{"id":"5b365cff-140a-40c5-969f-ff638f334e06","arxiv_id":"2506.21504","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Correlated, especially anti-correlated, acceptor vibrations create a large acceptor-acceptor reorganization energy that amplifies quantum vibronic pathways, yielding electron and energy transfer rate enhancements well beyond the naive factor of two.","lead":"A theoretical model of electron and energy transfer between a donor and two or more electron acceptors shows that the way the acceptor vibrations move together can make the transfer much faster than the simple sum of single-acceptor rates. The work explains the surprisingly large 4- to 5-fold rate boosts seen in recent experiments and gives design principles for multi-acceptor materials used in light harvesting and charge separation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 5.8-fold prediction and the claimed 4-fold agreement rest on an assumed anti-correlation geometry (α≈0.97, β≈−0.26, λ_AA=3λ) that is never computed for the actual molecule; the ratio drops to roughly 3–4 for less extreme choices, so the experimental comparison is not yet supported.","rationale":"I agree with the reader's weakest assumption. I also considered whether a more internal problem exists: the perturbative AA-pathway expansion is not shown to be converged for the anti-correlated case, and dephasing is neglected. Those concerns are secondary because even a converged exact calculation would still require a value for α/β and λ_AA. The fully correlated limit is benchmarked exactly, and the classical high-temperature upper bound of 2 is a useful independent check, so the framework itself has real support. The soft spot is parameter selection: the anti-correlated point is chosen to maximize the effect, and the paper's own Tables S1–S3 demonstrate that the predicted 5.8-fold enhancement is highly sensitive to that choice. Since Sec. 2.4 characterizes only electronic couplings, not vibrational correlation, the experimental comparison is not yet grounded in the molecular system. The proposed normal-mode/QM-MM calculation is a feasible, direct way to decide whether the experimental molecule actually inhabits the anti-correlated regime; until that check is done, the conditional verdict is appropriate.","tokens_in":44405,"tokens_out":7380,"duration_ms":84224,"concrete_test":"One decisive check: compute, from DFT normal modes (or QM/MM with the experimental DAA structure), the Huang–Rhys displacements for the D→A1, D→A2, and A1→A2 charge-transfer states, and reduce them to α and β (or directly to λ_AA and the reaction-coordinate angle θ). Then rerun the partial-summation rate at T=10 K using these molecule-specific α,β and the Sec. 2.4 couplings, retaining V_DA1≠V_DA2. If the inferred λ_AA is below 3λ or θ≤90°, the computed ratio will fall below about 4, confirming that the 4–5-fold agreement was an artifact of the assumed anti-correlation; if λ_AA≈3λ and θ≈120°, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the assignment of the experimental molecule to the anti-correlated regime. In Sec. 2.2, the anti-correlated simulation point α=(√(2+√3))/2≈0.97, β=−(√(2−√3))/2≈−0.26 is chosen so that the acceptor–acceptor reorganization energy of Eq. (5) equals 3λ=15,736 cm^-1. Tables S1–S3 show the entire quantitative story depends on this: at V_AA=400 cm^-1 and T=10 K, the two-acceptor/single-acceptor ratio is 5.79 for this point, but only 4.23 for uncorrelated (2λ), 2.93 for partially correlated (0.27λ), and 2.88 for fully correlated (0λ). The paper provides no calculation of α/β, or of λ_AA, for the Phelan molecule; Sec. 3.1 supports the assignment only with the qualitative statement that the A1→A2 dipole-moment change 'can be substantial.' The DFT in Sec. 2.4 computes electronic couplings (V_DA1=−144.8, V_DA2=−68.0, V_AA=575.8 cm^-1) but no vibrational correlation parameters, and the main simulations instead use symmetric V_DA=109.7 cm^-1 and V_AA≤400 cm^-1. Therefore the 'good agreement' with the measured 4–5-fold enhancement is not a test of the model for the actual molecule; it is an illustration at an assumed parameter point. If a realistic λ_AA is less than 3λ or the correlation angle is not >90°, the predicted ratio falls to roughly 3–4, and the claimed explanation of the experiment no longer follows.