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arxiv: 2603.02040 · v2 · submitted 2026-03-02 · ❄️ cond-mat.mes-hall

On-surface synthesis and aromaticity of large cyclocarbons

Pith reviewed 2026-05-15 16:59 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords cyclocarbonsaromaticityon-surface synthesisscanning tunnelling spectroscopytransport gapcarbon ringsannulenestip-induced chemistry
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The pith

Transport gaps in tip-synthesized carbon rings show aromatic 4n+2 species retain a larger gap than anti-aromatic 4n ones up to at least N=42, with the difference shrinking as rings grow larger.

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

The work creates monocyclic carbon rings containing up to 88 atoms on a salt surface by successive tip-induced bond rearrangements and fusions. Scanning-tunnelling spectroscopy records the transport gap for each ring, revealing a clear oscillation: rings whose atom count is a multiple of 4 (anti-aromatic) have smaller gaps than those with 4n+2 atoms (aromatic). This oscillation weakens with increasing size and is predicted to disappear, signalling the loss of distinct aromatic character. At N=42 the gap difference is still measurable and accompanying calculations find ring currents whose magnitude matches that of benzene. The results supply a direct experimental test of how aromaticity evolves in the pure-carbon limit of annulenes.

Core claim

Tip-induced chemistry on NaCl produces C20, C22, C42, C44, C46, C66 and C88; their measured transport gaps are smaller for N=4n than for N=4n+2 at small sizes, the amplitude of this alternation decreases with N, and large-active-space calculations predict ring currents at N=42 that remain comparable in strength to those in benzene.

What carries the argument

Transport gap extracted from scanning-tunnelling spectra, which reports the HOMO-LUMO separation modulated by aromatic stabilisation or destabilisation in the monocyclic carbon framework.

If this is right

  • Aromaticity remains detectable at N=42 with ring currents of benzene-like magnitude.
  • The 4n versus 4n+2 gap difference shrinks steadily and is expected to vanish at large N.
  • Larger cyclocarbons can serve as model systems for conductance and quantum-interference studies in atomic carbon wires.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the oscillation truly disappears, cyclocarbons beyond a few dozen atoms will behave electronically like ordinary conjugated chains rather than aromatic or anti-aromatic rings.
  • The same manipulation sequence could be used to insert heteroatoms or defects into the rings to test how aromaticity is locally quenched.
  • Persistent ring currents at N=42 imply that carbon rings of this size may still support delocalised currents useful for designing molecular-scale current loops.

Load-bearing premise

The gap recorded on the surface equals the intrinsic gap of the isolated cyclocarbon without substantial distortion from the substrate, charging, or tip-induced changes.

What would settle it

Finding identical transport gaps for C20 and C22, or for C42 and C44, on the same surface would falsify the reported aromaticity oscillation.

Figures

Figures reproduced from arXiv: 2603.02040 by Alberto Baiardi, Beren Dempsey, Fabian Paschke, Florian Albrecht, Harry L. Anderson, Igor Ron\v{c}evi\'c, Ivano Tavernelli, Jakob Eckrich, Leo Gross, Leonard-Alexander Lieske, Lisanne Sellies, Marco Vitek, Samuele Piccinelli, Stefano Barison, Yueze Gao.

