{"id":"0e2b2bcc-5c0a-4bd4-a6bf-a794f51ea700","arxiv_id":"2411.19670","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"IETS steps in phenalenyl on Au(111) at 22.5 and 35 mV are assigned to specific out-of-plane vibrational modes via spatial mapping and DFT simulations.","lead":"This paper shows that the inelastic tunneling steps seen in a single phenalenyl radical molecule on a gold surface are caused by molecular vibrations, not by spin flips. The result gives researchers a simple spatial-mapping method to tell vibrational and magnetic excitations apart in nanographene devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 22.5 mV IETS step is 2.5 meV above the calculated 20.0 meV k=1,2 modes, yet the paper offers no explanation for this discrepancy, leaving the central mode assignment quantitatively unsupported.","rationale":"The reader's weakest_assumption identified the gas-phase DFT approximation as the key risk, and the energy mismatch is a concrete symptom of that risk. I partially agree: the substrate-induced modification of vibrational modes is indeed a load-bearing assumption, and the 22.5 mV versus 20.0 meV discrepancy strengthens the concern. However, the reader listed the energy mismatch as a separate soundness issue rather than folding it into the weakest assumption; my concern is more specifically that the energy mismatch, combined with the qualitative nature of the map comparison, is the most direct quantitative challenge to the mode assignment. The proposed DFT-on-slab calculation would settle both the energy and the spatial-map questions. The verdict remains CONDITIONAL because the paper should either explain the energy shift or provide substrate-including calculations before the specific mode assignment is accepted; the general vibrational-origin conclusion is solid due to the spin-1/2 argument. Therefore no change to the reader's CONDITIONAL verdict is needed.","tokens_in":7880,"tokens_out":7297,"duration_ms":65334,"concrete_test":"Repeat the vibrational and electron-phonon coupling calculations for phenalenyl adsorbed on a Au(111) slab (or a sufficiently large Au cluster) using a dispersion-corrected functional, e.g. PBE-D3 or B3LYP with vdW corrections. Recompute all modes below 100 meV and the Bardeen tunneling maps from Eq. (1) with the same tip parameters (φ=5 eV, z_t=7 Å, z_S=1.6 Å). If the k=1,2 modes shift to ~22.5 meV, k=4 stays near 35 meV, and the simulated maps retain the triangular-ring/center intensity distribution, the assignment stands. If the energies shift differently, the eigenvectors change substantially, or additional modes gain significant |M_k|^2, the gas-phase assignment is not reliable and the paper's central claim would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim assigns the experimentally observed IETS steps to three out-of-plane vibrational modes: k=1,2 at 20.0 meV and k=4 at 35.4 meV. The k=4 assignment matches the 35 mV step almost exactly, but the k=1,2 assignment is off by 2.5 meV: the experimental step appears at ±22.5 mV while the calculated modes are 20.0 meV. In IETS, the step position directly measures the excitation energy of the adsorbed molecule, so a 12% discrepancy for one pair of modes but not the other is not explained by a simple global shift. The paper relies on gas-phase DFT (Gaussian 16, B3LYP, 6-311g(d,p)) throughout, and the adsorbed molecule is strongly hybridized with Au(111) as evidenced by the Kondo resonance. The spatial maps in Fig. 4 provide qualitative support, but the energy mismatch is the only quantitative check on the mode assignment. If the 22.5 mV feature is not the k=1,2 pair, then either the DFT calculation is missing a mode with significant electron-phonon coupling or the gas-phase vibrational description is unreliable for this system. The paper never discusses this discrepancy, and the Methods provide no substrate model or error estimate for the vibrational energies. This gap undermines confidence that the observed features are correctly assigned to the claimed modes, even though the general vibrational-origin conclusion is well supported by the spin-1/2 argument.