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REVIEW 2 major objections 6 minor 71 references

An analysis of the performance of coupled cluster methods for core excitations and core ionizations using standard basis sets

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Singly augmented triple-zeta basis sets, combined with the CC3/CCSDT hierarchy, are sufficient for low-energy K-edge core excitations and give CCSDT ionization energies within a few tenths of an electronvolt of experiment.

desk verdict A careful, useful benchmark for core-level CC calculations; the practical basis-set guidance is solid, but the absolute 0.3 eV agreement with experiment is less certain than the paper suggests. read the letter →

arxiv 1908.03635 v1 pith:ZD3436A3 submitted 2019-08-09 physics.chem-ph

Johanna P. Carbone , Lan Cheng , Rolf H. Myhre , Devin Matthews , Henrik Koch , Sonia Coriani This is my paper · ORCID
classification physics.chem-ph
keywords coreexcitationenergiesionizationcoupledclusterbasissetconvergencecore-valenceseparationcompleteextrapolationscalarrelativisticeffectsK-edgespectroscopy
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 benchmarks the coupled cluster hierarchy CC2, CCSD, CC3, and CCSDT for computing vertical core excitation and ionization energies at the oxygen, carbon, and nitrogen K-edges of water, ammonia, and carbon monoxide, using standard correlation-consistent and 6-311 basis sets. It aims to establish which basis-set and method combination is sufficient for quantitative comparison with X-ray absorption and photoelectron spectra. The central conclusion is that singly augmented triple-zeta bases such as aug-cc-pVTZ capture the low-lying non-Rydberg core excitations accurately, that the modest 6-311++G** set performs nearly as well, and that CCSDT in a core-valence basis reproduces the experimental ionization energies to within a few tenths of an electronvolt once scalar relativistic effects are added. This matters because core-level spectroscopy is widely used but practical quantum-chemical protocols have been hampered by the large basis-set and correlation errors that plague core-excited states; the paper supplies a simple cost-accuracy prescription.

What carries the argument

The load-bearing machinery is core-valence separation (CVS) applied within the coupled cluster response hierarchy, CC2-CCSD-CC3-CCSDT. CVS restricts the excitation operator to excitations out of a chosen core orbital, converting the hard diffuse core-hole problem into an ordinary single-reference excited-state calculation at each rung of the hierarchy. Around that core, the paper varies basis-set families (cc-pVXZ, singly and doubly augmented variants, core-valence cc-pCVXZ variants, and 6-311 sets), applies the $X^{-3}$ and exponential complete-basis-set extrapolation formulas to the excitation energies, and adds the spin-free exact two-component one-electron (SFX2C-1e) scalar relativistic correction on top of the CCSDT values. This machinery separates the two main error sources, one-electron basis incompleteness and many-body correlation truncation, so each can be assigned a concrete energy cost in eV.

What would settle it

A high-resolution X-ray photoelectron measurement of the O 1s ionization potential of water with an independently determined uncertainty below 0.05 eV would settle whether the claimed CCSDT agreement is real; if the accepted value shifts by 0.3 eV or more, the basis-set and method recommendations would need to be revised.

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Extended reading notes

Core claim

The paper's central discovery is a documented cost-accuracy ladder for core spectroscopy at the K-edges of O, C, and N. For the lowest core excitations in water, ammonia, and carbon monoxide, double-zeta basis sets overestimate the transition energy by 2 to 5 eV; moving to any triple-zeta correlation-consistent set cuts the error to about 1 eV, and adding a single diffuse layer (aug-cc-pVTZ) makes the singly augmented triple-zeta family sufficiently accurate for states with limited or no Rydberg character. The basis-set sequences converge monotonically, and the two-point $X^{-3}$ and three-point exponential extrapolations give essentially identical complete-basis-set limits. For core ionization energies, CCSD overshoots by 1.5 to 2 eV at the oxygen and nitrogen edges, CC3 lands about 1 eV low, and CCSDT in the largest core-valence sets leaves a residual of roughly -0.3 eV, with scalar relativistic effects adding +0.2 to +0.4 eV depending on the element. The paper also finds that CC2 produces compressed spectral profiles and erratic intensities, whereas CCSD gives stable relative intensities with a systematic overestimate that can be rigid-shifted; the smaller 6-311++G** basis offers nearly aug-cc-pVTZ quality for low-energy excitations.

