{"id":"6b196175-c815-430e-9af6-d6ff4c95b418","arxiv_id":"2510.25658","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"BSE@evGW0@PBE implemented in CP2K reproduces nanographene absorption after 1/L extrapolation and predicts a lowest bright exciton size of ~7.6 Å that TDDFT functionals cannot match in both size and spectrum.","lead":"This paper implements the GW plus Bethe-Salpeter equation (GW-BSE) method in the CP2K code, validates it against another implementation, and uses it to compute optical spectra and exciton sizes in nanographenes. The key result: the lowest bright exciton in these nanographenes has a size that saturates at about 7.6 Å, and standard TDDFT functionals cannot reproduce both this size and the full spectral shape.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Extrapolation from L≤13 to L=46 is the weakest point; sensitivity to fit form could shift peaks by >0.05 eV","rationale":"The reader's weakest assumption — the quadratic 1/L extrapolation — is indeed the most load-bearing part of the paper. The claim of 'excellent agreement with experiment' within 0.05 eV depends entirely on evaluating the fit at L≈46, far outside the fitted range. I considered whether the numerical truncation error (Table II) or the neglect of the Au(111) substrate is more serious, but both are secondary: the truncation error is a systematic numerical error that could be reduced by raising E_cut, and the substrate effect is an environmental model error that is common in this field and could be addressed by future work. In contrast, the extrapolation is intrinsic to the methodology: without it, the comparison to the 20-nm experimental ribbon is impossible. The concrete test of refitting with alternative functional forms directly probes whether the 0.05-eV agreement is a robust conclusion or an artifact of the assumed scaling. Since this concern is already reflected in the reader's CONDITIONAL verdict, no change to the verdict is needed.","tokens_in":30869,"tokens_out":6005,"duration_ms":53824,"concrete_test":"Refit the data in Fig. 4 using (i) a linear fit in 1/L and (ii) an exponential fit in L, and evaluate both at L=46. If the extrapolated Ω(1) and Ω(2) differ by more than 0.05 eV between fit forms, the quadratic extrapolation is not robust and the claimed agreement with experiment is not firmly established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of 0.05-eV agreement with experiment depends on the quadratic extrapolation Ω(p)(L)=a+b/L+c/L² (Sec. III, Fig. 4). Peak positions are computed only for L=4–13 (lengths up to ~6 nm) and then evaluated at L≈46 (20 nm), more than three times beyond the largest computed system. The functional form is motivated by a free-electron 1D-box model, but no evidence is provided that this scaling is valid at such large L. A deviation from the assumed 1/L+1/L² behavior — for example, a crossover to a different exponent or a nonmonotonic size dependence — would shift the extrapolated Ω(1) and Ω(2) by more than 0.05 eV, undermining the headline agreement. The paper also does not report uncertainties on the fit parameters, and the BSE energy cutoff (E_cut=10 eV) already changes the first peak by up to 45 meV for L=4 (Table II), which is comparable to the claimed accuracy. Taken together, the agreement with experiment could be fortuitous if the extrapolation form is not robust.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The authors report an implementation of GW-BSE in the CP2K code and validate it against FHI-aims on Thiel's set of 28 organic molecules, obtaining a mean absolute error of 2.7 meV with different analytic-continuation settings (4.7 meV with matched settings). They then apply BSE@evGW0@PBE to finite 7-armchair nanographenes of increasing length (L=4–13), extract the two lowest longitudinal absorption peaks, and extrapolate quadratically in 1/L to the experimental length of about 20 nm. The extrapolated values (2.09 eV and 2.26 eV) agree with experiment (2.05 eV and 2.31 eV) to within 0.05 eV. The paper also computes spatial descriptors of the lowest bright excitation, finding that its longitudinal size converges to about 7.6 Å, and compares with TDDFT using several exchange–correlation functionals, concluding that none reproduce both the BSE size and the full spectral shape.","tokens_in":31242,"tokens_out":9487,"duration_ms":88655,"significance":"If the finite-size extrapolation is robust, the paper is a valuable contribution: it makes available an open-source GW-BSE implementation in a widely used code, backed by a strong cross-code validation (MAE < 5 meV) and reproducible data (GitHub/Zenodo). The 0.05 eV agreement with experiment would be an encouraging demonstration of BSE for finite nanostructures. The