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REVIEW 3 major objections 5 minor 92 references

Nonadiabatic excited-state dynamics with quantum Monte Carlo-trained machine learning: azomethane as a stringent test

T0 review · 3 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Quantum Monte Carlo-trained neural force fields bring correlated wave-function accuracy to photodynamics: for azomethane they cut predicted C-N dissociation from 92% to 33% (cis) and 82% to 9.5% (trans), with a ~160 fs prompt dissociation c

desk verdict First credible multi-state QMC-trained ML force fields for nonadiabatic dynamics; the cis-azomethane story holds up, but the trans results lean on an extrapolated model and the abstract overstates the experimental match. read the letter →

arxiv 2607.16129 v1 pith:3L6NCGVM submitted 2026-07-17 physics.chem-ph physics.comp-ph

Alfonso Annarelli , Emiel Slootman , Claudia Filippi This is my paper · ORCID
classification physics.chem-phphysics.comp-ph
keywords quantumMonteCarlomachine-learnedforcefieldsnonadiabaticdynamicssurfacehoppingazomethanephotodynamicsconicalintersectionsC-Nbonddissociation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to establish that variational quantum Monte Carlo (QMC) can serve as a practical reference for machine-learned nonadiabatic photodynamics: neural-network force fields trained on QMC energies and forces can propagate large ensembles of surface-hopping trajectories with correlated wave-function accuracy. For azomethane, this changes the chemical story: fixed-active-space CASSCF predicts runaway C-N bond breaking (92% of cis trajectories within 400 fs), while the QMC-trained model keeps the torsional photoisomerization mechanism central and reduces dissociation to 33%; for trans-azomethane the reduction is even larger, from 82% to 9.5%. The same dynamics yields a small prompt dissociation component after internal conversion, with C-N cleavage beginning around 160 fs, in qualitative agreement with femtosecond-resolved mass-spectrometry experiments. If correct, this makes QMC-trained machine learning a practical route to correlated excited-state dynamics without the manual active-space choices that dominate current errors.

What carries the argument

The load-bearing object is a Jastrow-Slater variational wave function whose determinantal part comes from selected configuration-interaction expansions, optimized state-specifically with an orthogonality penalty and targeted at a common second-order perturbation correction across all geometries and states. The stochastic VMC energies and forces are converted by a neural-network force field into smooth multi-state potential-energy surfaces, which are then used in trajectory surface-hopping dynamics. Crucially, the determinantal expansion adapts its size to the geometry—hundreds of determinants near the cis minimum, only about 150 for dissociated fragments—so the method keeps balanced accuracy

What would settle it

Run direct on-the-fly VMC surface-hopping trajectories, without the neural-network surrogate, for a few dozen cis-azomethane initial conditions through the first conical intersection and out to roughly 400 fs; if the fraction of trajectories with a C-N bond longer than 2.25 Å, or the onset time of first bond cleavage, differs substantially from the ML model's ~33% and ~160 fs, the training-coverage assumption is falsified.

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Extended reading notes

Core claim

The paper's central claim is that stochastic variational Monte Carlo energies and forces, obtained from Jastrow-Slater wave functions with selected configuration-interaction expansions, can be turned by neural networks into smooth multi-state force fields and used for large-ensemble surface-hopping photodynamics. On azomethane, this changes the computed product distribution: CASSCF puts 92% (cis) and 82% (trans) of trajectories on a C-N dissociative path within 400 fs, while the QMC-trained model yields 33% and 9.5%, respectively, while preserving the expected torsion to the conical-intersection region. The QMC dynamics also shows a small but non-negligible prompt dissociation component afte

Load-bearing premise

The entire QMC training set is generated once from CASSCF adaptive-sampling trajectories, so if the true correlated surface visits geometries CASSCF never explores (for example different torsional or dissociation pathways), the QMC-trained force field must extrapolate beyond its training data, and the dissociation yields plus the ~160 fs prompt onset inherit that coverage bias.

Editorial extensions

If this is right

  • CASSCF's excess dissociation is a systematic error of the fixed-active-space reference rather than a sampling artifact, since the QMC and CASPT2 models share the same geometries and initial conditions yet fragment much less.
  • The torsional mechanism (normal and rotator pathways through two symmetry-related conical intersections) is robust across electronic-structure methods, shifting the open question to quantitative branching and dissociation yields.
  • The predicted ~160 fs onset of C-N cleavage after internal conversion gives time-resolved experiments a specific target to confirm or rule out an impulsive dissociation component.
  • A QMC-trained ML force field can be applied to the trans isomer without retraining, covering both photoisomerization directions with one correlated reference dataset.
  • One thousand-trajectory, 400 fs surface-hopping ensembles with correlated reference data are computationally feasible through the ML surrogate.

