{"id":"8ace3d27-883c-46cd-8ca3-26f3faedfcb1","arxiv_id":"2412.04958","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A coupled-trajectory surface hopping algorithm with collective energy sharing restores internal consistency and suppresses frustrated hops in fulvene and DMABN photodynamics.","lead":"This paper introduces a surface hopping method where trajectories share kinetic energy with the whole swarm when an electronic hop is attempted, aiming to fix three known problems at once: overcoherence, failed hops, and mismatched electronic populations. The method is tested on two benchmark molecules and shown to match more accurate quantum calculations, though the energy-sharing rules remain heuristic.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CCT-TSH's internal consistency and zero-frustration may be largely enforced by its deterministic active-state hop rule and collective energy-sharing reservoir rather than by the coupled-trajectory electronic dynamics, because the paper's tests never ablate Eq. 10's quantum-momentum coupling.","rationale":"The reader's weakest assumption focuses on the frozen-Gaussian quantum momentum approximation and its transferability beyond the two LVC systems. My concern is complementary and, in my view, at least as load-bearing: the numerical demonstrations do not isolate the coupled-trajectory electronic coupling (Eq. 10) from two other features that can produce the same results by construction. The paper itself says that the equity/overlap CCT-TSH results have no frustrated hops 'albeit by construction' (Section 3.2) and that the deterministic rule makes trajectories follow the largest electronic population (Sections 2 and 4), which directly couples F to P. A control with Q^alpha = 0 would disentangle these effects. This is not an accusation of circularity in the derivation, but a request for a decomposition of where the improvement actually comes from. The concern matters because the abstract and conclusions present coupled trajectories as the essential ingredient ('What is missing in surface hopping... coupling of the trajectories'), and if a Q=0 version performs equally well, the central claim must be substantially reframed. The paper also openly flags the arbitrariness of the energy-sharing implementation, and the Qmom variant that relies most directly on the quantum momentum fails. My concrete test is cheap, uses the same open-source code, and would settle the mechanism question directly. For these reasons I keep the reader's CONDITIONAL verdict but strengthen the justification: the requested revision should include a Q=0 ablation, not just an extra benchmark and parameter specification.","tokens_in":19221,"tokens_out":1927,"duration_ms":18933,"concrete_test":"Run CCT-TSH without the coupled-trajectory electronic term (set Q^alpha = 0 and Eq. 10 identically zero in the electronic evolution), keeping the deterministic largest-population hop rule and the equity-based or overlap-based energy sharing exactly as implemented. Compare P/F internal consistency, frustrated-hop counts, and diabatic populations for fulvene and DMABN against the full CCT-TSH results in Figs. 2, 5, 6 and 7. If the Q=0 control is nearly indistinguishable, the central claim that coupled-trajectory quantum-momentum coupling provides the decoherence/internal-consistency mechanism is not supported by the current tests. Also report one ab initio or non-LVC benchmark, as the reader requested.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The headline claim is that moving to coupled trajectories robustly cures decoherence, frustrated hops, and internal consistency at once. A load-bearing concern, reinforced by the paper's own text, is that the favorable CCT-TSH results are not cleanly attributable to the coupled-trajectory mechanism. Three built-in features of CCT-TSH can enforce the advertised behavior by construction: (1) the deterministic hopping rule 'trajectories evolve in the electronic state with the largest population' (Section 2 and Fig. 5/7 tests) directly aligns the active-state fraction F with the electronic population P, which is essentially the definition of internal consistency; (2) the equity/overlap energy-sharing schemes completely avoid frustrated hops 'by construction' (Section 3.2, Fig. 2 discussion), because energy is nevertheless drawn from a sufficiently large many-trajectory reservoir, irrespective of the quantum-momentum coupling; (3) the quantum-momentum coupling itself is already acknowledged to violate the zero-NACV ensemble sum rule and is patched a posteriori (Section 2 CT-TSH discussion), and the one CCT-TSH variant most directly built on this quantum momentum (Qmom-based) produces 120 frustrated hops and deviates in Fig. 6. The paper does not report a control calculation that isolates the contribution of Eq. 10's quantum-momentum coupling from the deterministic hopping and collective energy reservoir. Consequently, the evidence as presented supports 'a deterministic, ensemble-energy-conserving surface hopping variant works on two LVC models' more strongly than it supports the central mechanism claimed, that coupled trajectories encoding nonlocal quantum information (quantum momentum) are what overcome these issues at once.