Theoretical prediction for monitoring Jahn-Teller vibrational evolution using real-space tip-enhanced Raman imaging

Domain: physics
Published: 2026-01-09
Editorial outcome: minor_revision

Abstract
The Jahn-Teller effect (JTE) reduces the geometrical symmetry of a system with degenerate electronic states via vibronic coupling, playing a pivotal role in molecular and condensed systems. However, due to the intrinsic limitations of conventional techniques, only the electronic evolution in JTE can be measured. Herein, we theoretically propose that vibrational resolved tip-enhanced Raman scattering images can visualize the vibrational evolutions in JTE in real space. Taking an experimentally accessible single zinc phthalocyanine (ZnPc) molecule as a proof-of-principle example, not only the degenerate vibrational splitting but also the overlooked vibration mixing caused by the JTE in its anionic form can be characterized by Raman images. Leveraging Raman images, the controllable configuration of JTE distortion with partial isotopic substitution can be further identified. These findings establish a practical protocol to monitor the detailed vibrational evolutions when a single molecule experiences JTE, providing a pathway for visualization of spontaneous symmetry breaking in molecular and solid-state systems.

Introduction
The Jahn-Teller effect (JTE)1,2 describes a fundamental phenomenon that a degenerate system spontaneously reduces its geometry symmetry via the vibronic coupling to stabilize the total energy3–5. JTE represents a general mechanism of spontaneous symmetry breaking, which is responsible for various important observations across multiple disciplines, including spectroscopy, molecular and solid-state physics, stereochemistry, and materials science6–14. In practice, JTE can be efficiently induced by injecting or removing an electron from a degenerate electronic state15,16, particularly in systems containing transition metal ions7,17,18. Such a charge-induced JTE arises from the modification of electronic occupancy, which directly lifts the degeneracy of molecular orbitals and thereby triggers symmetry-lowering structural distortions. In this context, scanning probe microscopy (SPM) techniques provide a practical means to precisely control JTE in real space19,20.

Despite the success of SPM techniques in the visualization of JTE, most investigations were focused on imaging the symmetry breaking of electronic states21–25. Exclusive investigation on the electronic degrees of freedom in JTE has led to the current lack of understanding of its vibrational aspect, which results in potentially ambiguous assignments of accompanying frequency splitting, the mixing of vibrational wavefunctions upon symmetry reduction, and the possibility of controlling JTE distortions through atomic displacements. Recently, by leveraging the tip-enhanced Raman scatting (TERS)26–29, an experimental measurement has captured several spectral variations when a single zinc phthalocyanine (ZnPc) was negatively charged30, where vibrational frequency evolution was highlighted. Nevertheless, it still lacks further reports on imaging vibrational symmetry breaking, another essential aspect of JTE, although it is possible owing to the high spatial resolution of TERS31–35.

Recent TERS studies have demonstrated their ability to quantitatively map the spatial distribution of vibrational wavefunctions32,36–39. In this study, this technique is expected to be further extended to visualize the single-molecule JTE from the vibrational perspective. Taking the experimentally accessible ZnPc molecule as a proof-of-principle example, we theoretically propose that TERS images provide a practical means to monitor all the details of the vibrational evolution in JTE distortion. We demonstrate that, not only the splitting of degenerate vibrations but also the mixing of non-degenerate vibrations belonging to different irreducible representations of the high-symmetry point group, can be affirmatively observed in TERS images. For the latter case, we reveal that the mixing strength is determined by both the energy difference and spatial distribution overlap between the mixed modes. Moreover, we manifest that the controllable JTE distortions at the sub-ångström level achieved through partial isotope substitution can be unambiguously distinguished by high-resolution TERS imaging.

Results
Spectra characterization of charge-induced JTE
Figure 1a illustrates the experimental setup for injecting an electron into neutral ZnPc to induce JTE distortion. In the neutral state, ZnPc possesses a doubly degenerate lowest unoccupied molecular orbital. Upon adding an extra electron, this degeneracy is lifted, triggering a symmetry-lowering structural distortion. Previous experiments observed sudden changes in TERS spectra when the sample bias exceeded 0.3 V, which was assigned as a transition from the neutral to negatively charged state30. It should be stressed that owing to the insulating spacer layer introduced in Fig. 1a, the negatively charged ZnPc− has a sufficiently long lifetime for spectral measurements and even imaging30,40. Besides, the experiment explicitly ruled out molecular deformation induced by mechanical pressure from the tip apex. Specifically, the reproducible spectral evolution during tip approach and retraction confirmed that the observed spectral changes and symmetry reduction originated intrinsically from different charging states of ZnPc30. Calculations show that the JTE-induced geometrical distortion from the neutral D4h to the anionic D2h is quite subtle (the elongations along both the diagonal axes are 0.026 and 0.010 Å, respectively, as shown in Fig. 1b), which provides an ideal example for focusing exclusively on vibrational variation itself.

To efficiently excite the required highly localized plasmonic field for single-molecule TERS measurements, an incident light with a wavelength of 532 nm was employed in the experiments30. Under the same incident energy, our first-principles calculations accurately reproduce the corresponding observed Raman spectra of ZnPc powder30 except for few peaks with relative intensities below ≈5% of the strongest band (e.g., a peak around 800 cm−1, Fig. 1c). Theoretical analysis reveal that these peaks originate from Raman-inactive modes because of the symmetry breaking via molecular stacking and lattice interactions in ZnPc powder. This undesired symmetry breaking is absent for a single molecule. Thus, the experimentally adopted wavelength of 532 nm can be used without further calibration in the practical calculations for single-molecular TERS. Then, we adopt an effective field Hamiltonian approach (see “Methods” for details), in which the spatial amplitude distribution of the localized plasmonic field is incorporated as the quantized light-matter interaction operator33,41–44, to enable the quantitative simulation of bond-resolved TERS spectra. By placing a 3 Å spatially confined plasmon (SCP) at the same tip position in the experiments, i.e., above the joint position between the lobe and center of ZnPc (see the black cross in Fig. 1b), the calculated TERS spectra for both neutral ZnPc and anionic ZnPc− are in overall agreement with their experimental counterparts (Fig. 1d). Specifically, the two main bands in the calculated spectrum of ZnPc− are located at 1309 and 1512 cm−1, which are in good agreement with the experimental values of 1305 and 1518 cm−1. For neutral ZnPc, one main peak in the theoretical spectrum appears at 1348 cm−1, which is again in agreement with the experimentally measured band at 1340 cm−1. As a result, the calculated TERS spectrum of ZnPc− presents a 39 cm−1 redshift caused by JTE, which quantitatively agrees with the corresponding experimental observation of 35 cm−1.30 For another main band, although the frequency shifts are in qualitative agreement, the theoretically predicted blueshift (26 cm−1) is larger than that (7 cm−1) measured in the experiments30. This result arises from the sole frequency deviation of the peak for neutral ZnPc, i.e., the band around 1511 cm−1 observed in experiments, as shown in Fig. 1d. Further calculated and experimental Raman images (see “Methods” for details) for this band are in excellent agreement with each other (Supplementary Fig. 1), demonstrating the affirmative assignment of this main band. In addition, the JTE-induced shifts of other secondary bands in the calculated spectra also agree well with the experimentally observed redshifts (Supplementary Fig. 2). The reproduction of the measured references in both uniform and plasmonic fields validates the accurate descriptions of electronic and vibrational structures as well as their responses at the current theoretical level.

According to the calculations, the experimentally measured30 two dominant bands for ZnPc and ZnPc− (Fig. 1d) are assigned to different vibrational modes. Specifically, the degenerate ν108 and ν105 contribute to the dominant bands of ZnPc. In ZnPc−, these vibrations split as a consequence of JTE and are labeled with subscripts “a” and “b” hereafter. As a result, the dominant high-frequency band originates from the accidentally degenerate ν0103a and ν025, where the superscript “0” denotes the anionic form. Meanwhile, ν048 contributes to the dominant band with low frequency, with the shoulder assigned as ν0108b. Although this assignment is different from ref. 30, the observation of only a single splitting component, i.e., ν0108b in ZnPc−, indicates the spatial localization of degenerate vibrational modes during symmetry breaking induced by JTE.

Imaging the degenerate vibrational splitting
To directly visualize the localization, we turn to vibrationally resolved TERS imaging36–38,45,46. By moving tip positions and simultaneously collecting scattering intensities at a given Raman shift, the images of the two dominant bands of ZnPc under an experimentally feasible 3 Å SCP (Supplementary Figs. 3 and 4)37 were calculated as shown in Fig. 2a. Both images exhibit clear fourfold symmetrical patterns, which correspond to the Eu irreducible representation in D4h point group (see vibrational displacements in Fig. 2a). On the other hand, the dominant modes of ZnPc− give two-fold symmetric patterns (Fig. 2a), demonstrating the symmetry reduction from D4h to D2h owing to JTE. The individual contributions of component modes to images in Fig. 2a can be found in Supplementary Figs. 5–7. It should be stressed that, although bias voltages and a decoupled substrate were used to stabilized different charge states of ZnPc30, these effects on the vibrational modes and Raman images are negligible (Supplementary Figs. 8–10). This result is consistent with the general purpose of introducing the decouple layer in TERS experiments30 and should be attributed to the rigid backbone and flat adsorption configuration of ZnPc. For other systems with strong substrate-adsorbate interactions, adequately large cluster models with advanced charge localization calculations would be required for the accurate description of the substrate effects.

Detailed analysis reveal that at the central Zn position, the image of ν048 is constructive, which is opposite to the destructive feature in that of ν108. This result further confirms that the dominant bands observed in experiments30 originate from different vibrational modes. To determine the split modes of degenerate vibrations, for example, ν108 that involves vibrations at four interior nitrogen atoms, we focused a 3 Å SCP on the nitrogen atoms along different axes in ZnPc− (see the color-marked crosses in the inset of Fig. 2b). The calculated spectra manifest that when the SCP is located at one specific position, one split mode becomes active and another one is completely suppressed (Fig. 2b), which arises from the vibrational localization accompanying with the splitting of degenerate modes. These spectral outcomes of JTE under plasmonic fields are quite different from those under conventional uniform optical fields, where both split Raman bands can be simultaneously observed in the latter. As a result, the split modes (ν0108a and ν0108b) can be identified. Specifically, TERS images of these vibrations exhibit split patterns derived from the original ν108, with a destructive center, as anticipated (Fig. 2c).

With the correct assignment, the electronic and displacement redistribution effects can be unambiguously investigated for the splitting of degenerate vibrations when the molecule experiences a JTE distortion. Particularly, adding an extra electron to neutral D4h ZnPc would split the degenerate ν108 at 1348.0 cm−1 into a blue-shifted mode at 1352.5 cm−1 and a significantly red-shifted mode at 1319.6 cm−1. The Eu ν108 mode then becomes further localized, which results in two non-degenerate modes, i.e., a B2u mode (ν0108a) at 1345.6 cm−1 and a B3u mode (ν0108b) at 1323.5 cm−1 (Fig. 2c). The decomposition of electronic and vibrational effects is a general approach. The detailed analysis for other representative degenerate modes can be found in Supplementary Fig. 11. It should be stressed that the minor geometrical distortion caused by JTE in ZnPc enables the decomposition of these effects.