Figure 1
Figure 1. Figure 1: On-surface synthesis of C22 and C44. Laplace-filtered AFM data measured with CO￾funcƟonalized Ɵps and corresponding chemical structures. a, Precursor 1. b, Cyclo[22]carbon, C22. c, Two C22 molecules with a centre-to-centre-distance of 5 nm. d–i, GeneraƟon of C44 from two C22, along with an energy diagram (d) calculated using OX-BLYP30, including energies of transiƟon structures (red plateaus, for details s… view at source ↗
Figure 2
Figure 2. Figure 2: On-surface synthesis of C66 and C88. Sequence of Laplace-filtered AFM data (upper panels) and respecƟve chemical structures (boƩom panels). a, C22 adjacent to C44 L(24,22) . b, Lemniscate C66 L(24,24,22) formed by fusion (pulse parameters: Vp = 4.5 V, Δz = 8.5 Å, IP = 7 pA). c, Lemniscate C66 L(46,22) formed by ring-opening (VP = 4.5 V, Δz = 8 Å, IP = 9 pA). d, C66 formed by ring opening (VP = 4.7 V, Δz = … view at source ↗
Figure 3
Figure 3. Figure 3: Transport gaps of cyclocarbons. a, STS measured gaps Δexp , i.e., energy differences between the PIR and the NIR for the studied cyclocarbons on monolayer NaCl on Au(111) (for the STS spectra and estimation of errors, see Supplementary Fig. S34). The dashed line, which only serves as guidance, was obtained by fitting Δexp = ae –bN + c, with a, b, and c as parameters. b, Gas￾phase calculated IPEA gaps Δcalc… view at source ↗
Figure 4
Figure 4. Figure 4: Theory results for even cyclo[N]carbons up to N = 100. a, Ring current. b, Aromatic stabilization energy (ASE). c, Automerization barrier. Calculations were performed with OX￾BLYP30/def2-TZVP, further details in SI sections 10–15. d, Transport gaps Δcalc of C20 and C22. Ionization potentials (IP), electron affinities (EA), and Δcalc (IP – EA) were computed using Hartree￾Fock (HF), heat bath CI (HCI), SqDRI… view at source ↗
read the original abstract

Molecular rings of N carbon atoms, that is, cyclo[N]carbons, or C$_N$, can be formed by tip-induced chemistry [1-7]. Because of their monocyclic geometry, cyclocarbons are fundamentally important for testing theoretical models of aromaticity [8-11]. Here, we synthesized large cyclo[N]carbons, with N up to 88, by tip-induced chemistry on a NaCl surface and studied their aromaticity by measuring their transport gaps by scanning tunnelling spectroscopy. We first generated C$_{20}$ and C$_{22}$, and then fused multiple cyclocarbons [5-7] by means of atom manipulation, obtaining C$_{42}$, C$_{44}$, C$_{46}$, C$_{66}$ and C$_{88}$. In agreement with predictions obtained using a finely tuned density functional [12-15] and large active space approximate configuration interaction calculations executed on quantum hardware [16, 17], we observe a substantially smaller transport gap for C$_{20}$ (N = 4n) compared to C$_{22}$ (4n+2), and for C$_{44}$ (4n) relative to C$_{42}$ (4n+2). In larger cyclocarbons, the oscillation of the transport gap between anti-aromatic N = 4n and aromatic N = 4n+2 cyclocarbons becomes smaller, and is expected to eventually vanish with increasing N, indicating non-aromaticity. Our experimental results show that aromaticity persists at N = 42, and theory predicts ring currents comparable in magnitude to that of benzene in cyclocarbons of this size. In the future, such large cyclocarbons could be used to study conductance, quantum interference, and the effects of aromaticity in single atomic carbon wires and circuits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reports tip-induced on-surface synthesis of cyclocarbons up to C88 on NaCl, including fusion of smaller rings to form C42, C44, C46, C66 and C88. Scanning tunneling spectroscopy measurements reveal smaller transport gaps for N=4n species (C20, C44) than for N=4n+2 (C22, C42), with the oscillation amplitude decreasing at larger N; the authors interpret this as persistence of aromaticity up to N=42, consistent with tuned DFT and quantum-hardware CI calculations that predict ring currents comparable to benzene.

Significance. If the measured gaps faithfully report gas-phase aromatic character, the work provides the first experimental extension of Hückel aromaticity/anti-aromaticity to cyclocarbons beyond C22 and demonstrates that the oscillation survives to N=42 before expected damping. The combination of atomically precise synthesis, STS gap data, and comparison to large-scale quantum-hardware calculations constitutes a notable advance for testing aromaticity models in monocyclic carbon systems and for future single-molecule carbon-wire studies.

major comments (1)
  1. [Results and Discussion sections on STS gap measurements and interpretation] The central claim equates the observed STS transport-gap oscillation on NaCl directly to intrinsic free-molecule aromaticity (smaller gap for N=4n anti-aromatic vs. 4n+2 aromatic, persisting to N=42). No experimental controls are described to bound differential surface effects such as image-charge stabilization, substrate-induced bond-length alternation, or tip-induced charging that could vary systematically with ring size or parity. While agreement with gas-phase tuned DFT and quantum-hardware results is reported, this does not substitute for a control measurement (different decoupling layer or bias-dependent charging check) that would be required to make the interpretation load-bearing.
minor comments (2)
  1. [Abstract and Methods] The abstract and main text refer to 'finely tuned density functional' without specifying the tuning procedure or parameters in the main manuscript; a brief methods paragraph or SI reference would improve reproducibility.
  2. [Figure captions] Figure captions for the STS spectra should explicitly state the number of independent measurements and the fitting procedure used to extract transport gaps.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the positive assessment of the significance of our work and for the constructive major comment. We address the concern regarding the interpretation of the STS transport gaps below.

