{"id":"e1a59d63-da8d-422b-a981-7d6f7ef722b8","arxiv_id":"2607.11711","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"MCAO generates Dunning-style Cu Gaussian basis sets that control solid-state linear dependence while preserving molecular accuracy and enabling CBS RPA benchmarks for bulk Cu and CO adsorption.","lead":"A new optimization method (MCAO) produces correlation-consistent Gaussian basis sets for copper that stay numerically stable in solids and surfaces. This lets researchers run reliable complete-basis-set correlated calculations on metals and the CO/Cu(111) adsorption problem.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The central claim is that MCAO produces correlation-consistent Cu bases that are stable in solids/surfaces, recover molecular and PW bulk references, and enable controlled CBS RPA@PBE benchmarks (including scalar-relativistic AE CO/Cu(111)). The reader's weakest assumption correctly flags the single-material κ constraint and hand-chosen ε0/κ0, but the paper already tests the bases on the exact systems of interest (bulk + surface) and shows molecular fidelity and PW agreement. Limitations (Cu-only, parameter choices, condition-number-only penalty) are acknowledged and do not falsify the Cu results. No stronger technical soft spot (e.g., broken correlation consistency, uncontrolled BSSE/FSE, or contradictory benchmarks) appears. Verdict remains ACCEPT; no adjustment needed.","tokens_in":27436,"tokens_out":493,"duration_ms":4356,"concrete_test":"Recompute the SFX2C-1e RPA@PBE top/hollow E_ads and ΔE_ads of CO/Cu(111) with the published MCAO-cc-pV(T,Q)Z sets and the SI composite protocol (eqs. 19, 12–13); if values match Table S4 within ~0.02 eV, the surface-transferability claim holds.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest assumption (single-material κ penalty on fcc Cu with fixed ε0/κ0) is real but not load-bearing for the central claim. The paper is explicitly a Cu proof-of-concept; it directly validates the resulting MCAO-cc-pVXZ sets on the Cu dimer (Table I), bulk fcc Cu vs PW (Fig. 3, Table S3), and CO/Cu(111) surfaces (Fig. 5, SI §VI), with public basis files and auxiliary sets. Condition numbers remain controlled (Fig. 1, Table S2), polarization exponents stay near atomic cc-pVXZ (Fig. 2), and CBS RPA@PBE numbers are consistent with independent NAO/PW literature. No internal inconsistency or missing check undermines the stated claims for Cu.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript introduces material-constrained atomic optimization (MCAO), which augments standard atomic basis-set optimization with a penalty on the overlap-matrix condition number evaluated for representative solids (Eq. 2). As a proof of concept, Dunning-style MCAO-cc-pVXZ (X = D, T, Q) sets are generated for Cu under all-electron (nonrelativistic and SFX2C-1e), hard/soft ccECP, and small-/large-core GTH-PBE treatments. The sets remain numerically stable for fcc Cu and Cu(111) while recovering molecular Cu2 RPA binding energies (Table I), plane-wave PBE lattice constants/bulk moduli/band structures (Fig. 3), and enabling CBS-extrapolated RPA@PBE benchmarks of bulk Cu and CO adsorption on Cu(111) that isolate pseudopotential, relativistic, and basis-set errors relative to a scalar-relativistic all-electron reference (Figs. 4–5).","tokens_in":27687,"tokens_out":757,"duration_ms":7332,"significance":"Reliable CBS extrapolation for correlated methods on metals and metal surfaces has long been hindered by linear dependence of diffuse atomic Gaussians. MCAO offers a practical, continuous regularization that largely preserves correlation consistency and atomic character, and the Cu sets immediately supply useful scalar-relativistic all-electron Gaussian-basis RPA benchmarks for the CO/Cu(111) site-preference problem. Strengths include public basis and auxiliary-set files, direct validation against independent PW, molecular cc-pVXZ, NAO, and experimental references, and a controlled multi-Hamiltonian error analysis. The work is a solid, well-executed proof of concept that should be of immediate use to the solid-state correlated-wavefunction community.","major_comments":[],"minor_comments":[{"comment":"The abstract and introduction state that the sets remain stable for “Cu solids and surfaces,” yet the κ penalty is evaluated only on bulk fcc Cu (Eq. 2 and SI §III.B). A short explicit statement that surface stability is demonstrated a posteriori (via successful SCF and RPA on CO/Cu(111)) would avoid any ambiguity.","section":null},{"comment":"Figure 1 caption and SI Fig. S1: the precise definition of the k-point union used for κ (n_max_k = 5) is clear in the SI but