Imaging the non-degenerate vibrational mixing
The minor geometrical distortion also allows explicit visualization of another vibrational evolution, i.e., the mixing of non-degenerate vibrations in high-symmetry after experiencing JTE (Supplementary Table 1). For instance, the A2g-symmetric ν23 and B2g-symmetric ν65 in ZnPc would mix with each other, generating two B1g modes (ν023 and ν065) in ZnPc− (Fig. 3a). It should be stressed that the details of this mixing are inaccessible under the excitation of conventional uniform optical fields. As a result, this mixing feature in JTE is completely overlooked in previous studies. A detailed decomposition reveal that the electronic effect leads to redshifts of two modes, resulting in a frequency difference of 4.4 cm−1, as shown in Fig. 3a. It is noted that the displacements of ν23 and ν65 are all located on the lobes with an efficient overlap. Calculated induced dipole moments (Supplementary Figs. 12 and 13) determine that the mixing coefficient (see definition in Eq. (1)) between ν23 and ν65 is close to 1.0, which results in distinctly split patterns in ν023 and ν065 as shown in Fig. 3a.

The mixing coefficient could be analogously derived from the perturbational molecular orbital theory as (see a detailed derivation in Supplementary Note 7)

T = λS12 / ΔE

where λ is a fitting parameter, S12 is the overlap between two mixing vibrations, and ΔE is the energy difference. For well-overlapped modes, i.e., S12 close to 1, the mixing coefficient T is inversely proportional to the energy difference ΔE, which is exactly the case of mode mixing for ν23 and ν65. Most of the mixing modes are in this category (Supplementary Figs. 14–16). By collecting all these modes, the fitting parameter λ is determined to be 2.8 cm−1 (see the blue diamond scatters and red line in Fig. 3b and Supplementary Fig. 17).

The theoretical model also predicts another category with S12 = 0, where T becomes zero regardless of ΔE and λ. In fact, there are few modes belonging to this category. For instance, the electronic effect leads to ΔE of 24.3 cm−1 between the A1g-symmetric ν13 and B1g-symmetric ν53 modes. If they were well-overlapped modes, the predicted T would be 0.13. Nevertheless, with no mixing with each other, these two modes give two A1g-symmetric modes in ZnPc−, exhibiting nearly identical fourfold image characteristics to their respective counterparts in ZnPc (Fig. 3c). This result should be attributed to the lack of spatial overlap between ν13 and ν53 modes, which is the sufficient prerequisite of S12 = 0. We note that the frequencies of these two non-overlapping modes change after the JTE, which should be attributed to the symmetry-lowering distortion. Two additional cases fall into this category (see orange diamond scatters in Fig. 3b and Supplementary Fig. 18). We want to stress that the current protocol, i.e., using TERS images to monitor the splitting and determine mixing coefficients of molecular vibrations, can be readily extended to other charge-induced JTE systems (Supplementary Fig. 19) owing to the intrinsic characteristics of nonresonant Raman imaging that can visualize the molecular vibrational modes in real space.36–38

Identifying isotopically engineered JTE distortion
The last capability of TERS imaging proposed in the present work is the identification of the controllable distortion in JTE. To this end, partial isotope substitution is employed to control the direction of JTE distortion, which is experimentally synthesizable47,48 (Supplementary Note 9) and can be selected out via TERS imaging (Supplementary Fig. 20). Although the geometrical variation is as small as 0.010 and 0.026 Å (Fig. 1b), isotope substitutions of 13C and deuterium (D) in one diagonal axis can stabilize the ZnPc−’s elongation configuration along this axis, i.e., iso-1 (Fig. 4a). Calculated results reveal that at the experimental conditions of 7 K and 6 × 10−14 atm, iso-1 has a lower Gibbs free energy of 0.38 kJ mol−1 than the configuration elongated along the other direction (iso-2). The population of iso-1 is then determined to be 99.84% in the experimental conditions (Supplementary Note 10). Because of the almost identical geometries (Fig. 4a), iso-1 and iso-2 are indistinguishable in electronic structure-based SPM techniques even with functionalized tips49–51.

This challenge can be overcome by utilizing the sensitivity of TERS images to subtle variations in vibrational modes (Fig. 4b). Although the calculated TERS image of ν0i1 121a in iso-1 has the identical brightest lobe patterns to that of the counterpart in iso-2, two moderate patterns appear around the interior nitrogen atoms along the isotopic axis for ν0i2 121b in iso-2. Similarly, except for the identical brightest central patterns, moderate patterns arise around the non-isotopic lobes in ν0i1 116a image for iso-1. These results should be attributed to the subtle vibrational redistributions caused by the axial length difference at the sub-ångström level. The ability of TERS imaging to distinguishing such subtle vibrational variations requires highly localized SCP fields (Supplementary Fig. 21), providing an effective means for identifying different configurations arising from isotopic JTE distortion.

Methods
Effective field Hamiltonian for TERS
The polarizability of non-resonance Raman under a localized plasmon is evaluated as

ακρσ = ∂α / ∂Qκ |vi⟩ ⟨vf| ...

where ρ and σ represent the Cartesian coordinates, Qκ is vibration modes, |vi⟩ (|vf⟩) is the initial (final) vibrational states of the ground electronic state |Ψg⟩, and

α ρσ = 1/ω ...

with the absorption process operator under Raman scattering

Vbσ = 1/2 Σj (pbj,σgσ + gσpbj,σ) ...

where pbj = i∇j is the momentum operator of the jth electron, and gσ is the amplitude distribution function of localized plasmon in σ direction.

The incident light wavelength was set to 532 nm (2.33 eV), that employed in experiments30 to fulfill the non-resonance condition. The response algorithm was adopted to efficiently evaluate Eq. (3)43, and the central-finite-difference method with 1.0 × 10−3 amu1/2Bohr size was used to estimate the derivative in Eq. (2). For TERS, it is sufficient to evaluate the zz component of Raman polarizability41,52. In practical simulations, the amplitude distribution function gσ for a localized plasmon field was simulated by a s-type Gaussian function as

g = exp(−α(r−rD)2)

where α is exponent, and r represents the coordinate position of plasmon. Here, α can determine the full-width at half-maximum (FWHM), i.e., the size of the localized plasmon field with the relation of FWHM = 2√ln2/√α. Specifically, we set α to be 0.086 Bohr−2 for a 3 Å localized plasmon.

Finally, the intensity of Raman scattering can be calculated by

I = ω4/c4 |MsMd|2 |Fp|2 |ακzz|2

with scattering light frequency of ω, directional radiation factor Md owing to the corresponding nanostructures for the enhancement in the detection direction53, localized plasmon field enhancement factor M, Purcell factor Fp54 that accounts for the spontaneous emission enhancement, and the light speed c. In addition, using Eq. (2), the induced dipole could be calculated by

μ0,k = M Fp αk,0 E0

where E0 is the electric field amplitude of the incident light and the elements of tensor αk,0 are given by Eq. (2). The parameter of μ can represent the signs (positive/negative) of Raman polarizability, that associated with vibration phase55. The Raman polarizability and intensity under localized plasmon field were practically calculated by the FASTERS program56. In addition, all the Raman spectra in the main text were convoluted by a Lorentzian function with FWHM of 10 cm−1.

Computational details
First-principles calculations were based on density functional theory methods, implemented in the GAUSSIAN16 software package, A03 version57. We considered the physisorption of the molecule. In other words, we neglect the substrate, tip, and bias voltage, as shown in TERS setup (Fig. 1a) and the negligible charge transfer from tip. The geometrical structure, electronic structures, and vibrational modes of both neutral ZnPc and anionic ZnPc− molecules were calculated in the gas phase at the B3LYP level58 with the 6-311+G(d,p) basis set59,60, excluding any unphysical convergence of the electronic structures, in particular for anionic states. The effect of anharmonicity on vibrations can be neglected under the cryogenic temperature of 7 K in the TERS experiments (Supplementary Fig. 22)30 because of the rigid structure of ZnPc. In addition, we obtained the electronic effect on the vibrational frequency by computing the neutral-geometry using the vibrational normal modes of the neutral molecule as basis vectors.

