{"id":"f8fd78ee-91ed-48ab-8e7e-94889e6ca295","arxiv_id":"2601.13845","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Across 30 transition metals at the fixed icosahedral motif, sulfur adsorption is driven mainly by the metal–sulfur interaction with mostly modest distortion; Ti13, Zr13, Hf13 emerge as the balanced, structurally resilient group and dissociate SO2 without destroying the cluster.","lead":"This paper maps how atomic sulfur adsorbs onto 13-atom icosahedral metal clusters across 30 transition metals, using quantum chemistry plus interpretable machine learning. It identifies titanium, zirconium, and hafnium as the balanced group that binds sulfur strongly yet keeps the cluster intact — a practical lead for sulfur-tolerant nanocatalyst design.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Table 1's Hf13 SO2 rows violate the paper's own Eq. 4 by up to ~10 eV, undermining the SO2 validation of Hf13 as a resilient triad member.","rationale":"I read the paper in good faith. The survey is carefully scoped: the authors state the focus is composition rather than geometric motif, and they are transparent that Cr, Mo, W, and Re relax to motifs more stable than pristine ICO after adsorption. That fixed-ICO caveat is a real limitation but is acknowledged and does not invalidate the survey as a computational resource for the ICO motif. The more serious problem is internal. Table 1 is the validation centerpiece for the Ti/Zr/Hf recommendation, and its Hf13 rows fail Eq. 4 by amounts far exceeding the stated 0.001 eV/atom numerical precision. This is not a matter of PBE accuracy or external consensus; it is an arithmetic inconsistency within the manuscript's own decomposition. A reader relying on Table 1 cannot currently verify the claim that Hf13 is a structurally resilient SO2 dissociation platform. The reader's verdict was CONDITIONAL based partly on this concern; my stress test reinforces that condition. I do not recommend rejection because the error may be a typo or a mislabeled unit, and the broader survey conclusions may survive correction. However, the validation of the triad is not sound as printed. My agreement with the reader is 'partial' because the reader's stated weakest assumption was the fixed-ICO motif, whereas I identify the Hf13 decomposition inconsistency as the single most load-bearing issue; the reader did flag it as item (2), so there is substantial overlap.","tokens_in":20235,"tokens_out":6202,"duration_ms":53477,"concrete_test":"Recompute the Hf13/SO2 dissociative and molecular total energies, then evaluate Eq. 4 using single-point frozen-fragment energies at the optimized geometries (Eqs. 5–7). Require |Eads - (ΔEint + 13·ΔE_TM13_dis + ΔE_SO2_dis)| < 0.01 eV. If the discrepancy persists beyond rounding, correct Table 1 and rerun the ML-guided selection; if it is a typographical error, the corrected values must still place Hf13 in the same intermediate adsorption regime before the triad recommendation can stand.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that Ti13, Zr13, and Hf13 are validated 'resilient platforms' for S poisoning rests on the SO2 adsorption decomposition in Table 1. As printed, the Hf13 rows do not satisfy Eq. 4. For the dissociative Hf13 geometry: Eads = -12.681 eV, but ΔEint + 13·ΔE_TM13_dis + ΔE_SO2_dis = -25.100 + 13·0.342 + 5.879 = -14.775 eV (if ΔE_TM is per atom), or -18.879 eV (if ΔE_TM is total, as the Zr row seems to require). For the molecular Hf13 geometry the mismatch is even larger: -13.182 + 13·0.288 + 12.6225 = +3.185 eV versus Eads = -6.826 eV. No combination of the printed values reproduces Eads within rounding. Because Eq. 4 is the paper's own energy decomposition, this is an internal inconsistency in the exact table used to validate the triad. If the Hf13 numbers are wrong, the evidence that Hf13 exhibits 'strong binding with limited distortion' is unsupported, and the design recommendation loses one of its three pillars. This is more immediately load-bearing than the fixed-ICO assumption, which the authors explicitly scope as a compositional survey; the Table 1 error is a direct contradiction with the manuscript's own formalism.