Computing Reaction and Activation Energies of Pericyclic Reactions using a Symmetry-Adapted VQE Algorithm

Atul Kumar; Maitreyee Sarkar; Manikandan Paranjothy

REVIEW 3 major objections 5 minor 28 references

Computing Reaction and Activation Energies of Pericyclic Reactions using a Symmetry-Adapted VQE Algorithm

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Choosing each molecule's active space by a symmetry-matched fraction rule lets VQE reproduce CCSD reaction energies within 0.8 kcal/mol and activation energies within about 6 kcal/mol, even when absolute VQE energies are off by hundreds…

desk verdict Honest benchmark data, but the symmetry mechanism collapses for the C1 species where SMV just picks the largest active space. read the letter →

arxiv 2608.04751 v1 pith:KX4BVPUQ submitted 2026-08-05 physics.chem-ph

Maitreyee Sarkar , Manikandan Paranjothy , Atul Kumar This is my paper · ORCID

classification physics.chem-ph

keywords variationalquantumeigensolveractive-spaceselectionsymmetry-matchedfractionpericyclicreactionsDiels-AlderreactionAlder-eneerrorcancellationUCCSD

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 works to show that a symmetry-based rule for picking which electrons and orbitals enter a VQE calculation—the symmetry-matched fraction (SMF) criterion—can convert very inaccurate absolute energies into chemically useful reaction and activation energies for pericyclic reactions. Applying the same rule to the reactants, products, and transition states of a Diels-Alder and an Alder-ene reaction, the authors report reaction energies within 0.08 and 0.79 kcal/mol of CCSD reference values and activation energies within about 5 and 6 kcal/mol. This matters because pericyclic reactions are governed by orbital symmetry and their transition states are strongly correlated, making them demanding tests for near-term quantum algorithms. The practical upshot is that relative energetics—the quantities chemists compare with experiment—can survive even when absolute VQE errors are hundreds of kcal/mol, as long as active spaces are chosen consistently along the reaction coordinate.

What carries the argument

The symmetry-matched fraction (SMF) is the percentage of UCCSD excitation operators inside a candidate active space that transform as the same irreducible representation as the Hartree-Fock reference; the symmetry-matched value (SMV) is the raw count, used when all excitations belong to one irreducible representation (C1 species). For each reactant, product, and transition state, the authors scan active spaces from (2e,3o) to (8e,8o) drawn from orbital pools (four occupied plus four virtual for C2v/Cs species, four plus two for C1 products, four plus five for transition states), then select the active space with the largest SMF/SMV. Energies come from VQE with a UCCSD ansatz, parity mapping with tapering, and SLSQP optimization on a noiseless simulator. The machinery ensures that the truncation of the wavefunction is symmetry-consistent across the reaction coordinate, which is what allows the large absolute errors to cancel in reaction and activation energy differences.

What would settle it

Compute reaction and activation energies for at least one additional pericyclic reaction (or perform a permutation test on the energy tables already supplied in the Supporting Information), comparing the maximum-SMF/SMV combination against randomly selected or chemically intuitive active-space combinations; if the symmetry-selected combination is not consistently closer to CCSD than typical arbitrary combinations, the claimed systematic cancellation is falsified.

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Extended reading notes

Core claim

The central claim is that the cancellation of large absolute errors in energy differences is systematic when every species along the reaction coordinate is treated with the active space of highest SMF (or SMV for C1 species). Quantitatively: for the Diels-Alder reaction the SMF-VQE reaction energy is -34.31457 kcal/mol versus CCSD's -34.23219 (difference 0.08238 kcal/mol), and the activation energy is 19.36314 versus 24.34098 kcal/mol (difference 4.97784 kcal/mol); for the Alder-ene reaction the differences are 0.79230 and 6.24199 kcal/mol. These numbers rest on absolute VQE energies with average deviations of roughly 140-415 kcal/mol from CCSD. The same symmetry-guided criterion collapses 1008 (reaction) and 2592 (activation) possible active-space combinations for the Diels-Alder case and 558 and 1512 for the Alder-ene case into a single symmetry-consistent selection per energy. The paper further argues that active-space size alone is not a reliable guide: deviations are non-monotonic, and the transition states require the largest spaces (8e,8o) with 432 symmetry-matched excitations and 360 tapered variational parameters.

Load-bearing premise

The central assumption is that the hundreds-of-kcal/mol errors in absolute VQE energies cancel systematically in energy differences because active spaces are picked by the same SMF/SMV rule for every species; this cancellation is demonstrated for only two reactions, without error bars or a comparison against arbitrary active-space choices, so if it is a coincidence the reported accuracy would not generalize.