spatial-descriptor analysis provides a compact way to compare TDDFT and BSE excited-state character, and the finding that common hybrid functionals fail to simultaneously reproduce the size and spectral shape of the exciton is instructive. The claimed convergence of the exciton size to about 7.6 Å is an interesting falsifiable prediction. However, the central quantitative claim hinges on an extrapolation that is currently not sufficiently scrutinized, which tempers the significance until that point is addressed.","major_comments":[{"comment":"The central claim of 0.05 eV agreement with experiment rests on the quadratic 1/L extrapolation of Ω^(p)(L) from L=4–13 to L≈46 (~20 nm). The extrapolation extends more than three times beyond the largest computed system, yet the paper provides no confidence intervals on a,b,c, no residual analysis, and no test of the assumed functional form. For p=2, b/L contributes 68 meV at L=46; a modest error in b would shift the extrapolated value by tens of meV. The BSE energy cutoff (E_empty=10 eV) already shifts peak positions by up to 45 meV at L=4 (Table II), an error comparable to the claimed agreement. Please report fit uncertainties, test sensitivity to excluding small-L points and to alternate 1/L forms, and preferably compute at least one longer system. If the extrapolated values shift by more than ~50 meV, the 'excellent agreement' wording should be softened.","section":"Sec. III, Fig. 4 and Table I"},{"comment":"All production BSE calculations use E_empty^cut=10 eV (App. D). Table II shows that this cutoff shifts the first three peak positions by 35–45 meV for L=4 relative to the fully converged result, and Table III shows a 38 meV shift and 2.3% change in d_exc for the strongest excitation. This error is comparable to the claimed 0.05 eV agreement with experiment and is not included in the error budget of the extrapolated values. The authors should quantify the cutoff convergence at larger L (e.g., L=8,13) and report whether the extrapolated peak positions are stable with respect to cutoff corrections.","section":"App. B, Table II"},{"comment":"The experimental spectra (Ref. 118) are measured for nanographenes on noble-metal surfaces, while the calculations treat free-standing molecules. Substrate screening and image-charge effects can shift excitation energies by tens of meV and are not discussed. Without an estimate of the substrate-induced shift, the agreement to 0.05 eV is not fully interpretable. Please discuss this effect and, if possible, provide a rough estimate (e.g., via a dielectric screening model or literature values for similar GNRs on metal surfaces).","section":"Sec. III, Fig. 5"}],"minor_comments":[{"comment":"The abstract and Sec. II state a MAE 'below 3 meV', but this is for different analytic-continuation settings in CP2K (128 Padé, 500 grid) and FHI-aims (16 Padé, 100 grid). With matched settings the MAE is 4.7 meV (App. E, Fig. 10). Please report both values together to avoid overstatement.","section":"Abstract / App. E"},{"comment":"The direction nomenclature is inconsistent: Sec. III says 'seven carbon atoms in zigzag direction and ... L in armchair direction', while Sec. VI says the width is along the armchair direction and the length along the zigzag direction. The latter is the correct description of a 7-armchair nanographene; please fix the earlier sentence.","section":"Sec. III / Sec. VI"},{"comment":"The axis label '1/∞' is unconventional; consider labeling the limit as 0.","section":"Fig. 4"},{"comment":"The frequency-independent constant C in Eq. (24) is not determined, so the comparison of line shapes in Fig. 5 is qualitative. This should be stated explicitly.","section":"Eq. (24) / Fig. 5"},{"comment":"The main text quotes a converged size of ~7.6 Å from TDA. App. G shows that solving the full BSE (ABBA) changes d_exc by up to 0.32 Å at large L; this uncertainty should be reflected in the quoted value.","section":"App. G"},{"comment":"Typo: 'We fit the the obtained peak frequencies' should read 'We fit the obtained peak frequencies'.","section":"Fig. 4 caption"}],"recommendation":"major_revision","confidential_remarks":"The implementation and cross-code benchmark are convincing and the data availability is commendable. The main issue is the robustness of the finite-size extrapolation that underpins the 0.05 eV agreement claim. I believe the authors can address this with additional analysis (fit uncertainties, sensitivity tests, and possibly longer systems). The substrate-screening effect is also worth attention. If the extrapolation uncertainty is quantified and the claims adjusted accordingly, the paper would be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a solid, useful implementation paper. The GW-BSE module in CP2K is validated against FHI-aims on Thiel's set, and the agreement is genuinely good. They also release inputs, outputs, and code, which is real evidence and makes the work reproducible. The nanographene application is a nice showcase, not a breakthrough, but the 7.6 Å saturation of the exciton size and the demonstration that TDDFT with various hybrids cannot reproduce both the energy and the full spectral shape are concrete, citable results.