Reading between the lines

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

  • Inference: The stated yields may carry a training-coverage bias, because all QMC labels were computed at geometries that CASSCF adaptive sampling selected; a self-consistent extension would let the QMC-trained model propose new geometries and add QMC labels there, especially along the dissociation asymptote.
  • Inference: The ~160 fs prompt component is sensitive to the C-N bond-length criterion (2.25 Å here) and to Wigner sampling with zero-point energy; recomputing yields with a shorter threshold and classical Boltzmann sampling would show how much of this component is physical versus sampling-driven.
  • Inference: The same pipeline should transfer to other photochemical systems where active-space methods degrade at conical intersections or along bond-breaking coordinates, making method-dependent dynamics the norm rather than the exception.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces a workflow in which variational Monte Carlo (VMC) wave functions built from CIPSI expansions are used as reference data to train multi-state neural-network force fields for nonadiabatic molecular dynamics. The method is applied to gas-phase azomethane, with the QMC-based model compared against CASSCF- and MS-CASPT2-based models. The authors benchmark vertical excitation energies and forces along isomerization and dissociation pathways, then propagate 1000-trajectory surface-hopping ensembles from both cis- and trans-azomethane. Their central findings are that the QMC-trained dynamics preserves the torsional relaxation through conical intersections, strongly reduces the excessive C–N dissociation seen with CASSCF (from 92% to 33% at 400 fs for cis, and 82% to 9.5% for trans), and predicts a small prompt dissociation component after internal conversion with an onset around 160 fs, in qualitative agreement with femtosecond experiments.

Significance. If the results are robust, the paper establishes a practical route for large-ensemble photodynamics with correlated wave-function reference data, which is a significant methodological advance. The force benchmarks are careful and informative: they demonstrate that fixed-active-space methods have geometry-dependent errors near conical intersections and along dissociation, whereas the VMC/CIPSI protocol with a fixed target PT2 correction behaves more consistently. The large trajectory ensembles (1000 per method) are a strength, as is the explicit comparison with exFCI for vertical excitation energies. The main risk concerns extrapolation of the ML model outside the configuration space spanned by the CASSCF-generated training set, which is directly relevant to the headline dissociation yields and the claimed prompt-dissociation timescale.

major comments (3)
  1. [Section IV.D (trans-azomethane dynamics) and Section III (adaptive sampling)] The trans dynamics is performed with an ML model trained exclusively on the dataset generated from cis-initiated CASSCF adaptive sampling, as stated in Section IV.D. The justification that cis and trans trajectories probe the same torsional coordinate and C–N cleavage channels is plausible but not demonstrated. The trans simulation provides the key experimental comparison (Fig. 8 onset ~160 fs vs Diau–Zewail 70–100 fs), and the 9.5% dissociation yield and the claimed prompt component rest entirely on this model. If the model must extrapolate in the trans-side basin or in post-internal-conversion regions that are sparse in the 2320-configuration cis-generated set, these results could be artifacts of training-set coverage. Please provide quantitative evidence: for example, project the training set and the trans-initiated trajectories onto the ∠CNNC dihedral and C–N bond-length coordinates,
  2. [Section III (training set generation, final paragraph)] The 2320 configurations used to train all three ML models are generated once by adaptive sampling at the CASSCF(12,10) level, and the QMC, CASSCF, and CASPT2 reference data are computed on the same geometries. This creates a coverage bias: any region of configuration space that the QMC potential-energy surfaces visit but CASSCF dynamics does not will be under-sampled, and the QMC-trained force field must extrapolate there. Since the central claim is that QMC substantially changes the dynamics relative to CASSCF, the very regions where the method is most important may be exactly the ones not sampled. I ask the authors to demonstrate that the QMC-ML trajectories stay within the training distribution (e.g., by monitoring a distance-to-training-set metric or comparing the distribution of key internal coordinates visited in the QMC dynamics with those in the training set), or to augment the s
  3. [Section IV.B, Fig. 3 and surrounding discussion] For dissociated geometries, the excited-state force deviations of CASSCF and MS-CASPT2 relative to VMC/CIPSI exceed 20 kcal/mol/Å. The authors argue that this should not directly affect the dissociation dynamics because C–N breaking occurs on the ground state. However, the ML models are multi-state and the state-averaged orbitals from the excited-state description enter the ground-state potential through the common determinantal space and the training of the coupled ML model. Given that dissociation yields are a central quantitative result, this claim should be supported quantitatively — for example, by showing how the excited-state force errors propagate into ground-state forces at the sampled dissociation geometries, or by comparing dynamics with and without the problematic excited-state training points.
minor comments (5)
  1. [Abstract / Section V] The abstract states that the prompt-dissociation timescale is "consistent with" experiments, while Section V concludes "qualitative agreement" and notes dependence on the bond-length criterion and initial sampling. Please harmonize these phrasings so the abstract does not overstate the strength of the comparison.
  2. [Section II.A / intro] Minor typo: "neural-network force fields [25] as a smooth surrogates" should read "as smooth surrogates."
  3. [Figure 6 caption] The caption contains "cis-iniziated" — should be "cis-initiated."
  4. [Table II] For the trans rows, QMC yields are reported without uncertainty (e.g., 9.5% of 1000 trajectories has a 95% binomial confidence interval of roughly ±1.8%). Reporting the uncertainty would help assess the significance of differences between methods.
  5. [Section IV.A and Table I] The exFCI values are used as benchmark, but they are produced within the same CIPSI family. Although the paper is transparent about this, a sentence noting that exFCI is an extrapolated limit from the same selected-CI framework would help the reader judge the degree of independence.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QMC force-field dynamics is a genuine ab initio prediction; the CASSCF-sampled training set is a coverage limitation, not a circular reduction.

