Machine review of arXiv:2506.21504}
}
read the original abstract

Molecular structures with multiple donor, bridge, or acceptor units can display quantum interference effects that influence electron and energy transfer (ET and EnT) rates. Recent experiments found a 4- to 5-fold increase in ET rates for donor-acceptor structures with two acceptors compared to one. This result is surprising: simple classical or quantum analysis suggests a factor of two rate enhancement. We analyze the coupling interactions in multiple acceptor systems and find that rate enhancements beyond additive effects arise from acceptor-acceptor interactions that: 1) shift the reaction free energy, 2) change the donor-acceptor couplings, and 3) alter the reaction-coordinate motion. Consideration of these effects explains the observed rates in multi-acceptor systems and suggests strategies to tailor energy and electron transfer kinetics.

Figures

Figures reproduced from arXiv: 2506.21504 by the authors.

Figure 1
Figure 1. The donor-two-acceptor molecule studied in Ref. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Four cases of donor-acceptor vibrations. Each has a [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Leading-order pathways for an electron to remain on [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Transfer rate ratios for two- and one-acceptor tran [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: One and two-acceptor transfer rates, kDA and kDA1A2 , as a function of the free energy for ET/EnT to a single acceptor, ∆G = ED − EA1,2 . The red line indicates the rate for a one-acceptor system. The light-blue line indicates a statistical sum of two one￾acceptor tran…
Figure 6
Figure 6. Figure 6: ET/EnT rates for a donor coupled to three acceptors. [PITH_FULL_IMAGE:figures/full_fig_p027_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    How quantum coherence assists photosynthetic light-harvesting

    Str\"umpfer, J.; Sener, M.; Schulten, K. How quantum coherence assists photosynthetic light-harvesting. J. Phys. Chem. Lett. 2012, 3, 536--542

    work page 2012

  2. [2]

    C.; B\"ohm, M

    Jakowetz, A. C.; B\"ohm, M. L.; Zhang, J.; Sadhanala, A.; Huettner, S.; Bakulin, A. A.; Rao, A.; Friend, R. H. What controls the rate of ultrafast charge transfer and charge separation efficiency in organic photovoltaic blends. J. Am. Chem. Soc. 2016, 138, 11672--11679

    work page 2016

  3. [3]

    A.; Rao, A.; Pavelyev, V

    Bakulin, A. A.; Rao, A.; Pavelyev, V. G.; van Loosdrecht, P. H. M.; Pshenichnikov, M. S.; Niedzialek, D.; Cornil, J.; Beljonne, D.; Friend, R. H. The role of driving energy and delocalized states for charge separation in organic semiconductors. Science 2012, 335, 1340--1344

    work page 2012

  4. [4]

    S.; Beratan, D

    Lin, J.; Balamurugan, D.; Zhang, P.; Skourtis, S. S.; Beratan, D. N. Two-electron transfer pathways. J. Phys. Chem. B 2015, 119, 7589--7597

    work page 2015

  5. [5]

    T.; Zhang, J.; Huang, G.-J.; Wu, Y.-L.; Zarea, M.; Young, R

    Phelan, B. T.; Zhang, J.; Huang, G.-J.; Wu, Y.-L.; Zarea, M.; Young, R. M.; Wasielewski, M. R. Quantum coherence enhances electron transfer rates to two equivalent electron acceptors. J. Am. Chem. Soc. 2019, 141, 12236--12239

    work page 2019

  6. [6]

    L.; Zhang, P.; Beratan, D

    Terai, K.; Yuly, J. L.; Zhang, P.; Beratan, D. N. Correlated particle transport enables biological free energy transduction. Biophys. J. 2023, 122, 1762--1771

    work page 2023

  7. [7]

    V.; Ivanov, A

    Feskov, S. V.; Ivanov, A. I. Efficiency of intramolecular electron transfer from the second excited state of the donor in molecular triads D--A 1--A 2. Russ. J. Phys. Chem. A 2016, 90, 144--151

    work page 2016

  8. [8]

    L.; Zhang, P.; Lubner, C

    Yuly, J. L.; Zhang, P.; Lubner, C. E.; Peters, J. W.; Beratan, D. N. Universal free-energy landscape produces efficient and reversible electron bifurcation. Proc. Natl. Acad. Sci. U.S.A. 2020, 117, 21045--21051

    work page 2020

Show all 54 references
  1. [9]

    Cina, J. A. Dynamics of an excitation-transfer trimer: Interference, coherence, Berry’s phase development, and vibrational control of non-adiabaticity. J. Chem. Phys. 2023, 158

    2023

  2. [10]

