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REVIEW 2 major objections 4 minor 17 references

Aufbau suppressed coupled cluster as a post-linear-response method

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that Aufbau suppressed coupled cluster (ASCC) is nearly insensitive to which linear-response method seeds it, so a cheap CIS or TD-DFT calculation can be refined into energies close to those from the best excited-state…

desk verdict A solid, incremental method paper showing ASCC/PLASCC is mostly starting-point insensitive; the headline is slightly ahead of the conditional data. read the letter →

arxiv 2506.16680 v1 pith:BE6QXWUA submitted 2025-06-20 physics.chem-ph

Trine Kay Quady , Harrison Tuckman , Eric Neuscamman This is my paper · ORCID
classification physics.chem-ph
keywords Aufbausuppressedcoupledclusterpost-linear-responserefinementexcited-statechargetransferstatesorbitalrelaxationlinearresponseTD-DFTEOM-CCSD
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 sets out to establish that Aufbau suppressed coupled cluster (ASCC), when seeded with a starting state from any of the common linear-response methods, corrects that starting state so well that the final accuracy barely depends on which method produced the seed. The central evidence is a 138-state valence/Rydberg set plus seven charge-transfer states: PLASCC, the partially linearized form of ASCC, takes CIS, TD-DFT, EOM-CCSD, and ESMF starting points with mean unsigned errors of 0.87, 0.72, 0.36, and 0.11 eV and returns results with MUEs of 0.12 eV or less. In charge-transfer states the effect is largest: PLASCC from TD-DFT cuts the MUE by about a factor of 20, from well over 2 eV to roughly 0.1 eV. A sympathetic reader would care because it suggests that expensive state-by-state orbital optimizations such as ESMF may not be worth their cost when ASCC is available, and that simple linear-response calculations can serve as entry points to high-accuracy excited-state energetics.

What carries the argument

The load-bearing object is the ASCC wave function $|\Psi_{\mathrm{ASCC}}\rangle = e^{-\hat S^\dagger} e^{\hat T}|\phi_0\rangle$, in which $\hat T$ contains excitation operators and $\hat S^\dagger$ contains de-excitations. Applied to the Aufbau determinant $|\phi_0\rangle$, the product $\hat S^\dagger \hat T$ creates a second copy of the ground-state determinant with a controlled sign, so the Aufbau determinant can be suppressed or cancelled rather than simply occupied. PLASCC uses the same equations but drops a selected set of nonlinear diagrams, which prior perturbative analysis showed to be the balancing act that yields the best accuracy. The starting-point protocol is the second piece: for each linear-response method, the transition density matrix is rotated and truncated by singular value decomposition to one or two dominant configuration state functions, giving a compact reference for $\hat T$. The exponentiated singles operator is what carries the argument, because it can build in orbital relaxations that the starting method lacks, which explains why CIS and TD-DFT seeds, despite missing most relaxation physics, end up almost as accurate as ESMF seeds.

What would settle it

Recompute the ASCC and PLASCC errors on the full set of states without dropping non-converged cases, treating non-convergence as a failure; a specific check is the two charge-transfer CIS states where PLASCC did not converge (ammonia-oxygendifluoride 4 1A' and 3,5-difluoro-penta-2,4-dienamine 1 1A"). If including those states raises the TD-DFT-seeded PLASCC MUE well above 0.1 eV, or widens the spread across starting points, the central resilience claim is contradicted. If a continuation method converges those states and they land near the benchmark, the claim is confirmed.

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Extended reading notes

Core claim

The paper's central claim, stated on its own terms, is that ASCC performs its own orbital relaxations through its singles operator, so the quality of the starting point matters much less than in typical post-linear-response schemes. The evidence is in the convergence of error distributions: regardless of whether ASCC or PLASCC is initialized from CIS, TD-DFT with a range-separated hybrid functional, EOM-CCSD, or ESMF, the final MUEs cluster near 0.1 eV for valence and Rydberg states, and the small remaining differences track the starting point's ability to help convergence more than its raw energy accuracy. For the seven charge-transfer states, TD-DFT starting points with errors larger than 2 eV are transformed into PLASCC results with an MUE about 20 times smaller, while the already-accurate EOM-CCSD starting points improve by more than a factor of three. The paper concludes that ASCC is best understood as a high-accuracy post-linear-response refinement method, with ESMF retaining only a very small accuracy edge that is probably not worth its added cost.

Load-bearing premise

The claim of starting-point insensitivity is measured only on the subset of states where at least two starting points converged; if the states that are hardest for a starting method are also the ones most likely to fail to converge, the reported insensitivity is optimistic.

Editorial extensions

If this is right

  • PLASCC used after TD-DFT or CIS should give valence and Rydberg excitation energies with typical errors of a few tenths of an eV, close to the results obtained from EOM-CCSD or ESMF starting points.
  • For charge-transfer states, post-linear-response PLASCC reduces TD-DFT's mean unsigned error by roughly a factor of 20, and improves even EOM-CCSD's charge-transfer errors by more than a factor of three.
  • Because starting-point accuracy matters so little, users can choose the cheapest convenient linear-response seed without expecting a large accuracy penalty, provided the ASCC equations converge.
  • The practical case for ESMF's nonlinear orbital optimization weakens: its roughly 0.02 eV MUE advantage over linear-response starts may not justify its state-by-state cost.
  • ASCC's own orbital relaxation means that post-linear-response use should be treated as a general mode of ASCC, not a specialized correction.