Load-bearing premise

The results rest on the assumption that the experimental reference ionization and excitation energies are accurate to within a few tenths of an electronvolt and are directly comparable to vertical computed values; the paper reports no uncertainties on those references.

Editorial extensions

If this is right

  • For low-energy core excitations with little or no Rydberg character, a singly augmented triple-zeta basis such as aug-cc-pVTZ is sufficient; double augmentation adds little and is not needed for routine work.
  • The inexpensive 6-311++G** basis yields excitation energies of nearly aug-cc-pVTZ quality, so lower-cost calculations are possible without leaving standard basis-set families.
  • CC2 should not be used to judge spectral shapes at these edges, because its peak separations are underestimated and its intensities are erratic; CCSD with a rigid shift is a safer choice for relative intensities.
  • For core ionization energies, the practical ladder is CC2 (low), CCSD (high), CC3 (about 1 eV low), and CCSDT (residual about -0.3 eV), with a scalar relativistic correction of +0.2 to +0.4 eV needed to close the gap.
  • Either the two-point $X^{-3}$ or the three-point exponential extrapolation can be used to estimate complete-basis-set limits of core excitation energies; they give essentially the same answer.

Reading between the lines

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

  • An editor's inference: if the pattern is generic, the practical recipe from this paper is CCSD/aug-cc-pVTZ with a rigid shift for core-excitation spectra, and CC3 or CCSDT/aug-cc-pVTZ plus a scalar relativistic correction for ionization energies; this recipe has not been validated in the paper beyond the three molecules.
  • The near-cancellation that makes aug-cc-pVTZ look converged may not survive for states with strong Rydberg character; the paper itself notes that extra diffuse functions are then needed, so a natural extension is to benchmark Rydberg-dominated edges on the same method grid.
  • Because the scalar relativistic correction is core-specific and nearly independent of basis and method, heavier-element K-edges will require a properly relativistic CCSDT treatment, and the basis-set-size rules may transfer more reliably than the absolute energy offsets.
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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 / 6 minor

Summary. The paper reports a systematic benchmark of coupled cluster methods (CC2, CCSD, CC3, CCSDT) for vertical core excitation and ionization energies at the K-edges of O, C, and N in water, ammonia, and carbon monoxide. Calculations use the core-valence separation scheme and standard Dunning and Pople basis sets, including augmented and core-valence variants. The authors analyze basis-set convergence, estimate complete basis set limits via two extrapolation formulas, and examine scalar relativistic effects with SFX2C-1e. The main recommendations are that singly augmented triple-zeta basis sets suffice for low-energy core excitations with limited Rydberg character, that 6-311++G** is a low-cost alternative, and that CCSDT in the largest core-valence basis reproduces core ionization energies to about -0.3 eV, with relativistic effects adding about +0.3 eV.

Significance. If the conclusions hold, this benchmark provides practical and quantitative guidance for choosing basis sets and CC levels in core-level spectroscopy, a field where systematic accuracy studies are relatively scarce. The paper's strengths include a comprehensive dataset across a hierarchy of methods and basis series, internal consistency checks, and honest caveats about the non-rigorous nature of the CBS extrapolations. The SFX2C-1e relativistic corrections are shown to be nearly transferable across methods and basis sets, which is a useful practical result. The central basis-set ordering and the recommendation of aug-cc-pVTZ rely on internal convergence trends and are robust. The more fragile component is the absolute CCSDT accuracy claim, which depends on the comparability of the computed vertical energies to the experimental references from Ref. [71].