Experimental details
All experiment data acquisition were performed in a custom low-temperature and ultrahigh-vacuum scanning tunneling microscopy (STM) (Unisoku 1400) combined with optical detection systems at about 6 K under a base pressure of about 5 × 10−11 Torr. The Ag(100) step substrate was cleaned by several cycles of argon ion sputtering and annealing. Electrochemically etched sliver Ag tips were cleaned by electron-bombardment and argon-ion sputtering. Then, by controlling the tip indentation, an atomistic protrusion was formed as the TERS active tip. The ZnPc molecules were thermally evaporated onto the Ag(100) substrate covered by 3ML-NaCl at 6 K. The supplementary TERS mapping was performed under the following laser conditions: an excitation wavelength of 532 nm and a power of 0.2 mW entering the STM chamber through the glass window. The acquisition parameters were set at V = −1 V and I = 2 pA, with the tip precisely positioned above on the joint position between the molecular lobe and Zn ion. Subsequently, the feedback loop turned off to maintain a constant tip-sample distance. Mapping data were then acquired under these conditions. Each spectrum was acquired for 1 s, resulting in a 60 × 60 pixel image with a total size of 3 nm × 3 nm.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Yu, et. al presents a theoretical framework for visualizing the effects related to Jahn-Teller effects in tip-enhanced Raman spectroscopy experiments. The authors study how the vibrational modes would change upon charging a molecule. Interestingly, they also observe a spatial localization of the vibrational modes within the molecule, together with vibrational mixing. Lastly, the authors study the effect of isotopes on the vibrational features.\nThis work is timely, as many groups are pursuing Raman maps of single molecules. Moreover, there is a lot more theory/computational support needed in understanding the experimental results. Given the topic and the nature of the manuscript, I would be glad to recommend this manuscript for Nat. Comms. provided the authors satisfactorily respond to the points below.\nIn my opinion, there are two voids in this manuscript:\nFirst, the authors do not mention/nor estimate the role of the bias voltages in the Raman maps. While it is true that both neutral and anionic ZnPc can be stable on NaCl (or any other large band gap insulator), for their imaging different voltages need to be applied. Otherwise, the molecule would simply change its charge state. I understand that in some cases there will be a short voltage window at which both could charge states could co-exist, but this will be the minority of the cases.\nSecond, the authors discuss the spatial localization and splitting of vibrational modes – which I find commendable and very interesting. Yet, the experiments will take place on a surface. Would such effects still be present in asymmetric adsorption positions? How much change would it incur in the vibrational modes? As far as I understand from the ‘Methods’ section, the calculations are done on the gas-phase molecules. Why not take the geometries of the adsorbed molecules?\nHere are additional points:\n1) In the abstract I would reinforce to the reader about the theoretical nature of this work.\n2) Authors claim that the Raman spectra of ZnPc powder is accurately reproduced. Yet, some peaks are not present (around 800 cm-1), while some additional peaks appear (1250 cm-1). It is important to note as to why such discrepancy comes from.\n3) Continuing on the text progression: it is unclear as to why the authors compare spectra for ZnPc powder and then proceed to discuss the results of single molecules. I think the flow of the text would be better if this was explicitly linked and motivated in written form.\n4) It is unclear as to why the plasmon central position (black cross in Fig 1) is chosen in that particular location. The authors should clarified this in the manuscript.\n5) Fig 1c can be difficult to interpreted. I recommend that the authors include colors in the center positions to facilitate comparison.\n6) The overlooked vibrational mixing is quite a nice finding. But I think the authors could improve Fig 3, specifically by increasing the size of the arrows in panels a and c. I also do not think it is necessary to show the plot in b from 280 to 300 cm-1, instead more space can be used for panels a and c.", "reviewer_2": "The Jahn-Teller effect (JTE) is a fundamental principle in physics and chemistry, describing how geometric distortion in non-linear molecules lifts electronic degeneracy, thereby playing a crucial role in the properties of molecules and condensed matter systems. This manuscript by Yu et al. presents a theoretical study proposing the use of vibrationally resolved tip-enhanced Raman scattering (TERS) imaging to visualize the vibrational features in a single zinc phthalocyanine (ZnPc) molecule undergoing a charge-induced JTE. The authors report that this approach can image the splitting of degenerate vibrational modes, characterize a previously overlooked mixing of non-degenerate vibrations, and identify JTE distortion configurations engineered by partial isotopic substitution.\nHowever, I cannot recommend this work for publication in Nature Communications in its present form because of the lack of significant conceptual novelty and the discrepancies with existing experimental data. These issues, detailed below, need to be thoroughly addressed.\n1) While the proposed application is interesting, the work largely represents an incremental application of an established technique (TERS imaging) to a well-understood phenomenon (JTE). The fact that JTE induces structural distortions and symmetry changes in molecules is a cornerstone of the field, extensively studied by various experimental and theoretical methods. This manuscript proposes a real-space visualization, but the predicted outcomes (e.g., a change from four-fold to two-fold symmetry) are largely intuitive consequences of the effect. The study does not appear to provide a fundamental advance that challenges or significantly expands the conventional understanding of the JTE.\n2) The manuscript's central arguments are built upon the accurate assignment of vibrational modes, but the theoretical results show evident deviations from the cited experimental data (Ref. 16). For instance, in Figure 1c, the calculated frequency for the mode near 1486 cm−1 in neutral and charged ZnPc molecules does not align well with the experimentally measured peaks. More critically, the experimentally observed blueshift for this mode upon charging the molecule is much smaller than the shift predicted by the authors' calculations (Fig. 1c). This discrepancy casts considerable doubt on the reliability of the theoretical model. More robust analysis for the peak assignments is required.\n3) The ability to resolve the image differences in the TERS images shown in Figure 4 is highly dependent on the spatial confinement of the plasmonic field. The authors should discuss the influence of the plasmonic field's confinement on the identification of the JTE. Specifically, what level of spatial resolution is necessary to distinguish the subtle vibrational changes predicted in the manuscript?\n4) The study does not address the synthetic feasibility of the proposed isotopically substituted molecule. Proposing a theoretical case is useful only if it is experimentally realizable. The authors should consider to propose plans that are more readily verifiable in experiments to strengthen the link between their theory and practical application.\n5) Minor point: The section title \"Controlling JTE distortion by partial isotope substitution\" seems misleading. The section does not propose a method to control the distortion but rather to identify a pre-determined distortion in a chemically synthesized molecule. The section title should be changed.", "reviewer_3": "This paper introduces a TERS imaging protocol that visualizes how individual vibrational modes evolve as a single ZnPc molecule undergoes charge-induced Jahn-Teller distortion. The authors accurately reproduce normal Raman and previously reported TESR spectra for both neutral and anionic ZnPc, validating their plasmon-embedded field Hamiltonian approach. Although the JTE arises from vibronic coupling, previous works have mostly imaged symmetry-broken electronic orbitals; examining only the electronic component of the JTE thus limits these studies to partial observation. Direct imaging of the vibrational component is therefore crucial for enhancing the predictive accuracy of structure-property models, and the authors’ attempt to resolve and independently image the vibrational modes is both timely and valuable. However, the following points require further explanation.\n1. All Raman images in this paper are theoretical. The experimental data is only the 1D Raman spectrum, while the Raman images are entirely simulations created by virtually scanning the plasmon local field and calculating the polarizability and enhancement factor for each mode. Even at very low resolution, experimental data is needed to validate the theoretical Raman imaging.\n2. The calculation model assumes a 3Å Gaussian plasmon and fixed orientation. Sensitivity to apex shape, gap size and charge-transfer strength should be quantified to solve tip-apex dependence.\n3. When discussing symmetry splittings such as those arising from JTE, the relative frequency shifts are paramount, and temperature-induced offsets largely cancel out. Nonetheless, vibrational modes obtained under the idealized assumptions of 0 K and the harmonic approximation can diverge from those observed in real experimental environments. The manuscript should therefore include further clarification on how temperature and anharmonicity corrections were applied.\n4. The protocol is demonstrated for only one molecule (ZnPc). Establishing its universality would ideally involve applying the workflow to at least one additional system. Given that suh simulations may be computationally demanding, the authors could instead strengthen the manuscript by adding a discussion of how the approach could be extended to other molecular system and what challenges might be encountered.", "reviewer_4": "In this manuscript, the authors propose to use imaging based on tip-enhanced Raman scattering as a means of accessing vibrational states in molecules that undergo Kahn-Teller distortions. For that, they build computational methods to obtain effective Hamiltonian models for Raman polarizability and scattering cross sections taking into account vibrational states defined according to relevant irreducible representations for the pertinent point group symmetries. In the model, they use localized plasmon fields represented by Gaussian functions. Additional first-principles calculations based on DFT to obtain electronic structures and vibrational modes of the the ZnPc molecule. The outcomes of the computational modeling are compared with experimental data supported from external references.\nThrough theoretical insights, the authors propose that imaging with Raman techniques allows to identify specific vibrational modes and their spatial distribution, which becomes all-important when aiming at gathering information when molecules are subject to Jahn-Teller distortions. In particular, the authors can describe through their model the observed frequency shifts when the charge state of molecules is changed by electrical biases, inducing Jahn-Teller effects after the charge injection. They explore how the modes change upon symmetry lowering and explain why some of the modes resulting from the JT-induced splitting are observed in experiments and why others are not. Additionally, they propose that TERS experiments can be aimed at exploring mixing of vibrational modes that is forbidden for high-symmetry settings, but can become mixed when symmetry is lowered by JT effects. Lastly, they also show how TERS imaging could be used to probe changes in vibrational modes caused by isotopic substitutions.\nThe work is relevant because most of works have focused on the effects of JT on the electronic component, rather than the vibrational ones resulting from JT vibronic couplings. I believe that this is an interesting perspective for experimentalists to explore what Raman-based imaging can gather about vibronic states in molecules. Therefore, I judge this is work is relevant to the field.\nI have some comments:\nWhen referring to Ref. 16, the authors assume an interpretation of the spectral variations in ZnPc as charges are injected as arising from JT effects. However, if I am not wrong, the authors do not interpret directly such variations as resulting from JT effects. The sentence as it is written, presumes that the authors of that paper assume JT effects as the reason of the observed changes in spectra.