Reading between the lines

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

  • A natural, untested extension is to seed PLASCC from cheaper-than-EOM-CCSD methods such as CC2 or selectively expanded CIS; if the insensitivity holds, sub-0.1 eV accuracy might be reachable at reduced scaling.
  • The same orbital-relaxation argument suggests PLASCC could improve excited-state potential energy surfaces, where partial relaxation errors distort photochemistry; testing this along nuclear coordinates would show whether the insensitivity persists beyond vertical energies.
  • The winnowing step means the reported numbers condition on convergence; extending the code to two-CSF and three-CSF starting points, or counting non-convergence as an outcome, would show whether the resilience claim holds for the hardest states rather than only for the tractable ones.
  • If ASCC truly erases starting-point dependence, the practical distinction between state-specific and response-based excited-state methods blurs: expensive orbital optimization could become optional, with convergence control replacing accuracy as the main design problem.
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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

2 major / 4 minor

Summary. The paper investigates whether Aufbau suppressed coupled cluster (ASCC) and its partially linearized variant (PLASCC) can serve as post-linear-response corrections for electronically excited states, starting from CIS, TD-DFT/ωB97X-V, EOM-CCSD, or ESMF wave functions. The authors construct truncated starting points via singular value decompositions of transition density matrices or natural-orbital-based procedures, then solve ASCC/PLASCC equations. They report that on a reduced set of 138 valence and Rydberg excitations from the QUEST databases plus seven charge-transfer states, final ASCC/PLASCC excitation-energy errors are nearly independent of the starting point. In particular, PLASCC from TD-DFT reduces the charge-transfer MUE by a factor of about 20, from multi-electron-volt errors to ~0.1 eV. The paper concludes that ASCC's singles operator provides its own orbital relaxation, so the more expensive ESMF orbital optimization may not be necessary when ASCC is used.

Significance. If the central claim holds, the paper describes a practically valuable protocol: a high-accuracy, state-specific coupled-cluster correction that can be initialized from cheap linear-response methods. The study is built on well-established external benchmarks (QUEST and the Szalay charge-transfer set), uses a fixed SVD truncation threshold rather than parameters fitted to the target energies, and provides a large raw-data table in the supplementary information. The starting-point-insensitivity claim is falsifiable and is supported by a broad set of states. The main weakness is that the headline quantitative conclusions rely on a reduced test set with nonrandom exclusions and a very small charge-transfer sample, so the reported resilience is partly conditional on convergence outcomes.

major comments (2)
  1. [III.a, III.c, SI a] The central starting-point-insensitivity claim is measured on a reduced test set that excludes states where two or more starting points fail to converge or have more than two large CSFs. Because poor starting points fail to converge more often, the reported MUEs are conditional on the converged subset and are not computed on a common fixed set of states. This is not merely a hypothetical concern: the SI lists five ωB97X-V-based PLASCC failures (formaldehyde 1 1B2, formamide 3 1A′, isobutene 1 1B1, thioacetone 2 1A1, cyclopropenone 3 1B2) for which ESMF-based PLASCC converges with errors near 0.0–0.1 eV. Dropping those states from the ωB97X-V statistics can artificially lower its MUE and make it look closer to ESMF than it actually is. I request a sensitivity analysis: for each starting point, report the MUE on the maximal set where at least one starting point converges, with missing entries handled by a stated rule (for example, using the ESMF-based result as a proxy, or excluding the state from all methods so that all MUEs are on an identical subset). Without such an analysis, the headline 'insensitivity' claim is not fully supported by the data as presented.
  2. [III.d, Figure 5] The charge-transfer conclusion rests on only seven states, and two of the CIS-based PLASCC calculations fail to converge (ammonia-oxygendifluoride 4 1A′ and 3,5-difluoro-penta-2,4-dienamine 1 1A″). The CIS-based MUE is therefore computed over five states, and the '20 times smaller' MUE ratio for TD-DFT is a ratio of small-sample statistics that could be dominated by one or two large starting-point errors. The paper does disclose these exclusions, but the abstract's characterization of the charge-transfer improvement as 'especially stark' goes beyond what seven states can robustly support. Please provide a per-state error table for the charge-transfer set, explicitly identify which states contribute to each MUE, and include a stability analysis (for example, leave-one-out or bootstrap) to show that the reported improvement factors are not artifacts of a single outlier.
minor comments (4)
  1. [III.c] The sentence comparing starting-point MUEs from Figure 1 (which includes the seven charge-transfer states) to the post-ASCC/PLASCC MUEs from Figure 2 (which excludes them) is an apples-to-oranges comparison. Since TD-DFT's large charge-transfer errors inflate its Figure 1 MUE, this sentence overstates the improvement. The fair comparison is already provided in Figure 4, and the text should either refer to Figure 4 or recompute the starting-point MUEs on the same 138-state subset.
  2. [II.d] The EOM-CCSD starting-point construction (interleaving singular vectors with natural orbitals followed by Gram–Schmidt) is more ad hoc than the CIS/TD-DFT construction, and the paper does not provide the same numerical validation as it does for the TD-DFT case (where the construction agrees with the CIS-like approach to within 0.01 eV). A brief test or justification of the EOM-CCSD construction would increase confidence that this starting-point choice does not introduce an uncontrolled bias.
  3. [SI b] The raw-data table is extremely wide and difficult to parse in printed form. I recommend also providing the data as a machine-readable file (CSV or similar) to allow readers to recompute the statistics and test alternative inclusion rules.
  4. [III.d, Figure 5] The figure caption should state explicitly that the MUE insets are computed over the converged states only, and that the numbers of states differ across starting points (the insets do show this, but the caption does not draw attention to it).

