{"id":"d3808189-6481-44f8-9e64-33ad2d15b5dc","arxiv_id":"2607.10514","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Relativistic FS-RCCSDT and DFT calculations give the first detailed low-lying electronic states of TlO, TlO+ and TlO−, with De(TlO)≈2.66 eV and an unbound TlO+ ground state.","lead":"High-level relativistic calculations map the electronic states of TlO, TlO+ and TlO− and show the cation ground state is unbound. The numbers help interpret thermochromatography experiments on thallium and its superheavy homologue nihonium.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The Reader correctly isolates the strongest claim (unbound TlO+) and the methodological limitation of the thermochemical cycles. That limitation does not underwrite the unbound result: the FS-RCCSDT curves are obtained directly in the 2h0p sector and already show no minimum. The paper is transparent about the restricted radial range (R > 2.1 Å inaccessible at full triples) and about the multireference character that causes DFT and CCSD(T)+ΔSO to produce spurious shallow wells. These are acknowledged limitations, not hidden assumptions that reverse the claim. Independent support comes from the clear trend AlO+ > GaO+ > InO+ > TlO+ and from the isoelectronic HgO discussion. Consequently the Reader’s ACCEPT / high-confidence assessment stands; no verdict adjustment is warranted.","tokens_in":15756,"tokens_out":500,"duration_ms":6482,"concrete_test":"Recompute the lowest 0+, 0−, 1 and 2 components of TlO+ at FS-RCCSDT (or an equivalent intermediate-Hamiltonian FS-RCCSDT) on a denser radial grid for R = 1.7–2.5 Å with the same active space and counterpoise correction; if any component develops a local minimum deeper than ~0.05 eV relative to the Tl+(1S0)+O(3P2) asymptote, the unbound claim would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the ground state of TlO+ is unbound rests on the FS-RCCSDT potential curves themselves (Fig. 1 and Table I), which are purely repulsive for the low-lying 3Π and 1Σ+ components. The thermochemical cycle that reconstructs De(TlO+) is secondary and is not required to establish unbound character; the paper already notes that De(TlO+) cannot be obtained from that cycle precisely because the curves are repulsive. The cycle is used only for the bound species (TlO and TlO−) and employs well-established experimental EA(O) and IP(Tl). No internal inconsistency or method-level failure that would reverse the unbound conclusion is apparent.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript reports a systematic relativistic electronic-structure study of TlO, TlO+, and TlO−. Low-lying potential curves and spectroscopic constants are obtained primarily with the Fock-space coupled-cluster method including connected triples (FS-RCCSDT) and an intermediate-Hamiltonian treatment of the 2h0p sector, with cross-checks against two-component DFT/PBE0 and scalar-relativistic CCSD(T)+ΔSO. The central results are that neutral TlO is bound (De ≈ 2.66 eV at FS-RCCSDT) with three low-lying states (X 2Σ+1/2 and the 2Π components) that exhibit an avoided crossing, that TlO− is strongly bound (De ≈ 3.23 eV), and that the ground electronic state of TlO+ is unbound (purely repulsive low-lying 3Π and 1Σ+ components). Vertical IP and adiabatic EA of TlO, dipole moment, and static polarizability components are also reported, and the data are used to discuss possible formation of TlO on gold surfaces in thermochromatography experiments relevant to nihonium chemistry.","tokens_in":15903,"tokens_out":1242,"duration_ms":14096,"significance":"Spectra of TlO and its ions have never been observed, and prior theory is limited to a single composite De estimate and one DFT Re value. The present work supplies the first detailed map of low-lying states for all three charge states, establishes the unbound character of TlO+ from first-principles curves, and provides IP, EA, μ, and α that can be used for adsorption-energy estimates. The FS-RCCSDT protocol (additive triples, counterpoise correction, intermediate Hamiltonian) is a high-level standard for such systems; agreement of IP/EA/De with DFT and CCSD(T)+ΔSO to ~0.2 eV strengthens confidence. The results are directly relevant to ongoing gas-thermochromatography work on Tl and Nh and give a concrete, falsifiable prediction (repulsive TlO+ curves) that can guide future experiments and calculations on NhO.","major_comments":[{"comment":"Section II and Table II: Dissociation energies of the open-shell species are reconstructed via thermochemical cycles that insert experimental EA(O) and IP(Tl). While this is standard