\nIn Fig. 1 c, the blue shift of the resonance at 1486 cm-1 between neutral ZnPc and ZnPc- is very subtle. I recommend to make the shift more evident in the figure (e.g., adding a vertical dashed line).\nFor a more accessible reading, I recommend to add a schematic illustration in the main text of all the irreps and corresponding point-group symmetries (before and after JT) for the relevant modes in the spectral range covered by Fig. 1. When reading the paper, it was difficult to me to finally grasp the irreps of the modes discussed in that figure."}, "author_response": "Point-by-point response to the Referee #1’s comments:\nGeneral Comment: The manuscript by Yu, et. al presents a theoretical framework for\nvisualizing the effects related to Jahn-Teller effects in tip-enhanced Raman\nspectroscopy experiments. The authors study how the vibrational modes would change\nupon charging a molecule. Interestingly, they also observe a spatial localization of the\nvibrational modes within the molecule, together with vibrational mixing. Lastly, the\nauthors study the effect of isotopes on the vibrational features.\nThis work is timely, as many groups are pursuing Raman maps of single molecules.\nMoreover, there is a lot more theory/computational support needed in understanding\nthe experimental results. Given the topic and the nature of the manuscript, I would be\nglad to recommend this manuscript for Nat. Comms. provided the authors satisfactorily\nrespond to the points below.\nReply: We thank the Referee for the good summary and positive recommendation of\nour work. We have carefully addressed all the Referee’s specific comments and\nsuggestions, which significantly strengthen the conclusions of the present work. A\npoint-by-point response is provided below.\nIn my opinion, there are two voids in this manuscript:\nQ1: First, the authors do not mention/nor estimate the role of the bias voltages in the\nRaman maps. While it is true that both neutral and anionic ZnPc can be stable on NaCl\n(or any other large band gap insulator), for their imaging different voltages need to be\napplied. Otherwise, the molecule would simply change its charge state. I understand\nthat in some cases there will be a short voltage window at which both could charge\nstates could co-exist, but this will be the minority of the cases.\nR1: The Referee is right that, in rare cases, a short bias window that allows the\ncoexistence of two charge states may exist, which is convenient for theoretical\nsimulations. Nevertheless, as pointed out by the Referee, this is not the case for the\ncurrent study. Following the Referee’s suggestion, the effects of different voltages,\nwhich are required to stabilize different charge states of ZnPc, on Raman images have\nbeen evaluated in the current version.\nAccording to the experiment setup in Ref. 30, neutral and anionic ZnPc can be\nstabilized under the sample bias voltages of 0.1 and 0.5 V, respectively. In these\nscenarios, different electric fields will be applied to the adsorbate and thus could\ninfluence its vibrations. To test this effect, we recalculated Raman images for the two\nmain peak modes in Fig. 1c at these two bias voltages by assuming a gap size of 0.7\nnm, where the electron transfer between the tip and the adsorbate is negligible. As\nshown in Fig. R1, Raman images under the corresponding bias (bottom panels) are\nalmost identical to their bias-free counterparts (top panels) for both neutral and anionic\nZnPc. This result should be attributed to the rigid backbone and flat adsorption\nconfiguration of ZnPc. Thus, we can safely neglect the effect of the bias voltages on\nRaman images in the present work, as anticipated by the Referee.\nFig. R1 (Supplementary Fig. 9) Simulated Raman images of the main peaks in Fig.\n1c under the bias voltages (bottom panels) of 0.1 V (ZnPc, left) and 0.5 V (ZnPc−, right)\nas well as their bias-free counterparts (top panels).\nWe have added the computational details for practical Raman images simulations under\ndifferent bias voltages on page S5 (see “In addition, according to … can be safely\nneglected.”) in the revised Supplementary Information. The above discussions have\nalso been added on page 7 (see “Notably, although bias … configuration of ZnPc.”) in\nthe revised manuscript. Figure R1 has been added as Supplementary Fig. 9 in the\nrevised Supplementary Information.\nQ2: Second, the authors discuss the spatial localization and splitting of vibrational\nmodes – which I find commendable and very interesting. Yet, the experiments will take\nplace on a surface. Would such effects still be present in asymmetric adsorption\npositions? How much change would it incur in the vibrational modes? As far as I\nunderstand from the ‘Methods’ section, the calculations are done on the gas-phase\nmolecules. Why not take the geometries of the adsorbed molecules?\nR2: We thank the Referee for this instructive suggestion regarding the evaluation of the\neffects of the realistic substrate in experiments on Raman images. To this end, we first\noptimized the geometry of ZnPc adsorbed on a three-monolayer (3ML)-NaCl/Ag(100)\nsurface, which mimics the experimental conditions of TERS measurements in Ref. 30.\nHere, the alignment of ZnPc on the substrate is adopted from previous scanning\ntunnelling microscope measurements of the same system (see Fig. R2a below and Fig.\n1b in the newly added Ref. S9 in the revised Supplementary Information). Both\nexperimental and theoretical results demonstrate a symmetrical adsorption of ZnPc on\nthe substrate. As a result, the effects of asymmetric adsorption position, as worried by\nthe Referee, are absent in the current study. Furthermore, calculated results reveal that\nthe root mean square deviation (RMSD) between geometries of adsorbed and free ZnPc\nis as small as 0.057 Å (Fig. R2b), indicating that the adsorbed configuration is nearly\nidentical to that in the gas phase.\nFig. R2 (Supplementary Fig. 7) a Optimized adsorption configuration of ZnPc on a\n3ML-NaCl/Ag(100) substrate. b Calculated RMSD between free ZnPc (magenta) and\nadsorbed ZnPc (green).\nSubsequently, the substrate effects on the splitting of vibrational modes were evaluated.\nHere, we take the main peaks, i.e., degenerate E modes of v and v in Fig. 1c, as\nu 108 105\nthe representative modes. Calculated results show that the splitting of these E modes\nu\ncaused by the substrate is as small as ~0.3 cm-1 (left and middle bottom panels in Fig.\nR3), which retains their degeneracy compared with the tens of wavenumber differences\ncaused by the JTE splitting. This result can be attributed to the negligible effects of the\nsubstrate on the structure, as discussed above. Admittedly, the calculated vibrational\nmodes for the degenerate E modes of adsorbed and free ZnPc display superficial\nu\ndifferences as shown in Fig. R3. These variations can be reasonably attributed to the\ndifferent diagonalization algorithms employed in the codes used for practical\ncalculations of adsorbed (VASP) and free (Gaussian) ZnPc. Thus, owing to the essential\ndegenerate nature of v and v , calculated Raman images of these modes of the\n108 105\nadsorbed ZnPc are identical with the counterparts in the gas phase, as shown in Fig. R3\n(left and middle panels), because any linear combination of degenerate vibrational\nmodes is still the eigenvector of them.\nWe further evaluate the substrate effects on vibrational modes and Raman images of\nnon-degenerate modes, where the artificial interference from linear combinations is\nabsent. Here, we take an A mode as a representative. It is clearly shown that both the\n1g\nvibrational mode and the corresponding Raman image of adsorbed ZnPc are almost\nidentical to those of free ZnPc (right panel in Fig. R3). Therefore, the substrate effects\non either the vibrational modes or the Raman images of the neutral ZnPc can be safely\nneglected.\nFig. R3 (Supplementary Fig. 8) Simulated vibrational modes and Raman images of\nthe two degenerate E -bands (left and middle, corresponding to the most intensive\nu\nbands of the Raman spectrum in Fig. 1c) and a representative non-degenerate A band\n1g\n(right) for free (top) and adsorbed ZnPc (bottom), respectively.\nThe Referee is right that we deliberately performed calculations on the gas-phase\nmolecules. One reason is that the substrate has negligible effects on the Raman images\nof the neutral ZnPc, as demonstrated above. Another reason is that sophisticated\nmethods for charged systems are still unavailable under periodic boundary conditions\n(PBC), where the artificial neutralization countercharge must be added due to the long-\nrange nature of electrostatic interactions. As a result, we cannot guarantee the accuracy\nof the geometry of anionic ZnPc⁻ adsorbed on the infinity slab substrate in PBC. To\ncircumvent this, we assume that the substrate effects on the geometry can again be\nneglected as those on the neutral ZnPc. The calculated Raman spectrum of ZnPc⁻ in the\ngas phase nicely reproduces the TERS measurements in Ref. 30, as shown in Fig. 1c,\nwhich affirmatively validates this hypothesis. Therefore, the spatial localization and\nsplitting of vibrational modes of ZnPc⁻ caused by JTE can be confidently simulated in\nthe gas phase.\nIn summary, we demonstrate that the substrate only has negligible effects on the\ngeometries, vibrational modes, and Raman images for both neutral and anionic ZnPc.\nThus, practical calculations on the gas-phase molecules are indeed adequate in the\npresent work for explorations of charge-induced JTE effects for ZnPc adsorbed on the\n3ML-NaCl/Ag(100) substrate, which is also consistent with the general purpose of\nintroducing the NaCl decouple layer in TERS experiments.\nWe have added the above discussions on page 7 (see “Notably, although bias …\nconfiguration of ZnPc.”), on page 14 (see “In other words … charge transfer from tip.”)\nin the revised manuscript, and on page S4 (see “In the proposed setup of TERS …\nconfidently simulated in the gas phase.”) in the revised Supplementary Information.\nFigures R2 and R3 have been added as Supplementary Fig. 7 and Fig. 8, respectively,\nin the revised Supplementary Information.\nHere are additional points:\nQ3: In the abstract I would reinforce to the reader about the theoretical nature of this\nwork.\nR3: We thank the Referee for the suggestion about reinforcing the theoretical nature in\nthe abstract. During the revision process, we have included experimental images to\nvalidate the theoretical results for responding to other Referees’ comments.\nNevertheless, the theoretical leading nature of this work maintains. Therefore, in the\nrevised manuscript, we have emphasized the “theory-driven” nature in the abstract (see\n“Herein, we theoretically propose”) following the Referee’s suggestion, which benefits\nthe better understanding of readers for the current work.\nQ4: Authors claim that the Raman spectra of ZnPc powder is accurately reproduced.\nYet, some peaks are not present (around 800 cm-1), while some additional peaks appear\n(1250 cm-1). It is important to note as to why such discrepancy comes from.\nR4: We thank the Referee for this meticulous observation. We have labeled these two\npeaks by colors for clarity in Fig. R4. The peak around 800 cm-1 corresponds to a C−H\nout-of-plane bending mode of the A -irreducible representation, which is Raman\n2u\ninactive. Thus, the presence of Raman-inactive modes in the experimental spectrum can\nbe attributed to the symmetry breaking by molecular stacking and lattice interactions in\nZnPc powders. In TERS experiments, a single molecule is investigated. By definition,\nthis symmetry-breaking effect becomes absent.\nFig. R4 (updated Fig. 1b in the revised manuscript) The two peaks raised by the\nReferee have been marked by colors. The experimental spectrum of ZnPc powder has\nbeen updated with a better digitized sampling from Ref. 30.\nRegarding the peak around 1250 cm-1, we would like to clarify that it does not\ncorrespond to an additional mode. Its absence in the experimental Raman spectrum was\ndue to the insufficient sampling when extracting data from Ref. 30. We have updated\nthe experimental powder spectra with a better digitized sampling. Now, the shoulder\npeak around 1250 cm-1 appears in the experimental spectrum, which is consistent with\nthe theoretical calculations.\nWe have added the above discussions on page 5 (see “except for few peaks … absent\nfor a single molecule.”) and updated the experimental Raman spectrum of ZnPc powder\nin Fig. 1b in the revised manuscript.