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REVIEW 3 major objections 5 minor 39 references

Automated selection of nuclear coordinates for reduced dimensionality nonadiabatic dynamics

T0 review · 3 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Principal component analysis of full-dimensional surface-hopping trajectories identifies low-dimensional nuclear subspaces that reproduce the full dynamics, outperforming normal-mode variance selection on all three photochemical reactions t

desk verdict Useful proof-of-concept benchmark showing PCA beats NMV for reducing dimensionality in TSH dynamics, but the headline reduction ratios are in-sample and should be read with caution. read the letter →

arxiv 2509.09329 v1 pith:OOMBFIIC submitted 2025-09-11 physics.chem-ph

Vincent Delmas , Alessandro Nardi Nardi , Isabella C. D. Merritt , Anthony Ferté , Ignacio Fdez. Galván , Morgane Vacher This is my paper
classification physics.chem-ph
keywords dimensionalityreductionnonadiabaticdynamicstrajectorysurfacehoppingprincipalcomponentanalysisnormalmodevariancephotochemistryphotoisomerizationring-openingreactions
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

This paper aims to replace human guesswork in choosing which nuclear coordinates matter for excited-state dynamics. It proposes using principal component analysis (PCA) of geometries visited in cheap full-dimensional surface-hopping simulations to automatically pick a reduced set of coordinates, and tests the idea on three photochemical reactions. The authors report that PCA-based reduction reproduces the full-dimensional dynamics within a 10% error threshold using 16 of 24 dimensions for azomethane, 7 of 30 for butyrolactone, and 16 of 24 for furanone; the variance-based alternative, normal mode variance, is consistently worse. If correct, the protocol offers a systematic first step toward running expensive quantum-dynamics methods in a much smaller space.

What carries the argument

The central object is the variance-ranked linear basis constructed from full-dimensional trajectory geometries: after removing rotation and translation, geometries are expressed in ground-state normal modes, and either principal components (PCA) or individual normal modes (NMV) with the largest variance are kept. Reduced-dimensional dynamics are run by propagating only within the selected subspace, with gradients projected onto it on the fly; accuracy of electronic populations and key geometric coordinates is compared to the full-dimensional simulation via absolute relative error.

What would settle it

Run the same PCA selection from low-level TSH dynamics, then run reduced-dimension dynamics with a more accurate electronic-structure or quantum-dynamics method and check whether the PCA-selected subspace reproduces the higher-level full-dimensional results; failure would show the protocol selects coordinates tuned only to the low-level reference.

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Extended reading notes

Core claim

For all three molecules, both PCA and NMV can be used to select lower-dimensional spaces in which the full-dimensionality dynamics results are reproduced, but PCA always allows a more significant dimensionality reduction without loss of accuracy. Specifically, PCA reduces tAZM from 24 to 16 dimensions, Bulac from 30 to 7, and Fur from 24 to 16, while NMV reduces tAZM from 24 to 18, Bulac from 30 to 24, and gives no clear reduction for Fur. Accuracy is judged by absolute relative errors below 10% for two electronic and two geometric properties per molecule, comparing ensembles of 100 trajectory surface hopping simulations.

Load-bearing premise

The load-bearing premise is that the full-dimensional trajectory-surface-hopping dynamics used both to train the reduction and to define accuracy captures the essential photochemistry; if it does not, the selected subspace is only accurate relative to that biased benchmark.

Editorial extensions

If this is right

  • PCA-based reduction reproduces full-dimensional TSH electronic and geometric properties within 10% relative error for tAZM at 16 dimensions, Bulac at 7 dimensions, and Fur at 16 dimensions.
  • NMV is consistently less efficient: it allows reduction to 18 dimensions for tAZM, 24 for Bulac, and no clear reduction for Fur.
  • Variance alone does not guarantee accuracy; the identity of removed motions matters, so no universal variance threshold applies across systems.
  • The approach is intended as the coordinate-selection step before running higher-cost dynamics methods (e.g., DD-vMCG, quantum Ehrenfest, MCTDH) in the reduced subspace.