could be summarized in one sentence in the main-text caption for readers who do not consult the SI.","section":null},{"comment":"Table I: the def2-TZVP* and pob-TZVP entries usefully illustrate the cost of aggressive truncation; a one-line note that these are literature solid-friendly sets (not MCAO variants) would help non-specialist readers.","section":null},{"comment":"SI §VI.E and the main-text discussion of Cao et al.: the sensitivity of DZ/TZ-only extrapolations is important; a brief pointer in the main text to the quantitative difference between CBS(D,T) and CBS(T,Q) would strengthen the argument without lengthening the narrative.","section":null},{"comment":"A few typographical inconsistencies appear (e.g., “Y u” spacing in author names, occasional missing spaces around units). These are easily fixed in production.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is a clean, high-quality methods paper with immediate practical value. The single-material κ constraint is a legitimate scope limitation for a Cu proof-of-concept and is not a load-bearing flaw; the authors already flag element-specific refinements as future work. I see no reason to delay publication."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"Punchline: this is a useful methods paper that actually solves a daily pain point—diffuse atomic Gaussians blowing up in metallic Cu—while keeping Dunning-style correlation consistency so you can still do honest CBS work.\n\nWhat is new is the MCAO loss: atomic energy plus a continuous condition-number penalty on fcc Cu, iterated over valence/4p/polarization with fixed ε0 scales and a target κ0 of 1e9. That is cleaner than exponent truncation or fully solid-optimized bases, and more continuous than the discrete valence-set trick in GTH-cc-pVXZ. They ship AE, SFX2C-1e, hard/soft ccECP, and sc/lc GTH sets through QZ, with public basis and auxiliary files.\n\nThe evidence is direct. Cu2 RPA matches standard cc-pVXZ within ~0.02 eV/atom. Bulk PBE a0/B0 and bands recover PW for GTH-sc. CBS RPA a0/B0 and CO top/hollow ads energies line up with NAO and PW/PAW literature; lc GTH is correctly flagged as the outlier. Polarization exponents stay near atomic cc-pVXZ while the diffuse valence is compacted. Math and protocol are spelled out; SI covers k-mesh, BSSE, TDL, and def2 comparisons. Citation pattern is normal for this niche.\n\nSoft spots, in proportion: the κ penalty is only on bulk fcc Cu with a few hand-chosen ε0/κ0 and valence sizes. That is a real transferability question for other environments, but the paper is explicitly a Cu proof-of-concept and they do validate on the dimer, bulk, and the (111) surface. Not a load-bearing hole for the claims they make. Extending beyond Cu and tightening the multi-mode regularization are future work they already name.\n\nWho cares: people doing correlated Gaussian work on metals and surfaces who need stable CBS. I would send it to peer review without hesitation. Worth reading if you touch solid-state RPA/CC or basis design; not a field-rewriter, but a solid tool paper.","headline":"Practical MCAO fix for linear-dependent Cu Gaussian bases, with clean CBS RPA numbers for bulk Cu and CO/Cu(111); soft spots are real but not load-bearing.","tokens_in":28273,"tokens_out":552,"would_cite":true,"duration_ms":8639,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"MCAO builds correlation-consistent Gaussian bases for copper that stay stable in solids while still enabling complete-basis-set extrapolation.","keywords":["Gaussian basis sets","correlation-consistent bases","material-constrained atomic optimization","copper solids","complete-basis-set extrapolation","random-phase approximation","CO adsorption","linear dependence"],"falsifier":"Compute CBS-extrapolated RPA@PBE CO adsorption energies on Cu(111) with an independent all-electron scalar-relativistic method or a fully solid-optimized basis of equal quality; a site-preference energy that differs from the paper’s SFX2C-1e MCAO result by more than ~0.02 eV would falsify the claimed transferability and benchmark quality.","tokens_in":28347,"feed_emoji":"⚛️","tokens_out":935,"duration_ms":7054,"temperature":0.7,"pith_summary":"Standard molecular Gaussian basis sets fail in metals because their diffuse functions make the overlap matrix nearly singular. This paper introduces material-constrained atomic optimization (MCAO), which keeps ordinary atomic energy minimization as the main objective and adds a penalty on large condition numbers of the overlap matrix in a representative solid. Applied to copper, MCAO produces Dunning-style cc-pVXZ bases (double through quadruple zeta) for all-electron, scalar-relativistic, ECP, and