read point-by-point responses
  1. Referee: [Results and Discussion sections on STS gap measurements and interpretation] The central claim equates the observed STS transport-gap oscillation on NaCl directly to intrinsic free-molecule aromaticity (smaller gap for N=4n anti-aromatic vs. 4n+2 aromatic, persisting to N=42). No experimental controls are described to bound differential surface effects such as image-charge stabilization, substrate-induced bond-length alternation, or tip-induced charging that could vary systematically with ring size or parity. While agreement with gas-phase tuned DFT and quantum-hardware results is reported, this does not substitute for a control measurement (different decoupling layer or bias-dependent charging check) that would be required to make the interpretation load-bearing.

    Authors: We agree that surface-induced effects represent a valid concern for any STS measurement on a decoupling layer and that explicit experimental controls would strengthen the claim. The observed gap oscillation matches the parity dependence and damping trend predicted by our gas-phase tuned-DFT and quantum-hardware CI calculations; this quantitative agreement across multiple ring sizes makes a purely substrate-driven origin unlikely, as image-charge stabilization or bond-length alternation would need to reproduce the same 4n vs. 4n+2 alternation and its systematic reduction with N. In the revised manuscript we will add a dedicated paragraph in the Discussion that (i) estimates the magnitude of image-charge shifts using a simple electrostatic model, (ii) notes the absence of bias-dependent charging signatures in our dI/dV spectra, and (iii) discusses why substrate-induced bond-length alternation is expected to be small on NaCl for these symmetric rings. We cannot, however, perform new control experiments on an alternative decoupling layer within the scope of this revision, as the on-surface synthesis protocol and molecular stability are specific to NaCl. revision: partial

standing simulated objections not resolved
  • New experimental controls on a different decoupling layer or explicit bias-dependent charging checks cannot be supplied in the revised manuscript.

Circularity Check

0 steps flagged

No circularity; experimental synthesis and STS gaps are independent of cited theory

full rationale

The paper's core chain is tip-induced on-surface synthesis of C_N rings on NaCl followed by direct STS transport-gap measurements. These experimental steps produce the reported gap oscillations (smaller for N=4n than 4n+2, persisting to N=42) without reference to or equivalence with the DFT or quantum-hardware CI predictions, which are invoked only for post-hoc comparison and aromaticity interpretation. No equation or claim reduces a measured quantity to a fitted parameter or self-citation by construction; the cited theory papers supply independent benchmarks rather than load-bearing premises. The work is therefore self-contained as an experimental report.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard chemical assumptions about Hückel aromaticity and the interpretation of transport gaps as aromaticity indicators. The theory component invokes a finely tuned density functional whose specific parameters are referenced but not re-derived here.

free parameters (1)
  • tuned DFT parameters
    The density functional is described as finely tuned; exact values or fitting procedure are not restated in the abstract but are required for the theoretical predictions.
axioms (2)
  • domain assumption Hückel's 4n+2 / 4n rule determines aromatic vs anti-aromatic character in monocyclic systems
    Invoked to assign aromaticity labels and to interpret smaller transport gaps as anti-aromatic signatures.
  • domain assumption Transport gap measured by STS on NaCl faithfully reflects the gas-phase aromaticity of the cyclocarbon
    Central link between experiment and aromaticity classification; surface and tip effects are assumed negligible.

pith-pipeline@v0.9.0 · 5699 in / 1487 out tokens · 65712 ms · 2026-05-15T16:59:30.839939+00:00 · methodology

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Reference graph

Works this paper leans on

67 extracted references · 67 canonical work pages

  1. [1]

    M., Schulz, F., Gawel, P., Gross, L

    Kaiser, K., Scriven, L. M., Schulz, F., Gawel, P., Gross, L. & Anderson, H. L. An sp-hybridized molecular carbon allotrope, cyclo[18]carbon. Science 365, 1299–1301 (2019)

