{"id":"0882bd8d-8a61-4db5-87c1-63b9de6c1a5a","arxiv_id":"2607.25639","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In a two-parabola model of non-adiabatic electron transfer, the mean transition path time can reach roughly a tenth of the macroscopic reaction time at large diabatic coupling.","lead":"This paper simulates a two-parabola model of electron transfer using Langevin dynamics and Zhu–Nakamura surface hopping, measuring how long the microscopic transition across the barrier takes compared with the overall reaction. It finds that the microscopic transition path time can exceed about five percent of the total reaction time at large diabatic coupling, so the hop is not always effectively instantaneous.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim may conflate coordinate barrier-crossing time with electron-transfer time: the coordinate-only TPT counts non-reactive segments that reach +x0 while still in the reactant electronic state.","rationale":"The paper is a careful simulation study, and the Zhu-Nakamura plus Langevin approach is reasonable. The quantitative claim, however, stands or falls on what is meant by a 'microscopic transition process.' Since the two-parabola model's reaction coordinate does not by itself define the electronic state, a coordinate-only TPT includes trajectories that cross the barrier region but remain on the reactant diabatic surface. This is not a small edge case: in the non-adiabatic regime the hopping probability is high, so a trajectory approaching the crossing on the lower adiabat will often hop to the upper (reactant-like) adiabat and later recross. The mTPT then averages over the time spent in the barrier by all such unproductive excursions. The central claim that the timescale of the microscopic transfer process can be a non-negligible fraction of the macroscopic reaction time requires conditioning on actual product formation. The reader's identified x0 dependence is real but less threatening: Appendix B shows larger x0 shifts TPT to longer times, and since the authors choose the smallest x0, the reported ratio is a lower bound in x0. The unresolved conditioning issue can be decided by a straightforward re-analysis of the same trajectories, so the conditional verdict remains appropriate. No change to the reader's verdict is needed, but the justification for conditionality should shift from the x0 concern to the electronic-state conditioning concern.","tokens_in":8605,"tokens_out":14044,"duration_ms":159827,"concrete_test":"Recompute mTPT (and the ratio to tau) using the same trajectories but define a successful microscopic transition only if the segment starts at -x0 with reactant character and first reaches +x0 with product character — e.g., requiring the active adiabatic surface at +x0 to be the lower surface (|c_r|^2 < 1/2). Apply this to the (V, gamma) point highlighted in Sec. III.D, e.g., V=3.43 meV and the gamma value for which mTPT > 5% of tau. If the electronically conditioned mTPT is no longer >5% of tau, the central claim is an artifact of including non-reactive barrier recrossings; if it remains >5%, the claim survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim (Sec. III.D) treats the mean transition path time mTPT as the timescale of the microscopic electron-transfer event. But the TPT defined in Sec. II.C.2 is purely coordinate-based: a transition path is any segment from -x0 to +x0 that does not return to -x0. No condition is imposed on the active adiabatic state or the diabatic population at the endpoint. In a two-parabola model with hopping, a trajectory can reach +x0 while remaining on the upper adiabat, whose character at x0 is still reactant-like (|c_r,2|^2 ~ 1); such a segment is a non-reactive barrier excursion, not an electron-transfer event. In the non-adiabatic regime P_hop is large, so these non-reactive excursions are common and can dominate the average mTPT. Fig.8 shows repeated crossings of the crossing point within a single TPT; without conditioning on the final electronic state, the reported mTPT—and hence the >5% ratio—may be inflated by passages that never change chemical identity. The paper explicitly acknowledges the arbitrary x0 (Sec. II.C.2, App. B), but this more basic ambiguity is not addressed. Note that choosing the smallest x0 actually makes mTPT a lower bound with respect to x0, so the x0 dependence is not the main threat to the claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a symmetric two-parabola model of condensed-phase non-adiabatic electron transfer, propagating nuclear dynamics with Langevin equations and electronic transitions via Zhu–Nakamura hopping probabilities. It defines a transition path as any coordinate-space segment from -x0 to +x0 that does not return to -x0, and computes the mean transition path time (mTPT) and the macroscopic reaction time tau from the reactant population decay. The main finding is that mTPT depends primarily on the friction parameter gamma, tau depends primarily on the diabatic coupling V, and for V=3.43 meV the mTPT exceeds 5% of tau, suggesting that the microscopic electron-transfer event is not always negligible compared with the overall