\n\nThe main soft spot is the extrapolation to the experimental length. Peak positions are computed only for L=4–13, then a quadratic fit in 1/L is evaluated at L≈46, and the claimed 0.05 eV agreement with experiment depends entirely on that functional form. The paper does not report fit uncertainties, and the 10 eV BSE cutoff already shifts the first peak by up to 45 meV at L=4 — same order as the claimed accuracy. The free-standing model also ignores the Au(111) substrate used in the experiment. These caveats don't sink the paper, but they mean the \"excellent agreement\" language oversells what is really a suggestive match. I'd ask the authors to test the extrapolation with a second fit form or a couple of larger L values, and to either report uncertainties or soften the claim.\n\nA smaller point: the headline MAE of 2.7 meV comes from runs with different Padé parameters than the reference calculation; the matched-parameter MAE is 4.7 meV. It's disclosed in the appendix, but the abstract's \"below 3 meV\" is a bit generous.\n\nWhat the paper does well: the benchmark against FHI-aims is the real contribution, and the use of established spatial descriptors is careful. The TDDFT comparison is fair — hybrids get some descriptors right but not the full spectrum, which is a clean message. The code and data availability make this a useful reference for anyone doing excited-state calculations in CP2K.\n\nWho is this for? GW-BSE practitioners who want a second independent implementation in an open-source code, and CP2K users wanting to compute excitations in molecules or nanostructures. It deserves a serious referee. My recommendation: send it out, request a revision that addresses the extrapolation robustness and adjusts the experimental-claims wording.","headline":"A credible CP2K GW-BSE implementation backed by a strong cross-code benchmark; the sub-0.1 eV agreement with experiment is plausible but rests on a long extrapolation and should be read as suggestive, not definitive.","tokens_in":31715,"tokens_out":2004,"would_cite":true,"duration_ms":24865,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper shows that a many-body GW-BSE calculation reproduces the two lowest absorption peaks of 7-armchair nanographenes within 0.05 eV of experiment after a quadratic length extrapolation, and that the size of the lowest bright excitati","keywords":["Bethe-Salpeter equation","GW approximation","nanographenes","graphene nanoribbons","optical absorption spectra","excitons","time-dependent density functional theory","spatial descriptors"],"falsifier":"Compute BSE@evGW0@PBE absorption peaks for a nanographene with L=15 or L=20 (or use a more rigorous extrapolation with more data points) and check whether the peak positions follow the fitted quadratic curve; alternatively, measure the two experimental peak positions for ribbons of several well-characterized lengths to test the extrapolation.","tokens_in":30754,"feed_emoji":"🔬","tokens_out":8466,"duration_ms":66871,"temperature":0.7,"pith_summary":"The paper establishes that a many-body GW-BSE calculation (BSE@evGW0@PBE) can quantitatively reproduce the optical absorption of finite nanographene ribbons and, at the same time, predict the spatial extent of the bound electron-hole pair. After validating the new CP2K implementation against an established code on Thiel's molecular set (mean error under 3 meV), the authors compute spectra for ribbons of increasing length, extrapolate the two lowest bright peaks to the experimental ~20 nm length, and find agreement within 0.05 eV. They also compute the spatial descriptors of the lowest excitation and find that its size saturates at about 7.6 Å for ribbons longer than a few nanometers, indicating a bound exciton with intrinsic correlation length. A systematic TDDFT comparison shows that functionals with 0-65% exact exchange cannot simultaneously reproduce the BSE spectral shape and the exciton size. The work thus argues that many-body methods are needed for accurate excited-state description in nanoscale carbon nanostructures.","feed_headline":"Exciton size in nanographene ribbons: 7.6 Å, spectra within 0.05 eV","feed_subtitle":"Parameter-free calculation nails the two lowest absorption peaks and fixes the electron-hole