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arxiv: 2607.01801 · v1 · pith:FSVZMR3Enew · submitted 2026-07-02 · ⚛️ physics.chem-ph

Benchmarking SOPPA-based methods for the calculation of static and dynamic polarizabilities

Joep van den Brink , Michael Hilding Estes , Stephan P. A. Sauer This is my paper

Pith reviewed 2026-07-03 04:11 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords polarizabilitiesSOPPAbenchmarkingCCSDaromatic moleculesfrequency-dependentRPAHRPA
0
0 comments X

The pith

HRPA(D) and SOPPA(CCSD) match CCSD most closely for polarizabilities across 41 molecules

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

The paper computes static and frequency-dependent polarizabilities for 41 molecules with RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2) and SOPPA(CCSD) using the aug-cc-pVTZ basis set. It benchmarks these against CCSD references and finds a clear split: HRPA(D) is most accurate for non-aromatic molecules while SOPPA(CCSD) leads for aromatic molecules at low frequencies, with RPA becoming best at high frequencies for aromatics because it overestimates the lowest excitation energy. A sympathetic reader cares because these calculations determine how molecules respond to electric fields in spectroscopy and materials, and the work shows that doubles corrections deliver CCSD-level accuracy at lower cost.

Core claim

Benchmarking shows HRPA(D) and SOPPA(CCSD) provide the most accurate results overall for static and dynamic polarizabilities, with HRPA(D) best for non-aromatic molecules and SOPPA(CCSD) best for aromatic molecules at low frequencies. RPA becomes most accurate for aromatic molecules at higher frequencies due to overestimation of the lowest electronic excitation energy. Doubles corrections in RPA(D) and HRPA(D) achieve accuracy comparable to or better than SOPPA(CCSD) at lower computational cost.

What carries the argument

The performance split between aromatic and non-aromatic molecules when applying doubles corrections within RPA(D) and HRPA(D) versus full SOPPA(CCSD) for polarizability calculations.

Load-bearing premise

The selected 41 molecules and aug-cc-pVTZ basis set produce performance trends that generalize, and CCSD serves as a sufficiently accurate reference without its own errors changing the relative rankings.

What would settle it

Recalculating polarizabilities for the same or additional molecules with a larger basis set such as aug-cc-pVQZ and finding that the accuracy ordering of HRPA(D) and SOPPA(CCSD) reverses relative to CCSD.

Figures

Figures reproduced from arXiv: 2607.01801 by Joep van den Brink, Michael Hilding Estes, Stephan P. A. Sauer.

Figure 1
Figure 1. Figure 1: FIG. 1. Deviations of the polarizabilities calculated with various methods from the CCSD results [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Deviations of the static polarizabilities calculated with various methods from the CCSD [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Deviations of the static polarizabilities of all 41 individual molecules calculated with [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Deviations of the static polarizabilities calculated with various methods from the CCSD [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Deviations of the static polarizabilities calculated with various methods from the CCSD [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Deviations of the polarizabilities at 589 [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Deviations of the polarizabilities at 589 [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Deviations of the polarizabilities at 589 [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Deviations of the polarizabilities at 355 [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Deviations of the polarizabilities at 355 [PITH_FULL_IMAGE:figures/full_fig_p026_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Deviations of the polarizabilities at 355 [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The mean- and mean absolute deviations of all methods except RPA have in [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Deviations of the static polarizabilities (in au) calculated with various methods from the [PITH_FULL_IMAGE:figures/full_fig_p032_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Deviation of calculated polarizabilities (in au) from experimental values for N [PITH_FULL_IMAGE:figures/full_fig_p036_14.png] view at source ↗
read the original abstract

Static and frequency-dependent polarizabilities were computed for 41 molecules using RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2), and SOPPA(CCSD) with the aug-cc-pVTZ basis set and benchmarked against CCSD reference values and available experimental data. The analysis reveals a pronounced distinction between the performance of these methods for aromatic versus non-aromatic molecules. Across all frequencies, HRPA consistently yields substantially larger deviations from CCSD than the other approaches, whereas HRPA(D) and SOPPA(CCSD) provide the most accurate results overall. For static polarizabilities, HRPA(D) performs best for non-aromatic systems, followed by SOPPA(CCSD) and RPA(D), while SOPPA(CCSD) is most accurate for aromatic molecules. In the frequency-dependent regime, HRPA(D) remains the most accurate method for non-aromatic molecules, although RPA(D) shows greater consistency. For aromatic molecules, SOPPA(CCSD) performs best at low frequencies, with RPA offering intermediate accuracy but higher consistency than most other methods; at higher frequencies, RPA becomes the most accurate approach, followed by RPA(D), while SOPPA(CCSD) deteriorates. These trends highlight the importance of doubles corrections in RPA(D) and HRPA(D), which achieve accuracy comparable to or better than SOPPA(CCSD) at lower computational cost. The strong performance of RPA for aromatic molecules is attributed to its characteristic overestimation of the lowest electronic excitation energy. Comparison with experimental data confirms SOPPA(CCSD) as the most reliable method for static polarizabilities, while RPA and HRPA(D) provide the best agreement for frequency-dependent polarizabilities of aromatic systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper benchmarks RPA, RPA(D), HRPA, HRPA(D), SOPPA, SOPPA(CC2), and SOPPA(CCSD) for static and frequency-dependent polarizabilities of 41 molecules at the aug-cc-pVTZ level, using CCSD values as the primary reference and available experimental data for validation. It reports that HRPA(D) and SOPPA(CCSD) are the most accurate overall, with HRPA(D) best for non-aromatic molecules across frequencies and SOPPA(CCSD) best for aromatic molecules at low frequencies (RPA best at high frequencies for aromatics), while highlighting the value of doubles corrections.