and does not affect the unbound character of TlO+ (which follows directly from the repulsive FS-RCCSDT curves in Fig. 1), the manuscript should quantify the residual uncertainty that arises from the incomplete cancellation of basis-set and correlation errors between De(TlO−), EA(TlO), and the atomic data, or at least state an estimated error bar on De(TlO) and De(TlO−) beyond the ~0.2 eV method-to-method scatter already shown.","section":null},{"comment":"Fig. 1 caption and Section III: For TlO+ the FS-RCCSDT curves cannot be continued beyond R ≈ 2.1 Å because of amplitude-equation instability. The claim that the ground state is unbound is therefore based on the short-range repulsive wall and the absence of a minimum inside the accessible region. A short additional check (e.g., FS-RCCSD or intermediate-Hamiltonian continuation to larger R, or a single-point comparison at a larger distance with a different active-space choice) would make the purely repulsive character more robust against the possibility of a shallow long-range well.","section":null}],"minor_comments":[{"comment":"Table I: Vibrational constants marked with an asterisk are harmonic; the text (Section III) correctly notes that the (1)1/2 state of TlO will be strongly non-adiabatic already at low v. Adding a brief note in the table caption that the listed ωe for (1)1/2 is only a harmonic estimate would avoid misreading.","section":null},{"comment":"Section III, paragraph on high-lying states: The approximate Te values obtained in the 0h1p and 1h2p sectors are useful for context, but the estimated uncertainties (0.1 eV and ~0.6 eV) should be stated next to each number in the text for clarity.","section":null},{"comment":"Table III: Only FS-RCCSD and DFT/PBE0 dipole moments are given; a CCSD(T)+ΔSO value (or a short statement why it was omitted) would complete the method comparison already used for the energetic quantities.","section":null},{"comment":"References: The recent experimental thermochromatography papers on Tl (e.g., Wilson et al. 2025, Serov et al. 2013) are cited; a one-sentence pointer in the introduction to the corresponding Nh experiments would help non-specialist readers see the direct link.","section":null},{"comment":"Typographical: In the abstract and several places the cation is written TlO$^+$ while the anion is TlO$^-$; consistent use of the same math-mode style throughout would improve appearance.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The work is solid and well within the scope of a specialized chemical-physics journal. The thermochemical-cycle and short-range-curve limitations are real but secondary; they do not overturn the central unbound-TlO+ claim. I see no reason to request major new calculations beyond the modest checks suggested above. Fit for the journal is good."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing is that this is the first systematic FS-RCCSDT treatment of TlO, TlO+ and TlO−, and it cleanly shows the low-lying states of the cation are purely repulsive. That is new and useful for the thermochromatography groups who already treat Tl as the Nh proxy.\n\nWhat the paper does well is straightforward. They run a proper relativistic Fock-space protocol (additive triples, intermediate-Hamiltonian treatment of the 2h0p sector, counterpoise, GRPP that includes Breit/QED), map the avoided crossings between the 2Σ+1/2 and 2Π1/2 curves of the neutral, and give spectroscopic constants, vertical IP, adiabatic EA, dipole and polarizability. Cross-checks with PBE0 and CCSD(T)+ΔSO stay within ~0.2 eV on the thermochemistry. The Bader charges and the comparison to AlO+/GaO+/InO+ make the unbound-TlO+ result chemically plausible rather than a numerical accident. The discussion of non-adiabatic effects on the vibrational spectrum is honest and explains why older optical searches failed.\n\nSoft spots are real but secondary. Dissociation energies of the open-shell species are reconstructed thermochemically because the low Fock-space sectors cannot reach the atomic limits; they use experimental EA(O) and IP(Tl). That is standard and clearly stated, and it is not needed for the unbound claim itself—the PECs already show no minimum. High-lying states are only estimated at FS-RCCSD, and the DFT/CCSD(T) geometries for the multiconfigurational ground state of TlO are off by ~0.05 Å, which the authors themselves flag. No input files or raw curves are deposited, but that is common in this subfield.