full rationale

The central derivation chain is self-contained rather than circular. The ML force fields are trained on VMC/CIPSI ab initio energies and forces, with no experimental observables or target dynamics quantities entering the fit. The reported dissociation yields, onset times, and excited-state populations emerge from 1000 independent surface-hopping trajectories and are not encoded in the training labels. The training configurations are generated once via CASSCF adaptive sampling and then reused for QMC, CASSCF, and CASPT2 reference data, which introduces a genuine extrapolation/coverage risk—particularly for trans-azomethane, since the models are applied 'without additional trans-specific training'—but this is a limitation of the sampling distribution, not a case where the prediction reduces to its inputs by construction. The exFCI benchmark shares the CIPSI family with the VMC wave functions, but it is an extrapolated full-CI estimate used as a consistency check and is not load-bearing for the dynamical conclusions; the paper also benchmarks against CCSD(T), MS-CASPT2, and external experimental data. Self-citations to prior QMC/CIPSI method papers are methodological building blocks rather than load-bearing authority, and no uniqueness or ansatz is imported solely from those citations. No circular step can be exhibited from the paper's equations or fitted parameters.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central simulation pipeline rests on no invented physical entities. It does rest on a chain of methodological assumptions: the QMC force estimator, the state-specific penalty orthogonalization, the balanced-CIPSI protocol, the neural-network surrogate, the CASSCF-generated training distribution, the surface-hopping approximation, and the Wigner sampling. Of these, the most fragile is the training-distribution assumption: because QMC energies/forces are computed on geometries chosen by CASSCF dynamics, the QMC-trained model cannot rediscover pathways CASSCF never sampled. The free parameters listed are hand-set protocol values that affect quantitative yields; none are fitted to the experimental dissociation data.

