{"id":"8d342037-a6b6-4b8e-8c49-6f44c271929b","arxiv_id":"1908.03635","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"A systematic coupled cluster benchmark finds that aug-cc-pVTZ class basis sets are adequate for low-energy K-edge core excitations in small molecules, and that CCSDT plus scalar relativity reproduces core ionization energies within about 0.3 eV of experiment.","lead":"This paper benchmarks the coupled cluster hierarchy (CC2, CCSD, CC3, CCSDT) for K-edge core excitation and ionization energies of water, ammonia, and carbon monoxide across dozens of standard basis sets. It concludes that singly augmented triple-zeta basis sets are sufficient for low-energy core excitations, and that the Pople 6-311++G** basis offers comparable accuracy at lower cost.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"0.3 eV CCSDT claim rests on unquantified comparability of computed vertical IEs to Ref. 71 peak energies; a vibrational/error-bar test would settle it.","rationale":"The paper is a careful benchmark with a consistent methodology: CVS-CC-LR/EOM-CC across the CC2/CCSD/CC3/CCSDT hierarchy, multiple basis-set families, and scalar relativistic corrections. The qualitative conclusions (Dunning sets with X greater than or equal to 3 converge; augmentation helps; double augmentation is marginal for low-energy states; 6-311++G** is competitive; CCSD systematically overestimates; CC2 underestimates splittings) are directly visible in the tables and figures and do not depend on exact experimental values. I therefore do not see an internal inconsistency or a methodological red flag. The weakest point is the absolute calibration of the quantitative CCSDT/IE claim: it uses four experimental values from one 1993 reference, without error bars and without a vibrational analysis connecting experimental band maxima to vertical electronic energies. Since the claimed agreement after the relativistic shift is at the 0.1 eV level, unquantified offsets of that size are load-bearing. The reader's weakest_assumption identified essentially the same issue, and the proposed Franck-Condon plus error-bar check would settle it. This does not require changing the CONDITIONAL verdict; at most, it sharpens the wording of the conclusion.","tokens_in":12696,"tokens_out":11396,"duration_ms":122639,"concrete_test":"Compute the Franck-Condon vibrational profile of each core-ionized state at the CCSDT/aCVQZ level (or CCSD(T) with the core hole if CCSDT gradients are unavailable), using the neutral equilibrium geometry, and determine the energy of the band maximum relative to the vertical electronic energy. Then compare these band-maximum energies with the four experimental peak energies from Ref. 71, using documented error bars from the original measurements. If the vibrational offset exceeds about 0.1 eV or the experimental uncertainty is comparable to 0.3 eV, the CCSDT agreement claim should be restated with that uncertainty; if the offset is below 0.05 eV and Ref. 71 uncertainties are at most 0.1 eV, the concern is minor and the current conditional verdict stands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The quantitative anchor of the central claim is the statement in Section III.D that 'the CCSDT results in the largest core-valence set are about -0.3 eV from experiment (and relativistic effects are +0.3 eV).' This requires the four experimental values from Ref. 71 (539.78, 405.6, 296.2, 542.5 eV) to be accurate vertical energies with uncertainties well below 0.3 eV. The paper reports no error bars for these values and no discussion of whether experimental band maxima coincide with the vertical electronic energy at the equilibrium geometry used in the calculations. The nonrelativistic CCSDT/aCVQZ deviations are -0.32, -0.26, +0.16, and -0.38 eV for the four edges; after the Table III relativistic shifts they become +0.07, -0.05, +0.26, and 0.00 eV. The claimed '-0.3 / +0.3' cancellation is therefore an average over four points whose individual scatter is comparable to the claimed effect. Core-ionized states of these molecules can have vibrational progressions whose band maxima are displaced from the vertical transition by a few tenths of an eV, and gas-phase XPS calibration offsets of 0.1-0.2 eV are common. Without quantifying either, the close CCSDT/experiment agreement after the +0.3 eV relativistic shift could be partly coincidental. The basis-set ordering and the aug-cc-pVTZ recommendation are largely robust because they rest on internal convergence across cardinal numbers; the fragile part is the absolute 0.3 eV accuracy claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13012,"tokens_out":4783,"duration_ms":49270,"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":[{"comment":"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.","section":"Section III.D, Tables I-III"},{"comment":"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.","section":"Section III.D, Tables I-II"}],"minor_comments":[{"comment":"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'.","section":"Section III.D"},{"comment":"The citation '[39, 47 ?]' contains a question mark and an incomplete reference placeholder; this should be corrected before publication.","section":"Introduction, Ref. [39]"},{"comment":"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.","section":"Section III.B"},{"comment":"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.","section":"Table II"},{"comment":"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.","section":"Figures 6 and 7"},{"comment":"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.","section":"Section III.A and Concluding Remarks"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a solid benchmark study that fits the journal's scope. The main risk is the absolute accuracy claim in Section III.D, which depends on unquantified properties of the experimental references. The authors should be encouraged to address this by adding a sensitivity analysis or by softening the claim; the basis-set recommendations are likely sound and should not be delayed by this issue."