major comments (2)
  1. [Section III.D, Tables I-III] The statement that 'the CCSDT results in the largest core-valence set are about -0.3 eV from experiment (and relativistic effects are +0.3 eV)' rests on four experimental values from Ref. [71] for which no uncertainties are reported and whose vertical versus band-maximum character is not discussed. The individual nonrelativistic CCSDT/aCVQZ deviations are -0.32, -0.26, +0.16, and -0.38 eV for the four edges; after the Table III relativistic corrections they become +0.07, -0.05, +0.26, and 0.00 eV. The scatter across the four points is comparable to the size of the claimed effect, and core-ionized states can exhibit vibrational progressions and calibration offsets at the same scale. Please add a concrete sensitivity test, such as an estimate of vibrational broadening or a range of plausible experimental reference values, or explicitly reframe the -0.3/+0.3 eV statement as an indicative estimate rather than a demonstrated accuracy. This concern does not undermine the basis-set ordering, which is supported by internal convergence across cardinal numbers.
  2. [Section III.D, Tables I-II] The quantitative CCSDT accuracy statement is based on a single basis set, aCVQZ, for the O and N edges, with no CCSDT/aCV5Z or CCSDT/aV5Z data to show that the CCSDT results have reached basis-set convergence. The CC3 data show changes of roughly 0.05-0.1 eV between aCVTZ and aCVQZ, so the CCSDT/aCVQZ value may still be several hundredths of an eV from its basis-set limit. If the missing quintuple-zeta CCSDT points are computationally feasible, reporting them would strengthen the claim; otherwise, the text should state the expected uncertainty from the observed CC3 convergence pattern.
minor comments (6)
  1. [Section III.D] The word 'understimated' in the sentence 'The core IEs of the two types of oxygen K-edge (H2O and CO) are significantly understimated' is a typo and should read 'underestimated'.
  2. [Introduction, Ref. [39]] The citation '[39, 47 ?]' contains a question mark and an incomplete reference placeholder; this should be corrected before publication.
  3. [Section III.B] The sentence 'By fitting the results with a X^-3 formula, on the other hand, we could not reproduce the behaviour of the excitation energies' is ambiguous: the preceding text states that the two-point X^-3 and three-point exponential procedures give essentially identical CBS values, so it should be clarified whether the failure refers to fitting the entire series rather than to the two-point procedure.
  4. [Table II] Some entries are reported with three decimal places (e.g., 295.999) while most others use two; standardizing the precision across the table would improve readability.
  5. [Figures 6 and 7] The experimental spectra are said to be 'shifted and rescaled' to overlap with the computed bands, but the amount of the shift is not stated; reporting the shift value in the caption or text would make the comparison more transparent.
  6. [Section III.A and Concluding Remarks] The claim that 6-311++G** is 'almost comparable' to aug-cc-pVTZ for low-energy core excitations is supported mainly by figures and by data placed in the arXiv supplement; including a small table of representative excitation energies and deviations for the key states in the main text would make this recommendation more directly verifiable.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a self-contained benchmark study comparing fixed CC method/basis-set inputs to external experimental values, with no fitted parameters used as predictions.