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript proposes CCT-TSH, a surface hopping algorithm built from exact-factorization coupled-trajectory ideas. Electronic coefficients evolve via the standard Tully term plus a quantum-momentum coupling (Eq. 10); nuclei evolve on the active adiabatic surface; hops are chosen deterministically as the state with largest electronic population (or by fewest switches in a variant); and three schemes (equity, overlap, quantum-momentum) share kinetic energy among the swarm when a hop is energetically unfavorable. The method is tested on full-dimensional LVC models of fulvene (30 modes) and DMABN (57 modes). The equity and overlap schemes eliminate frustrated hops, restore near-agreement between electronic populations P and trajectory fractions F, and yield diabatic populations in good agreement with MCTDH reference data; the quantum-momentum scheme yields 120 frustrated hops in both systems and is less accurate.","tokens_in":19498,"tokens_out":7684,"duration_ms":77461,"significance":"If substantiated, the contribution is significant: it offers a practically implementable surface hopping variant in which internal consistency and absence of frustrated hops are achieved without a per-trajectory decoherence correction, and it connects the design to the exact factorization. The paper has concrete strengths: it uses an open-source implementation (G-CTMQC), provides a Supporting-Information script for generating inputs, uses external MCTDH benchmarks, and introduces no fitted parameters in the derivation. However, the evidence as presented does not cleanly attribute the improvements to the coupled-trajectory electronic term (Eq. 10); the deterministic hopping rule and collective energy reservoir can produce the same headline behaviors by construction, while the one scheme most directly tied to the quantum momentum performs worst. The manuscript therefore needs a control/ablation study and quantitative diagnostics before the broad claims in the abstract and conclusions can be accepted.","major_comments":[{"comment":"The manuscript does not report a control calculation that isolates the role of the coupled-trajectory electronic term, Eq. (10), from the two algorithmic features that can enforce the advertised behavior by construction: the deterministic hopping rule ('trajectories evolve in the electronic state with the largest population', Section 2) and the collective energy-sharing reservoir. Equity- and overlap-based CCT-TSH eliminate frustrated hops 'by construction' (Section 3.2), and deterministic hopping directly aligns the trajectory fraction F with the electronic population P. Since the conclusions claim that coupling of trajectories is 'the crucial ingredient' (Section 4), the authors should add an ablation, e.g., CCT-TSH with Eq. (10) switched off while retaining deterministic hopping and energy sharing, or an independent-trajectory energy-sharing benchmark, to rule out the alternative explanation that the energy reservoir alone is responsible for the improvements.","section":"Section 3.2 / Table 1 / Fig. 2"},{"comment":"The quantum-momentum-based energy-sharing scheme, which is the variant most directly built on the quantum momentum appearing in Eq. (10), produces 120 frustrated hops in both fulvene and DMABN and deviates from the other schemes in Fig. 6. The authors attribute this to the approximate nature of the quantum momentum (Sections 2 and 3.2). This is a load-bearing caveat: it shows that the coupled-trajectory electronic dynamics as implemented is not by itself the robust cure claimed in the abstract, and it weakens the attribution of the success of the equity/overlap schemes to the quantum-momentum coupling. Please discuss quantitatively the role of Eq. (10) in the successful schemes, for example by reporting the relative magnitude of the CT contribution to the electronic coefficient derivative and by comparing with the suggested ablation.","section":"Section 3.2 / Table 1 / Fig. 6"},{"comment":"The paper reports no quantitative measure of internal consistency (e.g., the maximum or time-integrated absolute difference between F and P) and no diagnostic of total-energy conservation of the swarm, although energy conservation of the swarm is the basis of the energy-sharing schemes. Adding such diagnostics is necessary to support the qualitative statements that internal consistency is 'restored closely' and