reaction timescale.","tokens_in":8986,"tokens_out":6384,"duration_ms":65533,"significance":"If the central claim is robust, the paper provides a concrete counterexample to the common assumption that microscopic ET events are instantaneous relative to macroscopic reaction times in the non-adiabatic regime. The study combines a well-established non-adiabatic transition theory (Zhu–Nakamura) with Kramers-like Langevin dynamics and performs systematic scans over V and gamma, which is a useful methodology. The comparison with the analytical P_hop=0 TPT distribution also helps to interpret the non-adiabatic effects. However, the quantitative claim (mTPT > 5% of tau) rests on a coordinate-only definition of a transition path that does not condition on the electronic state being the product state, and the lack of statistical error bars on the reported mean values weakens the quantitative conclusions. The qualitative separation of timescales (gamma controls mTPT, V controls tau) is supported by the figures, but the specific ratio claims require further analysis.","major_comments":[{"comment":"The transition path is defined purely by reaching +x0 in the coordinate, with no condition on the electronic state. In the non-adiabatic regime (small V), the upper adiabatic surface has predominantly reactant diabatic character at positive x (Eq. 6 gives |c_r,2|^2 ~ 1 for small V), so a trajectory can reach +x0 on the upper adiabat without undergoing electron transfer. Figure 8 shows multiple recrossings within a TPT but does not distinguish reactive from non-reactive segments. The central claim (e.g., mTPT > 5% of tau at V=3.43 meV) may therefore be inflated by non-reactive barrier excursions. Please re-analyze TPTs conditioned on the final state being the product (e.g., |c_p|^2 > 1/2 at +x0) or at least report the fraction of coordinate-only TPTs that are non-reactive in the parameter range where the ratio exceeds 5%.","section":"§II.C.2, §III.D, Fig. 8"},{"comment":"The mTPT depends on the arbitrarily chosen boundary x0. The paper states that results \"did not vary significantly\" with x0, but Appendix B explicitly says the TPT distribution shifts to longer durations as x0 increases when gamma is large. Since the central quantitative claim is the ratio mTPT/tau, a robustness analysis showing the ratio across the six tested x0 values is needed. Without it, the reader cannot assess how much of the >5% figure is due to the specific choice x0=2.06 amu^(1/2) Å.","section":"§II.C.2, §V.B"},{"comment":"No statistical error bars are reported for tau or mTPT. For a quantitative claim such as \"the mTPT is greater than 5% of tau,\" standard errors or confidence intervals are necessary to determine whether the difference is significant. With 10,000 trajectories for population dynamics and 100,000 for TPT analysis, the estimates may be precise, but correlated events (multiple TPTs from one trajectory) could reduce the effective sample size. Please include error estimates, especially for the mTPT/tau ratio.","section":"§III (Figs. 4-10)"}],"minor_comments":[{"comment":"Typographical error: \"out scope\" should be \"our scope\". Also, \"logistic scale\" in several figure captions (Figs. 5, 6, 9, 10, 11) should be \"logarithmic scale\" (or \"log scale\").","section":"§II.D"},{"comment":"The identification of tau=1/k with the mean first-passage time is reasonable for a two-state Markov process, but the phrase \"time constant\" is ambiguous because the exponential decay in Eq. (14) has time constant 1/(2k). Since tau=1/k is larger than 1/(2k), the ratio mTPT/tau is conservative; please clarify the definition in the text.","section":"§II.C.1, Eq. (14)"},{"comment":"The sentence \"because the sign after b^4 is minus\" is unclear. Please spell out the formula for the case of opposite-slope crossings; the Zhu–Nakamura formula contains both plus and minus variants, and the reader should not have to infer the sign convention.","section":"Eq. (9)"}],"recommendation":"major_revision","confidential_remarks":"The central physical question is timely and the simulations are straightforward, but the coordinate-only TPT definition is the main obstacle: the paper's headline quantitative claim may conflate solvent barrier crossings with actual electron transfer. The authors should be asked to condition the TPT on the electronic state or to demonstrate that non-reactive crossings are negligible in the regime where the claim is made. Adding error bars and an x0-robustness check would also strengthen the paper. I recommend major revision rather than rejection because the core finding is plausible and the requested analyses are within the scope of the existing simulation framework."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a straightforward, well-executed simulation study that brings transition path time analysis to non-adiabatic electron transfer in a symmetric two-parabola model. The new bit is the numerical finding that the mean TPT is controlled by friction whereas the overall rate is controlled by diabatic coupling, and that under strong coupling the mTPT can be ~5% or more of the reaction time. That qualitative separation is worth knowing.