{"id":"b1fc96f1-e7d6-44fc-9119-a623cc88de24","arxiv_id":"2607.26728","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"A small ExTG-contracted Gaussian basis for ²Li Rydberg states (n≤7, S–G) delivers >10⁻² eV EOM-CCSD accuracy and beats a larger universal Rydberg basis.","lead":"A compact Gaussian basis set is built for lithium Rydberg states up to n=7 (S–G), reaching few-meV accuracy at EOM-CCSD with far fewer functions than prior sets. It matters because routine quantum-chemistry codes need small, accurate diffuse bases before Rydberg chemistry of molecules becomes practical.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper’s strongest claim is narrowly computational and is directly supported by external benchmarks (Tables II–IV). The HF-Koopmans contraction is an approximation, but the numerical evidence shows it transfers to the correlated level at the stated accuracy for this atom; residual errors are consistent with the method, not with basis failure. The reader already flags the undemonstrated polyatomic leap and rates the work CONDITIONAL for that reason; that assessment is appropriate and needs no further downward adjustment. A single uncontracted recomputation would close the only remaining quantitative loophole around contraction loss. Novelty and significance remain mid-scale tooling improvements, consistent with the reader’s scores.","tokens_in":12896,"tokens_out":503,"duration_ms":11700,"concrete_test":"Recompute the full set of EOM-CCSD excitation energies in Table II with the uncontracted ExTG primitive sets (i.e., without the LCAO contraction step of §II.C) and with the extra E_lim_HF S function restored; if any state shifts by more than ~1 meV relative to the contracted AAQZ-ExTG-Ry7G values, the contraction/Koopmans premise would be quantitatively imperfect. Otherwise the claim is reinforced.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader’s weakest-assumption concern (HF-Koopmans virtuals of closed-shell Li+ remaining adequate contracted functions for ROHF-EOM-CCSD of neutral 2Li) is already stress-tested by the paper itself. Tables II–IV show that the contracted AAQZ-ExTG-Ry7G / Ry3P+nL bases recover external non-relativistic reference excitation energies and the IP to a few meV (better than 10^-2 eV) at EOM-CCSD, matching or beating both the authors’ prior ETG basis and a Kaufmann-style universal set of comparable scope. Residual ~3.5 meV systematic offsets track the IP error and are therefore attributable to the EOM-CCSD/correlation treatment (or missing relativity), not to a failure of the HF map. The molecular-extension framing is prospective only and does not underwrite the Li claim. Consequently the central accuracy-and-compactness claim for 2Li stands on the tabulated external comparisons; no further load-bearing internal inconsistency is evident.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript develops a compact Gaussian basis (AAQZ-ExTG-Ry7G and the state-selective AAQZ-ExTG-Ry3P+nL) for 2Li Rydberg states up to n=7 and angular momenta S–G. Building on a Koopmans/HF virtual-orbital optimization of Li+ with exponentially tempered Gaussian (ExTG) primitives added to aug-ANO-pVQZ, the authors report ROHF-EOM-CCSD excitation energies and a CCSD ionization potential accurate to a few meV (better than 10^{-2} eV) relative to high-level non-relativistic references and experiment. The new bases are compared favorably to the authors’ earlier ETG-based 2023Sm set and to a Kaufmann-style universal primitive set of comparable scope, while using substantially fewer primitives and contracted functions. One-dimensional orbital cuts are used to illustrate a regular logarithmic nodal structure of the Rydberg orbitals out to tens of Å (and, with the prior basis, to ~10 µm for 25S).","tokens_in":13216,"tokens_out":1304,"duration_ms":40490,"significance":"If the tabulated accuracy and compactness hold, the work is a practical methodological contribution to ab initio Rydberg chemistry: it shows that carefully contracted, system-tailored Gaussians can describe high-n Rydberg states of Li at few-meV accuracy with basis sizes compatible with standard quantum-chemistry codes, including a minimal state-selective construction that adds only a handful of functions. The external benchmarks against ECG/Hy-CI-type references, experiment, and a Kaufmann-style universal set, together with the explicit size comparison in Table I, are genuine strengths. The ExTG parameterization and the documented reduction of near-linear-dependence issues relative to ETG are useful technical results. The molecular-extension framing is appropriately prospective and does not underwrite the Li claim.","major_comments":[{"comment":"§III.B and Tables II–III: The residual errors for S–F states systematically approach ~−3.5 meV and track the ~4 meV IP underestimation (Table IV), while G states show an opposite-sign ~+6 meV residual. The manuscript attributes the overall few-meV accuracy to the basis at EOM-CCSD, but does not cleanly separate basis incompleteness from EOM-CCSD/correlation (and missing relativity) error. A short, explicit discussion—e.g., that the common