that the schemes give 'almost identical' population decays. Please include the corresponding error norms or energy-conservation curves.","section":"Section 3.2 / Figs. 2, 5, 7"}],"minor_comments":[{"comment":"There are typos: '4-(dimethyloamino)benzonitrile' in the Abstract should be '4-(dimethylamino)benzonitrile'; 'dfferent' in the Fig. 6 caption and 'occurences' in the Conclusions should be corrected.","section":"Abstract and Fig. 6 caption"},{"comment":"References 29 and 93 appear to cite the same paper by Gómez, Spinlove, and Worth with different publication years; please verify and cite it once to avoid confusion.","section":"References 29 and 93"},{"comment":"The caption states that the lighter lines show different velocity rescaling/inversion choices for TSH, TSH-ED, and CT-TSH, but it is not stated whether the CCT-TSH curves shown in the same figure are individual runs or averages; please clarify the color/line coding and report the spread over the three energy-sharing schemes.","section":"Fig. 2"},{"comment":"The symbol q is introduced as a pseudo-velocity but is then used in Eqs. (14) and (15) without an explicit definition; please define it (e.g., q_alpha = Q_alpha/M) just before the equations and use the same notation consistently.","section":"Eqs. (14) and (15)"},{"comment":"The statement that the frozen-Gaussian reconstruction of the quantum momentum 'violates the physical conditions' and must be imposed a posteriori is an important limitation; it should be restated in the Conclusions so that readers who do not read Section 2 in detail are aware of this caveat.","section":"Section 2 and Conclusions"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope and has the strength of a reproducible open-source implementation with external MCTDH benchmarks. The main technical issue is attribution: the paper needs an ablation study separating the quantum-momentum coupling from deterministic hopping and the collective energy reservoir. The self-citation density is understandable given the direct lineage from CT-MQC/CT-TSH, but duplicate references (29 vs 93) should be normalized."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this paper. It introduces something new: three schemes for sharing kinetic energy among a swarm of trajectories when a hop is attempted, plus a deterministic hopping rule based on the largest electronic population. And the equity- and overlap-based variants do deliver on the paper's main promises—no frustrated hops, internal consistency, and diabatic populations close to MCTDH on the fulvene and DMABN LVC benchmarks. But the paper advertises the coupled-trajectory quantum-momentum term as the key to overcoming all three problems at once, and that attribution is not actually supported by the tests. The energy reservoir and the deterministic hop rule could be doing most of the work; there is no control run that switches off Eq. (10) while keeping the rest.\n\nWhat's genuinely good: the energy-sharing idea is a real departure from the usual per-trajectory velocity rescaling, and the paper is transparent about its heuristic character. The deterministic hop rule is clean and physically motivated from the exact-factorization picture. The implementation is in the open-source G-CTMQC code, the input generator is provided, and the benchmarks are external MCTDH results. The paper also openly reports that the quantum-momentum-based sharing scheme produces 120 frustrated hops and that the frozen-Gaussian quantum momentum violates a sum rule and needs an ad hoc patch.\n\nThe soft spots are real but not fatal. First, the missing ablation: run CCT-TSH with the same energy sharing and deterministic hops but without the C_CT term to see how much the quantum momentum actually contributes. If the results barely change, the abstract-level claim oversells the coupled-trajectory mechanism. Second, the frustrated-hop removal for equity/overlap is by construction, as the authors admit; it's a reservoir effect, not evidence that the nonlocal coupling works. Third, internal consistency is likely helped by the largest-population rule, which directly ties the active state to the propagated electronic populations. Fourth, there is no uncertainty analysis for CCT-TSH over the velocity-rescaling variants—they say results don't change dramatically but show no spread. Finally, both tests are LVC models; an ab initio or non-LVC test would make the robustness claim credible.