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":44837,"tokens_out":4163,"duration_ms":46805,"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":[{"comment":"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.","section":"Sec. 2.2, Eq. (5), Table S3"},{"comment":"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.","section":"Sec. 2.4 vs. Sec. 3.1, Fig. 4"},{"comment":"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.","section":"Sec. 2.3 and SI Sec. S6"}],"minor_comments":[{"comment":"The equations contain stray '⇐' symbols after the integrals, which appear to be LaTeX artifacts; these should be removed.","section":"Eqs. (7)–(9)"},{"comment":"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).","section":"Sec. 3.1"},{"comment":"Reference 17 is incomplete: 'J. Am. Chem. Soc. 2024, (17)' lacks the article number or page range.","section":"Ref. 17"},{"comment":"The caption refers to 'First:' and 'Second:' but the figure does not label its two panels; adding (a) and (b) labels would improve clarity.","section":"Fig. 4 caption"},{"comment":"The SI contains several OCR-style artifacts (e.g., 'Vibrnoic Hamiltonian', garbled equation cross-references) that should be cleaned up before publication.","section":"Supporting Information"}],"recommendation":"major_revision","confidential_remarks":"The framework is promising and the fully correlated benchmark is a genuine strength, but the paper currently overstates the experimental validation because the anti-correlated parameter point is assumed rather than derived for the Phelan molecule. A revision that either computes alpha/beta (or lambda_AA) for the actual system, or explicitly presents the experimental comparison as a conditional illustration, would be appropriate for this journal. The convergence of the pathway truncation in the general case should also be addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a real mechanism, not a numerical artifact, but the paper oversells the experiment comparison. The new idea is that acceptor–acceptor reorganization energy, arising from correlated (especially anti-correlated) reaction-coordinate motion, can give non-additive rate enhancement beyond the statistical factor of N and beyond the symmetric-superposition sqrt(2) coupling boost. That is a genuine addition to the earlier Phelan picture. The fully correlated limit is treated analytically, the partial summation is benchmarked against the exact two-state Fermi golden rule there, and the agreement is good. The code is available and the DFT couplings are a concrete attempt to connect to the experimental molecule. These are real strengths.\n\nThe soft spots are where the reader and stress-test put them. The headline quantitative claim—the 5.82 ratio at V_AA=400 cm^-1, T=10 K that is compared to the measured 4–5x enhancement—rests on choosing alpha≈0.97, beta≈−0.26 so that the AA reorganization energy is exactly 3λ. That choice is not derived for the Phelan molecule. The paper offers only a qualitative dipole-moment argument, and the DFT section computes electronic couplings, not the vibrational correlation parameters. Without that, the 'good agreement' is really an illustration at an assumed parameter point, not a test. The stress-test note is right: for uncorrelated (2λ) the ratio is 4.23, for partially correlated 0.27λ it is 2.93, and for fully correlated it is 2.88. So the experimental claim is not load-bearing for the mechanism, but it is currently unsupported.\n\nTwo smaller issues. The truncation order of the pathway expansion in the general anti-correlated case is not stated explicitly; the SI shows infinite-order resummation in the AA coupling when the acceptor vibrational Hamiltonians are identical, but for the anti-correlated case I did not see convergence control. Dephasing is neglected by design, which is acceptable for a first mechanism paper but should be flagged as a limitation. The paper does acknowledge the golden-rule regime, so I don't want to overstate this.\n\nWho is this for? Physical chemists working on charge/energy transfer in multi-chromophore systems, and experimentalists who want design rules. A serious referee should see it, but the revision needs either a real calculation of alpha/beta for the experimental molecule or a clear reframing: this is a mechanism paper, not yet an explanation of the specific 4-fold experiment. I'd take it to review.","headline":"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.","tokens_in":45343,"tokens_out":1750,"would_cite":false,"duration_ms":18783,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["electron transfer","energy transfer","multi-acceptor systems","vibronic coupling","reaction-coordinate correlation","acceptor-acceptor reorganization energy","non-additive rate enhancement","quantum interference"],"falsifier":"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.","tokens_in":44167,"feed_emoji":"⚡","tokens_out":18355,"duration_ms":171936,"temperature":0.7,"pith_summary":"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.","feed_headline":"Two-acceptor transfer runs 5.8-fold faster when vibrations oppose","feed_subtitle":"Model traces the 4-fold rate gain to out-of-phase acceptor vibrations amplified by low temperature.