{"id":"986c8c9a-809e-4784-bd52-6b1a1c7f134f","arxiv_id":"1908.05219","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Using local quasi-diabatic states, the authors run on-the-fly non-adiabatic simulations of ethylene with PLDM and SQC, getting population dynamics close to AIMS and better than surface hopping here.","lead":"This paper demonstrates the first ab-initio on-the-fly use of the quasi-diabatic (QD) scheme for non-adiabatic molecular dynamics, interfacing diabatic quantum dynamics methods with adiabatic electronic structure calculations. It shows that two trajectory-based methods (PLDM and SQC) can simulate ethylene photodynamics in close agreement with a wavepacket benchmark, suggesting the scheme opens up many diabatic methods for realistic simulations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The AIMS benchmark in Fig. 2 may not be at the same electronic structure level as the QD runs; if so, the close agreement does not validate the central claim.","rationale":"The reader's primary weakest assumption was the local validity of the crude-adiabatic/QD basis over dt=0.1 fs, with the AIMS benchmark level listed as a secondary fragility. I agree that the AIMS benchmark level is the more directly load-bearing concern: the paper's headline comparison rests on it, and the manuscript is internally ambiguous (calling Ref. 55 CASPT2 in one paragraph and CASSCF in another). The QD basis approximation is a legitimate concern but is mitigated by the statement that dt=0.5 fs gives the same single-trajectory results, and it can be controlled by reducing dt. The benchmark mismatch, if real, would invalidate the central numerical evidence. I therefore keep the reader's CONDITIONAL verdict unchanged: the claim is plausible and the method is clearly presented, but the benchmark level must be verified or corrected before acceptance. I recommend checking the reference level directly rather than assuming bad faith, since a CASSCF AIMS curve may exist in Ref. 55 alongside the CASPT2 curve.","tokens_in":13252,"tokens_out":7409,"duration_ms":73866,"concrete_test":"Identify the exact electronic structure level of the AIMS populations plotted in Fig. 2 by inspecting Refs. 54 and 55 (or by contacting the authors). If the AIMS data are from MS-CASPT2, rerun AIMS (or use the MCE results of Ref. 17) at the identical SA-3-CASSCF(2,2)/6-31G* level, with the same initial Wigner sampling and two-state subspace, and compare directly to QD-PLDM/QD-SQC populations and errors.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is that QD-PLDM and QD-SQC populations agree closely with AIMS, which is treated as the 'almost exact solution' of the CAS(2,2) ethylene model. But the QD simulations are performed at the SA-3-CASSCF(2,2)/6-31G* level, while the text explicitly attributes Ref. 55 to AIMS 'using CASPT2 level of the electronic structure calculations that include dynamical correlation.' If the AIMS curve in Fig. 2 comes from MS-CASPT2 rather than CASSCF, then the comparison is between different electronic Hamiltonians: close agreement could be coincidental and would not validate the QD interface at the level actually used. The later statement that the AIMS results are 'performed at the CASSCF level of theory (54, 55)' conflicts with the CASPT2 attribution, so the benchmark level is ambiguous in the manuscript itself. Resolving this is necessary before the headline claim can be accepted.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents the first on-the-fly ab initio application of the quasi-diabatic (QD) propagation scheme, in which adiabatic states at a reference geometry are used as local diabatic states during each short nuclear propagation segment and are dynamically updated along the trajectory. The authors interface this QD scheme with two diabatic quantum dynamics methods, PLDM and SQC, and use it to simulate the nonadiabatic photodynamics of ethylene at the SA-3-CASSCF(2,2)/6-31G* level. The central claim, stated in the abstract and conclusions, is that QD-PLDM and QD-SQC produce adiabatic population dynamics in close agreement with an AIMS benchmark and that both outperform decoherence-corrected FSSH. In addition, the paper analyzes representative reactive trajectories and product populations, arguing that the QD-based simulations correctly capture the competing nonradiative decay pathways through different conical intersections. The manuscript also provides the formal expressions for the quasi-diabatic potential and gradient matrix elements (Eqs. 3-7), emphasizing that no global diabatic surfaces or representation reformulation of the dynamics methods are required.","tokens_in":13453,"tokens_out":8957,"duration_ms":87963,"significance":"If the central claim holds, the paper is a significant methodological advance: it demonstrates that a broad class of diabatic quantum dynamics approaches can be coupled directly to adiabatic electronic structure calculations, eliminating the need