\nQ5: Continuing on the text progression: it is unclear as to why the authors compare\nspectra for ZnPc powder and then proceed to discuss the results of single molecules. I\nthink the flow of the text would be better if this was explicitly linked and motivated in\nwritten form.\nR5: We thank the Referee for this helpful suggestion. To achieve high-resolution\nRaman images, the prerequisite is the effective excitation of the plasmon between the\ntip and the substrate by selecting a specific wavelength of the incident laser. In\nexperiments, a laser with a wavelength of 532 nm was adapted (see Ref. 30 for details).\nUsually, this wavelength needs to be calibrated in linear response simulations owing to\nthe systematic error of the used density functional theory. The purpose of comparing\nthe experimental spectrum of ZnPc powder and theoretical predictions is indeed to\ncalibrate the wavelength used in the practical calculations for single molecules.\nFortunately, using experimentally adopted 532 nm, we can quantitatively reproduce the\nRaman spectra of the ZnPc powder, which highlights the accuracy of the theoretical\nlevel used in the present work. As a result, we used the same wavelength as that used\nin TERS experiments for subsequent response simulations of single molecules.\nWe have clarified this motivation on page 5 (see “Thus, the experimentally …\ncalculations for single-molecular TERS.”) in the revised manuscript, which enhances\nthe flow of connection from powder to single molecules, as anticipated by the Referee.\nQ6: It is unclear as to why the plasmon central position (black cross in Fig 1) is chosen\nin that particular location. The authors should clarified this in the manuscript.\nR6: We thank the Referee for this important clarification. In Fig. 1c, we aim to align\nwith the experimental TERS spectra. According to Ref. 30, the tip position for TERS\nmeasurement is placed between the lobe and the center. Thus, we choose the plasmon\ncentral position in our simulations to correspond to the tip position adapted in the\nexperiment.\nWe have added this clarification on page 5 (see “spatially confined plasmon … the lobe\nand center”) in the revised manuscript.\nQ7: Fig 1c can be difficult to interpreted. I recommend that the authors include colors\nin the center positions to facilitate comparison.\nR7: We thank the Referee for this instructive suggestion. Now, the center positions of\neach main peak in the calculated spectra have been filled with the same colors as the\ncorresponding spectra, which makes the comparison more facilitative (Fig. R5).\nBesides, to improve the clarity and readability of Fig. 1c, and to respond to other\nReferees’ comments, we have labeled the irreducible representations in Fig. 1c and\nadded two dashed lines to guide the peak shifts, as shown in Fig. R5.\nFig. R5 The revised Fig. 1c that includes colors in the center positions as well as labeled\nirreducible representations and guidelines to facilitate comparison in the revised\nmanuscript.\nQ8: The overlooked vibrational mixing is quite a nice finding. But I think the authors\ncould improve Fig 3, specifically by increasing the size of the arrows in panels a and\nc. I also do not think it is necessary to show the plot in b from 280 to 300 cm-1, instead\nmore space can be used for panels a and c.\nR8: We thank the Referee for this suggestion regarding the improvement of Fig. 3.\nAccordingly, we have revised Fig. 3 by enlarging the arrows in panels a and c, removing\nthe data for 280–300 cm-1 range in Fig. 3b, and reorganizing the figure layout (see Fig.\nR6 for detailed revisions). To ensure completeness, we have moved the original Fig. 3b\nthat includes the 280–300 cm-1 range as Supplementary Fig. 16 in the revised\nSupplementary Information.\nFig. R6 The revised Fig. 3 that enlarges the arrows in panels a and c, removes the data\nfor 280–300 cm-1 range panel b, and optimizes the layout in the revised manuscript.\nPoint-by-point response to the Referee #2’s comments:\nGeneral Comment: The Jahn-Teller effect (JTE) is a fundamental principle in physics\nand chemistry, describing how geometric distortion in non-linear molecules lifts\nelectronic degeneracy, thereby playing a crucial role in the properties of molecules and\ncondensed matter systems. This manuscript by Yu et al. presents a theoretical study\nproposing the use of vibrationally resolved tip-enhanced Raman scattering (TERS)\nimaging to visualize the vibrational features in a single zinc phthalocyanine (ZnPc)\nmolecule undergoing a charge-induced JTE. The authors report that this approach can\nimage the splitting of degenerate vibrational modes, characterize a previously\noverlooked mixing of non-degenerate vibrations, and identify JTE distortion\nconfigurations engineered by partial isotopic substitution.\nHowever, I cannot recommend this work for publication in Nature Communications in\nits present form because of the lack of significant conceptual novelty and the\ndiscrepancies with existing experimental data. These issues, detailed below, need to be\nthoroughly addressed.\nReply: We thank the Referee for giving us an opportunity to highlight the novelty and\nclarify the differences between theoretical and experimental results. As noted by the\nReferee, the Jahn-Teller effect (JTE) utilizes vibronic coupling to lift electronic\ndegeneracy of non-linear molecules. By definition, the vibrational aspect is equally\nimportant as the electronic component in JTE. Nevertheless, owing to the lack of\nappropriate tools, only the electronic component of JTE is extensively investigated in\nthe literature. In this work, we propose that by leveraging spatially confined plasmons,\nhigh-resolution TERS imaging is an ideal means to visualize the vibrational evolution\nwhen a molecule undergoes JTE. In this scenario, the spectral outcomes are totally\ndifferent from those excited by uniform fields (see following R1 for details). In other\nwords, we provide a novel approach for high-resolution probing of the vibrational\naspect in JTE, which comprehensively deepens its fundamental understanding.\nAfter careful and comprehensive comparison, we find that, as pointed out by the\nReferee, there is indeed a difference for one peak between the theoretically predicted\nspectra and the experimental measurements. Otherwise, the calculated spectra are in\noverall agreement with the experimental data. To achieve a definitive assignment of the\nonly questionable peak, we seek assistance from our experimental collaborators. The\nnewly updated experimental Raman imaging of this peak shows excellent agreement\nwith the theoretical prediction, confirming the consistency between our calculations\nand the experimental data (see following R2 for details).\nOverall, with the help of the Referee, we have highlighted the conceptual novelty and\neliminated the potential discrepancy with the experimental data. These improvements\nhave significantly enhanced the robustness and reliability of the present work. We hope\nthat the current revision meets the publication criteria of Nature Communications.\nFollowing is a point-by-point response to the Referee’s detailed comments.\nQ1: While the proposed application is interesting, the work largely represents an\nincremental application of an established technique (TERS imaging) to a well-\nunderstood phenomenon (JTE). The fact that JTE induces structural distortions and\nsymmetry changes in molecules is a cornerstone of the field, extensively studied by\nvarious experimental and theoretical methods. This manuscript proposes a real-space\nvisualization, but the predicted outcomes (e.g., a change from four-fold to two-fold\nsymmetry) are largely intuitive consequences of the effect. The study does not appear\nto provide a fundamental advance that challenges or significantly expands the\nconventional understanding of the JTE.\nR1: We thank the Referee for allowing us to highlight the novelty of our work in a\nrevision. We agree with the Referee that in the present work, an advanced vibrationally\nresolved technique, i.e., high-resolution TERS imaging, is used to investigate the JTE\nthat involves vibronic coupling. While the electronic structure changes associated with\nJTE distortion have been extensively studied both theoretically and experimentally, the\nequally important vibrational aspect has not yet been investigated with high spatial\nresolution. To this end, high-resolution TERS imaging is a candidate, in which the\nspatially confined plasmon (SCP) is a prerequisite. In this context, the spectral\noutcomes of JTE are quite different from those under uniform optical fields. As pointed\nout by the Referee, the latter, in particular, the frequency splitting of the degenerate\nvibrations, is well known. Specially:\n1) As a consequence of structural distortions induced by JTE, a degenerate mode (E\nu\nmodes in the present work) should split into two modes. Intuitively, we can expect that\none corresponding Raman band splits into two Raman bands. This is true under uniform\noptical fields. Nevertheless, accompanied by the splitting, a localization of the\ncorresponding vibrational mode occurs. Because SCP can only shine on a part of the\nmolecule, in this context, the spectral outcome of JTE only results in one band when\nthe SCP is located at one specific position (see Fig. 2b in the main text for details). On\nthe other hand, the localization of the split modes can be visualized by TERS imaging\n(see Fig. 2c in the main text for details), which is inaccessible under the conventional\nuniform optical fields. In other words, our work expands the understanding even for the\nwell-studied frequency splitting in JTE.\n2) Fundamental group theory tells us that symmetry reduction can cause different\nirreducible representations under high symmetry to become the same irreducible\nrepresentation under low symmetry, i.e., vibrational modes mixing after JTE-induced\ndistortions. However, group theory only tells us that the mixing exists, but not how it\noccurs in detail. Again, conventional uniform optical fields cannot investigate the\ndetails of this mixing. As a result, this feature in JTE is overlooked in previous studies.\nIn the present work, we reveal that TERS imaging is a perfect means for studying the\nmode mixing in JTE. Not only modes’ evolution but also mixing coefficients can be\nprecisely determined by TERS imaging, providing a fundamental understanding of the\nJTE.\n3) Typically, the distortions induced by JTE are unbiased. Although partial isotopic\nsubstitution could, in principle, modulate JTE distortions, precisely distinguishing these\nstructural variations is a challenge. In the present work, we demonstrate that because of\nits sensitivity to subtle variations in vibrational modes, TERS imaging can effectively\nidentify isomers with different isotopic substitutions. This finding paves the way for\nfurther applications of the vibrational aspect in JTE.\nOverall, this work focuses on the visualization of the vibrational aspect in JTE, a highly\nimportant yet difficult-to-investigate subject due to the lack of appropriate tools. We\ndemonstrate that high-resolution TERS imaging is an emerging tool for this purpose,\nwhere the spectral outcomes are totally different from those under uniform fields. The\nfindings in the present work not only provide a deep and fundamental understanding of\nthe JTE effect but also pave the way for its further practical applications. Therefore, we\nbelieve that our work represents a substantial advance rather than an incremental\ncontribution to JTE.\nWe have added the above discussions on page 7 (see “when the SCP is located …\nobserved in the latter.”), on page 8 (see “It should be stressed … overlooked in previous\nstudies.”), and on page 11 (see “this challenge can … variations in vibrational modes”)\nin the revised manuscript.\nQ2: The manuscript's central arguments are built upon the accurate assignment of\nvibrational modes, but the theoretical results show evident deviations from the cited\nexperimental data (Ref. 16). For instance, in Figure 1c, the calculated frequency for\nthe mode near 1486 cm-1 in neutral and charged ZnPc molecules does not align well\nwith the experimentally measured peaks. More critically, the experimentally observed\nblueshift for this mode upon charging the molecule is much smaller than the shift\npredicted by the authors' calculations (Fig. 1c). This discrepancy casts considerable\ndoubt on the reliability of the theoretical model. More robust analysis for the peak\nassignments is required.\nR2: We totally agree with the Referee that the accurate assignment of vibrational modes,\nin particular the frequency shifts, is essential in the present work. The Referee is right\nthat in Fig. 1c, we compared the calculated TERS spectra of different charge states\n(neutral and anionic) with the experimentally measured counterparts. Notably, the\nexperimental spectra were measured at the same tip position. Thus, we must reproduce\nthem with the same conditions, i.e., simulating spectra of both neutral and anionic ZnPc\nat the same SCP center position. Admittedly, this is an extreme challenge.