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper delivers what it promises: a systematic CC2–CCSDT benchmark for K-edge excitations and ionizations in water, ammonia, and CO across a wide range of standard basis sets. The data set is large, internally consistent, and the qualitative conclusions follow from the tables. The recommendation that singly augmented triple-zeta bases suffice for low-lying excitations, with 6-311++G** as a cheaper stand-in, is well supported by internal convergence trends. The scalar relativistic corrections are cleanly isolated and method-independent, which is a useful result in itself. Credit where due: the authors are transparent about the ad hoc nature of the CBS extrapolations and do not oversell the spectral simulations.\n\nThe soft spot is exactly where your stress-test lands. The claim that CCSDT is within about 0.3 eV of experiment rests on four experimental values from Ref. 71 with no stated uncertainties. The individual deviations after the relativistic shift are +0.07, -0.05, +0.26, and 0.00 eV, so the 'cancellation' is an average hiding scatter comparable to the effect being claimed. The paper never addresses whether the experimental band maxima correspond to vertical transitions at the equilibrium geometries used, and vibrational progressions or calibration offsets of a few tenths of an eV are plausible in core-level spectra. That does not sink the paper, but it does mean the absolute accuracy claim should be softened or qualified. The basis-set ordering and the aug-cc-pVTZ recommendation are robust because they rest on the internal convergence of the computed values across cardinal numbers, not on the experimental comparison.\n\nMinor gaps: a few data points are missing at CC3 and CCSDT for the largest bases, and the CBS estimates carry no uncertainty assessment. Neither issue affects the main recommendations.\n\nOverall, this is a useful reference benchmark for practitioners in computational core-level spectroscopy. It does not break new methodological ground, but it fills a practical gap in a careful, honest way. It deserves a serious referee, though the authors should be asked to address the experimental comparability issue and report uncertainties if possible.","headline":"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.","tokens_in":13551,"tokens_out":1450,"would_cite":true,"duration_ms":16852,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["core excitation energies","core ionization energies","coupled cluster","basis set convergence","core-valence separation","complete basis set extrapolation","scalar relativistic effects","K-edge spectroscopy"],"falsifier":"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.","tokens_in":12506,"feed_emoji":"⚛️","tokens_out":10254,"duration_ms":89752,"temperature":0.7,"pith_summary":"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.","feed_headline":"Singly augmented triple-zeta bases suffice for core spectra","feed_subtitle":"Full-triples coupled cluster lands within a few tenths of an eV of measured K-edge energies.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the experimental core ionization and excitation energies of water, ammonia, and carbon monoxide used as the reference in all comparisons.","marker":"[71]"},{"why":"Introduces the core-valence separation implementation within CC linear response and equation-of-motion CC on which all core-edge calculations rely.","marker":"[43]"},{"why":"Earlier basis-set analysis of core-excitation methods whose extrapolation strategy this study follows.","marker":"[17]"},{"why":"Provides the ADC hierarchy benchmark for core-level spectra that this study parallels and compares against.","marker":"[18]"},{"why":"Efficient CCSDT implementations used to obtain full-triples core excitation and ionization energies.","marker":"[61, 62]"},{"why":"Spin-free exact two-component one-electron theory used to compute the scalar relativistic corrections.","marker":"[63–65]"},{"why":"Supply the $X^{-3}$ and exponential extrapolation formulas used to estimate complete-basis-set limits.","marker":"[69, 70]"},{"why":"Efficient CC3 implementation used for all approximate-triples calculations.","marker":"[60]"}],"fun_headline_variants":["Core spectra: singly augmented triple-zeta is the sweet spot","For K-edges, one diffuse layer on triple-zeta suffices","Singly augmented triple-zeta: the basis set for core spectra","Triple-zeta plus one diffuse layer: enough for core edges"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Core spectra: singly augmented triple-zeta is the sweet spot","For K-edges, one diffuse layer on triple-zeta suffices","Singly augmented triple-zeta: the basis set for core spectra","Triple-zeta plus one diffuse layer: enough for core edges"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000649,"raw_usage":{"total_tokens":2964,"prompt_tokens":919,"completion_tokens":2045,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":535,"completion_tokens_details":{"reasoning_tokens":1970}},"tokens_in":535,"tokens_out":2045,"duration_ms":20169,"temperature":1.0,"reasoning_tokens":1970,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:06:59.171306+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"M.; Ma, Y.; Chen, C","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental core ionization and excitation energies of water, ammonia, and carbon monoxide used as the reference in all comparisons."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the core-valence separation implementation within CC linear response and equation-of-motion CC on which all core-edge calculations rely."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Earlier basis-set analysis of core-excitation methods whose extrapolation strategy this study follows."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the ADC hierarchy benchmark for core-level spectra that this study parallels and compares against."},{"cited_title":"H.; Koch, H","cited_arxiv_id":null,"evidence_quote":"Efficient CC3 implementation used for all approximate-triples calculations."}],"review_version":1}