Editorial extensions

If this is right

For the two reactions tested, reaction energies are reproduced within 1 kcal/mol of CCSD (0.08 and 0.79 kcal/mol) and activation energies within about 5-6 kcal/mol, despite absolute errors of 140-415 kcal/mol.
The SMF/SMV criterion reduces the combinatorial search over active spaces to a single choice per energy, eliminating the need for chemical intuition to pick active spaces.
Transition states are the resource bottleneck: both require an (8e,8o) active space with 432 symmetry-matched excitations and 360 tapered variational parameters, consistent with their near-degeneracy.
Larger active spaces do not always improve VQE energetics within the truncated framework; the symmetry character of excitations, not active-space size, is the relevant selection principle.
The protocol directly transfers from the earlier ring-strain studies to pericyclic reactions, indicating it may be a general strategy for reaction energetics in resource-constrained VQE.

Reading between the lines

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

If the cancellation observed here is systematic, the SMF/SMV rule could serve as a parameter-free error-mitigation strategy for NISQ-era reaction energetics, complementing hardware error mitigation.
A natural testable extension is a permutation analysis over the already-tabulated active-space energies: checking whether the maximum-SMF combination ranks better than typical random active-space combinations would quantify how often the criterion is genuinely predictive.
Because C1 species have no symmetry distinction among excitations, the SMV criterion reduces to preferring larger excitation manifolds; testing more low-symmetry, substituted pericyclic reactions would clarify whether the rule is symmetry physics or simply a richness preference.
The same logic may apply to other truncated correlated methods, such as selected CI or density matrix embedding, where absolute errors are large but relative energies along a reaction coordinate matter, suggesting SMF-style selection as a general truncation principle.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the paper has real benchmark numbers, but its central mechanism—symmetry-guided cancellation of errors—does not hold for the C1 species, which are most of the molecules here. For those, the SMV criterion reduces to picking the largest active space. That needs to be confronted before the interpretation can be trusted.

What's new: applying the group's earlier SMF/SMV active-space selection to Diels-Alder and Alder-ene reactions, including transition states, with VQE/UCCSD at STO-3G. The new numbers in Tables III and IV are cleanly reported, absolute errors are shown honestly, and the selection rule is defined independently of the target energies. No fitting to CCSD is involved, so the reported reaction and activation energy differences are genuine predictions of the protocol as described.

The soft spot is serious. Section III.C notes that in C1 symmetry all excitations share one irrep, so SMF is 100% for every candidate. The paper then falls back on SMV, which is just the numerator—the total number of excitations. Maximizing SMV is equivalent to maximizing active-space size. Five of the eight species (Diels-Alder product and TS; Alder-ene ene, product, TS) are C1, and Table V confirms that the selection for all of them is the largest active space in the pool. So the symmetry criterion is doing no work for exactly the species that determine the reaction and activation energies. The agreement with CCSD might be a size effect or a lucky cancellation; the paper gives no baseline over second-largest or random active spaces, no error bars, and only two reactions. The claim that symmetry-consistent selection produces the cancellation is accordingly overstated.

That said, the paper is not wrong about the data. The observation that large absolute VQE errors can still yield chemically usable relative energies is worth examining, even if the selection rule is blunter than advertised. A reviewer should ask for a clear discussion of the C1 degeneracy, a comparison against at least one alternative active-space choice, and ideally a few more reactions to see whether the cancellation generalizes.

This deserves a serious referee: the numbers are real, the method is reproducible from the text, and the flaw is in the interpretation, not the computation. I'd take it, but only as a conditional.

Referee Report

3 major / 5 minor

Summary. The paper applies a symmetry-based active-space selection criterion (SMF/SMV) to VQE/UCCSD calculations of the Diels–Alder and Alder–ene reactions in the STO-3G basis, and compares the resulting reaction and activation energies with CCSD reference values. The authors report that, although absolute VQE energies deviate from CCSD by roughly 140–415 kcal/mol per species, the SMF/SMV-selected active spaces yield reaction energies within 0.08 and 0.79 kcal/mol and activation energies within about 5–6 kcal/mol of CCSD. The paper further claims that this systematic cancellation of errors arises from the symmetry consistency of the selected active spaces across reactants, products, and transition states, and that the protocol reduces the large combinatorial space of active-space choices to a single selection per reaction.