offset matches the IP error and is therefore largely method- rather than basis-limited, and why G differs—would make the central “better than 10^{-2} eV” claim more precise and less easy to over-read as pure basis quality.","section":"§III.B, Tables II–IV"},{"comment":"§II.A–C and the transferability claim: The contracted functions are optimized exclusively on closed-shell RHF virtual energies of Li+ under Koopmans’ theorem, then used for ROHF-EOM-CCSD of neutral 2Li. Tables II–IV already show that this map works to a few meV for Li, so the central atomic claim stands. However, the abstract and §IV present the protocol as “an important step towards” polyatomic Rydberg work without stating what would have to be re-validated for open-shell cores or multi-center systems (orbital relaxation, core–Rydberg correlation, choice of ion-core reference). A brief, concrete caveat on the scope of the demonstrated transfer would keep the prospective claim proportionate to the evidence.","section":"§II.A–C; Abstract; §IV"}],"minor_comments":[{"comment":"Abstract and §IV: the phrase “higher than 10^{-2} eV accuracy” is ambiguous (larger accuracy vs. accuracy better than 10^{-2} eV). Prefer “better than 10^{-2} eV” or “errors below 10^{-2} eV,” consistent with the body text.","section":"Abstract; §IV"},{"comment":"§I: “but my need to obtain just a few” → “may need”.","section":"§I"},{"comment":"§III: “thoroughfully” → “thoroughly”.","section":"§III"},{"comment":"Table I footnote and basis naming: AAQZ-ExTG-Ry3P is described as adding two S and two P contracted Rydberg functions; ensure the table’s contracted counts and the “+ nL” usage in the text/tables are fully consistent so a reader can reconstruct the state-selective sets without the GENBAS file.","section":"Table I; §III.A"},{"comment":"Figures 1–3 and SI: the logarithmic radial cuts are central to the nodal-structure claim; adding a brief note on normalization/scale of the plotted amplitude (and that only the m-aligned component is shown for ℓ>0) would aid reproducibility.","section":"§III.C; Figs. 1–3"},{"comment":"References: several high-precision Li Rydberg benchmarks are cited; a single sentence placing the present EOM-CCSD/basis errors relative to residual relativistic/QED effects (already partly in the IP comparison) would help non-specialist readers.","section":"§III.B"}],"recommendation":"minor_revision","confidential_remarks":"Solid, incremental improvement on the authors’ 2023 PCCP basis: the ExTG reparameterization and especially the drastic reduction to a state-selective AAQZ-ExTG-Ry3P+nL set are the real advances. No load-bearing inconsistency with the external benchmarks. Suitable for a methods-oriented chemical physics journal after minor revision; I would not require new molecular calculations for acceptance of the Li claim."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The real deliverable here is a compact, usable Li Rydberg Gaussian set (AAQZ-ExTG-Ry7G and the state-selective Ry3P+nL add-on) that recovers EOM-CCSD excitations and the IP to a few meV through n=7, S–G, while using far fewer primitives and contracted functions than the authors’ 2023 ETG basis and fewer functions than a Kaufmann-style universal set on the same aug-ANO-pVQZ core.\n\nWhat is new is not the Koopmans/HF-virtual idea (that was the 2023 PCCP paper) or ExTG itself (their earlier He work), but the re-parameterization that cuts the primitive count roughly in half, the minimal state-selective construction (only two S + two P extras for higher nL), the head-to-head vs Kaufmann primitives, and the orbital-cut analysis—including the previously unpublished 25S cut from the old basis that reaches ~10 µm. Tables II–IV are clean: errors cluster near −3.5 meV for most S–F states (G ~+6 meV), state-selective vs full basis differs by ≲0.1 meV, and the IP sits ~4 meV below experiment in lockstep with the excitation offsets. That pattern points to residual correlation/relativity, not a broken HF map. Circularity is low; validation is external.\n\nSoft spots are modest and mostly framing. The molecular “important step” language is prospective only—no polyatomic numbers. Optimizer artifacts and full ExTG parameters are not dumped, so exact reproduction needs more than the GENBAS file. G-state signs flip relative to the S–F trend, and the paper does not explain why. None of that undercuts the Li claim the tables actually support.