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports low-temperature STM/IETS measurements on the phenalenyl radical (S = 1/2) adsorbed on Au(111). The authors observe symmetric conductance steps at bias voltages of ±22.5 mV and ±35 mV. Using the absence of spin excitations for a spin-1/2 center, the spatial distribution of the step intensities, and DFT-based Bardeen simulations of vibration-assisted tunneling, they assign the features to three out-of-plane vibrational modes: a degenerate pair at 20.0 meV (k = 1, 2) and a mode at 35.4 meV (k = 4). They conclude that the steps are off-resonant vibrational excitations and that the approach can discriminate vibrational from magnetic IETS features in nanographenes.","tokens_in":8134,"tokens_out":3066,"duration_ms":29094,"significance":"If the conclusions hold, this work provides a practical method for distinguishing vibrational from spin excitations in IETS of magnetic nanographenes, which is an important issue for the field of pi-magnetism. The paper has clear strengths: the spin-1/2 argument rigorously rules out conventional spin-flip excitations; the DFT-based Bardeen simulations use no free parameters fitted to the IETS maps, with fixed tip parameters and standard B3LYP/6-311g(d,p); and the simulated mode energies and spatial maps are compared directly with experiment. The central vibrational-origin conclusion is well supported. However, the quantitative assignment of the 22.5 mV feature to the 20.0 meV modes is not adequately justified, and the gas-phase DFT assumption is not discussed in light of the strong molecule-substrate hybridization evidenced by the Kondo resonance.","major_comments":[{"comment":"The manuscript assigns the experimental step at ±22.5 mV to the calculated degenerate modes k = 1, 2 at 20.0 meV, while the ±35 mV step matches the k = 4 mode at 35.4 meV almost exactly. The 2.5 meV (12%) discrepancy for the lower-energy pair is never commented on. Since the IETS step position is a direct measure of the excitation energy of the adsorbed molecule, this mismatch is quantitatively material. A global rigid shift due to the substrate or DFT error cannot explain why one pair of modes matches to within 0.4 meV while the other is off by 2.5 meV. The authors should discuss the expected accuracy of the gas-phase vibrational energies, consider anharmonicity or surface-induced renormalization, or provide additional evidence that the 22.5 mV feature indeed corresponds to the k = 1, 2 pair rather than to some other mode. Without this discussion, the quantitative mode assignment for one of the two features is not yet established.","section":"Main text, discussion of Fig. 1d and Fig. 3"},{"comment":"The DFT calculations are performed for an isolated gas-phase molecule, whereas the experiment is performed on a molecule strongly hybridized with Au(111), as evidenced by the pronounced Kondo resonance. The manuscript does not state what effect the surface is expected to have on the vibrational energies, the SOMO shape, or the electron-phonon coupling. This is a load-bearing assumption because both the mode energies and the simulated spatial maps are used for the assignment. The authors should either justify the transferability of gas-phase results to the adsorbed system or show that the conclusions are robust to, for example, different DFT functionals, basis sets, or a simplified substrate model. Such a test would directly address the correctness risk of the assignment.","section":"Methods (first paragraph) and Fig. 4 comparison"},{"comment":"The statement that the \"conformity between simulated and measured maps accordingly proofs\" that the steps are caused by off-resonant vibrational excitations is stronger than the evidence presented. The comparison is visual and qualitative, and for the 22.5 mV step the authors acknowledge that the subtraction procedure overestimates the Kondo background and creates six darker areas. While the central dark region is a genuine signal, a quantitative comparison metric (e.g., a normalized cross-correlation or a line-cut overlay) would strengthen the claim. This is not a fatal flaw, but it should be addressed so that the spatial evidence is as convincing as the spin-1/2 argument.","section":"Fig. 4c-e and Conclusion"}],"minor_comments":[{"comment":"There is a typo: \"integrataion plane\" should be \"integration plane.\"","section":"Text near Eq. (1)"},{"comment":"\"Deconstructive interference\" should be \"destructive interference.\"","section":"Paragraph discussing Fig. 2 and Kondo resonance"},{"comment":"\"Dislocations of the carbon atoms\" should likely be \"displacements of the carbon atoms,\" since the text refers to normal-mode motion, not lattice defects.","section":"Section on k = 1, 2 modes (Fig. 4a discussion)"},{"comment":"\"Proofs\" should be \"proves\" (or \"demonstrates\"). Also, \"exctitation\" in the sentence before Eq. (1) should be \"excitation.