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the central experimental observation — the 4- to 5-fold ET rate enhancement in the anthracene–1,4-benzoquinone donor–two-acceptor molecule — and the earlier coupling-based explanation this paper extends.","marker":"[5]"},{"why":"Provides additional two-acceptor experimental rate data and, together with Ref. 15, serves as the nearly parallel (pi-stacked) dipole case that the model predicts should show only additive enhancement.","marker":"[13]"},{"why":"Reports the zinc porphyrin–two-NDI acceptor measurement whose nearly parallel charge-transfer dipoles make it the comparison system with small acceptor–acceptor reorganization energy.","marker":"[15]"},{"why":"Documents the four-fold faster ET of perylene–(NDI)4 versus single-NDI species, one of the multi-acceptor observations the theory is built to explain.","marker":"[16]"},{"why":"Reports long-lived charge separation in a donor linked to four acceptors, extending the multi-acceptor rate data beyond two acceptors.","marker":"[17]"},{"why":"Supplies the generalized Marcus theory used to prove that classical high-temperature vibrations cap the two-acceptor enhancement at twice the single-acceptor rate.","marker":"[24]"},{"why":"Provides the diagrammatic many-body formalism on which the partial summation of vibronic pathways is based.","marker":"[29]"},{"why":"Supplies the electron-transfer dynamical model and the Lorentzian spectral density used for the vibrational bath in the rate simulations.","marker":"[30]"},{"why":"Provides the nonequilibrium golden rule population formula that underlies the rate calculation and the exact two-state benchmark in the fully correlated limit.","marker":"[32]"},{"why":"The generalized Mulliken–Hush method used to compute the diabatic couplings ($V_{DA1}$, $V_{DA2}$, $V_{A1A2}$) of the experimental molecule from DFT-computed transition dipoles.","marker":"[44]"}],"fun_headline_variants":["Out-of-phase acceptor vibrations drive 5.8x rate boost","Correlated motion explains non-additive transfer gains","Two acceptors beat one: out-of-phase vibrations amplify rates","Correlated acceptor motion yields 5.8x non-additive rate boost","Vibrational coupling boosts two-acceptor electron transfer 5.8x"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Out-of-phase acceptor vibrations drive 5.8x rate boost","Correlated motion explains non-additive transfer gains","Two acceptors beat one: out-of-phase vibrations amplify rates","Correlated acceptor motion yields 5.8x non-additive rate boost","Vibrational coupling boosts two-acceptor electron transfer 5.8x"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00105,"raw_usage":{"total_tokens":4427,"prompt_tokens":977,"completion_tokens":3450,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":593,"completion_tokens_details":{"reasoning_tokens":3360}},"tokens_in":593,"tokens_out":3450,"duration_ms":26542,"temperature":1.0,"reasoning_tokens":3360,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:23:51.437378+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"T.; Zhang, J.; Huang, G.-J.; Wu, Y.-L.; Zarea, M.; Young, R","cited_arxiv_id":null,"evidence_quote":"Supplies the central experimental observation — the 4- to 5-fold ET rate enhancement in the anthracene–1,4-benzoquinone donor–two-acceptor molecule — and the earlier coupling-based explanation this paper extends."},{"cited_title":"T.; Schultz, J","cited_arxiv_id":null,"evidence_quote":"Provides additional two-acceptor experimental rate data and, together with Ref. 15, serves as the nearly parallel (pi-stacked) dipole case that the model predicts should show only additive enhancement."},{"cited_title":"M.; Krzyaniak, M","cited_arxiv_id":null,"evidence_quote":"Reports the zinc porphyrin–two-NDI acceptor measurement whose nearly parallel charge-transfer dipoles make it the comparison system with small acceptor–acceptor reorganization energy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the four-fold faster ET of perylene–(NDI)4 versus single-NDI species, one of the multi-acceptor observations the theory is built to explain."},{"cited_title":"M.; Williams, M","cited_arxiv_id":null,"evidence_quote":"Reports long-lived charge separation in a donor linked to four acceptors, extending the multi-acceptor rate data beyond two acceptors."},{"cited_title":"B.; Kassal, I","cited_arxiv_id":null,"evidence_quote":"Supplies the generalized Marcus theory used to prove that classical high-temperature vibrations cap the two-acceptor enhancement at twice the single-acceptor rate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the diagrammatic many-body formalism on which the partial summation of vibronic pathways is based."},{"cited_title":"N.; Beratan, D","cited_arxiv_id":null,"evidence_quote":"Supplies the electron-transfer dynamical model and the Lorentzian spectral density used for the vibrational bath in the rate simulations."},{"cited_title":"D.; Evans, D","cited_arxiv_id":null,"evidence_quote":"Provides the nonequilibrium golden rule population formula that underlies the rate calculation and the exact two-state benchmark in the fully correlated limit."},{"cited_title":"E.; Yeganeh, S.; Cave, R","cited_arxiv_id":null,"evidence_quote":"The generalized Mulliken–Hush method used to compute the diabatic couplings ($V_{DA1}$, $V_{DA2}$, $V_{A1A2}$) of the experimental molecule from DFT-computed transition dipoles."}],"review_version":1}