to construct global diabatic potentials or rederive equations of motion in the adiabatic representation. The demonstration uses a realistic, non-model test case (ethylene photodynamics) and compares against an independent wavepacket benchmark rather than fitting parameters, which is a strong validation strategy for a methods paper. The formal QD equations in Eqs. 3-7 are internally consistent, and the absence of trajectory-specific fitted parameters (the SQC square-window parameter being a fixed methodological constant) strengthens the credibility of the reported comparison. The reactive-trajectory and product-population analyses also add mechanistic value beyond the population curves. However, the benchmark-level ambiguity and the lack of statistical uncertainties mean that the quantitative strength of the headline comparison is not yet established.","major_comments":[{"comment":"The level of electronic structure behind the AIMS benchmark is ambiguous and this ambiguity is load-bearing. The text attributes Ref. 55 to AIMS using CASPT2, yet the same paragraph calls the benchmark 'the almost exact quantum dynamics of the CAS(2,2) ethylene model' provided by AIMS, and the later discussion refers to 'AIMS results performed at the CASSCF level of theory (54, 55)'. If the filled circles in Fig. 2 come from MS-CASPT2 rather than CASSCF, the comparison is between different electronic Hamiltonians and the close agreement in Fig. 2B/C would not validate the QD interface at the SA-3-CASSCF level actually used in the QD simulations. The authors should state explicitly which electronic structure level produced the AIMS curves in Fig. 2, cite the correct reference, and, if the benchmark is CASPT2, provide the corresponding CASSCF-level AIMS result for a consistent comparison.","section":"Results and Discussion, Fig. 2"},{"comment":"No statistical uncertainties are reported for the 120-trajectory population curves, although the QD-SQC curve is visibly noisy and the differences among methods in the bottom panels are comparable in size to the apparent noise. The claims of 'close agreement with AIMS' and of outperforming FSSH should be supported by error bars or confidence intervals obtained from trajectory statistics, and ideally by a convergence test with respect to the number of trajectories for at least one of the QD methods.","section":"Fig. 2 and Calculation Details"},{"comment":"The central quasi-diabatic approximation, namely that the crude adiabatic states at a fixed reference geometry form a valid local diabatic basis over the propagation segment, is only tested indirectly through agreement with AIMS. The statement that dt = 0.5 fs reproduces the single-trajectory result is not a convergence test of the ensemble population dynamics. A direct convergence study with respect to the nuclear time step (e.g., dt = 0.05, 0.1, and 0.2 fs) would substantiate the finite-step approximation embodied in Eqs. 3-5 and rule out the possibility that the close agreement in Fig. 2 is accidental.","section":"Eq. 2 and Calculation Details"}],"minor_comments":[{"comment":"Equation 4 contains typographical errors: 'Vαβ(R0))' should read 'Vαβ(R0)' in both occurrences.","section":"Eq. 4"},{"comment":"The phrase 'ab-inito' should be 'ab initio', and the term 'dibabatic' near the end of the Introduction should be 'diabatic'.","section":"Abstract and Significance Statement"},{"comment":"The y-axis label 'Strucutre proportion' is misspelled and should read 'Structure proportion'.","section":"Fig. 4"},{"comment":"The sentence 'Fig. 3 presets three representative reactive trajectories' should read 'presents'.","section":"Fig. 3 caption"},{"comment":"The sentence 'a much larger time-step dt = 0.5 fs can be used and generates the same results at the single trajectory level' is vague; the reference time step and the metric used to compare single trajectories should be specified.","section":"Calculation Details"},{"comment":"The supporting information is referenced several times but is not included in the manuscript; if it is not part of the submission package, the key technical details (phase tracking of adiabatic states and Löwdin orthonormalization) should be summarized in the main text.","section":"Materials and Methods"}],"recommendation":"major_revision","confidential_remarks":"The main obstacle is the ambiguity surrounding the AIMS benchmark: the paper appears to cite a CASPT2-focused reference (Ref. 55) for a benchmark that the surrounding text labels as the CAS(2,2)/CASSCF model. Before resubmission, the authors should verify which calculation generated the filled circles in Fig. 2 and adjust the citation and wording accordingly. The paper is otherwise within the scope of the journal and the methodological demonstration is of interest if the benchmark issue is resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real news here is straightforward: this is the first ab initio on-the-fly application of the quasi-diabatic (QD) propagation scheme, and it works. The authors take two diabatic methods, PLDM and SQC, and run them on ethylene photodynamics with SA-3-CASSCF(2,2)/6-31G* surfaces, without building a global diabatic model or reformulating the dynamics into the adiabatic representation. That is a concrete capability demonstration, and the population dynamics agree reasonably with their chosen benchmark and beat decoherence-corrected FSSH in this case. The method section is honest about the local nature of the basis, and the equations for the QD potentials and gradients are standard and sound. I also appreciate that they openly note the QD scheme does not strictly avoid derivative-coupling-like quantities; it trades them for overlap matrices and gradients, which is a fair and useful framing. No fitted parameters, 120 trajectories, Wigner sampling—this is a careful simulation study, not a toy.\n\nNow the soft spots, in proportion. The biggest one is the AIMS benchmark. The text says in one place that AIMS used CASPT2 (ref 55 is a MS-CASPT2 paper) and in another that AIMS is at CASSCF level (refs 54, 55). That is an internal inconsistency in the manuscript itself, and it matters. If the AIMS curve in Fig. 2 is from a CASPT2 calculation, then the comparison is between different electronic Hamiltonians, and close agreement between QD-PLDM and AIMS would be partly coincidental, not a clean validation of the QD interface at the CASSCF level used. The authors need to resolve this—state explicitly which electronic structure level the AIMS benchmark used and, if it was CASPT2, make clear that the comparison is illustrative rather than a strict validation. That is a load-bearing ambiguity, not a style nit.\n\nSecond, there are no error bars on the trajectory populations. With 120 trajectories, sampling noise in the nonadiabatic decay window is non-negligible, and the small reported differences between QD-PLDM and QD-SQC could be within noise. The SQC population is visibly noisy and they note the windowing issue, but they do not quantify it. A simple bootstrap over trajectories would address this.\n\nThird, the SI is referenced but not included in the preprint. For a method paper whose whole point is enabling others to do the same thing, missing the numerical details (overlap computation, phase tracking, Löwdin steps) is a real impediment. Code release would be even better.\n\nIs the central argument sound? The core idea—crude adiabatic states as a local diabatic basis with dynamical updating—is not new here; it is in their earlier work, and they cite it properly. The contribution is the first realistic on-the-fly test, and that is a legitimate contribution. If the AIMS level is clarified and error bars are added, the central claim should hold up. I would not desk-reject this. The community needs more real-molecule tests of diabatic methods, and this is a credible step. Send it to a referee who knows both mapping-based dynamics and ethylene photochemistry, and ask pointed questions about the benchmark level and the statistical significance of the differences. It deserves serious review, not a rubber stamp.\n\nWho is this for? People working on nonadiabatic dynamics methods and their interfacing with electronic structure. I would bring it to a reading group focused on semiclassical dynamics, and I would probably cite it as the first on-the-fly QD application once the SI and benchmark details are settled.","headline":"A genuinely useful first on-the-fly demonstration of the QD scheme, but the AIMS benchmark level is ambiguous and the comparison deserves a hard look before the headline claim is taken at face value.","tokens_in":13976,"tokens_out":889,"would_cite":true,"duration_ms":11336,"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":"The quasi-diabatic scheme lets diabatic quantum dynamics methods run directly on adiabatic ab initio data, with ethylene dynamics matching AIMS and outperforming FSSH.","keywords":["quasi-diabatic scheme","non-adiabatic molecular dynamics","on-the-fly simulation","partial linearized density matrix","symmetric quasi-classical approach","CASSCF","ethylene photodynamics","conical intersections"],"falsifier":"Run QD-PLDM ethylene photodynamics at nuclear time steps of 0.05, 0.1, and 0.5 fs and check whether the S1/S0 population curves converge; significant step-size dependence would indicate the frozen quasi-diabatic basis is not converged at the tested step sizes.","tokens_in":13077,"feed_emoji":"⚛️","tokens_out":9723,"duration_ms":77625,"temperature":0.7,"pith_summary":"This paper claims that a 'quasi-diabatic' (QD) propagation scheme—using the adiabatic electronic states at a fixed reference geometry as a local diabatic basis over each short nuclear propagation segment—provides a seamless interface between diabatic quantum dynamics methods and conventional adiabatic electronic structure calculations. The authors demonstrate the scheme on the first ab initio on-the-fly