\"","section":"Conclusion"},{"comment":"The subtraction procedure for the maps (constant-height maps at different biases) is described only briefly. Stating whether the maps were normalized or drift-corrected before subtraction, and how the bias offsets were chosen, would improve reproducibility.","section":"Fig. 4c caption and main text"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and the central vibrational-origin conclusion is likely correct. The main issue is the unexplained energy discrepancy for the 22.5 mV feature, which is a quantitative weak point in an otherwise convincing qualitative story. If the authors can either resolve this discrepancy or provide a more robust justification for the gas-phase DFT assignment, the paper would be acceptable. I have not identified any concerns about novelty or citation practices."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short take: the paper does what it claims. It shows that the inelastic steps in phenalenyl on Au(111) are vibrational and not spin excitations. The S=1/2 argument is clean, and the spatial dI/dV maps are a convincing fingerprint. The specific assignment to three out-of-plane modes is very likely correct, but the paper is too quiet about the 12% gap between the calculated 20.0 meV and the measured 22.5 mV step. That is the main thing to fix.\n\nWhat's new: spatial IETS mapping applied to a triangulene radical to separate vibrational from magnetic excitations. The method itself is not new—Refs. 39–41 already did the heavy lifting—but this is the first clear demonstration in the nanographene context. It gives the community practical guidance on which vibrational modes to expect when doing IETS on these molecules, which will help interpreting spectra of larger spin chains where vibrational and magnetic signals overlap.\n\nWhat's solid: the S=1/2 argument rules out spin excitations, so the steps have to be inelastic excitations of some other kind. The DFT-Bardeen simulation uses standard parameters and no fitting to the measured maps, so the circularity burden is low. The symmetry reasoning for why only three modes couple is physically transparent and matches the observed spatial patterns.\n\nSoft spots: the 22.5 mV vs 20.0 meV discrepancy for k=1,2 is never discussed. It is not a fatal blow—DFT harmonic frequencies can easily be off by 10%—but the authors should say so and give a rough error estimate. It is also surprising that k=4 matches almost exactly while k=1,2 do not; a brief comment on mode-dependent errors would help. Gas-phase DFT is a real limitation given the Kondo-resolved hybridization with Au(111), though the spatial maps suggest the SOMO remains well localized. The agreement between measured and simulated maps is asserted as 'very good' but not quantified; a normalized cross-correlation or similar would strengthen the claim.\n\nThis paper is for experimentalists and theorists working on triangulene-based spin chains, especially those doing IETS. It is a useful methodological confirmation, not a breakthrough.\n\nRecommendation: it deserves a serious referee. I would send it to review and ask for a revision that addresses the energy discrepancy, adds a note on DFT accuracy, and quantifies the map agreement. The central conclusion holds up.","headline":"Clear evidence that the IETS steps in phenalenyl are vibrational rather than spin excitations, with a plausible mode assignment that needs one honest paragraph about a 2.5 meV discrepancy.","tokens_in":8749,"tokens_out":3400,"would_cite":true,"duration_ms":30568,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The inelastic tunneling steps at ±22.5 mV and ±35 mV in a single phenalenyl radical on Au(111) are off-resonant vibrational excitations of three out-of-plane modes, not spin excitations.","keywords":["inelastic electron tunneling spectroscopy","phenalenyl radical","triangulene","vibrational excitation","Kondo resonance","scanning tunneling microscopy","electron-phonon coupling","open-shell nanographene"],"falsifier":"Measure phenalenyl on a weakly coupled decoupling layer, such as NaCl on Cu(111), and repeat the below/above-step map subtraction. If the step energies shift by more than a few meV or the maps lose the predicted triangular-ring and center patterns, the gas-phase mode assignment and the vibrational mechanism would fail; conversely, if the maps were to follow the Kondo/spin-density