Significance. If the reported cancellation is robust, the approach could be a useful practical heuristic for resource-constrained VQE simulations of correlated molecular systems, because it would make chemically meaningful relative energies accessible despite large absolute-energy errors in a minimal-basis, noiseless-simulator setting. The paper's strengths include the explicit enumeration of all candidate active spaces, the definition of the selection rule independently of the target energetics, and the quantification of the combinatorial reduction. However, the significance is substantially limited by the small number of reactions (two), the absence of uncertainty estimates, and the fact that for C1-symmetric species the criterion degenerates to a size-maximization rule, so the central symmetry-based mechanism is not actually operative for most of the species that determine the reported energy differences.

major comments (3)

[Tables III and IV] For the five C1-symmetric species in this study (Diels–Alder product and TS; Alder–ene ene, product, and TS), all UCCSD excitation operators transform as the single irreducible representation of the C1 point group, so SMF = 100% for every candidate active space. Consequently SMV equals the total number of excitations, and maximizing SMV is mathematically identical to maximizing the number of excitations; within the finite orbital pools of Tables I and II this always selects the largest available active space, namely (8e,6o) in the (4o,2v) pool and (8e,8o) in the (4o,5v) pool, exactly as Table V reports. The paper acknowledges that SMF is identical for C1 species but does not state that the criterion reduces to a size-maximization heuristic. The central interpretation—that symmetry-consistent active-space selection produces systematic error cancellation—is therefore not operative for the product and transition states that determine the reported reaction and activation energies. Please provide control calculations (e.g., second-largest, smallest, or randomly selected active spaces, or a comparison against the distribution of all combinatorial energy differences) to determine whether the observed agreement is a symmetry effect or simply a size effect.
[Section IV.C] The claim of systematic cancellation rests on only two reactions and two activation-energy comparisons, with no uncertainty estimates. The absolute per-species VQE errors are 140–415 kcal/mol, so the reported agreement requires that errors for species along the same reaction coordinate are highly correlated. Without a distribution of reaction and activation energies over the combinatorial space—which the authors already enumerate (e.g., 1008 combinations for the Diels–Alder reaction energy)—or repeated-run statistics to account for optimizer variability, the reported agreement could be accidental. Please quantify the spread of energy differences over all active-space combinations and locate the SMF/SMV-selected values within that distribution to demonstrate that the selection is not merely cherry-picking a favorable outlier.
[Section IV.C] The statement that "the symmetry-guided framework adapts non-uniformly across the reaction coordinate and does not simply favor the largest active spaces for all molecular species" is misleading. It is true that the Cs and C2v species in this study can select compact active spaces, but for every C1 species the criterion selects the largest active space in the pool. The apparent non-uniform behavior is entirely driven by the two non-C1 species (diene and dienophile in Diels–Alder; enophile in Alder–ene), and the claim overstates the role of symmetry. Please rephrase this passage to explicitly acknowledge that for C1 species the criterion reduces to a maximum-excitation-count rule, and discuss how this affects the mechanistic interpretation of the error cancellation.

minor comments (5)

[Supporting Information] The abstract contains the typo "Diel-Alder" (should be "Diels-Alder"); the same typo appears in the Supporting Information figure caption "Diene and Dieneophile" (should be "dienophile").
[Section III.A] The main text states that absolute energies are provided in the Supporting Information, but the SI contains only comparison figures (S5 and S6) without numeric tables. Please include a table of absolute VQE and CCSD energies for all species and all active spaces considered, to allow readers to reproduce the reported differences and the cancellation analysis.
[Section III.C] The paper specifies that CCSD/STO-3G single-point energies are computed on M05-2X/cc-pVDZ geometries, but it does not report the point-group symmetry enforcement or the irrep labels used in the SMF/SMV analysis. Please state explicitly which Abelian point group was used for each species and how the orbital irreps were assigned (e.g., from NWChem output) to make the selection reproducible.
[Section III.C] Reference [14] is cited as "The Journal of Physical Chemistry A (2026)" without volume, article number, or DOI, and reference [28] is an arXiv preprint; please update these citations and briefly describe how the symmetry-matched fraction criterion was validated in those earlier works, since the present paper relies heavily on that prior framework.
[Section III.C] The sentence "Active spaces with the largest SMF values were selected" is correct for the general case but could be misleading for C1 species, where all SMF values are identical; the subsequent text clarifies that SMV is used, but the initial wording might confuse readers. Please rephrase to state upfront that for C1 species the selection uses SMV (or, equivalently, the total excitation count).

Circularity Check

1 steps flagged · score 2.0 of 10

No significant circularity; the C1 SMV criterion degenerates to excitation-count maximization by definition, but the energetic comparison to CCSD is independent and unfitted.

self definitional [Section III.C, Eq. (1), and the paragraph beginning 'As organic molecules generally possess lower symmetry'; Table V]
"SMF = Nsame-irrep/Ntotal-excitations × 100 (1) ... The numerator in the above expression will be referred to as the symmetry-matched value (SMV). ... In C1 symmetry, all excitations belong to the same irreducible representation, resulting in identical SMF values for all active spaces. In such cases, the SMV was used to guide active-space selection instead of the SMF."