\nWe want to stress that the theoretical spectra are in overall agreement with the\nexperimental results. Specifically, the two main peaks in the calculated spectrum of\nanionic ZnPc− are located at 1309 and 1512 cm-1, which are in good agreement with\nexperimental values of 1305 and 1518 cm-1. Furthermore, in the theoretical spectrum\nof neutral ZnPc, one of the main peaks appears at 1348 cm-1, which is again in\nagreement with the experimentally measured band at 1340 cm-1. As a result, the\ntheoretically predicted redshift (39 cm-1) for this band caused by JTE quantitatively\nagrees with the experimental observation (35 cm-1). The only deviation arises from\nanother main peak of neutral ZnPc, whose experimentally measured frequency is\naround 1511 cm-1. In the calculated spectrum, this band appears around 1486 cm-1. For\nthis band, although the frequency shifts are in qualitative agreement, the theoretically\npredicted blueshift (26 cm-1) is larger than that (7 cm-1) measured in experiments, as\npointed out by the Referee. Because the majority of the peaks in the theoretical\ncalculations and experimental measurements are in excellent agreement, it is reasonable\nto believe that the only difference arises from the imperfections of the theoretical model\nand the inherent accuracy of the computational level itself.\nFig. R7 (Supplementary Fig. 1) Experimental (1511 cm-1, left) and calculated (1486\ncm-1, right) Raman images of the main peak in the neutral ZnPc TERS spectra in Fig.\n1c. The confinement of the plasmonic field was set to 10 Å in simulations to satisfy the\nexperimental resolution. Both experimental and theoretical image sizes are 3 nm×3 nm.\nTo provide an affirmative assignment of the experimental main peak at 1511 cm-1 as\nthe theoretically predicted v mode, we seek the help of the authors of Ref. 30 to\n105\nmeasure the TERS image of this peak. They kindly conducted measurements for us.\nThe experimental Raman image (Fig. R7, left panel) displays a dark center and four\nbright patterns localized around the lobes of the ZnPc, which is in good agreement with\nthe calculated Raman image of v . Therefore, the mode assignment of the 1511 cm-1\n105\npeak is validated by experiments, which demonstrates that our assignment of the TERS\npeaks for ZnPc in different charge states is robust, as required by the Referee.\nFig. R8 (Supplementary Fig. 2b) Experimental (top) and calculated (bottom) TERS\nimages of representative vibrations for a fully optimized magnesium porphyrin system.\nThe confinement of the plasmonic field in simulations was set to 1.5 Å that was\nachieved in the experiments (Ref. 37).\nIn addition, we note that during the above imaging, the confinement of the plasmonic\nfield is not as good as that in Ref. 30. This is because, within the time period given by\nthe Editor for the revision, it is experimentally not feasible to achieve the optimal\nconditions for imaging. To address this, we have reproduced the imaging results for a\nfully optimized similar system reported in Ref. 37 (from the same experimental group),\nas shown in Fig. R8. The results demonstrate that the confinement of the plasmonic\nfield can be even better (1.5 Å) than that used for monitoring JTE (3 Å) in the present\nwork.\nWe have added the above discussions on page 5 (see “two main bands in the\ncalculated … affirmative assignment of this main band.”), on page 6 (see “under an\nexperimentally … (Supplementary Figs. 2-3)37”) in the revised manuscript, and on page\nS1 (see “Supplementary Section 1”), on page S2 (see “During the above imaging …\nhighly optimized imaging setup.”) in the revised Supplementary Information. All\ndetails relevant to the experimental TERS imaging have been added on page 14 (see\nsection of “Experimental details”) in the revised manuscript. Figures R7 and R8 have\nbeen added as Supplementary Figs. 1 and 2b in the revised Supplementary Information.\nQ3: The ability to resolve the image differences in the TERS images shown in Figure 4\nis highly dependent on the spatial confinement of the plasmonic field. The authors\nshould discuss the influence of the plasmonic field's confinement on the identification\nof the JTE. Specifically, what level of spatial resolution is necessary to distinguish the\nsubtle vibrational changes predicted in the manuscript?\nR3: We agree with the Referee that the spatial confinement of the plasmonic field is\ncritical to resolve the image differences in the TERS images shown in Fig. 4. Following\nthe Referee’s suggestion, to find what level of spatial resolution is necessary to\ndistinguish the subtle vibrational changes, we calculated the Raman images of the\nrelevant modes (v and v , Fig. 4b in the main text) under a series of plasmonic\n116a 116b\nsizes of 1.5, 3, 4, 5, and 8 Å, as shown in Fig. R9. As the plasmonic size increases, the\nimage patterns associated with the subtle vibrational changes become gradually blurred.\nWhen plasmonic size is set to 5 Å, the TERS images of v and v become similar\n116a 116b\nbut still distinguishable owing to the “wing” feature located at the non-isotopically\nsubstituted lobes. When the plasmonic size is set to 8 Å, this feature disappears,\nresulting in indistinguishable Raman images. Thus, we can conclude that a spatial\nconfinement of the plasmonic field of at least 5 Å is required to reliably identify the\nvibrational subtle differences in partially isotope-substituted ZnPc.\nFig. R9 (Supplementary Fig. 20) Calculated Raman images of the vibrational modes\nin Fig. 4b in the main text under different sizes of SCP fields.\nWe have added the above discussions on page 11 (see “requires highly localized …\n(Supplementary Fig. 20),”) in the revised manuscript and on page S14 (see\n“Supplementary Section 10”) in the revised Supplementary Information. Figure R9 has\nbeen added as Supplementary Fig. 20 in the revised Supplementary Information.\nQ4: The study does not address the synthetic feasibility of the proposed isotopically\nsubstituted molecule. Proposing a theoretical case is useful only if it is experimentally\nrealizable. The authors should consider to propose plans that are more readily\nverifiable in experiments to strengthen the link between their theory and practical\napplication.\nR4: We thank the Referee for the valuable suggestion about the feasibility of the\nproposed partially isotope-substituted ZnPc, which definitely strengthens our predicted\npractical applications for JTE. After searching the literature, we find that ZnPc can be\nsynthesized experimentally from four precursors through a cycloaddition reaction (see\nthe newly added Ref. 47 for details). Therefore, the proposed partially isotope-\nsubstituted ZnPc is indeed experimentally realizable, as anticipated by the Referee.\nSpecifically, the precursor phathalic-13C anhydride is commercially available from the\n6\nwhich can then be converted into a potassium/cesium salt in the presence of excess\n13CO and a suitable metal catalyst to undergo carbon isotope exchange (CIE), thereby\n2\nintroducing 13C at the two carboxyl positions. The fully 13C-labeled acid then undergoes\nH/D exchange on the aromatic ring in the presence of D gas and a Pd/C (or Ir) catalyst.\nwith acetic anhydride. Subsequently, isotopically substituted phthalic anhydride (A)\nundergoes a cycloaddition reaction with standard phthalic anhydride (B) in a 1:1 molar\nratio to synthesize various structures (see the newly added Ref. 48 for details). The most\nabundant products are ortho-substituted AABB and para-substituted ABAB.\nFig. R10 (Supplementary Fig. 19) Calculated Raman images of the vibration around\n1503 cm-1 for ortho-substituted (AABB, top) and para-substituted (ABAB, bottom)\nZnPc. The skeletons of the isotope-substituted lobe are marked in green in the Raman\nimage.\nWe can further use TERS imaging to select the isotopomer ABAB that is the proposed\none for the JTE applications. To this end, we choose a vibration (around 1503 cm-1) that\nis localized on the non-isotopically substituted lobes as an example. Calculated TERS\nimages of this vibration can clearly distinguish AABB and ABAB isotopomers, as\nshown in Fig. R10. Therefore, the partially isotope-substituted ZnPc proposed in the\npresent work is feasible to synthesize and can be selected out in experiments, which\nstrengthens the link between our theoretical results and practical application, as\nrequired by the Referee.\nWe have added the above discussions on page 10 (see “which is experimentally\nsynthesizable … (Supplementary Fig. 19).”) in the revised manuscript and on page S13\n(see “Supplementary Section 8”) in the revised Supplementary Information. Figure R10\nhas been added as Supplementary Fig. 19 in the revised Supplementary Information.\nQ5: Minor point: The section title \"Controlling JTE distortion by partial isotope\nsubstitution\" seems misleading. The section does not propose a method to control the\ndistortion but rather to identify a pre-determined distortion in a chemically synthesized\nmolecule. The section title should be changed.\nR5: We thank the Referee for this suggestion. We have changed the section title to\n“Identifying JTE distortion engineered by partial isotope substitution” in the revised\nmanuscript.\nPoint-by-point response to the Referee #3’s comments:\nGeneral Comment: This paper introduces a TERS imaging protocol that visualizes how\nindividual vibrational modes evolve as a single ZnPc molecule undergoes charge-\ninduced Jahn-Teller distortion. The authors accurately reproduce normal Raman and\npreviously reported TESR spectra for both neutral and anionic ZnPc, validating their\nplasmon-embedded field Hamiltonian approach. Although the JTE arises from vibronic\ncoupling, previous works have mostly imaged symmetry-broken electronic orbitals;\nexamining only the electronic component of the JTE thus limits these studies to partial\nobservation. Direct imaging of the vibrational component is therefore crucial for\nenhancing the predictive accuracy of structure-property models, and the authors’\nattempt to resolve and independently image the vibrational modes is both timely and\nvaluable. However, the following points require further explanation.\nReply: We thank the Referee for acknowledging our work as timely and valuable. We\nalso thank the Referee for the constructive comments, which significantly improved the\nquality of the present work. Our point-by-point response is provided below.\nQ1: All Raman images in this paper are theoretical. The experimental data is only the\n1D Raman spectrum, while the Raman images are entirely simulations created by\nvirtually scanning the plasmon local field and calculating the polarizability and\nenhancement factor for each mode. Even at very low resolution, experimental data is\nneeded to validate the theoretical Raman imaging.\nR1: We thank the Referee for encouraging us to provide an experimental validation of\nthe theoretical Raman imaging even at very low resolution. To this end, we seek the\nhelp of our experimental collaborator by asking them to measure the TERS image of\nthe main peak, i.e., v , in Fig. 1c. The observed Raman image is in excellent agreement\n105\nwith the theoretical simulation (Fig. R11), although the resolution is quite low\nconsisting with the Referee’s foresight. Specifically, both experimental and theoretical\nimages display a dark center and four bright patterns localized around the lobes of the\nZnPc.\nFig. R11 (Supplementary Fig. 1) Experimental (left) and calculated (right) Raman\nimages of the main peak in the neutral ZnPc TERS spectrum in Fig 1c. The confinement\nof the plasmonic field was set to 10 Å in simulations to satisfy the experimental\nresolution. Both experimental and theoretical image sizes are 3 nm×3 nm.\nFig. R12 (Supplementary Fig. 2) a Molecular structure of magnesium porphyrin\n(MgP). b Experimental (top) and calculated (bottom) TERS images of representative\nvibrations for a fully optimized magnesium porphyrin system. The confinement of the\nplasmonic field in simulations was set to 1.5 Å that was achieved in the experiments\n(Ref. 37).\nAs the Referee anticipated, the resolution in Fig. R11 is not as good as that in Ref. 30\nand our simulations. This is because, within the time period given by the Editor for the\nrevision, it is experimentally not feasible to achieve the optimal conditions for imaging.