positions, a spin origin would be indicated.","tokens_in":7631,"feed_emoji":"🔬","tokens_out":10944,"duration_ms":88944,"temperature":0.7,"pith_summary":"The paper studies a single phenalenyl radical, a triangular carbon molecule with one unpaired spin, adsorbed on Au(111). It asks whether the symmetric conductance steps seen in inelastic electron tunneling spectroscopy (IETS) are magnetic or vibrational, and concludes they are vibrational. The authors map the spatial distribution of the inelastic tunneling probability by subtracting constant-height conductance images taken below and above each step, and compare those maps with density-functional-theory simulations. The experimental maps match the simulated patterns for three out-of-plane vibrational modes: two degenerate modes at 20.0 meV and one at 35.4 meV. This matters because IETS is a standard probe of spin excitations in carbon nanostructures, and vibrational steps can masquerade as magnetic ones; the spatial fingerprint provides a practical way to tell them apart.","feed_headline":"Carbon radical's tunneling steps are vibrations, not spins","feed_subtitle":"Spatial maps and density-functional simulations pin the 22.5 mV and 35 mV signals to three out-of-plane modes.","key_machinery":"The central object is the vibrationally perturbed SOMO wavefunction, $\\delta\\Psi_{m,k} = \\delta Q_k (\\partial \\Psi_m/\\partial Q_k)$, whose overlap with an s-wave tip orbital enters the tunneling matrix element. For each mode $k$, the equilibrium structure is displaced by $\\pm\\delta Q_k/2$, the resulting change in the SOMO is computed with DFT, and the tunneling matrix element gives the inelastic intensity. The mechanism is off-resonant vibration-assisted tunneling, with strong intensity only when the mode's out-of-plane displacement has the same local symmetry as the SOMO phase: the degenerate $k=1,2$ modes (20.0 meV) create a threefold triangular ring with a node in the center, while the $k=4$ mode (35.4 meV) is centered on the molecule.","core_discovery":"The paper establishes that the symmetric differential-conductance steps observed at $\\pm 22.5$ mV and $\\pm 35$ mV on a single phenalenyl radical on Au(111) are off-resonant vibrational excitations, not spin excitations. A single $S=1/2$ radical has no spin-flip excited state in zero magnetic field, and the maps of step intensity do not follow the singly occupied molecular orbital (SOMO) or its Kondo signature; instead, DFT-based simulations of the vibrationally perturbed wavefunction reproduce the measured maps. The steps are assigned to the degenerate out-of-plane modes $k=1,2$ at 20.0 meV and to mode $k=4$ at 35.4 meV, and the agreement of the below/above-step map subtraction with simulation is the decisive evidence.","pith_inferences":["Editorial inference: the same map-subtraction protocol should separate vibrational from magnetic IETS steps in triangulene dimers and chains, where both types of excitation can appear at similar energies.","Editorial inference: if substrate hybridization does not strongly renormalize the modes, the 20.0 meV and 35.4 meV energies serve as a fingerprint for identifying phenalenyl on other metal surfaces.","Editorial inference: the symmetry-matching rule suggests that for larger triangulenes the number of strongly coupled vibrational modes will remain small, which should simplify the interpretation of spin IETS on those systems."],"forward_implications":["In IETS of a single $S=1/2$ nanographene radical, symmetric conductance steps cannot be spin excitations, and the spatial maps shown here identify them as vibrational.","The inelastic intensity is controlled by the vibrationally perturbed wavefunction, not the elastic orbital density, so IETS maps can be concentrated where the elastic signal is suppressed.","Only vibrational modes whose out-of-plane motion shares the local symmetry of the SOMO phase couple strongly; for phenalenyl these are exactly the 20.0 meV and 35.4 meV modes.","Choosing a tip position at the molecule's edge suppresses vibrational background, which is a practical guideline for measuring spin excitations in triangulene-based systems.","The below/above-step map-subtraction protocol yields directly the spatial distribution of the inelastic tunneling probability and can be applied to other molecular adsorbates."],"supporting_citations":[{"why":"provides the on-surface deprotonation route and identifies the phenalenyl radical's S=1/2 ground state.","marker":"[12]"},{"why":"introduces