\n\nThis is for people who run EOM-CCSD (or similar) on Rydberg or anionic systems and hit basis-size walls in standard packages. Worth a serious referee; I would engage with the basis if I needed Li Rydberg numbers soon. Send it out.","headline":"Solid methods paper: a smaller ExTG-contracted Li Rydberg basis that hits few-meV EOM-CCSD accuracy through n=7 S–G and beats a Kaufmann-style universal set at lower cost.","tokens_in":13883,"tokens_out":533,"would_cite":true,"duration_ms":9401,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A compact tailored Gaussian basis recovers lithium Rydberg states to better than 0.01 eV.","keywords":["Rydberg states","Gaussian basis sets","lithium","EOM-CCSD","exponentially tempered Gaussians","Koopmans theorem","basis-set optimization","diffuse orbitals"],"falsifier":"Recompute the same ROHF-EOM-CCSD excitation energies for the higher-n F and G states against a large explicitly correlated or STO Full-CI reference; if the few-meV systematic offset grows or reverses while the universal basis does not, the claimed accuracy and superiority of the tailored ExTG contraction fail.","tokens_in":13758,"feed_emoji":"⚛️","tokens_out":902,"duration_ms":28739,"temperature":0.7,"pith_summary":"This paper builds a small Gaussian basis that accurately describes the Rydberg excited states of atomic lithium up to principal quantum number n = 7 and angular momenta S through G. The authors variationally optimize exponentially tempered diffuse Gaussians on the virtual orbitals of Li+, contract them, and add the resulting few functions to a standard correlation basis. At the EOM-CCSD level the excitation energies and ionization potential then agree with the best available non-relativistic references to a few meV, while the basis stays smaller than both an earlier even-tempered set and a comparable universal Rydberg Gaussian set. One-dimensional orbital plots show a clean, regular nodal pattern on a logarithmic radial scale that extends tens of angstroms from the nucleus. The protocol is presented as a practical step toward routine ab initio Rydberg work on larger atoms and molecules without enormous diffuse bases.","feed_headline":"Small Gaussian basis hits Li Rydberg states to 0.01 eV","feed_subtitle":"Tailored ExTG functions beat universal sets with fewer primitives and reach tens of angstroms","key_machinery":"Exponentially tempered Gaussian (ExTG) primitives, variationally optimized as Hartree–Fock virtual orbitals of closed-shell Li+ under Koopmans’ theorem and then contracted into a handful of Rydberg basis functions that are simply added to aug-ANO-pVQZ.","core_discovery":"At the EOM-CCSD level the new AAQZ-ExTG-Ry7G basis, and its still smaller state-selective form AAQZ-ExTG-Ry3P plus one extra nL function, yields lithium Rydberg excitation energies up to n = 7 (S–G) and the ionization potential accurate to better than 10^{-2} eV, outperforming an analogous universal Kaufmann-style Gaussian Rydberg basis while using fewer functions.","pith_inferences":["If the HF-to-EOM-CCSD transfer holds for open-shell molecular cores, the same few-function augmentation could make Rydberg PESs routine in polyatomics without custom continuum bases.","The observed logarithmic regularity of nodes suggests a simple radial scaling that could supply starting ExTG parameters for other atoms without full re-optimization.","Breakdown of the map under strong core polarization would likely appear first as n-dependent error growth in the ionization-potential limit rather than in the lowest valence states."],"forward_implications":["State-selective high-n calculations need only two extra S, two extra P, and one nL contracted Rydberg function on top of a standard basis.","The same optimization protocol can generate compact Rydberg bases for larger atoms.","Properly tempered and contracted Gaussians can describe orbitals that extend tens of angstroms (and, with the earlier larger set, even to ~10 µm).","The ExTG form reduces the near-linear-dependence problems that appear with ordinary even-tempered diffuse sets."],"fun_headline_variants":["Compact Gaussian basis hits Li Rydberg states to 0.01 eV","Fewer primitives beat universal sets on Li Rydberg energies","Small ExTG basis reaches Li n=7 Rydbergs within 0.01 eV","State-selective Gaussian set tops Kaufmann basis for Li","AAQZ-ExTG-Ry basis yields 0.01 eV Li Rydberg accuracy"],"cache_read_input_tokens":128,"weakest_assumption_plain":"That Hartree–Fock virtual orbitals optimized on the Li+ cation remain accurate enough contracted functions for the correlated Rydberg states of neutral lithium once few-meV accuracy is required.","fun_headline_variants_meta":{"raw":{"variants":["Compact Gaussian basis hits Li Rydberg states to 0.01 eV","Fewer primitives beat universal sets on Li Rydberg energies","Small ExTG basis reaches Li n=7 Rydbergs within 0.01 eV","State-selective Gaussian set tops Kaufmann basis for Li","AAQZ-ExTG-Ry basis yields 0.01 eV Li Rydberg accuracy"]},"model":"grok-4.5","effort":"low","cost_usd":0.00512,"raw_usage":{"total_tokens":1393,"prompt_tokens":755,"num_sources_used":0,"completion_tokens":87,"cost_in_usd_ticks":51204000,"prompt_tokens_details":{"text_tokens":755,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":551,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":755,"tokens_out":87,"duration_ms":8184,"temperature":1.0,"reasoning_tokens":551,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-30T22:48:52.725539+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Recompute the same ROHF-EOM-CCSD excitation energies for the higher-n F and G states against a large explicitly correlated or STO Full-CI reference; if the few-meV systematic offset grows or reverses while the universal basis does not, the claimed accuracy and superiority of the tailored ExTG contraction fail.","supporting_citations":[],"review_version":1}