    L.; Gouterman, M

    Fulton, R. L.; Gouterman, M. Vibronic coupling. I. Mathematical treatment for two electronic states. J. Chem. Phys. 1961, 35, 1059--1071

    1961

  3. [11]

    Isolating non-adiabatically enhanced ground state quantum beats through two-dimensional electronic spectroscopy

    Sahu, A.; Tiwari, V. Isolating non-adiabatically enhanced ground state quantum beats through two-dimensional electronic spectroscopy. J. Chem. Phys. 2025, 162

    2025

  4. [12]

    E.; Mauck, C

    Hartnett, P. E.; Mauck, C. M.; Harris, M. A.; Young, R. M.; Wu, Y.-L.; Marks, T. J.; Wasielewski, M. R. Influence of anion delocalization on electron transfer in a covalent porphyrin donor--perylenediimide dimer acceptor system. J. Am. Chem. Soc. 2017, 139, 749--756

    2017

  5. [13]

    T.; Schultz, J

    Phelan, B. T.; Schultz, J. D.; Zhang, J.; Huang, G.-J.; Young, R. M.; Wasielewski, M. R. Quantum coherence in ultrafast photo-driven charge separation. Faraday Discuss. 2019, 216, 319--338

    2019

  6. [14]

    Photoinduced Cascading Charge Transfer in Perylene Bisimide-Based Triads

    Loong, H.; Zhou, J.; Jiang, N.; Feng, Y.; Xie, G.; Liu, L.; Xie, Z. Photoinduced Cascading Charge Transfer in Perylene Bisimide-Based Triads. J. Phys. Chem. B 2022, 126, 2441--2448

    2022

  7. [15]

    M.; Krzyaniak, M

    Bancroft, L.; Zhang, J.; Harvey, S. M.; Krzyaniak, M. D.; Zhang, P.; Schaller, R. D.; Beratan, D. N.; Young, R. M.; Wasielewski, M. R. Charge transfer and spin dynamics in a zinc porphyrin donor covalently linked to one or two naphthalenediimide Acceptors. J. Phys. Chem. A 202...

    2021

  8. [16]

    Fisher, J. M. Fundamental Electron Transfer Dynamics in Donor-Acceptor Compounds: One-, Two-, and Four-Pathway Systems. Ph.D.\ thesis, Northwestern University, 2023

    2023

  9. [17]

    M.; Williams, M

    Fisher, J. M.; Williams, M. L.; Palmer, J. R.; Powers-Riggs, N. E.; Young, R. M.; Wasielewski, M. R. Long-Lived Charge Separation in Single Crystals of an Electron Donor Covalently Linked to Four Acceptor Molecules. J. Am. Chem. Soc. 2024,

    2024

  10. [18]

    D.; Silbey, R

    Jang, S.; Newton, M. D.; Silbey, R. J. Multichromophoric F \"o rster resonance energy transfer. Phys. Rev. Lett. 2004, 92, 218301

    2004

  11. [19]

    D.; Silbey, R

    Jang, S.; Newton, M. D.; Silbey, R. J. Multichromophoric F \"o rster resonance energy transfer from B800 to B850 in the light harvesting complex 2: evidence for subtle energetic optimization by purple bacteria. J. Phys. Chem. B 2007, 111, 6807--6814

    2007

  12. [20]

    Theory of multichromophoric coherent resonance energy transfer: A polaronic quantum master equation approach

    Jang, S. Theory of multichromophoric coherent resonance energy transfer: A polaronic quantum master equation approach. J. Chem. Phys. 2011, 135

    2011

  13. [21]

    D.; Jordanides, X

    Scholes, G. D.; Jordanides, X. J.; Fleming, G. R. Adapting the F \"o rster theory of energy transfer for modeling dynamics in aggregated molecular assemblies. J. Phys. Chem. B 2001, 105, 1640--1651

    2001

  14. [22]

    Scholes, G. D. Long-range resonance energy transfer in molecular systems. Annu. Rev. Phys. Chem. 2003, 54, 57--87

    2003

  15. [23]

    D.; Fleming, G

    Scholes, G. D.; Fleming, G. R. On the mechanism of light harvesting in photosynthetic purple bacteria: B800 to B850 energy transfer. J. Phys. Chem. B 2000, 104, 1854--1868

    2000

  16. [24]

    B.; Kassal, I

    Taylor, N. B.; Kassal, I. Generalised Marcus theory for multi-molecular delocalised charge transfer. Chem. Sci. 2018, 9, 2942--2951

    2018

  17. [25]

    R.; Ratner, M

    Zarea, M.; Powell, D.; Renaud, N.; Wasielewski, M. R.; Ratner, M. A. Decoherence and quantum interference in a four-site model system: Mechanisms and turnovers. J. Phys. Chem. B 2013, 117, 1010--1020