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a combined DFT and machine-learning study of atomic sulfur adsorption on 13-atom icosahedral transition-metal nanoclusters (TM13) for 30 metals across the 3d–5d series. Using PBE-D3 with vibrational analysis, the authors compute adsorption energies and decompose them into interaction and distortion contributions, together with structural, electronic, and vibrational descriptors. Unsupervised k-means clustering and supervised regression with LOFO feature ranking are used to identify Ti13, Zr13, and Hf13 as a chemically resilient triad, and explicit SO2 adsorption calculations on these three clusters are presented as validation. The central claim is that these isoelectronic metals combine strong S binding with limited structural perturbation, making them promising sulfur-tolerant subnanometer catalysts.","tokens_in":20447,"tokens_out":7471,"duration_ms":80742,"significance":"If the results hold, the paper provides a broad, open dataset of S adsorption descriptors for 30 transition-metal icosahedral nanoclusters and a transparent workflow connecting DFT descriptors to poisoning trends. The computational protocol is standard and well documented, with convergence tests, vibrational confirmation of minima, and a public repository for inputs, outputs, and ML workflows. The energy decomposition is exact bookkeeping, and the LOFO analysis across three regressors is a reasonable interpretability strategy. However, the SO2 validation table contains internal inconsistencies that directly affect the Ti/Zr/Hf recommendation, and the fixed-ICO assumption is not verified for the selected metals. These issues must be resolved before the central claims can be accepted.","major_comments":[{"comment":"The Hf13 rows in Table 1 violate the decomposition Eq. (4). For dissociative Hf13, ΔE_int + 13·ΔE_TM13_dis + ΔE_SO2_dis = -25.100 + 13(0.342) + 5.879 = -14.775 eV (or -18.879 eV if ΔE_TM13_dis is interpreted as total), which does not reproduce the reported E_ads = -12.681 eV. For molecular Hf13, the same sum gives +3.185 eV (per-atom) or -0.272 eV (total), versus E_ads = -6.826 eV. The Zr13 dissociative row only satisfies Eq. (4) if ΔE_TM13_dis = 0.360 eV is treated as a total energy, contradicting the column header '(eV/atom)'. Because Table 1 is the direct DFT validation of the Ti/Zr/Hf 'resilient platform' claim and of the 'strong, predominantly dissociative' SO2 conclusion, these inconsistencies are load-bearing. The authors must correct the units and recompute/report the decomposition for all six rows, and re-examine the Hf13 SO2 results in particular.","section":"Table 1; Eq. (4)"},{"comment":"The paper fixes all 30 TM13 clusters to the ICO motif, stating that it is the lowest-energy configuration for several TM13 NCs (refs [33,59]), but it does not verify that ICO is the global or even a representative minimum for each element. The manuscript's own §3.2 reports that Cr, Mo, W, and Re can relax to motifs more stable than the pristine ICO geometry, so for these metals the reported S adsorption energies on the relaxed ICO may not be the operative ones. More importantly for the central recommendation, no ground-state check is reported for Ti, Zr, and Hf. If their lowest-energy 13-atom isomers are not ICO, the statement that the ICO framework 'remains largely preserved' upon SO2 adsorption is not evidence of catalytic resilience. I request a concrete test: compare S adsorption on low-energy non-ICO motifs (e.g., decahedral, fcc/hcp, amorphous) for Ti13, Zr13, and Hf13, or perform","section":"§2 Atomic Configurations; §3.2; Conclusions"},{"comment":"The k-means clustering uses k=10 chosen 'based on the idea' that small chemically similar groups would form, without an elbow/silhouette analysis or stability check. The Ti/Zr/Hf selection is attributed to these cluster assignments (Figure 4 and §3.3), and the paper is titled around interpretable, physics-informed learning. Because the ML grouping is a central part of the selection rationale, the arbitrary k is a gap. The authors should report the model-selection criterion and a stability analysis showing that Ti/Zr/Hf remain in the same cluster for a range of k (e.g., 3–12) and across