  2. [2]

    Sun, L., Zheng, W., Gao, W., Kang, F., Zhao, M. & Xu, W. On-surface synthesis of aromatic cyclo[10]carbon and cyclo[14]carbon. Nature 623, 972–976 (2023)

  3. [3]

    M., Christensen, K

    Gao, Y., Albrecht, F., Rončević, I., Ettedgui, I., Kumar, P., Scriven, L. M., Christensen, K. E., Mishra, S., Righetti, L. & Rossmannek, M. et al. On-surface synthesis of a doubly anti-aromatic carbon allotrope. Nature 623, 977–981 (2023)

  4. [4]

    Sun, L., Zheng, W., Kang, F., Gao, W., Wang, T., Gao, G. & Xu, W. On-surface synthesis and characterization of anti-aromatic cyclo[12]carbon and cyclo[20]carbon. Nat. Commun. 15, 7649 (2024)

  5. [5]

    Albrecht, F., Rončević, I., Gao, Y., Paschke, F., Baiardi, A., Tavernelli, I., Mishra, S., Anderson, H. L. & Gross, L. The odd-number cyclo[13]carbon and its dimer, cyclo[26]carbon. Science 384, 677–682 (2024)

  6. [6]

    Guo, Y., Yun, Y., Xiang, W., Xu, G., Sun, L. & Xu, W. On-surface synthesis of cyclo[20]carbon and cyclo[30]carbon from cyclo[10]carbon. Nat. Commun. 16, 11507 (2025)

  7. [7]

    Guo, Y., Hua, L., Yun, Y., Xu, G., Sun, L. & Xu, W. Ouroboros: from linear carbons to cyclic carbons, cyclo[25]carbon and cyclo[50]carbon. J. Am. Chem. Soc. https://doi.org/10.1021/jacs.6c00225 (2026)

  8. [8]

    V., Valiev, R

    Baryshnikov, G. V., Valiev, R. R., Kuklin, A. V., Sundholm, D. & Ågren, H. Cyclo[18]carbon: insight into electronic structure, aromaticity and surface coupling. J. Phys. Chem. Lett. 10, 6701–6705 (2019)

  9. [9]

    V., Valiev, R

    Baryshnikov, G. V., Valiev, R. R., Nasibullin, R. T., Sundholm, D., Kurten, T. & Ågren, H. Aromaticity of even-number cyclo[n]carbons (n = 6–100). J. Phys. Chem. A 124, 10849–10855 (2020)

  10. [10]

    L., Patrick, C

    Anderson, H. L., Patrick, C. W., Scriven, L. M. & Woltering, S. L. A short history of cyclocarbons. Bull. Chem. Soc. Jpn. 94, 798–811 (2021)

  11. [11]

    J., Rossmannek, M., Tavernelli, I., Gross, L

    Rončević, I., Leslie, F. J., Rossmannek, M., Tavernelli, I., Gross, L. & Anderson, H. L. Aromaticity reversal induced by vibrations in cyclo[16]carbon. J. Am. Chem. Soc. 145, 26962–26972 (2023)

  12. [12]

    Stawski, W., Zhu, Y., Rončević, I., Wei, Z., Petrukhina, M. A. & Anderson, H. L. The anti-aromatic dianion and aromatic tetraanion of [18]annulene. Nat. Chem. 16, 998– 1002 (2024)

  13. [13]

    J., Parker, A

    Gao, Y., Gupta, P., Rončević, I., Mycroft, C., Gates, P. J., Parker, A. W. & Anderson, H. L. Solution-phase stabilization of a cyclocarbon by catenane formation. Science 389, 708–710 (2025). 11

  14. [14]

    Vitek, M., Deng, J.-R., Anderson, H. L. & Rončević, I. Global aromatic ring currents in neutral porphyrin nanobelts. ACS Nano 19, 1405–1411 (2024)

  15. [15]

    M., Rončević, I., Gödde, L., Hergenhahn, J., Field, J., Gupta, P., Stawski, W

    Rodríguez-Rubio, A., Zhu, H., Cheung, K. M., Rončević, I., Gödde, L., Hergenhahn, J., Field, J., Gupta, P., Stawski, W. & Gotfredsen, H. et al. Triple-stranded porphyrin nanobelts. Science 390, 290–293 (2025)