the inelastic-tunneling step mechanism whose threshold energy defines the vibrational excitation energy.","marker":"[27]"},{"why":"supplies the gas-phase DFT calculations used for vibrational energies and perturbed wavefunctions.","marker":"[32]"},{"why":"characterizes the Kondo resonance of phenalenyl on Au(111), which marks the SOMO location and supports the spin-exclusion argument.","marker":"[33]"},{"why":"gives the vibrationally perturbed wavefunction formalism that underlies the off-resonant excitation probability.","marker":"[39]"},{"why":"supports the symmetry-matching rule between vibrational displacement and orbital phase.","marker":"[40]"},{"why":"provides the DFT-based recipe for computing off-resonant vibrational tunneling intensities beyond the Franck-Condon model.","marker":"[41]"},{"why":"provides the tunneling matrix element formula used to simulate the inelastic intensity maps.","marker":"[42]"}],"fun_headline_variants":["Tunneling steps on phenalenyl are vibrations, not spins","Radical's inelastic tunneling peaks are vibrations, not spin flips","Phenalenyl radical's IETS steps originate from vibrations","Spatial maps pin phenalenyl's 22 mV steps to vibrations"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculations treat the molecule as isolated in the gas phase, so the argument assumes that sitting on Au(111) does not significantly change the vibrational modes or their coupling to the electron, even though the surface strongly screens the unpaired spin.","fun_headline_variants_meta":{"raw":{"variants":["Tunneling steps on phenalenyl are vibrations, not spins","Radical's inelastic tunneling peaks are vibrations, not spin flips","Phenalenyl radical's IETS steps originate from vibrations","Spatial maps pin phenalenyl's 22 mV steps to vibrations"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000558,"raw_usage":{"total_tokens":2593,"prompt_tokens":821,"completion_tokens":1772,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":437,"completion_tokens_details":{"reasoning_tokens":1695}},"tokens_in":437,"tokens_out":1772,"duration_ms":12300,"temperature":1.0,"reasoning_tokens":1695,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:58:22.325780+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure phenalenyl on a weakly coupled decoupling layer, such as NaCl on Cu(111), and repeat the below/above-step map subtraction. If the step energies shift by more than a few meV or the maps lose the predicted triangular-ring and center patterns, the gas-phase mode assignment and the vibrational mechanism would fail; conversely, if the maps were to follow the Kondo/spin-density positions, a spin origin would be indicated.","supporting_citations":[{"cited_title":"Observation of the Magnetic Ground State of the Two Smallest Triangular Nanographenes","cited_arxiv_id":null,"evidence_quote":"provides the on-surface deprotonation route and identifies the phenalenyl radical's S=1/2 ground state."},{"cited_title":"C.; Lambe, J","cited_arxiv_id":null,"evidence_quote":"introduces the inelastic-tunneling step mechanism whose threshold energy defines the vibrational excitation energy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the gas-phase DFT calculations used for vibrational energies and perturbed wavefunctions."},{"cited_title":"C.; Krane, N.; Drost, R.; Sobrino, N.; Bernhardt, A.; Jur\\' c c ek, M.; Fasel, R.; Ruffieux, P.; Liljeroth, P.; Jacob, D","cited_arxiv_id":null,"evidence_quote":"characterizes the Kondo resonance of phenalenyl on Au(111), which marks the SOMO location and supports the spin-exclusion argument."},{"cited_title":"Theory of Single Molecule Vibrational Spectroscopy and Microscopy","cited_arxiv_id":null,"evidence_quote":"gives the vibrationally perturbed wavefunction formalism that underlies the off-resonant excitation probability."},{"cited_title":"Symmetry Dependence of Vibration-Assisted Tunneling","cited_arxiv_id":null,"evidence_quote":"supports the symmetry-matching rule between vibrational displacement and orbital phase."},{"cited_title":"L.; Franke, K","cited_arxiv_id":null,"evidence_quote":"provides the DFT-based recipe for computing off-resonant vibrational tunneling intensities beyond the Franck-Condon model."},{"cited_title":"before\" the step) were subtracted from the higher energy maps (taken","cited_arxiv_id":null,"evidence_quote":"provides the tunneling matrix element formula used to simulate the inelastic intensity maps."}],"review_version":1}