example, the photodynamics of ethylene at the SA-3-CASSCF(2,2)/6-31G* level, running two diabatic methods, partial linearized density matrix (PLDM) and symmetric quasi-classical (SQC) dynamics. They report that QD-PLDM and QD-SQC population dynamics agree closely with the ab initio multiple spawning (AIMS) benchmark and outperform decoherence-corrected fewest-switches surface hopping (FSSH). If the claim holds, the scheme removes the need to construct global diabatic surfaces or reformulate diabatic dynamics into the adiabatic representation, giving many recently developed quantum dynamics approaches a direct route to on-the-fly ab initio simulation and realistic test cases.","feed_headline":"Quasi-diabatic scheme matches AIMS, beats FSSH on ethylene","feed_subtitle":"The quasi-diabatic trick lets PLDM and SQC run on adiabatic CASSCF data, matching AIMS.","key_machinery":"The central object is the quasi-diabatic basis, defined per short propagation segment by freezing the adiabatic states at the reference geometry $R_0\\equiv R(t_0)$: $|\\Phi_\\alpha(R_0)\\rangle \\equiv |\\Phi_\\alpha(R(t_0))\\rangle$ for $t\\in[t_0,t_1]$. This basis makes the derivative coupling vanish inside the segment and converts the electronic Hamiltonian into a matrix with off-diagonal couplings, computed as $V_{\\alpha\\beta}(R(t_1))=\\sum_{\\lambda\\nu}S_{\\alpha\\lambda}\\,E_\\lambda(R(t_1))\\,\\delta_{\\lambda\\nu}\\,S^\\dagger_{\\beta\\nu}$ with overlap matrix $S_{\\alpha\\lambda}=\\langle\\Phi_\\alpha(R_0)|\\Phi_\\lambda(R(t_1))\\rangle$, and using nuclear gradients $\\nabla V_{\\alpha\\beta}(R(t_1))$ built from the full nuclear dependence of the adiabatic states. These quantities avoid the singular derivative couplings and non-adiabatic couplings that can destabilize other approaches near conical intersections, and they supply the mapping-Hamiltonian forces needed by PLDM and SQC. This machinery is what carries the seamless interface between diabatic dynamics and adiabatic electronic structure.","core_discovery":"The central discovery is that non-adiabatic dynamics methods formulated in a diabatic representation do not need global diabatic states to run on the fly. During each short time segment $t\\in[t_0,t_1]$, the QD scheme defines the quasi-diabatic basis as the adiabatic states at the segment's starting geometry, $|\\Phi_\\alpha(R_0)\\rangle \\equiv |\\Phi_\\alpha(R(t_0))\\rangle$. In this basis derivative couplings vanish within the segment, while the electronic Hamiltonian $V_{\\alpha\\beta}(R(t))$ acquires off-diagonal elements obtained by linear interpolation between the diagonal values at $R(t_0)$ and the overlap-transformed values at $R(t_1)$, with gradients $\\nabla V_{\\alpha\\beta}(R(t_1))$ computed from adiabatic energies and state overlaps. Using PLDM and SQC as diabatic dynamics engines, the paper presents the first ab initio on-the-fly ethylene photodynamics driven by CASSCF, obtains S1/S0 population dynamics in close agreement with AIMS and better than FSSH over 200 fs, and recovers the competing non-radiative pathways through the twisted-pyramidalized and ethylidene conical intersections, with about half the trajectories traversing each channel.","pith_inferences":["If the QD basis approximation is as good as this one-molecule test suggests, the same interface should work for any electronic structure method that can supply adiabatic energies, gradients, and state overlaps—for example, methods describing charge transfer or Rydberg states—provided the reference geometry is refreshed often enough to track changing electronic character.","A direct convergence test of the nuclear time step (e.g., dt = 0.05 vs 0.1 vs 0.5 fs) would isolate the error coming from the frozen-basis assumption; the paper uses dt = 0.1 fs and notes 0.5 fs works at the single-trajectory level but does not report a systematic population convergence study.","The QD scheme's replacement of derivative couplings by overlap matrices suggests a natural route for interfacing with machine-learned or otherwise approximate representations of $V_{\\alpha\\beta}$ and gradients, potentially extending on-the-fly diabatic dynamics to larger systems where analytic couplings are unavailable.","For systems with more than two coupled states, the scheme will need careful treatment of state-tracking phase conventions and orthonormalization (both mentioned in the SI), and a many-state generalization would be a natural next validation."],"forward_implications":["Any diabatic quantum dynamics method that only needs a local electronic Hamiltonian matrix and its gradients can be coupled directly to standard adiabatic electronic structure packages, without representation reformulation or global diabatization.","QD-PLDM and QD-SQC reproduce the AIMS benchmark populations for the CAS(2,2) ethylene model, while decoherence-corrected FSSH relaxes too quickly; the QD-based methods are thus more accurate than a widely used trajectory surface hopping method