Reading between the lines

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

  • Because both the full and reduced dynamics use the same SA-CASSCF TSH method, the 10% threshold measures reduction error relative to that level of theory, not absolute photochemical accuracy; validating against a more accurate method or experiment is a natural next step.
  • PCA's mixing of all normal modes into each principal component may implicitly accommodate some anharmonic or large-amplitude motion better than truncating individual modes; testing on systems with stronger anharmonicity would clarify this.
  • The protocol could be iterated: a cheap TSH run selects a subspace, a higher-level reduced-dimension run then refines the selection, potentially improving the subspace without a full-dimensional high-level calculation.
  • Although the coordinate selection is automated, the choice of electronic and geometric properties used to define error still involves human input; different property choices might rank the two methods differently.
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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 manuscript proposes an automated protocol for selecting reduced nuclear-coordinate subspaces for mixed quantum-classical trajectory surface hopping (TSH) simulations. Full-dimensional TSH trajectories are analyzed by principal component analysis (PCA) or by ranking ground-state normal modes by their variance (NMV); the reduced subspace is then used to re-run TSH dynamics, and accuracy is measured as the absolute relative error (ARE, Eq. 1) of selected electronic and geometric properties against the full-dimensional reference. The protocol is applied to trans-azomethane, butyrolactone, and furanone. The central quantitative claims are that PCA allows reduction from 24 to 16, 30 to 7, and 24 to 16 dimensions, respectively, while NMV allows 24 to 18 and 30 to 24, with no clear reduction for furanone; PCA outperforms NMV in all cases.

Significance. If the reported reduction ratios are robust, the protocol would be a useful practical tool for constructing reduced-dimensional models of nonadiabatic dynamics in an automated, reproducible way, without manual selection of reaction coordinates. Strengths of the paper include the honest re-simulation of the reduced dynamics in the projected subspace rather than a post-processing reconstruction, the display of raw trends including non-monotonic error curves, the absence of free parameters fitted to the ARE, and the explicit grounding of the 10% threshold in the ensemble-convergence estimates of Ref. 33. The robustness check with respect to the number of analyzed trajectories is a useful addition. The main caveats are that the evaluation is in-sample and at the same electronic-structure level used to build the subspace, so the specific minimal dimensionalities should be read as internal-consistency results until an out-of-sample or cross-method validation is supplied.

major comments (3)
  1. [Section 2.1, Figure 2, Eq. (1), Section 3] The PCA/NMV bases are built from the same full-dimensional trajectory ensemble used as the ARE reference (Eq. 1). The quoted minimal dimensionalities (16/7/16 for PCA; 18/24 for NMV) may therefore be optimistically biased. The fewer-trajectories robustness test in Section 4/SI does not break this training/evaluation coupling. Also, the manuscript does not state whether the reduced runs reuse the same initial conditions as the reference ensemble. This is load-bearing for the quantitative claims. Please state this explicitly and provide a held-out test, e.g., build the basis from one half of the 100 trajectories and evaluate reduced dynamics against full-dimensional dynamics from the other half. If infeasible, state the in-sample nature as a limitation and present the ratios as upper-bound estimates.
  2. [Introduction, Section 4, Conclusions] The stated motivation is to use low-level TSH dynamics to select a subspace in which more expensive, higher-accuracy dynamics can be run. However, the validation is entirely at the same TSH/SA-CASSCF level, so the selected subspace is only shown to reproduce the low-level dynamics. The manuscript acknowledges this assumption but still uses it to support the claim that the approach opens routes to higher-level simulations. A concrete demonstration for at least one system, e.g., PCA selection from TSH trajectories followed by reduced-dynamics comparison against a full-dimensional run at a second electronic-structure level, would substantiate transferability. Without it, the transferability statement should be presented as a proposal, not as an established result.
  3. [Section 4 (coordinate system limitation)] The protocol uses ground-state normal modes as the global coordinate basis, and the Discussion acknowledges that normal modes have known limitations for large-amplitude motions. Two of the three test systems are ring-opening reactions involving large-amplitude bond breaking, so this is not a marginal issue. The empirical results show that PCA in this basis works for the studied cases, but the generality of the method would be better supported by testing at least one alternative coordinate definition (e.g., mass-weighted Cartesian PCA or a curvilinear internal-coordinate basis) or by restricting the claims to modest-amplitude processes. As written, the acknowledged limitation is flagged but not addressed.
minor comments (5)
  1. [Section 3.1] The text says 'for the NMV a loss of accuracy at 18 dimensions' but the conclusion states NMV can reduce to 18 dimensions. Please reconcile whether the last accurate dimensionality is 18 or whether accuracy is lost when going from 18 to 17 dimensions.
  2. [Section 4] The sentence 'the electronic properties most clearly differentiate between the two methods (Figure 3(b))' appears to reference the wrong panel; electronic-property AREs are shown in Figure 3(c).
  3. [Section 4, Figure 9] The sentence 'For Fur (e), the evolution of error with variance is comparable...' should refer to Figure 9(f), as Figure 9(e) is the Bulac panel.
  4. [Section 3.2] The electronic AREs for Bulac are described as 'relatively low (less than 0.2)'. Since the acceptance threshold is 0.1, it would be clearer to state explicitly whether these values are below the threshold or only low relative to the other error curves.
  5. [Section 2.1] The text first says full dimensionality is 3N_at dimensions and later reports reductions in terms of 3N_at-6. Please clarify that the rotational and translational degrees of freedom are removed by the Kabsch alignment and normal-mode projection before PCA/NMV, so the quoted dimensionalities are internal-coordinate dimensionalities.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the PCA/NMV subspaces are variance-based and the reduced-dynamics ARE is measured against separately rerun full-dimensional TSH dynamics, not reconstructed from the basis.