initializations. If the grouping is not robust, the claim that the ML provides 'a solid, data-driven reason' for the triad selection is overstated.","section":"§2 Machine Learning Models; §3.3"}],"minor_comments":[{"comment":"There are several typos: 'Nanoclustes' in the keywords, 'physic-informed' in §2, and inconsistent spacing in 'V ASP'. A careful proofread is needed.","section":"Throughout"},{"comment":"The ΔE_SO2_dis column is labeled 'eV/atom' but the distortion energy of an adsorbate is defined per molecule in Eq. (7). Please correct the units. The vibrational frequencies at the bottom of the table should be labeled with the mode number or assignment, and the units (cm^-1) made explicit.","section":"Table 1"},{"comment":"The text says SOC was 'included and tested' but also says all findings originated from PBE-D3 optimizations. Please clarify explicitly whether the production energies include SOC or only the tested protocols in the SI.","section":"§2 Computational Details"},{"comment":"The group cross-validation procedure is described only vaguely. Please specify the group definition (e.g., by d-series or by cluster), the split ratio, and report R²/MAE values for each model. The bar chart in Figure 6 would benefit from error bars or a scatter plot with parity line.","section":"Figure 6; §2 ML Models"},{"comment":"The LOFO panels report ΔR², ΔMAE, and ΔRMSE, but the heatmap color scales are not defined in the caption, and negative deltas (redundant features) need interpretation. Also, the list of descriptors used in the models should be stated explicitly in the main text, not only in the Methods.","section":"LOFO Analysis; Figure 5"}],"recommendation":"major_revision","confidential_remarks":"The Table 1 inconsistency is the most serious issue and should be resolved before publication. The near-identical ΔE_int values in the Ti and Zr dissociative rows (-25.416 and -25.41) and the large Hf13 mismatches suggest the table entries should be rechecked against the raw DFT outputs. The fixed-ICO scope is acknowledged by the authors as a compositional survey, but the conclusions generalize beyond that scope; a targeted check for Ti/Zr/Hf would substantially strengthen the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis is a genuinely useful computational survey: 30 transition metals on the fixed ICO motif, atomic sulfur adsorption with a clean energy decomposition, vibrational fingerprints, and a modest interpretable-ML layer. The DFT work is careful—convergence tests, no imaginary modes, spin-polarized PBE-D3—and the authors are explicit that the ML is a rationalization layer, not a replacement for first principles. The periodic trends (interaction-dominated adsorption, moderate distortion for most metals, d-band center correlation) are supported by the reported numbers. The Ti/Zr/Hf selection as a balanced group is a reasonable output of the clustering.\n\nThe soft spots are real, and one is concrete. Table 1, used to validate the SO2 case study, does not satisfy the paper's own Eq. 4 for several rows. For dissociative Hf13, the printed components sum to about −14.8 eV, not the listed −12.7 eV; for molecular Hf13 the mismatch is ~10 eV. Zr13 dissociative also fails by a large margin. This is not rounding. The paper's central triad validation loses one of its three pillars until those numbers are corrected or the decomposition is re-explained.\n\nThe fixed-ICO assumption is acknowledged but still load-bearing. The authors note that Cr, Mo, W, and Re relax to motifs more stable than pristine ICO after adsorption, which means the poisoning-mechanism trends for those elements are conditioned on a geometry that may not be operative. That should be scoped explicitly, or per-element motif stability should be checked.\n\nThe ML claims are modest, but the \"predict for new samples\" framing overstates what 30 datapoints and same-data LOFO can do. That is a minor overstatement, not a fatal flaw. The GitHub link has no commit hash or inventory, so reproducibility is promised but not yet evidenced.