\n\nWho gets value from this: surface hopping practitioners who want a concrete way to eliminate frustrated hops and restore internal consistency without ad hoc decoherence corrections. A serious referee should be assigned; the paper is coherent, reproducible, and the method will likely be used regardless of whether the mechanism attribution survives scrutiny. My own verdict is conditional: publish after an ablation and a non-LVC test.","headline":"Energy-sharing surface hopping that fixes frustrated hops and internal consistency on two LVC benchmarks, but the coupled-trajectory mechanism is oversold.","tokens_in":20111,"tokens_out":4977,"would_cite":true,"duration_ms":48785,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Treating the trajectory swarm as a single energy-sharing entity yields a surface hopping scheme that restores internal consistency, removes frustrated hops, and matches quantum reference calculations in two molecular tests.","keywords":["surface hopping","nonadiabatic molecular dynamics","coupled trajectories","quantum momentum","frustrated hops","internal consistency","decoherence","exact factorization"],"falsifier":"Run the overlap-based energy-sharing scheme on a model in which the nuclear density separates into two well-separated branches that later re-enter a nonadiabatic coupling region; if the swarm populations deviate from a converged wavepacket calculation, or if trajectories in one branch share energy for hops occurring in the other, the local character of the hop is lost and the frozen-Gaussian quantum momentum is the component to blame.","tokens_in":18997,"feed_emoji":"⚛️","tokens_out":9687,"duration_ms":94487,"temperature":0.7,"pith_summary":"Surface hopping is the workhorse of photochemical dynamics, but in its standard independent-trajectory form it overestimates electronic coherence, produces frustrated hops when a trajectory lacks kinetic energy to climb to the final state, and gives two inconsistent estimates of electronic populations. This paper claims the cure is to treat the swarm of trajectories as a single coupled object, not as independent copies. The proposed coupled-trajectory surface hopping scheme adds a quantum-momentum term that carries nuclear delocalization into the electronic evolution, and when a hop is attempted it lets the whole swarm share kinetic energy through three alternative rules (equity, overlap, quantum-momentum-weighted). On full-dimensional linear-vibronic-coupling models of fulvene and DMABN, the equity and overlap versions remove frustrated hops, restore internal consistency, and give diabatic populations in good agreement with converged quantum reference calculations.","feed_headline":"Swarm energy sharing fixes surface hopping's three classic flaws","feed_subtitle":"Coupled trajectories remove frustrated hops, restore population consistency, and match quantum reference decays.","key_machinery":"The central object is the coupled-trajectory surface hopping scheme with energy sharing, built from the exact factorization of the molecular wavefunction. The nuclear swarm is used to reconstruct the nuclear density, and the gradient of that density enters the electronic coefficient evolution as a quantum momentum term, which is the decoherence channel. The load-bearing mechanism for the other two issues is energy sharing: at a hop attempt, the hopping trajectory first gives all of its kinetic energy, and the remaining deficit is redistributed to the other trajectories by rescaling their velocities either proportionally to their kinetic energy (equity) or proportional to their Gaussian overlap with the hopping trajectory (overlap), with a third option splitting the cost by nonadiabatic-coupling and quantum-momentum weights. The active state can also be chosen deterministically as the state of largest electronic population rather than by a stochastic fewest-switches rule.","core_discovery":"The central claim is that moving away from an independent-trajectory picture is the one strategy that addresses decoherence, frustrated hops, and internal consistency simultaneously. In the new algorithm, each nuclear trajectory still evolves on an adiabatic potential and hops between electronic states, but the electronic coefficients are corrected by a coupled-trajectory term depending on the quantum momentum, and the active state can be chosen deterministically as the most populated state. At a hop attempt, if the cost exceeds the hopping trajectory's kinetic energy, the deficit is taken from the kinetic energy of other trajectories, so the swarm as a whole conserves energy and the hop is not frustrated. In the two molecular models tested, the equity- and overlap-based sharing schemes eliminate frustrated hops, make the trajectory-count and electronic-population estimates agree, and reproduce the reference diabatic population decay.","pith_inferences":["The near-identical performance of the equity and overlap schemes suggests the essential ingredient may be swarm-level energy conservation rather than the specific sharing rule; a minimal scheme that pools kinetic energy from all trajectories could be tested directly.","The paper does not test cases where the swarm splits into well-separated spatial branches, so