Significance. If the performance trends hold, the work supplies practical guidance on cost-accuracy trade-offs for response-property calculations and underscores the utility of HRPA(D) as a lower-cost alternative to SOPPA(CCSD). The explicit separation of aromatic versus non-aromatic behavior and the dual comparison to both CCSD and experiment are useful features.

major comments (2)
  1. [Abstract] Abstract and main analysis: the central distinction (HRPA(D) superior for non-aromatics, SOPPA(CCSD) for aromatics at low frequency) is obtained by treating CCSD/aug-cc-pVTZ as ground truth. Because CCSD omits triples and higher excitations whose contributions to polarizabilities are known to be larger near low-lying states, and because aromatic and non-aromatic molecules differ systematically in their excitation spectra, any class-dependent CCSD error would directly affect the reported ordering. No higher-level reference (e.g., CCSDT or CC3) or basis-set extrapolation is presented to test this possibility.
  2. [Abstract] Abstract: while experiment is invoked to confirm SOPPA(CCSD) for static polarizabilities, the frequency-dependent rankings (especially the reversal favoring RPA at high frequencies for aromatics) rest entirely on the CCSD reference. Without a quantitative assessment of how CCSD errors vary with frequency or molecular class, the claim that these trends generalize remains load-bearing and unverified.
minor comments (2)
  1. The criteria used to classify the 41 molecules as aromatic or non-aromatic, the exact frequency grid, and the statistical measures (MAE, max error, etc.) should be stated explicitly in the methods section.
  2. A short discussion of why aug-cc-pVTZ was chosen uniformly and whether basis-set incompleteness errors are expected to cancel equally across the tested propagators would improve transparency.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments on our benchmarking study. We address the two major comments point-by-point below, acknowledging the limitations of the CCSD reference while noting the practical constraints of the study.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main analysis: the central distinction (HRPA(D) superior for non-aromatics, SOPPA(CCSD) for aromatics at low frequency) is obtained by treating CCSD/aug-cc-pVTZ as ground truth. Because CCSD omits triples and higher excitations whose contributions to polarizabilities are known to be larger near low-lying states, and because aromatic and non-aromatic molecules differ systematically in their excitation spectra, any class-dependent CCSD error would directly affect the reported ordering. No higher-level reference (e.g., CCSDT or CC3) or basis-set extrapolation is presented to test this possibility.

    Authors: We agree that CCSD is an approximate reference and that the neglect of triples (and higher) excitations could introduce class-dependent errors, particularly given differences in excitation spectra between aromatic and non-aromatic molecules. For the 41-molecule set at aug-cc-pVTZ, however, CCSDT or CC3 calculations remain computationally prohibitive. We have therefore adopted CCSD as the highest feasible correlated reference, consistent with prior benchmarking studies in the field. Where experimental data exist, they support the static-polarizability ordering. We will revise the manuscript to add an explicit discussion of this limitation and its potential impact on the reported aromatic/non-aromatic distinction. revision: partial

  2. Referee: [Abstract] Abstract: while experiment is invoked to confirm SOPPA(CCSD) for static polarizabilities, the frequency-dependent rankings (especially the reversal favoring RPA at high frequencies for aromatics) rest entirely on the CCSD reference. Without a quantitative assessment of how CCSD errors vary with frequency or molecular class, the claim that these trends generalize remains load-bearing and unverified.

    Authors: We acknowledge that the frequency-dependent rankings rely on the CCSD reference, as experimental frequency-dependent polarizabilities are available for only a small subset of the molecules. The static results, by contrast, are cross-validated against experiment. A quantitative decomposition of CCSD errors as a function of frequency or molecular class would require higher-level data that are not feasible for the full set. In the revised manuscript we will clarify that the frequency-dependent trends are reported relative to CCSD and note the absence of a direct error analysis with respect to frequency or aromaticity. revision: partial

standing simulated objections not resolved
  • Higher-level reference calculations (CCSDT, CC3) or basis-set extrapolations for the full 41-molecule set to quantify class- and frequency-dependent CCSD errors.

Circularity Check

0 steps flagged

Benchmarking against independent CCSD references and experiment shows no circularity in performance claims

full rationale

The paper computes polarizabilities for 41 molecules with multiple propagator methods and directly compares deviations to CCSD/aug-cc-pVTZ values plus experimental data. No equations or results reduce by construction to fitted inputs, self-definitions, or self-citation chains; the reported rankings (HRPA(D) vs SOPPA(CCSD) by molecular class) are statistical outcomes of those external comparisons. Minor self-citations to prior SOPPA implementations are present but not load-bearing for the benchmark conclusions, which remain falsifiable against the cited references.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The study relies on standard quantum-chemistry assumptions about reference methods and basis sets without introducing new fitted parameters or postulated entities.

axioms (2)
  • domain assumption CCSD calculations with the chosen basis provide reliable reference polarizabilities for benchmarking
    Used as the primary benchmark throughout the abstract.
  • domain assumption The aug-cc-pVTZ basis set is adequate to reveal relative method performance
    Applied uniformly to all methods and molecules.

pith-pipeline@v0.9.1-grok · 5857 in / 1323 out tokens · 33442 ms · 2026-07-03T04:11:25.543241+00:00 · methodology

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