\n\nThis is for people who need numbers for SHE chromatography modeling or who care about heavy-element oxides. The math and citation pattern look solid; nothing is circular. I would send it to peer review without hesitation and would cite the De and unbound-TlO+ results myself if I were writing on Nh chemistry.","headline":"Solid first high-level map of TlO/TlO+/TlO− states; the unbound TlO+ claim is direct from the PECs and the work is ready for referees.","tokens_in":16528,"tokens_out":556,"would_cite":true,"duration_ms":5592,"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":"The ground state of TlO+ is unbound, while neutral TlO remains bound at about 2.66 eV.","keywords":["thallium monoxide","TlO","relativistic Fock-space coupled cluster","spin-orbit coupling","dissociation energy","thermochromatography","nihonium","superheavy elements"],"falsifier":"A laboratory measurement of the TlO+ dissociation energy or a spectroscopic observation of a bound vibrational progression in the cation ground state would directly test the claim that the ground electronic state is unbound.","tokens_in":16647,"feed_emoji":"⚛️","tokens_out":627,"duration_ms":6791,"temperature":0.7,"pith_summary":"This paper maps the low-lying electronic states and key energetic properties of thallium monoxide and its ions for the first time at high relativistic accuracy. It finds that neutral TlO is a bound molecule whose ground state is mixed by spin-orbit coupling, while the ground electronic state of the TlO+ cation is purely repulsive and therefore unbound. Dissociation energies, electron affinity, ionization potential, dipole moment and polarizability are reported, and the results are used to interpret how Tl-containing molecules form during gas thermochromatography experiments that also serve as models for the superheavy element nihonium. The unbound character of TlO+ implies that the neutral molecule is more likely to form on a surface than in the gas phase after an ion is neutralized.","feed_headline":"TlO+ ground state is unbound; neutral TlO holds at 2.66 eV","feed_subtitle":"First high-accuracy map of TlO states guides thermochromatography of thallium and nihonium","key_machinery":"Relativistic Fock-space coupled-cluster theory with full iterative triples (FS-RCCSDT), applied in the 1h0p and 2h0p sectors relative to closed-shell TlO- as the Fermi vacuum, together with thermochemical cycles that recover dissociation energies from computed electron affinities and ionization potentials plus experimental atomic data.","core_discovery":"High-level relativistic Fock-space coupled-cluster calculations that include connected triple excitations show that the ground electronic state of the TlO+ cation is unbound: its low-lying 3Pi and 1Sigma+ components remain repulsive once spin-orbit coupling is taken into account. Neutral TlO, by contrast, is bound, with a dissociation energy of approximately 2.66 eV, an adiabatic electron affinity of 2.03 eV and a vertical ionization potential of 10.16 eV.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["TlO+ ground state unbound; TlO binds at 2.66 eV","Relativistic CC shows TlO+ unbound, TlO De ~2.66 eV","First high-accuracy TlO states map TlO+ as unbound","TlO EA 2.03 eV, IP 10.16 eV; cation ground state free","Spin-orbit makes TlO+ repulsive; neutral holds 2.66 eV"],"cache_read_input_tokens":128,"weakest_assumption_plain":"Dissociation energies of the open-shell species cannot be obtained inside the low Fock-space sectors and must be reconstructed from thermochemical cycles that insert experimental atomic electron affinity and ionization potential values.","fun_headline_variants_meta":{"raw":{"variants":["TlO+ ground state unbound; TlO binds at 2.66 eV","Relativistic CC shows TlO+ unbound, TlO De ~2.66 eV","First high-accuracy TlO states map TlO+ as unbound","TlO EA 2.03 eV, IP 10.16 eV; cation ground state free","Spin-orbit makes TlO+ repulsive; neutral holds 2.66 eV"]},"model":"grok-4.5","effort":"low","cost_usd":0.005776,"raw_usage":{"total_tokens":1514,"prompt_tokens":731,"num_sources_used":0,"completion_tokens":116,"cost_in_usd_ticks":57760000,"prompt_tokens_details":{"text_tokens":731,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":667,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":731,"tokens_out":116,"duration_ms":5712,"temperature":1.0,"reasoning_tokens":667,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T11:07:44.355079+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A laboratory measurement of the TlO+ dissociation energy or a spectroscopic observation of a bound vibrational progression in the cation ground state would directly test the claim that the ground electronic state is unbound.","supporting_citations":[],"review_version":1}