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REVIEW 3 major objections 5 minor 42 references

Vibrational excitations in magnetic triangular nanographenes

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2411.19670 v1 pith:UG5HTMWU submitted 2024-11-29 cond-mat.mes-hall

Nils Krane , Elia Turco , Annika Bernhardt , Michal Juríček , Roman Fasel , Pascal Ruffieux This is my paper · ORCID
classification cond-mat.mes-hall
keywords inelasticelectrontunnelingspectroscopyphenalenylradicaltriangulenevibrationalexcitationKondoresonancescanningmicroscopyelectron-phononcouplingopen-shellnanographene
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Main text, discussion of Fig. 1d and Fig. 3] 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.
  2. [Methods (first paragraph) and Fig. 4 comparison] 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.
  3. [Fig. 4c-e and Conclusion] 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.
minor comments (5)
  1. [Text near Eq. (1)] There is a typo: "integrataion plane" should be "integration plane."
  2. [Paragraph discussing Fig. 2 and Kondo resonance] "Deconstructive interference" should be "destructive interference."
  3. [Section on k = 1, 2 modes (Fig. 4a discussion)] "Dislocations of the carbon atoms" should likely be "displacements of the carbon atoms," since the text refers to normal-mode motion, not lattice defects.
  4. [Conclusion] "Proofs" should be "proves" (or "demonstrates"). Also, "exctitation" in the sentence before Eq. (1) should be "excitation."
  5. [Fig. 4c caption and main text] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the mode assignment is tested against experimental spatial maps, and the DFT/Bardeen inputs are not fitted to the measured IETS data.

full rationale

The paper's central claim is that the IETS steps at ±22.5 mV and ±35 mV arise from three out-of-plane vibrational modes calculated with gas-phase DFT (B3LYP/6-311G(d,p)) and Bardeen tunneling matrix elements. The calculation inputs—work function 5 eV, tip height 7 Å, integration plane 1.6 Å—are fixed and not adjusted to reproduce the experimental maps. The measured spatial distributions in Fig. 4c are the external benchmark against which the simulated maps are compared; no fitted parameter is renamed as a prediction. The energy comparison (20.0 meV vs 22.5 mV and 35.4 meV vs 35 mV) also provides an independent quantitative check, even if the 2.5 meV offset for the lower mode is a possible accuracy concern rather than circularity. The only relevant self-citation (Ref. 41, Reecht et al., which shares an author) is used as a methodological reference for the electron-phonon coupling simulation; the method is stated in the paper and validated by the experimental comparison, so it is not load-bearing as a self-citation. Ref. 12, also with overlapping authors, establishes the spin-1/2 ground state but is independently supported by the Kondo signal and by Lieb/Ovchinnikov-type spin rules. No step in the derivation defines the predicted quantity in terms of the experimental observable or imports a uniqueness theorem from the authors' prior work.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim depends on the gas-phase DFT approximation for an adsorbed molecule, the Bardeen tunneling model with an s-wave tip, the Lorente-Persson electron-phonon coupling framework, and the rule-out of spin excitations for S=1/2. Three technical parameters (workfunction, tip height, integration plane) are chosen by hand but not fitted to the experimental maps. No new entities are postulated.

free parameters (3)
  • Tip workfunction phi = 5 eV
    Assumed in the Bardeen integral for the simulated tunneling matrix elements; a typical value for metal tips, not fitted to the experimental IETS maps.
  • Tip height z_t = 7 A
    Assumed distance of the s-wave tip above the molecule in the Bardeen calculation; not fitted to the data.
  • Integration plane position z_S = 1.6 A
    Chosen plane for the Bardeen surface integral; not fitted to the data.
assumptions (4)
  • domain assumption Gas-phase DFT (B3LYP/6-311g(d,p)) describes the vibrational modes and SOMO wavefunction of phenalenyl on Au(111) accurately enough for mode assignment.
    The DFT is run on a single molecule in vacuum, while the experiment is on a molecule on Au(111) with strong Kondo screening. The paper does not discuss how the substrate might shift modes or alter the SOMO.
  • domain assumption Bardeen's tunneling formalism with an s-wave tip at 7 A height and a planar integration surface captures the relative inelastic tunneling probabilities.
    Used in Eq. (1) to compute |Mk|2; the s-wave tip and the chosen geometry are approximations that are not independently validated in the paper.
  • standard math The off-resonant vibrational excitation probability is proportional to the tunneling matrix element of the vibrationally perturbed molecular orbital delta Psi_m,k (Lorente-Persson theory).
    Taken from Refs. 39-41; the paper adopts this framework without re-deriving it.
  • domain assumption A single S=1/2 spin has no excited spin state in zero magnetic field, so the IETS steps cannot be spin excitations.
    Standard result for an isolated spin-1/2; the paragraph after Figure 1 uses this to rule out magnetic origin.

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Cite this review

Pith. "Pith review of Vibrational excitations in magnetic triangular nanographenes." pith.science (2026). https://pith.science/paper/UG5HTMWU

@misc{pith2026241119670,
  author       = {Pith},
  title        = {Pith review of: Vibrational excitations in magnetic triangular nanographenes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UG5HTMWU}},
  note         = {Machine review of arXiv:2411.19670}
}
read the original abstract

Inelastic electron tunneling spectroscopy (IETS) is a powerful measurement technique often used in scanning tunneling spectroscopy to probe excited states of various nanostructures, e.g., the magnetic properties of complex spin systems. The observed excited states can be of magnetic and vibrational origin and it is therefore necessary to differentiate between these two excitation mechanisms. Here, we investigate the spin S = 1/2 phenalenyl radical on Au(111). IETS measurements feature inelastic excitations, whereas the spatial distribution of their intensity excludes any spin excitations. Comparison to theoretical simulations proves the vibrational origin of those excitations and allows us to assign the observed features to distinct vibrational modes.

Figures

Figures reproduced from arXiv: 2411.19670 by the authors.

Figure 1
Figure 1. Chemical structure of the phenalenyl radical (a) and perspective view of its singly [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. dI/dV spectra taken along a line across a phenalenyl molecule. (a) The Kondo resonance is strongest when the tip is positioned at the edges of the phenalenyl, whereas the inelastic steps appear in the center. Feedback opened for each spectrum at −60 mV/1 nA. The spectra are vertically offset for clarity. (b) STM image of phenalenyl, indicating the po￾sitions where spectra were acquired. The scale bar indicates 0.5 n… view at source ↗
Figure 3
Figure 3. Tunneling matrix elements |Mk| 2 for all vibrational modes ¯hω < 100 meV (full circles), as well as elastic tunneling (hollow circles), for three different tip positions (see inset). Only the modes k = 1, 2 (20 meV) and k = 4 (35 meV) show significant intensities. The markers for mode k = 1 are displayed as stars for better distinction from k = 2. Inset: Simulated dI/dV map of elastic tunneling matrix elements into … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Spatial mapping of vibrational excitation intensities. (a) Structure of phenalenyl [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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