free parameters (7)
  • Jastrow distance-rescaling parameter κ = 0.6 a.u.
    Set by hand in the two-body Jastrow factor (Ref. [54]); controls short-range electron correlation and therefore the reference forces.
  • Penalty strength λ10 = 1 a.u.
    Orthogonality constraint strength in Eq. 4; chosen 'sufficiently large' to separate states; affects excited-state purity and hence both PESs.
  • Node-cutoff ε = 0.1 a.u.
    Force-estimator regularization (Ref. [45]); the value determines how close to the nodes the guiding wave function is allowed to go and affects the force labels.
  • Target PT2 energy correction = -0.616 a.u.
    Convergence target for all CIPSI expansions; a hand-set protocol parameter that directly sets the number of determinants (748–2856 vs 149) and the balance between geometries and states.
  • Dissociation bond-length threshold = 2.25 Å
    Operational criterion for counting C–N cleavage; the reported yields (33%, 47%, 92%, 9.5%, 29.7%) depend on this value, as the authors acknowledge.
  • ML hyperparameters (SPaiNN) = reported in SI
    Network architecture, training schedule, and early-stopping criteria for the force fields; not given in the main text and not deposited in a public archive.
  • Decoherence decay factor = 0.1 a.u.
    Standard energy-based decoherence parameter (Ref. [68]); affects hopping statistics and excited-state lifetimes.
assumptions (7)
  • domain assumption The VMC force estimator (Eq. 2) with a guiding wave function finite at the nodes (node-cutoff ε = 0.1 a.u.) yields unbiased atomic forces.
    Invoked to compute all QMC reference forces; relies on Refs. [41–45] and the chosen ε; a biased force estimator would directly bias the ML training labels.
  • domain assumption State-specific energy minimization with the penalty term (Eq. 4, λ10 = 1 a.u.) produces orthogonal approximations to S0 and S1.
    From Ref. [24]; the dynamics requires two clean adiabatic states; if the penalty is too weak, state mixing distorts PESs and nonadiabatic transitions.
  • ad hoc to paper Imposing the same target PT2 correction (−0.616 a.u.) across all geometries and states gives balanced wave-function quality.
    Central protocol choice; not deduced from first principles; validated only by convergence tests reported in the SI, and it controls the determinant content of the wave functions.
  • domain assumption The SpaiNN equivariant neural network can accurately interpolate VMC/CIPSI energies and forces from 2320 configurations over the sampled configuration space.
    The ML surrogate is the source of all dynamics; test-set errors are relegated to the SI and not provided in the main text.
  • ad hoc to paper Adaptive sampling at the CASSCF(12,10) level yields a training set that covers the configuration space visited by the QMC-trained dynamics.
    The full ML dataset is generated once at CASSCF level; any region QMC would visit but CASSCF does not is extrapolation. This is the paper's most fragile premise.
  • domain assumption Curvature-driven trajectory surface hopping with energy-based decoherence (decay 0.1 a.u.) reproduces the outcome of full nonadiabatic propagation.
    Supported by Refs. [61–69] and a CASSCF/MS-CASPT2 comparison in the SI, but not independently proven for the QMC-trained surfaces.
  • domain assumption Wigner harmonic sampling of initial conditions is appropriate for the fs dynamics; zero-point leakage into dissociative coordinates does not invalidate the relative method comparison.
    The authors note Wigner ZPE can accelerate dissociation relative to Boltzmann sampling, acknowledging this assumption is load-bearing for the absolute yields.

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Cite this review

Pith. "Pith review of Nonadiabatic excited-state dynamics with quantum Monte Carlo-trained machine learning: azomethane as a stringent test." pith.science (2026). https://pith.science/paper/3L6NCGVM

@misc{pith2026260716129,
  author       = {Pith},
  title        = {Pith review of: Nonadiabatic excited-state dynamics with quantum Monte Carlo-trained machine learning: azomethane as a stringent test},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3L6NCGVM}},
  note         = {Machine review of arXiv:2607.16129}
}
read the original abstract

We introduce quantum Monte Carlo (QMC)-trained multi-state machine-learned (ML) force fields for nonadiabatic excited-state dynamics, targeting photochemical processes in which the electronic character changes along the reaction path and a consistent correlated description is required. In this framework, variational Monte Carlo wave functions combine compact selected configuration-interaction expansions with a Jastrow factor that explicitly accounts for dynamical correlation, while neural networks convert the stochastic QMC data into smooth potential energy surfaces for large surface-hopping ensembles. We apply this approach to azomethane, a demanding test case involving torsional relaxation through conical-intersection regions and C--N bond dissociation on the hot ground state. Benchmark calculations support the accuracy of the QMC reference data and show robust force convergence across isomerization and dissociation geometries. The QMC-trained dynamics preserves the expected photoisomerization mechanism, strongly reduces the excessive C--N breaking obtained with complete active space self-consistent field, and predicts a small but non-negligible prompt dissociation component after internal conversion, with a timescale consistent with femtosecond-resolved mass-spectrometry experiments. These results establish QMC-ML as a practical route to nonadiabatic photochemical dynamics with accurate wave-function reference data.

Figures

Figures reproduced from arXiv: 2607.16129 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representation of gas-phase [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Force comparison along the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Force comparison along a C–N dissociation pathway. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Polar representation of 100 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Excited-state population as a function of time for [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Fractions of azomethane trajectories in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Excited-state population as a function of time for [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. C–N bond-length analysis for the QMC-trained [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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