\n\nVerdict: the atomic-S survey is a solid, citable resource. The SO2 validation section and Table 1 need a careful correction before the design guidelines are relied on. I would send this to peer review, with a request to fix the table and to soften the generalization claims.","headline":"Solid 30-metal S-adsorption survey with a real internal inconsistency in the SO2 validation table; worth refereeing after fixes.","tokens_in":21150,"tokens_out":2822,"would_cite":true,"duration_ms":28429,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["31.15.E-","68.43.-h","82.65.+r"],"model":"deepseek-v4-flash","headline":"The paper's central claim: across 30 icosahedral 13-atom transition-metal clusters, sulfur adsorption is dominated by the electronic interaction term, and the isoelectronic Ti13, Zr13, Hf13 group offers a sulfur-tolerant balance between str","keywords":["sulfur poisoning","transition-metal nanoclusters","icosahedral clusters","density functional theory","interpretable machine learning","d-band center","adsorption energy decomposition","SO2 dissociation"],"falsifier":"Perform a global structure search (e.g., basin hopping or genetic algorithm) for each of the 30 TM13 clusters without constraining to the icosahedral motif, then recompute atomic sulfur adsorption on the lowest-energy isomer. If for any of the metals flagged with negative distortion energies the non-ICO isomer gives significantly different adsorption energies or a different preferred site, the claim that ICO-based trends represent the operative sulfur-poisoning behavior would be overturned.","tokens_in":20016,"feed_emoji":"🛡️","tokens_out":6326,"duration_ms":62904,"temperature":0.7,"pith_summary":"This paper tries to establish a transferable, data-driven picture of how atomic sulfur poisons 13-atom transition-metal nanoclusters and which metals withstand it best. The authors fix all 30 metals (3d–5d series) to the icosahedral cluster motif and combine dispersion-corrected density functional theory with interpretable machine learning. They find that adsorption energy is dominated by the metal–sulfur interaction term, while distortion of the cluster cage is usually moderate; a few metals, notably Cr, Mo, W, and Re, show large negative distortion energies, meaning their icosahedral scaffold can reorganize into more stable motifs on adsorption. Clustering and regression analyses single out the isoelectronic trio Ti13, Zr13, and Hf13 as a middle regime: sulfur binds strongly enough to activate S-containing molecules yet not so strongly that the cluster falls apart. Explicit SO2 calculations on these three clusters show dissociative, strong adsorption with the icosahedral cage largely preserved, offered as validation and as design guidance for sulfur-tolerant subnanometer catalysts.","feed_headline":"30-metal screening picks Ti, Zr, Hf as sulfur-tolerant clusters","feed_subtitle":"DFT plus machine learning finds 13-atom icosahedral clusters that bind sulfur strongly but resist structural damage.","key_machinery":"Central engine is the fixed icosahedral (ICO) 13-atom motif—one central atom plus 12 surface atoms—used for all 30 metals, and the adsorption-energy decomposition Eads = ΔEint + ΔEdis(TM13), which splits the electronic interaction between frozen fragments from the energy penalty or gain of distorting the cluster. Around this decomposition, the paper organizes DFT-derived descriptors (binding energy, bond length and effective coordination, d-band center, HOMO–LUMO gap, charge transfer, vibrational frequencies and zero-point energy) into a descriptor space that feeds k-means clustering and leave-one-feature-out regression to rank which descriptors generalize best.","core_discovery":"On its own terms, the paper's central claim is that on the fixed icosahedral (ICO) 13-atom motif, sulfur adsorption on all 30 transition metals is governed primarily by the electronic metal–sulfur interaction, with moderate geometric distortion of the metal cage for most metals, and that an interpretable machine-learning analysis of the DFT-derived descriptors identifies the isoelectronic Ti13, Zr13, Hf13 group as a chemically resilient intermediate-binding regime. Explicit SO2 calculations on those three clusters find strong dissociative adsorption (S–O bonds stretched past 4 Å) while the ICO cage remains essentially