\nTo address this, we have reproduced the imaging results for a fully optimized similar\nsystem reported in Ref. 37 (Fig. R12). The results demonstrate that the confinement of\nthe plasmonic field can be even better (1.5 Å) than that used for monitoring JTE (3 Å)\nin the present work. These results demonstrate that in the near future, experiments will\nbe fully capable of measuring the predicted TERS images, thereby deepening the\nfundamental understanding of JTE.\nWe have added above discussions on page 6 (see “Further calculated and\nexperimental … of this main band.” and “under an experimentally … (Supplementary\nFigs. 2-3)37”) in the revised manuscript, and on page S1 (see “Supplementary Section\n1”), on page S2 (see “During the above imaging … highly optimized imaging setup.”)\nin the revised Supplementary Information. All details relevant to the experimental\nTERS imaging have been added on page 14 (see section of “Experimental details”) in\nthe revised manuscript. Figures R11 and R12 have been added as Supplementary Figs.\n1 and 2 in the revised Supplementary Information.\nQ2: The calculation model assumes a 3Å Gaussian plasmon and fixed orientation.\nSensitivity to apex shape, gap size and charge-transfer strength should be quantified to\nsolve tip-apex dependence.\nR2: We thank the Referee for this constructive suggestion. As noted by the Referee, the\napex shape and the gap size directly determine the spatial resolution of Raman imaging.\nAs shown in Fig. R13a (adapted from the newly added Ref. S3 in the revised\nSupplementary Information), the lateral size, i.e., the full width at half maximum\n(FWHM), of the plasmonic field can be evaluated as FWHM=√𝑅𝑑, where R is the\ncurvature of the apex shape and d is the gap size. In practical simulations, we used a\nso-called “pico-cavity” silver tip as realized in Ref. S3 in the revised Supplementary\nInformation, where a single silver atom decorates the apex. As a result, R is set to 1.45\nÅ.\nFig. R13 (Supplementary Fig. 3) a Schematic illustration of tip shape and gap size in\na “pico-cavity”, adapted from Ref. S3 in the revised Supplementary Information. b\nSimulated TERS images at gap sizes ranging from 0.7 to 3 nm with an atom-decorated\nsilver tip. The FWHMs of the corresponding SCP are labeled at the bottom. c\nDifferential charge density map at a tip–molecule distance of 2 Å.\nBy taking into account the thickness of the three NaCl decouple layer (4.1 Å, see the\nnewly added Ref. S4 in the revised Supplementary Information for details), a series of\ngap sizes of 0.7, 1.0, 1.5, 2.0, and 3.0 nm are considered, corresponding to the\nplasmonic sizes of 3.2, 3.8, 4.6, 5.4, and 6.6 Å. Taking one main peak, i.e., v ,\nas a\n108\nrepresentative, calculated results reveal that increasing the gap size leads to a decreased\nresolution, as shown in Fig. R13b. When the gap size exceeds 2.0 nm, the image can\nno longer resolve vibrational details of four-fold patterns in the molecular center. In\naddition, the 3.2 Å plasmon with a 0.7 nm gap size can be rationalized as the 3 Å\nplasmon for monitoring JTE in the current work.\nTo address the possible charge transfer effect between the tip and ZnPc, we placed an\nAg cluster 2 Å above the molecule, which is consistent with the gap size of 0.7 nm.\nCalculated results reveal that the differential charge density between the tip and\nmolecule is less than 0.003 e/bohr3 (Fig. R13c). Further Bader charge analysis shows\nthat the total charge transfer is less than 0.1 e, which falls within the error margin of the\nmethod. Thus, the charge transfer between the tip and ZnPc is negligible for 3 Å TERS\nimaging in the current work, as anticipated by the Referee.\nWe have added the above discussions on page 6 (see “under an experimentally …\n(Supplementary Figs. 2-3)37”), on page 14 (see “and the negligible … from tip.”) in the\nrevised manuscript, and on page S2 (see “Specifically, the tip-apex … SCP in the\ncurrent work.”) in the revised Supplementary Information. Figure R13 has been added\nas Supplementary Fig. 3 in the revised Supplementary Information.\nQ3: When discussing symmetry splittings such as those arising from JTE, the relative\nfrequency shifts are paramount, and temperature-induced offsets largely cancel out.\nNonetheless, vibrational modes obtained under the idealized assumptions of 0 K and\nthe harmonic approximation can diverge from those observed in real experimental\nenvironments. The manuscript should therefore include further clarification on how\ntemperature and anharmonicity corrections were applied.\nR3: We thank the Referee for highlighting the effects of temperature and anharmonicity.\nIn fact, the experiments were carried out at an ultralow temperature of 7 K (see Ref. 30\nfor details), which corresponds to a characteristic frequency of 5 cm-1. Because the\nconsidered frequencies are significantly larger than this value (typically > 1000 cm-1),\nthe initial vibrational state stays in the ground state (n =0) and the final state stays in\nv\nthe first excited state (n =1). Thus, the finite temperature effect on frequency is\nv\nnegligible in our simulations.\nFig. R14 (Supplementary Fig. 21) Calculated potential energy surface along the\nvibrational mode of v (cyan triangles) and fitted by a Morse potential (magenta line).\n108\n' \nwe fit the potential energy surface by a Morse potential of 𝑉(𝑟) = 𝐷 '1−𝑒\"#(%\"%! )+\n!\n(Fig. R14). As a result, the dissociation energy D and Morse parameter α are\ne\ndetermined to be 9.5×105 kcal/mol and 4.8×10-3 bohr-1amu-1/2, respectively. Based on\nthis fitted Morse potential, the energy difference between the ground (n =0) and the first\nv\nexcited state (n =1) is evaluated to be 1348.5 cm-1. In other words, at the cryogenic\nv\ntemperature of 7 K, the anharmonic frequency of v is 1348.5 cm-1, which is almost\n108\nidentical to the calculated harmonic frequency of 1348.0 cm-1. This result is consistent\nwith the fact that the anharmonicity constant x is as small as 1.01×10-6, which can be\ne\nattributed to the rigid structure of ZnPc. Therefore, the effect of anharmonicity on\nfrequency can be safely neglected again.\nWe have added the above discussions on page 14 (see “The effect of anharmonicity …\nrigid structure of ZnPc.”) in the revised manuscript and on page S14 (see\n“Supplementary Section 11”) in the revised Supplementary Information. Figure R14\nhas been added as Supplementary Fig. 21 in the revised Supplementary Information.\nQ4: The protocol is demonstrated for only one molecule (ZnPc). Establishing its\nuniversality would ideally involve applying the workflow to at least one additional\nsystem. Given that suh simulations may be computationally demanding, the authors\ncould instead strengthen the manuscript by adding a discussion of how the approach\ncould be extended to other molecular system and what challenges might be encountered.\nR4: We thank the Referee for the constructive suggestion about the universality of the\npresent work. To address this, we have applied the proposed protocol for a single copper\nporphyrin (CuP) molecule, which has different ligands (porphyrin vs. phthalocyanine)\nand a central metallic ion (Cu vs. Zn) from ZnPc. When CuP experiences charge-\ninduced JTE, the calculated Raman images, similar to those of ZnPc, can again\nfaithfully reflect the splitting of degenerate modes and the coupling between different\nirreducible representations, as shown in Fig. R15. Now, the universality of the current\nprotocol has been numerically demonstrated, as required by the Referee. The principle\nof this universality is attributed to the intrinsic characteristics of Raman imaging that\ncan visualize the molecular vibrational modes in real space, a feature theoretically\nproposed by our group and experimentally validated by others.\nFig. R15 (Supplementary Fig. 18) Evolution of vibrational modes from CuP to CuP–.\na Splitting of the degenerate E mode. b Mixing of well-overlapped A and B modes.\nu 2g 2g\nThe electronic effect of the excess electron on the vibrational energy was indicated by\narrows.\nWe also thank the Referee for the suggestion about discussing the challenges of\nextending the current simulations to other molecular systems. Notably, current charge-\ninduced JTE involves neutral and anionic states. Choosing an appropriate theoretical\nlevel to accurately describe the electronic structures at different charge states, especially\nthe anionic state, is crucial for practical simulations of TERS images. Usually, a diffuse\nbasis set has to be selected for the extra electron. Furthermore, owing to Janak's theorem,\nthe eigenvalue of the HOMO in anionic states must be negative. Otherwise, the\ncalculations will converge to unphysical solutions. All of these issues can pose\nchallenges to achieving accurate TERS image calculations, which have been carefully\nchecked in the present simulations.\nWe have added the above discussions on page 10 (see “We want to stress …\nmodes in real space.36–38”), on page 14 (see “The eigenvalues of … particular for anionic states.”),\nand on page S12 (see “Supplementary Section 7”) in the revised\nSupplementary Information. Figure R15 has been added as Supplementary Fig. 18 in the revised Supplementary Information.\nPoint-by-point response to the Referee #4’s comments:\nGeneral Comment: In this manuscript, the authors propose to use imaging based on\ntip-enhanced Raman scattering as a means of accessing vibrational states in molecules\nthat undergo Kahn-Teller distortions. For that, they build computational methods to\nobtain effective Hamiltonian models for Raman polarizability and scattering cross\nsections taking into account vibrational states defined according to relevant irreducible\nrepresentations for the pertinent point group symmetries. In the model, they use\nlocalized plasmon fields represented by Gaussian functions. Additional first-principles\ncalculations based on DFT to obtain electronic structures and vibrational modes of the\nthe ZnPc molecule. The outcomes of the computational modeling are compared with\nexperimental data supported from external references.\nThrough theoretical insights, the authors propose that imaging with Raman techniques\nallows to identify specific vibrational modes and their spatial distribution, which\nbecomes all-important when aiming at gathering information when molecules are\nsubject to Jahn-Teller distortions. In particular, the authors can describe through their\nmodel the observed frequency shifts when the charge state of molecules is changed by\nelectrical biases, inducing Jahn-Teller effects after the charge injection. They explore\nhow the modes change upon symmetry lowering and explain why some of the modes\nresulting from the JT-induced splitting are observed in experiments and why others are\nnot. Additionally, they propose that TERS experiments can be aimed at exploring\nmixing of vibrational modes that is forbidden for high-symmetry settings, but can\nbecome mixed when symmetry is lowered by JT effects. Lastly, they also show how\nTERS imaging could be used to probe changes in vibrational modes caused by isotopic\nsubstitutions.\nThe work is relevant because most of works have focused on the effects of JT on the\nelectronic component, rather than the vibrational ones resulting from JT vibronic\ncouplings. I believe that this is an interesting perspective for experimentalists to explore\nwhat Raman-based imaging can gather about vibronic states in molecules. Therefore,\nI judge this is work is relevant to the field.\nReply: We thank the Referee for the comprehensive summary of our work. We also\nthank the Referee for the instructive suggestions that significantly improve the quality\nof the present work. A point-by-point response to the Referee’s comments is provided\nbelow.\nI have some comments:\nQ1: When referring to Ref. 16, the authors assume an interpretation of the spectral\nvariations in ZnPc as charges are injected as arising from JT effects. However, if I am\nnot wrong, the authors do not interpret directly such variations as resulting from JT\neffects. The sentence as it is written, presumes that the authors of that paper assume JT\neffects as the reason of the observed changes in spectra.\nR1: We thank the Referee for pointing out this inappropriate citation of Ref. 16 in the\nprevious manuscript. Following the suggestion of the Referee, we have modified the\ninappropriate description during the interpretation of the spectral variations in the\nrevised manuscript (see “an experimental … was negatively charged” on page 3). Now,\nRef. 16 is appropriately cited.\nQ2: In Fig. 1 c, the blue shift of the resonance at 1486 cm-1 between neutral ZnPc and\nZnPc- is very subtle. I recommend to make the shift more evident in the figure (e.g.,\nadding a vertical dashed line).