    2013

  18. [26]

    L.; Zhang, P.; Ru, X.; Terai, K.; Singh, N.; Beratan, D

    Yuly, J. L.; Zhang, P.; Ru, X.; Terai, K.; Singh, N.; Beratan, D. N. Efficient and reversible electron bifurcation with either normal or inverted potentials at the bifurcating cofactor. Chem 2021, 7, 1870--1886

    2021

  19. [27]

    D.; Wasielewski, M

    Powell, D. D.; Wasielewski, M. R.; Ratner, M. A. Redfield Treatment of Multipathway Electron Transfer in Artificial Photosynthetic Systems. J. Phys. Chem. B 2017, 121, 7190--7203

    2017

  20. [28]

    P.; Phelan, B

    Lin, C.; O’Connor, J. P.; Phelan, B. T.; Young, R. M.; Wasielewski, M. R. Ultrafast Charge Transfer Dynamics in a Slip-Stacked Donor--Acceptor--Acceptor System. J. Phys. Chem. A 2023,

    2023

  21. [29]

    Mattuck, R. D. A guide to Feynman diagrams in the many-body problem, 2nd ed.; Dover Publications, 1992

    1992

  22. [30]

    N.; Beratan, D

    Onuchic, J. N.; Beratan, D. N.; Hopfield, J. J. Some aspects of electron-transfer reaction dynamics. J. Phys. Chem. 1986, 90, 3707--3721

    1986

  23. [31]

    N.; de Andrade, P

    Onuchic, J. N.; de Andrade, P. C. P.; Beratan, D. N. Electron tunneling pathways in proteins: a method to compute tunneling matrix elements in very large systems. J. Chem. Phys. 1991, 95, 1131--1138

    1991

  24. [32]

    D.; Evans, D

    Coalson, R. D.; Evans, D. G.; Nitzan, A. A nonequilibrium golden rule formula for electronic state populations in nonadiabatically coupled systems. J. Chem. Phys. 1994, 101, 436--448

    1994

  25. [33]

    G.; Nitzan, A.; Ratner, M

    Evans, D. G.; Nitzan, A.; Ratner, M. A. Photoinduced electron transfer in mixed-valence compounds: Beyond the golden rule regime. J. Chem. Phys. 1998, 108, 6387--6393

    1998

  26. [34]

    Newton, M. D. Quantum chemical probes of electron-transfer kinetics: the nature of donor-acceptor interactions. Chem. Rev. 1991, 91, 767--792

    1991

  27. [35]

    S.; Waldeck, D

    Skourtis, S. S.; Waldeck, D. H.; Beratan, D. N. Inelastic electron tunneling erases coupling-pathway interferences. J. Phys. Chem. B 2004, 108, 15511--15518

    2004

  28. [36]

    S.; Beratan, D

    Skourtis, S. S.; Beratan, D. N. Theories of structure-function relationships for bridge-mediated electron transfer reactions. Adv. Chem. Phys. 1999, 106, 377--452

    1999

  29. [37]

    K.; Jonas, D

    Tiwari, V.; Peters, W. K.; Jonas, D. M. Electronic energy transfer through non-adiabatic vibrational-electronic resonance. I. Theory for a dimer. J. Chem. Phys. 2017, 147

    2017

  30. [38]

    Solvent effects on the electron transfer reactions in supramolecular systems

    Najbar, J.; Tachiya, M. Solvent effects on the electron transfer reactions in supramolecular systems. J. Photochem. Photobiol., A 1996, 95, 51--59

    1996

  31. [39]

    Calculation of electron transfer rates using mixed quantum classical approaches: Nonadiabatic limit and beyond

    Xie, W.; Bai, S.; Zhu, L.; Shi, Q. Calculation of electron transfer rates using mixed quantum classical approaches: Nonadiabatic limit and beyond. J. Phys. Chem. A 2013, 117, 6196--6204

    2013

  32. [40]

    F.; Mendive-Tapia, D.; Bearpark, M

    Izmaylov, A. F.; Mendive-Tapia, D.; Bearpark, M. J.; Robb, M. A.; Tully, J. C.; Frisch, M. J. Nonequilibrium Fermi golden rule for electronic transitions through conical intersections. J. Chem. Phys. 2011, 135, 234106

    2011

  33. [41]

    Nonequilibrium Fermi’s golden rule charge transfer rates via the linearized semiclassical method

    Sun, X.; Geva, E. Nonequilibrium Fermi’s golden rule charge transfer rates via the linearized semiclassical method. J. Chem. Theory Comput. 2016, 12, 2926--2941

    2016

  34. [42]