distance at 7.6 Å.","key_machinery":"The central machinery is the Bethe-Salpeter equation built on eigenvalue-self-consistent GW quasiparticle energies (BSE@evGW0@PBE), which treats the electron-hole pair via the statically screened Coulomb interaction W0(ω=0). The spatial analysis uses the size of the excitation des = sqrt(⟨|r_e - r_h|²⟩), decomposed into electron-hole separation, electron and hole spreads, and a correlation coefficient. The finite-size analysis uses a quadratic fit Ω(p)(L)=a+b/L+c/L², motivated by a one-dimensional free-electron model, to extrapolate peak positions from L=4-13 to the experimental length L≈20 nm.","core_discovery":"The central result is that the BSE@evGW0@PBE approach, implemented in the CP2K code, reproduces the two lowest longitudinal absorption peaks of 7-armchair nanographenes within 0.05 eV of experimental peak positions after a quadratic 1/L extrapolation to the experimental length, and that the spatial size of the lowest bright excitation converges to ~7.6 Å with increasing ribbon length. The paper further shows that TDDFT with any tested functional (PBE, BLYP, PBE0, B3LYP, HSE06, CAM-B3LYP, and PBEh with 0-100% exact exchange) fails to reproduce both the full spectral shape and the exciton size, highlighting the need for explicit electron-hole interaction and screening.","pith_inferences":["If the quadratic 1/L scaling holds beyond L=13, a direct BSE calculation at L=15 or L=20 should land on the fitted curve; a deviation would indicate the extrapolated agreement is fortuitous.","The predicted exciton radius could be measured experimentally (e.g., via two-photon absorption or scanning tunneling spectroscopy), offering a direct test of the ~7.6 Å value.","The descriptor framework introduced here (size of excitation, correlation coefficient) could serve as a quantitative benchmark for judging improved TDDFT kernels, such as range-separated hybrids with optimally tuned screening."],"forward_implications":["The same GW-BSE workflow can now be applied to other finite nanostructures (nanoribbons, quantum dots, molecular aggregates) in CP2K, providing optical spectra and exciton sizes without empirical tuning.","The saturation of the exciton size at ~7.6 Å in 7-armchair ribbons implies that optical properties of longer ribbons are governed by a local exciton with well-defined radius, not by ribbon length.","TDDFT with standard hybrid functionals, even at 25-65% exact exchange, is insufficient for predicting both spectral shape and exciton spatial extent; quantitative exciton properties in nanographenes require many-body methods.","The quadratic 1/L extrapolation connects computationally accessible finite flakes to experimentally synthesized ~20 nm ribbons, enabling quantitative comparison with experiment."],"fun_headline_variants":["GW-BSE: nanographene spectra to 0.05 eV, exciton size 7.6 Å","Nanographene exciton size pinned at 7.6 Å by GW-BSE, TDDFT fails","Exciton size 7.6 Å, spectra within 0.05 eV in nanographene","Many-body effects essential: GW-BSE beats TDDFT for nanographene excitations","GW-BSE nails nanographene spectra within 0.05 eV and exciton size 7.6 Å"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The agreement with experiment rests on the quadratic 1/L extrapolation of the two peak positions from short ribbons (L=4-13) to the experimental length of about 20 nm; if the true length dependence deviates from this functional form at longer lengths, the claimed 0.05 eV agreement would not hold.","fun_headline_variants_meta":{"raw":{"variants":["GW-BSE: nanographene spectra to 0.05 eV, exciton size 7.6 Å","Nanographene exciton size pinned at 7.6 Å by GW-BSE, TDDFT fails","Exciton size 7.6 Å, spectra within 0.05 eV in nanographene","Many-body effects essential: GW-BSE beats TDDFT for nanographene excitations","GW-BSE nails nanographene spectra within 0.05 eV and exciton size 7.6 Å"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001171,"raw_usage":{"total_tokens":4670,"prompt_tokens":727,"completion_tokens":3943,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":471,"completion_tokens_details":{"reasoning_tokens":3821}},"tokens_in":471,"tokens_out":3943,"duration_ms":23910,"temperature":1.0,"reasoning_tokens":3821,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T07:25:02.298098+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute BSE@evGW0@PBE absorption peaks for a nanographene with L=15 or L=20 (or use a more rigorous extrapolation with more data points) and check whether the peak positions follow the fitted quadratic curve; alternatively, measure the two experimental peak positions for ribbons of several well-characterized lengths to test the extrapolation.","supporting_citations":[],"review_version":1}