pseudopotential treatments. The bases stay numerically stable for bulk copper and Cu(111) surfaces, recover molecular dimer binding energies and plane-wave bulk properties, and allow complete-basis-set RPA calculations that separate pseudopotential, relativistic, and basis-set errors. The same protocol yields scalar-relativistic all-electron RPA benchmarks for the long-standing CO adsorption site preference on Cu(111).","feed_headline":"Stable copper Gaussian bases that still reach the CBS limit","feed_subtitle":"MCAO keeps atomic correlation consistency while taming linear dependence in metals and surfaces","key_machinery":"Material-constrained atomic optimization (MCAO): the loss L = E_atom + (ε0/κ0) max_M κ(α; M) that regularizes ordinary atomic exponent optimization by a linear penalty on the largest overlap-matrix condition number evaluated for a reference solid (fcc Cu), while retaining Dunning-style valence and polarization hierarchies.","core_discovery":"Material-constrained atomic optimization produces correlation-consistent Gaussian basis sets for copper that remain numerically stable in periodic solids and surfaces while preserving molecular accuracy and systematic complete-basis-set convergence. With those bases, CBS-extrapolated RPA@PBE calculations supply controlled all-electron scalar-relativistic reference values for bulk copper and for CO adsorption energies on the top and hollow sites of Cu(111).","pith_inferences":["If the same condition-number target works for other late 3d metals, MCAO could become a default generator of solid-stable correlation-consistent bases across the transition series.","Extending the penalty from the single largest eigenvalue to a soft threshold over the full small-eigenvalue spectrum may further improve stability without extra compactness.","The same MCAO bases could serve as the orbital basis for periodic coupled-cluster or quantum Monte Carlo studies of CO/Cu(111), testing whether the RPA site preference survives higher-order correlation."],"forward_implications":["Gaussian-basis correlated-wavefunction calculations on copper metals and surfaces can now reach the complete-basis-set limit without ad-hoc exponent truncation.","Pseudopotential, ECP, and scalar-relativistic errors for bulk copper and CO/Cu(111) can be isolated on a common CBS footing against an all-electron reference.","The MCAO protocol supplies a practical route to Dunning-style bases for other transition metals once an analogous solid-state condition-number target is chosen.","Cross-code comparisons of the CO adsorption puzzle can use the same MCAO bases to remove basis-set incompleteness as a confounding factor."],"fun_headline_variants":["MCAO yields stable correlation-consistent Gaussian bases for Cu solids","Material-constrained optimization tames linear dependence in copper bases","Correlation-consistent Cu bases that remain stable for solids and surfaces","MCAO-cc-pVXZ sets enable CBS RPA benchmarks for bulk Cu and CO ads","Atomic bases for copper that preserve CBS limits in periodic systems"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"A condition-number penalty tuned only on bulk face-centered-cubic copper is assumed to keep the bases stable and accurate for copper surfaces and other local environments without destroying correlation consistency.","fun_headline_variants_meta":{"raw":{"variants":["MCAO yields stable correlation-consistent Gaussian bases for Cu solids","Material-constrained optimization tames linear dependence in copper bases","Correlation-consistent Cu bases that remain stable for solids and surfaces","MCAO-cc-pVXZ sets enable CBS RPA benchmarks for bulk Cu and CO ads","Atomic bases for copper that preserve CBS limits in periodic systems"]},"model":"grok-4.5","effort":"low","cost_usd":0.005446,"raw_usage":{"total_tokens":1459,"prompt_tokens":779,"num_sources_used":0,"completion_tokens":75,"cost_in_usd_ticks":54460000,"prompt_tokens_details":{"text_tokens":779,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":605,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":779,"tokens_out":75,"duration_ms":5749,"temperature":1.0,"reasoning_tokens":605,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T03:41:26.647555+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute CBS-extrapolated RPA@PBE CO adsorption energies on Cu(111) with an independent all-electron scalar-relativistic method or a fully solid-optimized basis of equal quality; a site-preference energy that differs from the paper’s SFX2C-1e MCAO result by more than ~0.02 eV would falsify the claimed transferability and benchmark quality.","supporting_citations":[],"review_version":1}