    S.; Rubtsov, I

    Xiao, D.; Skourtis, S. S.; Rubtsov, I. V.; Beratan, D. N. Turning charge transfer on and off in a molecular interferometer with vibronic pathways. Nano Lett. 2009, 9, 1818--1823

    2009

  35. [43]

    Lepage, G. P. Adaptive multidimensional integration: VEGAS enhanced. J. Comput. Phys. 2021, 439, 110386

    2021

  36. [44]

    E.; Yeganeh, S.; Cave, R

    Subotnik, J. E.; Yeganeh, S.; Cave, R. J.; Ratner, M. A. Constructing diabatic states from adiabatic states: Extending generalized Mulliken--Hush to multiple charge centers with Boys localization. J. Chem. Phys. 2008, 129

    2008

  37. [45]

    partial-summation

    Nuomin, H. partial-summation. https://github.com/Beratan-Lab-Duke/partial-summation, 2024

    2024

  38. [46]

    L.; Palmer, J

    Williams, M. L.; Palmer, J. R.; Young, R. M.; Wasielewski, M. R. Charge Transfer Dynamics in Supramolecular Tessellations Composed of Aromatic Donors and Chiral Tris (naphthalenediimide) Triangular Acceptors. J. Am. Chem. Soc. 2024, 146, 34130--34140

    2024

  39. [47]

    J.; Verhoeven, J

    Brouwer, A.; Eijckelhoff, C.; Willemse, R. J.; Verhoeven, J. W.; Schuddeboom, W.; Warman, J. M. Two-step sequential light-induced electron transfer in a simple trichromophoric donor-donor-acceptor system. J. Am. Chem. Soc. 1993, 115, 2988--2989

    1993

  40. [48]

    H.; Kim, Y

    Yonemoto, E. H.; Kim, Y. I.; Schmehl, R. H.; Wallin, J. O.; Shoulders, B. A.; Richardson, B. R.; Haw, J. F.; Mallouk, T. E. Photoinduced electron transfer reactions in zeolite-based donor-acceptor and donor-donor-acceptor diads and triads. J. Am. Chem. Soc. 1994, 116, 10557--10563

    1994

  41. [49]

    J.; Verhoeven, J

    Willemse, R. J.; Verhoeven, J. W.; Brouwer, A. M. Reversible charge migration in the excited state of an electron Donor-Donor-Acceptor system detected via delayed charge transfer fluorescence. J. Phys. Chem. 1995, 99, 5753--5756

    1995

  42. [50]

    E.; Pandey, L.; Barlow, S.; Tiwari, S

    Polander, L. E.; Pandey, L.; Barlow, S.; Tiwari, S. P.; Risko, C.; Kippelen, B.; Bredas, J.-L.; Marder, S. R. Benzothiadiazole-dithienopyrrole donor--acceptor--donor and acceptor--donor--acceptor triads: synthesis and optical, electrochemical, and charge-transport properties. ...

    2011

  43. [51]

    S.; Gierschner, J.; Yoon, S.-J.; Park, S

    Kwon, M. S.; Gierschner, J.; Yoon, S.-J.; Park, S. Y. Unique piezochromic fluorescence behavior of dicyanodistyrylbenzene based donor--acceptor--donor triad: mechanically controlled photo-induced electron transfer (eT) in molecular assemblies. Adv. Mater. 2012, 24, 5487--5492

    2012

  44. [52]

    Lin, J.-A.; Li, S.-W.; Liu, Z.-Y.; Chen, D.-G.; Huang, C.-Y.; Wei, Y.-C.; Chen, Y.-Y.; Tsai, Z.-H.; Lo, C.-Y.; Hung, W.-Y.; others Bending-type electron donor--donor--acceptor triad: dual excited-state charge-transfer coupled structural relaxation. Chem. Mater. 2019, 31, 5981--5992

    2019

  45. [53]

    U.; Miao, J.; Meng, H

    Zhao, J.; Yao, C.; Ali, M. U.; Miao, J.; Meng, H. Recent advances in high-performance organic solar cells enabled by acceptor--donor--acceptor--donor--acceptor (A--DA'D--A) type acceptors. Mater. Chem. Front. 2020, 4, 3487--3504

    2020

  46. [54]

    Charge-Separated States Determined Photoinduced Electron Transfer Efficiency in a DDA System in an External Electric Field

    Wang, X.; Wang, H.; Zhang, M.; Pullerits, T.; Song, P. Charge-Separated States Determined Photoinduced Electron Transfer Efficiency in a DDA System in an External Electric Field. J. Phys. Chem. C 2023, 127, 2805--2817 mcitethebibliography main_renamed.tex0000664000000000000000...

    2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.