on this test.","Because the QD scheme replaces derivative couplings with well-behaved overlap and gradient quantities, methods built on it may be numerically robust near trivial crossings and conical intersections where derivative couplings become singular.","The scheme enables realistic ab initio test cases—such as ethylene photodynamics—to assess approximate diabatic dynamics methods, and here it correctly predicts the competing non-radiative channels (ethylidene and twisted-pyramidalized conical intersections, and H2 dissociation)."],"supporting_citations":[{"why":"It introduces the quasi-diabatic propagation scheme that this paper applies to on-the-fly ethylene dynamics.","marker":"[40]"},{"why":"It defines the partial linearized density matrix (PLDM) path-integral approach used as one of the two diabatic dynamics methods.","marker":"[30]"},{"why":"It defines the symmetric quasi-classical (SQC) window approach used as the second diabatic dynamics method.","marker":"[50]"},{"why":"It supplies the AIMS population dynamics used as the benchmark that QD-PLDM and QD-SQC are compared against.","marker":"[55]"},{"why":"It provides the implemented AIMS method and the conical-intersection pathways that the QD trajectories reproduce.","marker":"[54]"},{"why":"It gives the decoherence-corrected FSSH method that the QD approaches are claimed to outperform.","marker":"[66]"},{"why":"It provides the efficient many-electron wavefunction-overlap computation used to construct the quasi-diabatic transformation matrices.","marker":"[71]"},{"why":"It supplies the nonadiabatic dynamics interface in which the QD-PLDM and QD-SQC simulations are implemented.","marker":"[63]"}],"fun_headline_variants":["Diabatic dynamics on the fly without global surfaces","First on-the-fly diabatic dynamics with CASSCF","QD scheme lets diabatic methods run on adiabatic data","Ethylene photodynamics: QD matches AIMS, beats FSSH","No global diabats: QD enables on-the-fly PLDM and SQC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the adiabatic electronic states frozen at each segment's starting geometry remain an accurate local basis through the whole short propagation segment, and that the AIMS benchmark describes the same electronic-structure-level dynamics; if either fails, the reported agreement would not be meaningful.","fun_headline_variants_meta":{"raw":{"variants":["Diabatic dynamics on the fly without global surfaces","First on-the-fly diabatic dynamics with CASSCF","QD scheme lets diabatic methods run on adiabatic data","Ethylene photodynamics: QD matches AIMS, beats FSSH","No global diabats: QD enables on-the-fly PLDM and SQC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000864,"raw_usage":{"total_tokens":3765,"prompt_tokens":982,"completion_tokens":2783,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":598,"completion_tokens_details":{"reasoning_tokens":2692}},"tokens_in":598,"tokens_out":2783,"duration_ms":19777,"temperature":1.0,"reasoning_tokens":2692,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:20:22.604648+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run QD-PLDM ethylene photodynamics at nuclear time steps of 0.05, 0.1, and 0.5 fs and check whether the S1/S0 population curves converge; significant step-size dependence would indicate the frozen quasi-diabatic basis is not converged at the tested step sizes.","supporting_citations":[{"cited_title":"Mandal, S","cited_arxiv_id":null,"evidence_quote":"It introduces the quasi-diabatic propagation scheme that this paper applies to on-the-fly ethylene dynamics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It defines the partial linearized density matrix (PLDM) path-integral approach used as one of the two diabatic dynamics methods."},{"cited_title":"Cotton and William H","cited_arxiv_id":null,"evidence_quote":"It defines the symmetric quasi-classical (SQC) window approach used as the second diabatic dynamics method."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the AIMS population dynamics used as the benchmark that QD-PLDM and QD-SQC are compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It provides the implemented AIMS method and the conical-intersection pathways that the QD trajectories reproduce."},{"cited_title":"Critical appraisal of the fewest switches algorithm for surface hopping","cited_arxiv_id":null,"evidence_quote":"It gives the decoherence-corrected FSSH method that the QD approaches are claimed to outperform."},{"cited_title":"Efficient and flexible computation of many-electron wave function overlaps","cited_arxiv_id":null,"evidence_quote":"It provides the efficient many-electron wavefunction-overlap computation used to construct the quasi-diabatic transformation matrices."},{"cited_title":"Nonadiabatic dynamics: The sharc approach","cited_arxiv_id":null,"evidence_quote":"It supplies the nonadiabatic dynamics interface in which the QD-PLDM and QD-SQC simulations are implemented."}],"review_version":1}