full rationale

The claimed result is that PCA/NMV-selected subspaces can host reduced-dimensional TSH dynamics that reproduce full-dimensional TSH dynamics within a 10% ARE threshold. The workflow (Section 2.1, Figure 2) constructs the PCA or NMV basis from geometric variances of full-dimensional trajectories; the accuracy metric (Eq. 1) then compares ensemble-averaged electronic and geometric properties of separately propagated reduced-dimensional trajectories with the full-dimensional ensemble. Nothing in the construction forces the selected electronic or geometric properties to agree: PCA maximizes retained geometric variance, not any of the four target properties, and the paper itself reports non-monotonic ARE as dimensions are reduced (Section 3.2) and shows that explained variance alone does not predict error (Section 4, Figure 9). The reduced-dynamics accuracy is therefore an empirical outcome, not a tautology. The protocol's use of the same TSH/SA-CASSCF level to generate both the basis and the reference is an acknowledged scope assumption (Introduction: 'the suggested protocol assumes that the lower-level dynamics is able to capture the relevant features of the investigated process'), and the limitation of ground-state normal modes for large-amplitude motion is explicitly acknowledged in Section 4. These are correctness/robustness caveats, not circular reductions. The few self-citations (Refs. 27 and 33) concern reaction parameters and trajectory-convergence checks and are not load-bearing for the PCA-vs-NMV comparison. No equation or construction in the paper reduces to its own input by definition.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The ledger for the central claim is light: no invented entities, no fitted potential parameters, and no coefficients tuned to force agreement between reduced and full dynamics. The main imported assumptions are methodological: TSH at the SA-CASSCF level is a valid reference, normal modes are adequate coordinates for large-amplitude motion, 100-trajectory ensembles are converged at every tested dimensionality, and variance in the full-dimensional trajectories marks dynamical importance. The free parameters are choices in the evaluation procedure: the 10% ARE threshold that turns error curves into 'reduction possible' statements, and the human-selected property sets (Table 1) that define the accuracy metric.

free parameters (2)
  • ARE accuracy threshold = 10% relative error
    Declared in Section 3.1 as the boundary between accurate and inaccurate dynamics. The headline reduction numbers (16, 7, 16) are the minimal dimensionalities whose total ARE stays below this threshold, so the quantitative claims are conditioned on this choice. It is justified by Ref. 33 convergence estimates but remains a human choice; sensitivity analysis is not given.
  • Evaluated property set for the accuracy metric = two electronic and two geometric properties per molecule (Table 1)
    AREtotal averages over these four properties (eq. 2). The Discussion states 'This process involves human input.' Different property choices could shift the reported reduction ratios; for Fur the authors note the total error is less decisive than the geometric error alone.
assumptions (4)
  • domain assumption TSH with SA-CASSCF/6-31G(d) faithfully captures the photochemistry of the three systems
    Stated in the Introduction: 'the suggested protocol assumes that the lower-level dynamics is able to capture the relevant features of the investigated process'. Both the reduction basis and the accuracy reference come from this method, so any bias in the reference propagates into the reduction numbers.
  • domain assumption Ground-state normal modes remain adequate coordinates for large-amplitude reactive motion
    The protocol works in normal mode coordinates from the ground-state minimum (Section 2.1). The Discussion acknowledges 'normal modes are known to present limitations in case of large amplitude motions', which is directly relevant to the ring-opening reactions (Bulac, Fur).
  • domain assumption 100-trajectory ensembles are converged at every tested dimensionality
    Section 2.3 justifies 100 trajectories for full dimensionality via Ref. 33, but each reduced-dimensionality ensemble is a separate 100-trajectory run and its convergence is not separately established; ARE values are reported without error bars.
  • domain assumption Explained variance in the full-dimensional ensemble marks dynamical importance
    Both selection methods rank coordinates by variance (Section 2.1). The paper itself demonstrates the failure of this assumption for NMV (Figure 4: low-variance modes 16 and 17 are load-bearing for tAZM isomerisation), so the assumption's validity is method- and system-dependent.