the local character of overlap-based sharing remains open; a model with two distant wavepacket branches crossing the same coupling region would stress it.","Because the quantum-momentum-based sharing still suffers many frustrated hops, the frozen-Gaussian reconstruction of the nuclear density is the most likely weak point; replacing it with an adaptive or higher-order density estimate is a natural next step."],"forward_implications":["In the fulvene model, the equity- and overlap-based schemes produce zero frustrated hops even when the velocity is rescaled only along the nonadiabatic coupling vector, where standard surface hopping records hundreds of frustrated hops.","CCT-TSH achieves internal consistency without an external decoherence correction: the fraction of trajectories on a state and the averaged electronic population agree.","On DMABN, the equity- and overlap-based schemes again remove frustrated hops and give S2 populations close to the decoherence-corrected surface hopping reference.","The overlap-based scheme with deterministic active-state selection matches the quantum reference diabatic populations in both molecules, indicating that deterministic hopping is a viable alternative to stochastic fewest-switches hopping.","Changing the velocity-rescaling scheme, or initializing the swarm with positions-only instead of Wigner sampling, changes the populations somewhat but does not destroy internal consistency or reintroduce frustrated hops."],"supporting_citations":[{"why":"Establishes the coupled-trajectory surface hopping algorithm and the quantum-momentum coupling term that the new scheme extends.","marker":"[19]"},{"why":"Supplies the full-dimensional linear vibronic coupling models and the benchmark populations for fulvene and DMABN.","marker":"[29]"},{"why":"Documents the molecular Tully models and shows how sensitive surface hopping results are to algorithm parameters.","marker":"[32]"},{"why":"Provides an ensemble-level, energy-conserving surface hopping formulation whose average hopping idea CCT-TSH adapts.","marker":"[36]"},{"why":"Offers a deterministic hopping alternative that CCT-TSH adopts for active-state selection.","marker":"[50]"},{"why":"Derives the exact electron-nuclear factorization giving the coupled evolution equations and the quantum momentum.","marker":"[54]"},{"why":"Identifies the quantum momentum as the channel through which nuclear delocalization induces electronic decoherence.","marker":"[56]"},{"why":"Argues for energy conservation over the whole swarm of trajectories, the principle the energy-sharing schemes implement.","marker":"[72]"},{"why":"Defines the energy-based decoherence-corrected surface hopping variant used as the main comparison baseline.","marker":"[96]"}],"fun_headline_variants":["Coupled trajectories fix decoherence, frustrated hops, and consistency","Swarm energy sharing solves three classic surface hopping flaws","One strategy: share energy across trajectories to fix surface hopping","Coupled-trajectory method overcomes classic surface hopping failures","Energy-sharing swarm restores consistency in surface hopping dynamics"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The scheme stands or falls on the assumption that a sum of frozen Gaussians centered on the trajectories gives a reliable quantum momentum for the electronic evolution and the energy sharing, even though the paper notes this reconstruction violates a physical no-transfer condition and must be imposed by hand.","fun_headline_variants_meta":{"raw":{"variants":["Coupled trajectories fix decoherence, frustrated hops, and consistency","Swarm energy sharing solves three classic surface hopping flaws","One strategy: share energy across trajectories to fix surface hopping","Coupled-trajectory method overcomes classic surface hopping failures","Energy-sharing swarm restores consistency in surface hopping dynamics"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000651,"raw_usage":{"total_tokens":2934,"prompt_tokens":845,"completion_tokens":2089,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":461,"completion_tokens_details":{"reasoning_tokens":2017}},"tokens_in":461,"tokens_out":2089,"duration_ms":13965,"temperature":1.0,"reasoning_tokens":2017,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:06:13.195753+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the overlap-based energy-sharing scheme on a model in which the nuclear density separates into two well-separated branches that later re-enter a nonadiabatic coupling region; if the swarm populations deviate from a converged wavepacket calculation, or if trajectories in one branch share energy for hops occurring in the other, the local character of the hop is lost and the frozen-Gaussian quantum momentum is the component to blame.","supporting_citations":[],"review_version":1}