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: ASCC energies are solved from starting-point-seeded CC equations and benchmarked against external references; no fitted parameter is renamed as a prediction.

full rationale

The paper's central claim is that ASCC/PLASCC final excitation energies are insensitive to the linear-response starting point. The final energies are obtained by solving the ASCC amplitude equations (Eqs. 3-4) after using the truncated starting point only to define the zeroth-order operator space; they are not equal to the starting-point energies by construction. No parameter is fitted to the benchmark targets: the 0.2 SVD truncation threshold is a fixed methodological choice, and the QUEST and Szalay CT references are external benchmarks. Self-citations to the authors' prior ASCC work (refs 17-19) supply the method's working equations and perturbative analysis, but the post-linear-response behavior is a new empirical result tested against those external references, so the self-citations are not load-bearing in a circular sense. The paper's exclusion of states where two or more starting points fail to converge (Sec. III.a) creates a selection-bias risk for the quantitative insensitivity claim, but that is a correctness/robustness concern, not a derivation that reduces the prediction to its input by construction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. It depends on the ASCC/PLASCC formalisms from the authors' prior work, on a fixed SVD truncation threshold, and on external benchmark data. The main non-standard input is the 0.2 threshold, which is not fitted to the target data but is nonetheless a hand-set parameter.

free parameters (1)
  • singular value truncation threshold = 0.2
    Singular values of the starting point's transition density matrix (or ESMF C matrix) below 0.2 are discarded before constructing the ASCC starting point. This constant is chosen once and applied to all states, not fitted to benchmark energies.
assumptions (4)
  • domain assumption For one-CSF starting points, the zeroth-order ASCC wave function exactly matches the truncated starting point; the S and T operators are then expanded around this zeroth-order (Eqs. 5-6).
    This is the foundation of the ASCC working equations and comes from prior work (Refs. 17, 18).
  • domain assumption The truncated SVD of a response vector (CIS TDM or ESMF C) preserves the physically relevant character of the excited state when singular values above 0.2 are retained.
    The entire starting point preparation rests on this; no test is shown for the 0.2 threshold's sensitivity.
  • domain assumption Benchmark excitation energies from QUEST (exFCI or EOM-CCSDT) and the Szalay CT set are accurate enough to serve as ground truth.
    The paper relies on these external references without re-assessment.
  • ad hoc to paper The partially linearized PLASCC truncation is a balanced approximation that should not qualitatively distort the ASCC potential surface.
    PLASCC is introduced in prior work (Ref. 18) as a pragmatic balancing of diagrams; this paper inherits it without a new derivation.

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Cite this review

Pith. "Pith review of Aufbau suppressed coupled cluster as a post-linear-response method." pith.science (2026). https://pith.science/paper/BE6QXWUA

@misc{pith2026250616680,
  author       = {Pith},
  title        = {Pith review of: Aufbau suppressed coupled cluster as a post-linear-response method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BE6QXWUA}},
  note         = {Machine review of arXiv:2506.16680}
}
read the original abstract

We investigate the ability of Aufbau suppressed coupled cluster theory to act as a post-linear-response correction to widely used linear response methods for electronically excited states. We find that the theory is highly resilient to shortcomings in the underlying linear response method, with final results from less accurate starting points nearly as good as those from the best starting points. This pattern is especially stark in charge transfer states, where the approach converts starting points with multi-eV errors into post-linear-response results with errors on the order of 0.1 eV. These findings highlight the ability of Aufbau suppressed coupled cluster to perform its own orbital relaxations and raise the question of whether initializing it with an orbital relaxed reference is worth the trouble.

Figures

Figures reproduced from arXiv: 2506.16680 by the authors.

Figure 1
Figure 1. FIG. 1. Distributions of excitation energy errors for CIS, TD [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Excitation energy error distributions for ASCCSD (left) and PLASCCSD (right) on our reduced test set of valence and Rydberg [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. ASCC (left) and PLASCC (right) excitation energy error distributions for different starting points broken out by state type: results for [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Excitation energy error distributions on our reduced valence and Rydberg set for TD-DFT/ [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Unsigned errors in charge transfer excitation energies. Er [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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