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Pith. "Pith review of Automated selection of nuclear coordinates for reduced dimensionality nonadiabatic dynamics." pith.science (2026). https://pith.science/paper/OOMBFIIC

@misc{pith2026250909329,
  author       = {Pith},
  title        = {Pith review of: Automated selection of nuclear coordinates for reduced dimensionality nonadiabatic dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OOMBFIIC}},
  note         = {Machine review of arXiv:2509.09329}
}
read the original abstract

Poor scaling of dynamics simulations with number of dimensions is currently a major limiting factor in the simulation of photochemical processes. In this work, we investigate ways to reduce the dimensionality of many-atom systems with a view toward enhancing computational efficiency while maintaining accuracy. Using mixed quantum-classical Trajectory Surface Hopping (TSH) simulations of three photoreactive molecules - trans-azomethane (tAZM), butyrolactone (Bulac), and furanone (Fur) - we explore two different dimensionality reduction techniques: Principal Component Analysis (PCA) and Normal Mode Variance (NMV). Dynamics simulations are run in full dimensionality and reduced dimensionality, employing either PCA or NMV, and the impact of the dimensionality reduction on selected electronic and geometric properties of the dynamics is evaluated. For all three molecules, both PCA and NMV can be used to select lower-dimensional spaces in which the full-dimensionality dynamics results are reproduced. PCA reduction outperforms NMV in all systems, allowing for a more significant dimensionality reduction without loss of accuracy. The improved accuracy of PCA is, for tAZM, mostly seen in the electronic properties while for both Fur and Bulac the advantage is clear in the ring-opening reaction itself as well. The present approach opens routes to simulation of larger photochemically relevant systems, through the use of automated dimensionality reduction, avoiding human bias.

Figures

Figures reproduced from arXiv: 2509.09329 by the authors.

Figure 1
Figure 1. (a) trans-to-cis isomerisation of azomethane, (b) ring opening of butyrolactone, and (c) ring opening of furanone. Re￾action times and excitation wavelength are taken from refs 26 and 27. This article is structured as follows: in Section 2 the method￾ology is introduced, including the dimensionality reduction procedure, the electronic and geometric properties used to evaluate the reactions, as well as the computatio… view at source ↗
Figure 2
Figure 2. First the dynamics are performed in full dimen [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 2
Figure 2. Workflow of the dimensionality reduction procedure, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figures from the paper (7 more)
Figure 3
Figure 3. Figure 3: Simulation results for trans-azomethane. Distribution (%) of the trans, mix, and cis conformers at the end of the dynamics simulations as a function of number of dimensions, for both PCA (a) and NMV (b) reduction methods. Evolution of the electronic (c), geometric (d) …
Figure 4
Figure 4. Figure 4: The two normal modes (mass weighted, hydrogen [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Simulation results for butyrolactone. Top panel: evolution (%) of C-O bond break as a function of time (fs) for each dimensionality, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: The four normal modes removed when decreasing from [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Simulation results for furanone. Evolution (%) of C-O bond break in function of time (fs) and dimensions for the PCA (a) and [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: (a) Normal mode 10 removed when reducing from 10 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Top panel: evolution of the explained variance (%) by the PCA (blue) and NMV (orange) methods, as a function of the retained [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

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    Sellner, B.; Ruckenbauer, M.; Stamboli \'c , I.; Barbatti, M.; Aquino, A. J. A.; Lischka, H. Photodynamics of Azomethane : A Nonadiabatic Surface-Hopping Study . J. Phys. Chem. A 2010, 114, 8778--8785 mcitethebibliography main-rev3.tex000066400000000000000000001566111506051356...

    2010

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.