By Eq. (1), SMV is Nsame-irrep. For a C1 species every UCCSD excitation transforms as the sole irreducible representation, so Nsame-irrep = Ntotal-excitations identically, making SMV = Ntotal-excitations by construction. 'Maximize SMV' is therefore exactly 'maximize the total number of excitations.' Within the finite pools used (4o2v for products and the ene; 4o5v for transition states), this selects AS(8e,6o) and AS(8e,8o), the largest active spaces, exactly as Table V reports for the product, TS, and ene species. Thus the 'symmetry-consistent' mechanism adds no independent constraint for five of the eight species; the selection reduces to a size-maximization heuristic.

full rationale

The central energetic claims are not circular. SMF/SMV values are computed from symmetry labels of UCCSD excitation operators using Eq. (1), before any comparison with CCSD, and the CCSD reference is external rather than used to tune the active-space choice. For the C2v and Cs species (diene, dienophile, enophile), the criterion selects non-maximal active spaces such as AS(2e,3o) for the enophile with SMF = 100, so the selection has independent content there. The self-citations to the authors' prior SMF work (refs 14 and 28) are not load-bearing because the criterion is defined in the present paper and tested against new CCSD data. The one definitional degeneracy is the C1 case documented above: for those species SMV collapses to the total excitation count, so the selected active spaces are the largest by construction. This affects the interpretation of the selection mechanism but not the derivation of the reported energy differences. The small sample size and lack of error bars are robustness concerns, not evidence of circularity. Overall, the paper's main numerical result is self-contained and not forced by its inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No numerical constants are fitted to the target reaction energies. The hand-chosen parameters are the orbital pools and active-space ranges in Tables I and II, which constrain the SMF/SMV selections. The principal structural assumption is the SMF criterion itself, carried over from the authors' earlier papers; the paper does not independently validate it against other selection methods.

free parameters (2)

Orbital pool composition per point group = 4 occupied + 4 virtual (C2v/Cs), 4 + 2 (C1 reactants/products), 4 + 5 (transition states)
Hand-chosen in Tables I and II; defines the candidate active spaces and therefore the selected SMF/SMV active spaces.
Active-space scan range = (2e,3o) to (8e,8o); min and max orbitals in Tables I and II
Chosen by hand; this range limits the set of active spaces from which the symmetry criterion selects.

assumptions (5)

domain assumption UCCSD ansatz within the chosen active space is flexible enough to describe the correlated ground states and transition states.
Invoked in Sections II.A and III.B; if the ansatz is not sufficiently expressive, the reported energies are variational truncations rather than approximations to the active-space ground state.
domain assumption CCSD/STO-3G single-point energies at DFT geometries are a valid reference for reaction and activation energies.
Used throughout Section III.A; the paper never cross-checks against experiment or higher-level methods, so all stated errors are relative to this reference.
domain assumption M05-2X/cc-pVDZ optimized geometries are accurate enough that single-point energies at these geometries represent the reaction path.
Geometry optimizations are done at DFT level per Section III.A; transition states are not characterized with frequency calculations in the text.
ad hoc to paper Excitations transforming as the same irreducible representation as the HF reference are the ones that should define the active space.
This is the defining assumption of the SMF criterion (Eq. 1), introduced in the authors' prior work and applied here; no independent benchmark is given within this paper.
standard math Parity mapping with tapering preserves the relevant low-lying spectrum.
Standard fermion-to-qubit mapping assumption used in Section III.B; it does not change the electronic energy.

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Cite this review

Pith. "Pith review of Computing Reaction and Activation Energies of Pericyclic Reactions using a Symmetry-Adapted VQE Algorithm." pith.science (2026). https://pith.science/paper/KX4BVPUQ

@misc{pith2026260804751,
  author       = {Pith},
  title        = {Pith review of: Computing Reaction and Activation Energies of Pericyclic Reactions using a Symmetry-Adapted VQE Algorithm},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KX4BVPUQ}},
  note         = {Machine review of arXiv:2608.04751}
}

read the original abstract

Pericyclic reactions provide stringent tests for quantum simulations because their mechanisms are governed by orbital symmetry and involve correlated transition states. In this work, we employ the variational quantum eigensolver (VQE) combined with a previously established symmetry-guided active-space selection protocol based on symmetry-matched fractions (SMF-VQE) to simulate Diel-Alder and Alder-ene reactions in complex systems involving extended pi-conjugation and multiple bonding. Although absolute electronic energies obtained from the current protocol exhibit significant deviations from the values computed using CCSD method, the symmetry-guided active spaces yield substantial cancellation of deviations in the energy differences. As a result, reaction energies are predicted with error (relative to CCSD) less than one kcal per mol, while activation energies are reproduced within about five to six kcal per mol. The symmetry-guided protocol also reduces the large combinatorial space of active-space choices to a single symmetry-consistent selection for each reaction.

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Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya,et al., Quantum chemistry in the age of quantum computing, Chem. Rev.119, 10856 (2019)

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