\nR2: We thank the Referee for this constructive suggestion about making Fig.1c more\nreadable. Following the suggestion, we have added guidelines in Fig.1c in the revised\nmanuscript, which makes the frequency shifts of the main peaks more evident (Fig.\nR16). In addition, to address the other Referee’s comment, the center positions of each\nmain peak in the calculated spectra have been filled with the same colors as the\ncorresponding spectra, which makes the comparison more facilitative.\nFig. R16 The revised Fig. 1c that includes colors in the center positions, labels\nirreducible representations, adds guidelines, and inserts an illustration table for the\npoint group changes in the revised manuscript.\nQ3: For a more accessible reading, I recommend to add a schematic illustration in the\nmain text of all the irreps and corresponding point-group symmetries (before and after\nJT) for the relevant modes in the spectral range covered by Fig. 1. When reading the\npaper, it was difficult to me to finally grasp the irreps of the modes discussed in that\nfigure.\nR3: We thank the Referee for this valuable suggestion. We have labeled all the\nirreducible representations associated with the peaks that are discussed in the main text\nin the revised Fig. 1c. In addition, an illustration table that lists corresponding point\ngroup symmetry of relevant vibrational modes in the spectral range before and after the\nJT effect has also been added in Fig. 1c. All these revisions (see above Fig. R16) provide\na more convenient understanding of the discussed modes, significantly improving the\npaper’s readability, as anticipated by the Referee."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors properly addressed all my comments. Some of which emphasize that simple calculations can render all the intricate Jahn-Teller effects in respect to Raman simulations.\nAs other reviewers stated, this paper will certainly serve as a good guide to experimentalists as well as to other theoreticians when trying to interpret some of the results.\nI do not fully agree with the authors in that negatively charged molecules can't be calculated properly. Of course, in a periodic boundary condition the final geometry may be difficult. But one can always perform cluster calculations and then feed this to calculate other quantities.\nOverall, I commend the authors work and am happy to accept this publication in its present form.", "reviewer_2": "In the response, the authors have largely replied to my comments. Indeed, the largest novelty of this manuscript is to propose theoretically to study the real-space vibrational features of a single molecule under Jahn-Teller effect with high-resolution TERS. They also show that a spatial confinement of the plasmonic field of at least 5 Å is required to reliably identify the vibrational subtle differences.\nI recommend to consider the acceptance of the manuscript without further review. Nevertheless, I have one suggestion that would significantly strengthen the paper’s conclusion.\nThe response to my Comment 2 concerning the v105 mode remains the weakest part. The evident quantitative discrepancy in the charge-induced shift (predicted ~26 cm 1 vs. experimental ~7 cm 1) is still a point of concern. While the authors correctly highlight the agreement of the v108 mode and provide a new low-resolution spatial image (Fig. R7), the overall argument for the model’s reliability in capturing JTE-induced shifts is weakened by this evident discrepancy in the other key mode. To make the paper’s conclusion more robust, I suggest that the authors briefly add the analysis of more additional JTE-affected vibrational mode from their dataset. By supplementing the analysis with more modes that are well-matched (similar to v108 mode), the authors can more robustly validate their model’s reliability in capturing JTE physics and better substantiate their theoretical claims.", "reviewer_3": "Although the experimental Raman images exhibit very low spatial resolution as expected, the authors’ attempt to compare these measurements with the theoretical images presented in the manuscript is commendable. Moreover, by extending their protocol to an additional system–CuP beyond ZnPc–the authors successfully demonstrate the broader applicability of their approach. Such an imaging protocol, capable of visualizing molecular vibrational modes directly in real space, has the potential to significantly improve the predictive accuracy of structure-property models.\nOverall, the authors have responded thoroughly to the reviewer’s comments, and the revisions made to the manuscript, together with the supplementary information, sufficiently address the points raised. The reviewer therefore recommends acceptance of the revised manuscript.", "reviewer_4": "In their revised manuscript, the authors have satisfactorily addressed my remarks. In particular, now they have included a table of irreducible representations of the analyzed modes, before and after JT effects taking place. They have also modified Fig 1.c to make more visible the shifts in the modes cause by the JT effects. I believe that with these modifications, the paper can be accepted."}, "author_response": "Point-by-point response to the Referee #1’s comments:\nGeneral Comment: The authors properly addressed all my comments. Some of which\nemphasize that simple calculations can render all the intricate Jahn-Teller effects in\nrespect to Raman simulations.\nAs other reviewers stated, this paper will certainly serve as a good guide to\nexperimentalists as well as to other theoreticians when trying to interpret some of the\nresults.\nI do not fully agree with the authors in that negatively charged molecules can't be\ncalculated properly. Of course, in a periodic boundary condition the final geometry\nmay be difficult. But one can always perform cluster calculations and then feed this to\ncalculate other quantities.\nOverall, I commend the authors work and am happy to accept this publication in its\npresent form.\nReply: We sincerely thank the Referee for acknowledging our revisions and\nrecommending publication of our manuscript.\nWe fully agree with the Referee that accurate geometry optimizations for charged\nmolecules would be very difficult in periodic boundary conditions. We also agree with\nthe Referee that reliable calculations for such systems are definitely possible with\nappropriate cluster models. In principle, one could extract a sufficiently large NaCl/Ag\ncluster (a rough estimation of ~800 atoms) to take into account the substrate effects on\nanionic ZnPc. Such first-principles calculations would substantially increase the\ncomputational cost. Moreover, it is necessary to ensure that the excess charge is indeed\nlocalized on the adsorbate rather than on the metal cluster in the practical calculations.\nThis cluster model approach is essential for systems with strong substrate-adsorbate\ninteractions and will be adopted in our future related works.\nWe have added the above discussion on page 8 (see “For other systems with strong\nsubstrate-adsorbate interactions, adequately large cluster models with advanced charge\nlocalization calculations would be required for the accurate description of the substrate\neffects.”) in the revised manuscript.\nPoint-by-point response to the Referee #2’s comments:\nGeneral Comment: In the response, the authors have largely replied to my comments.\nIndeed, the largest novelty of this manuscript is to propose theoretically to study the\nreal-space vibrational features of a single molecule under Jahn-Teller effect with high-\nresolution TERS. They also show that a spatial confinement of the plasmonic field of at\nleast 5 Å is required to reliably identify the vibrational subtle differences.\nI recommend to consider the acceptance of the manuscript without further review.\nNevertheless, I have one suggestion that would significantly strengthen the paper’s\nconclusion.\nThe response to my Comment 2 concerning the v105 mode remains the weakest part.\nThe evident quantitative discrepancy in the charge-induced shift (predicted ~26 cm−1\nvs. experimental ~7 cm−1) is still a point of concern. While the authors correctly\nhighlight the agreement of the v108 mode and provide a new low-resolution spatial\nimage (Fig. R7), the overall argument for the model’s reliability in capturing JTE-\ninduced shifts is weakened by this evident discrepancy in the other key mode. To make\nthe paper’s conclusion more robust, I suggest that the authors briefly add the analysis\nof more additional JTE-affected vibrational mode from their dataset. By supplementing\nthe analysis with more modes that are well-matched (similar to v108 mode), the authors\ncan more robustly validate their model’s reliability in capturing JTE physics and better\nsubstantiate their theoretical claims.\nReply: We sincerely thank the Referee for acknowledging the revisions and novelty of\nour work, as well as for the recommendation of acceptance of the manuscript. We also\nthank the Referee for the additional valuable suggestion about the analysis of more JTE-\naffected vibrational modes.\nFig. R1 (Supplementary Fig. 2) Two additional sets of JTE-induced shifts in the calculated (Theo.)\nand experimental (Exp.) TERS spectra of neutral ZnPc and anionic ZnPc⁻. The cyan-shaded regions\nhighlight the spectral windows for the JTE-induced frequency shifts.\nIn the previous version, we focused on the main peaks of the TERS spectra. Following\nthe Referee’s advice, we have checked the secondary TERS signals as highlighted by\nthe cyan-shaded regions in Fig. R1. In these spectral windows, the calculated peak\npositions exhibit redshifts of 5.9 (1165.2 cm−1 vs. 1159.3 cm−1) and 14.7 cm-1 (1425.9\ncm−1 vs. 1411.2 cm−1) under charge-induced JTE, which quantitatively reproduce the\nexperimentally observed redshifts of 7.8 (1138.2 cm−1 vs. 1130.4 cm−1) and 16.2 cm-1\n(1411.7 cm−1 vs. 1395.5 cm−1), respectively. The consistency of these additional JTE-\ninduced shifts, together with the v mode discussed in the main text, provides a more\n108\nrobust validation of our model’s reliability in capturing JTE-related spectral changes.\nWe have added the above analysis on page 6 (see “In addition, the JTE-induced shifts\nof other secondary bands in the calculated spectra also agree well with the\nexperimentally observed redshifts (Supplementary Fig. 2).”) in the revised manuscript\nand on page S2 (see “We have checked … capturing JTE-related spectral changes.”) in\nthe revised Supplementary Information. Figure R1 has been added as Supplementary\nFig. 2 in the revised Supplementary Information.\nPoint-by-point response to the Referee #3’s comments:\nGeneral Comment: Although the experimental Raman images exhibit very low spatial\nresolution as expected, the authors’ attempt to compare these measurements with the\ntheoretical images presented in the manuscript is commendable. Moreover, by\nextending their protocol to an additional system–CuP beyond ZnPc–the authors\nsuccessfully demonstrate the broader applicability of their approach. Such an imaging\nprotocol, capable of visualizing molecular vibrational modes directly in real space, has\nthe potential to significantly improve the predictive accuracy of structure-property\nmodels.\nOverall, the authors have responded thoroughly to the reviewer’s comments, and the\nrevisions made to the manuscript, together with the supplementary information,\nsufficiently address the points raised. The reviewer therefore recommends acceptance\nof the revised manuscript.\nReply: We sincerely thank the Referee for the commendation of our revisions and for\nrecommending acceptance of the revised manuscript. The Referee’s encouraging\ncomments about experimental validation and extension of our protocol significantly\nenhance the broad applicability of the present proposed real-space TERS imaging for\nvisualizing Jahn-Teller vibrational evolution. We are very grateful for this support.\nPoint-by-point response to the Referee #4’s comments:\nGeneral Comment: In their revised manuscript, the authors have satisfactorily\naddressed my remarks. In particular, now they have included a table of irreducible\nrepresentations of the analyzed modes, before and after JT effects taking place. They\nhave also modified Fig 1.c to make more visible the shifts in the modes cause by the JT\neffects. I believe that with these modifications, the paper can be accepted.\nReply: We sincerely thank the Referee for acknowledging our revisions and the\npositive recommendation for acceptance. The Referee’s suggestions significantly\nimprove the readability of Fig. 1. Besides, following the Editor’s requirement, we have\nmoved the table of the irreducible representations to Fig. 1’s caption. We appreciate the\nReferee’s supportive comments on our work."}]

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