\n\nThe methods are appropriate: Langevin dynamics with Zhu-Nakamura hopping, a clear definition of the reactant population, and a sensible check against the known analytical TPT distribution for the no-hopping limit. They also test six values of the boundary x0 and show the distribution shape is fairly stable, and they use 100,000 trajectories for the TPT statistics. The main claims are read directly from trajectory statistics, not produced by fitting parameters.\n\nSoft spots, in order of importance.\n\nFirst, the TPT definition is purely coordinate-based. A transition path is any segment that goes from −x0 to +x0 without returning to −x0; nothing checks whether the trajectory actually changes its electronic state. On the upper adiabat at +x0 the system is still mostly reactant-like, so a path that reaches +x0 while hopping onto the upper surface is a failed or non-reactive barrier excursion, not an electron transfer. In the non-adiabatic regime, hopping to the upper surface is common, so such excursions can contaminate the mTPT and inflate the ratio to τ. The paper shows (Fig. 8) that paths often cross the crossing point many times; without conditioning on the final diabatic/adiabatic population, the reported mTPT is not clearly an electron-transfer time. This is a load-bearing ambiguity for the central claim. The authors should either condition the TPT on the electronic state at +x0, or explicitly reframe the result as a coordinate-barrier-crossing time rather than an ET time.\n\nSecond, no statistical error bars are reported for mTPT or τ. With 100,000 trajectories the errors are probably small, but a couple of bootstrap intervals would make the \">5% of τ\" claim easier to trust.\n\nThird, the x0 dependence is actually less threatening than the paper makes it seem: they pick the smallest x0, which gives the shortest TPTs, so their ratio is a lower bound with respect to that parameter. The Appendix could say that explicitly.\n\nThe analytical reference curves use ω' = ω for the inverted parabola, which is a coarse approximation, but it is only a benchmark and does not drive the conclusions.\n\nOverall, the paper is clear and the simulations look honest. It deserves a serious referee, but the referee should push for a clearer definition of what \"transition\" means electronically and a robustness check that conditions on the final state. I wouldn't cite the quantitative conclusion in my own work until that is resolved.","headline":"The paper is a clean computational study of transition path times in a two-parabola model, but the central quantitative claim that the microscopic ET event can take >5% of the macroscopic time rests on a coordinate-only TPT definition that may count non-reactive barrier excursions as transfers.","tokens_in":9420,"tokens_out":4800,"would_cite":false,"duration_ms":51233,"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":"In the non-adiabatic regime of a two-parabola electron-transfer model, the microscopic crossing time can be a non-negligible fraction of the overall reaction time, challenging the usual 'instantaneous transfer' assumption.","keywords":["electron transfer","non-adiabatic dynamics","transition path time","two-parabola model","Langevin dynamics","diabatic coupling","timescale separation","Kramers theory"],"falsifier":"Run the same Langevin curve-crossing hopping simulation with a substantially smaller x0 (e.g., 0.1 amu^1/2 Å) and recompute mTPT/τ for V = 3.43 meV; if the ratio falls below 1% across the γ range, the central 'non-negligible' claim would not survive the boundary choice. Alternatively, compare with a full quantum-mechanical simulation of the two-parabola model to see whether the classical hopping treatment overestimates the microscopic crossing time.","tokens_in":8550,"feed_emoji":"⚡","tokens_out":7281,"duration_ms":69916,"temperature":0.7,"pith_summary":"The paper tests a common assumption in condensed-phase electron-transfer theory: that the actual electronic transition event is instantaneous compared with the slow nuclear rearrangement that brings the system to the crossing region. Using a symmetric two-parabola model driven by Langevin dynamics with non-adiabatic hopping probabilities, the authors simulate both the reactant population decay and the distribution of transition path times (TPTs) over a wide range of diabatic couplings V and friction strengths γ. They find that the mean transition path time (mTPT) is primarily controlled by friction, while the macroscopic reaction time τ is primarily controlled by V, and that these two timescales can approach each other: for V = 3.43 meV the mTPT exceeds 5% of τ. A sympathetic reader would care because this quantitative result marks a regime where the separation of timescales underpinning many rate theories breaks down.","feed_headline":"Electron jumps can take 5% of reaction time","feed_subtitle":"Simulations of a two-parabola model show the instantaneous-jump picture fails for strong diabatic coupling.","key_machinery":"The central object is the transition path time (TPT), defined as the duration of a trajectory's first passage from a point -x0 on the reactant side to a symmetric