full rationale

This paper is an assessment study rather than a derivation chain. The quantities it reports—vertical core excitation and ionization energies for water, ammonia, and carbon monoxide—are computed from defined CC hierarchies (CC2, CCSD, CC3, CCSDT), fixed basis sets, the CVS scheme, and experimental equilibrium geometries; none of these inputs is defined in terms of the target energies, and no parameter is fitted to the experimental reference values before making the comparisons. The CBS extrapolation in Section III.B applies Eqs. (1)-(2) to the computed excitation energies, but the paper explicitly states that these formulas 'are not rigorous expressions for the basis set dependence of energies, but serve as an estimate of the trend,' and the central basis-set recommendation (singly augmented triple-zeta sets are sufficient for low-energy core excitations) rests on the observed monotonic convergence across cardinal numbers and the direct comparison with experimental values, not on the extrapolated CBS numbers. The 'about -0.3 eV from experiment (and relativistic effects are +0.3 eV)' statement in Section III.D is a direct reading of Table I/II and Table III values against external experimental data; it is not a fitted input disguised as a prediction. Self-citations (e.g., Refs. 43, 46, 48, 60-62) provide implementation descriptions and previously reported relativistic trends; they are methodological support rather than load-bearing premises that force the conclusions. Concerns about unquantified experimental uncertainties or the comparability of computed vertical energies to band maxima would be correctness or robustness issues, not circularity. The analysis is therefore self-contained against external benchmarks with no step that reduces to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central benchmark claims rely on the CVS approximation, on experimental geometries, on the correctness of the Dalton and CFOUR implementations, and on the applicability of standard extrapolation formulas. No new physical entities are introduced. The CBS extrapolation parameters are fitted to the computed energies but do not enter the main conclusions except as convergence estimates.

free parameters (3)
  • ECBS (extrapolated basis-set limit energy) = not tabulated numerically; plotted in Fig. 5 for aug-cc-pCVXZ
    Obtained by least-squares fitting or two/three-point extrapolation of computed excitation energies with Eq. 1 or 2. These values are estimates and are not central to the qualitative benchmark conclusions.
  • A (X^-3 amplitude) = not reported
    Fit coefficient in Eq. 1 for each basis set series and method. Used only for CBS estimates.
  • A and B (exponential amplitudes) = not reported
    Fit coefficients in Eq. 2 for each basis set series and method. Used only for CBS estimates.
assumptions (4)
  • domain assumption Core-valence separation (CVS) is a valid approximation for K-edge core excitations in these molecules.
    The CVS scheme restricts excitations to the core orbital and is implemented as described in Ref. 43. The benchmark relies on this approximation being accurate for the low-energy core-excited states considered.
  • domain assumption Experimental geometries are accurate enough for computing vertical excitation and ionization energies.
    The paper states 'Accurate experimental equilibrium geometries were adopted' for all three systems. Vertical transition energies are geometry-dependent, but small geometry uncertainties are expected to have minor effects on the qualitative conclusions.
  • domain assumption The coupled cluster implementations in Dalton and CFOUR are correct for core-level properties.
    The paper relies on previously validated implementations of CC-LR, EOM-CC, and CVS. No independent verification is provided in this work.
  • domain assumption Standard basis set extrapolation formulas (Eqs. 1 and 2) can be applied to excitation and ionization energies.
    The authors explicitly note that these formulas are not rigorous for excitation energies and serve as an estimate. The CBS values are used to support qualitative convergence statements, not as precise predictions.

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Cite this review

Pith. "Pith review of An analysis of the performance of coupled cluster methods for core excitations and core ionizations using standard basis sets." pith.science (2026). https://pith.science/paper/ZD3436A3

@misc{pith2026190803635,
  author       = {Pith},
  title        = {Pith review of: An analysis of the performance of coupled cluster methods for core excitations and core ionizations using standard basis sets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZD3436A3}},
  note         = {Machine review of arXiv:1908.03635}
}
read the original abstract

An extensive analysis has been carried out of the performance of standard families of basis sets with the hierarchy of coupled cluster methods CC2, CCSD, CC3 and CCSDT in computing selected Oxygen, Carbon and Nitrogen K-edge (vertical) core excitation and ionization energies within a core-valence separated scheme in the molecules water, ammonia, and carbon monoxide. Complete basis set limits for the excitation energies have been estimated via different basis set extrapolation schemes. The importance of scalar relativistic effects has been established within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e).

Figures

Figures reproduced from arXiv: 1908.03635 by the authors.

Figure 1
Figure 1. FIG. 1. H [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. CO, Carbon K-edge. Basis set convergence of the first two vertical core excitation energies with [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. CO, Oxygen K-edge. Basis set convergence of the first two vertical core excitation energies with [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. NH [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. H [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. H [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. NH [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

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