intact, which the authors take as direct validation of the trend-guided se","pith_inferences":["Editorial inference: because the analysis fixes the ICO motif, the predicted poisoning mechanisms and the Ti/Zr/Hf designation hold only if ICO is a representative shape for each metal; a global isomer search for the anomalous Cr, Mo, W, Re cases would test whether the descriptor rankings survive.","Editorial inference: the same descriptor pipeline could be applied to other poisoning species (e.g., H2S or phosphorus) or to bimetallic 13-atom clusters to see whether the interaction/distortion decomposition and the Ti/Zr/Hf resilience persist.","Editorial inference: the dissociative SO2 adsorption at low coverage suggests these clusters are worth testing in catalytic settings such as hydrodesulfurization or SO2 electroreduction, provided the dissociated fragments can be removed rather than remaining permanently bound.","Editorial inference: the clustering groups could double as an experimental roadmap—if size-selected Ti13, Zr13, and Hf13 clusters can be synthesized, direct measurements of sulfur binding and SO2 activation would provide a strong test of the computational trends."],"forward_implications":["If correct, the dominance of the interaction term means sulfur-tolerance trends can be predicted mainly from electronic descriptors such as the d-band center, not just from geometric rigidity.","The Ti13, Zr13, Hf13 trio becomes a concrete family of candidate sulfur-tolerant subnanometer catalysts; their dissociative SO2 adsorption suggests they may activate sulfur–oxygen bonds rather than merely accumulate sulfur.","The descriptor ranking from leave-one-feature-out analysis gives a short menu of pristine-cluster properties that generalize to predict sulfur adsorption on new clusters, enabling cheaper screening beyond the 30 metals.","For Cr, Mo, W, and Re, negative distortion energies imply sulfur adsorption can drive the cluster toward a different motif, so their poisoning behavior may depend strongly on isomer choice or environmental conditions.","The flattened binding-energy curve after sulfur adsorption suggests that adsorbed sulfur tends to equalize metal cluster stabilities, so poisoning risk may be more uniform across metals than bulk trends imply."],"fun_headline_variants":["Ti, Zr, Hf clusters resist sulfur poisoning","13-atom clusters: Ti, Zr, Hf tolerate sulfur","ML+DFT finds sulfur-tolerant nanoclusters","Sulfur adsorption mapped on 30 metal clusters","Icosahedral clusters: strong sulfur binding, low damage"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Every conclusion is computed on clusters that were started in, and mostly keep, the icosahedral shape; if for some metals—especially Cr, Mo, W, and Re—the true lowest-energy 13-atom cluster has a non-icosahedral structure, the adsorption energies, site preferences, and poisoning picture could be different.","fun_headline_variants_meta":{"raw":{"variants":["Ti, Zr, Hf clusters resist sulfur poisoning","13-atom clusters: Ti, Zr, Hf tolerate sulfur","ML+DFT finds sulfur-tolerant nanoclusters","Sulfur adsorption mapped on 30 metal clusters","Icosahedral clusters: strong sulfur binding, low damage"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000265,"raw_usage":{"total_tokens":1505,"prompt_tokens":868,"completion_tokens":637,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":612,"completion_tokens_details":{"reasoning_tokens":558}},"tokens_in":612,"tokens_out":637,"duration_ms":7273,"temperature":1.0,"reasoning_tokens":558,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T09:24:49.987493+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a global structure search (e.g., basin hopping or genetic algorithm) for each of the 30 TM13 clusters without constraining to the icosahedral motif, then recompute atomic sulfur adsorption on the lowest-energy isomer. If for any of the metals flagged with negative distortion energies the non-ICO isomer gives significantly different adsorption energies or a different preferred site, the claim that ICO-based trends represent the operative sulfur-poisoning behavior would be overturned.","supporting_citations":[],"review_version":1}