point x0 on the product side, excluding trajectories that return to -x0. The dynamical model is a symmetric two-parabola diabatic surface pair with a constant coupling V, propagated by Langevin dynamics with friction γ and Gaussian noise, with non-adiabatic transitions decided by an exact curve-crossing hopping probability at the avoided crossing. Comparing the TPT distribution and its mean with the population-decay time constant τ obtained by exponential fitting is what carries the argument.","core_discovery":"The central claim is that, even in the non-adiabatic regime where individual electronic transitions are fast, the time a trajectory spends inside the barrier region can be a non-negligible fraction of the mean first-passage time. The numerical evidence shows that the mean transition path time scales mainly with solvent friction γ and depends only weakly on the diabatic coupling V, whereas the macroscopic reaction time τ decreases strongly with V (roughly k ∝ V²). As a consequence, the ratio mTPT/τ can reach values above 5% when V is large, so the conventional picture in which the microscopic transfer is effectively instantaneous may not be quantitatively valid in this parameter range.","pith_inferences":["The quantitative 'non-negligible' claim is defined with respect to an arbitrary boundary x0; because the paper chooses the smallest of six tested values and the TPT distribution lengthens with increasing x0, the claim is a conservative lower bound for the tested model, but it should be verified for even smaller x0 before being used as a universal statement.","The same TPT machinery could be applied to asymmetric (finite driving force) electron transfer, where the crossing point is displaced and the TPT distribution may become skewed; how the ratio mTPT/τ behaves there is untested.","One could connect mTPT/τ to experimentally accessible coherence or time-resolved spectral signatures of the transition state, providing a link between this trajectory-based quantity and observable electron-transfer dynamics.","The finding that mTPT is governed mainly by γ suggests that in high-friction solvents the 'instantaneous' assumption fails more easily; this gives a testable prediction: increasing solvent friction should increase the microscopic transfer time even if the overall rate is unchanged."],"forward_implications":["For large diabatic couplings, rate theories that treat the electronic transition as instantaneous may underestimate the actual time spent in the transition region by an order of magnitude.","Because mTPT and τ are controlled by different parameters (γ vs V), friction and electronic coupling affect different stages of the reaction; tuning solvent friction can change the microscopic crossing time without proportionally changing the rate.","The TPT distribution shifts to shorter times as V increases, so non-adiabatic transitions preferentially select high-momentum crossing trajectories, shortening the individual microscopic event even as the overall reaction accelerates.","The similarity between the simulated mTPT and the analytical no-hopping (P_hop=0) results indicates that the two-parabola barrier shape, not the hopping probability itself, dominates the average crossing time.","The ratio mTPT/τ provides a concrete, computable diagnostic for when the instantaneous-transfer assumption is acceptable in a given electron-transfer model."],"fun_headline_variants":["Electron transfer time can be 5% of total reaction","Non-adiabatic jumps not instant: up to 5% of time","Strong coupling makes electron jumps measurable","Instantaneous-jump assumption fails for electron transfer"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The quantitative conclusion that mTPT is a non-negligible fraction of τ depends on the arbitrary choice of the reaction-coordinate boundaries ±x0 that define a transition path; with a smaller x0 the crossing region narrows and the measured mTPT may shrink, potentially dropping below the quoted 5% threshold.","fun_headline_variants_meta":{"raw":{"variants":["Electron transfer time can be 5% of total reaction","Non-adiabatic jumps not instant: up to 5% of time","Strong coupling makes electron jumps measurable","Instantaneous-jump assumption fails for electron transfer"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1007,"prompt_tokens":667,"completion_tokens":340,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":411,"completion_tokens_details":{"reasoning_tokens":274}},"tokens_in":411,"tokens_out":340,"duration_ms":3955,"temperature":1.0,"reasoning_tokens":274,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T01:48:26.342957+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same Langevin curve-crossing hopping simulation with a substantially smaller x0 (e.g., 0.1 amu^1/2 Å) and recompute mTPT/τ for V = 3.43 meV; if the ratio falls below 1% across the γ range, the central 'non-negligible' claim would not survive the boundary choice. Alternatively, compare with a full quantum-mechanical simulation of the two-parabola model to see whether the classical hopping treatment overestimates the microscopic crossing time.","supporting_citations":[],"review_version":1}