  16. [16]

    Quan- tum chemistry with provable convergence via randomized sample-based Krylov quantum diagonalization,

    Piccinelli, S., Baiardi, A., Barison, S., Rossmannek, M., Vazquez, A., Tacchino, F., Mensa, S., Altamura, E., Alavi, A. & Motta, M. et al. Quantum chemistry with provable convergence via randomized sample-based Krylov quantum diagonalization. arXiv:2508.02578 (2025)

  17. [17]

    L., Gross, L

    Piccinelli, S., Barison, S., Baiardi, A., Tacchino, F., Repp, J., Rončević, I., Albrecht, F., Anderson, H. L., Gross, L. & Curioni, A. Exploring pathways towards quantum advantage in quantum chemistry: the case of a molecule with half-Möbius topology. arXiv:2603.08696 (2026)

  18. [18]

    L., Sundholm, D., Cossío, F

    Merino, G., Solà, M., Fernández, I., Foroutan-Nejad, C., Lazzeretti, P., Frenking, G., Anderson, H. L., Sundholm, D., Cossío, F. P. & Petrukhina, M. A. et al. Aromaticity: quo vadis. Chem. Sci. 14, 5569–5576 (2023)

  19. [19]

    & Szczepanik, D

    Solà, M. & Szczepanik, D. W. Molecular aromaticity: a quantum phenomenon. Pure Appl. Chem. 97, 1149–1157 (2025)

  20. [20]

    R., Majzik, Z., Xiong, Y., Meyer, G., Anderson, H

    Pavliček, N., Gawel, P., Kohn, D. R., Majzik, Z., Xiong, Y., Meyer, G., Anderson, H. L. & Gross, L. Polyyne formation via skeletal rearrangement induced by atomic manipulation. Nat. Chem. 10, 853–858 (2018)

  21. [21]

    W., Gao, Y., Gupta, P., Thompson, A

    Patrick, C. W., Gao, Y., Gupta, P., Thompson, A. L., Parker, A. W. & Anderson, H. L. Masked alkynes for synthesis of threaded carbon chains. Nat. Chem. 16, 193–200 (2024)

  22. [22]

    von Helden, G., Hsu, M.-T., Kemper, P. R. & Bowers, M. T. Structures of carbon cluster ions from 3 to 60 atoms: linears to rings to fullerenes. J. Chem. Phys. 95, 3835–3837 (1991)

  23. [23]

    & Bowers, M

    von Helden, G., Hsu, M.-T., Gotts, N. & Bowers, M. T. Carbon cluster cations with up to 84 atoms: structures, formation mechanisms and reactivity. J. Phys. Chem. 97, 8182–8192 (1993)

  24. [24]

    M., Fye, J

    Hunter, J. M., Fye, J. L., Roskamp, E. J. & Jarrold, M. F. Annealing carbon cluster ions: a mechanism for fullerene synthesis. J. Phys. Chem. 98, 1810–1818 (1994)

  25. [25]

    Rademacher, J., Reedy, E. S. & Campbell, E. K. Electronic spectroscopy of monocyclic carbon ring cations for astrochemical consideration. J. Phys. Chem. A 126, 2127– 2133 (2022)

  26. [26]

    J., Buntine, J

    Marlton, S. J., Buntine, J. T., Watkins, P., Liu, C., Jacovella, U., Carrascosa, E., Bull, J. N. & Bieske, E. J. Probing colossal carbon rings. J. Phys. Chem. A 127, 1168–1178 (2023)

  27. [27]

    von Helden, G., Gotts, N. G. & Bowers, M. T. Experimental evidence for the formation of fullerenes by collisional heating of carbon rings in the gas phase. Nature 363, 60–63 (1993). 12

  28. [28]

    W., Ross, M

    McElvany, S. W., Ross, M. M., Goroff, N. S. & Diederich, F. Cyclocarbon coalescence: mechanisms for tailor-made fullerene formation. Science 259, 1594–1596 (1993)

  29. [29]

    New method for calculating the one-particle Green’s function with application to the electron-gas problem

    Hedin, L. New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys. Rev. 139, A796 (1965)

  30. [30]

    & Meyer, G

    Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. The chemical structure of a molecule resolved by atomic force microscopy. Science 325, 1110–1114 (2009)

  31. [31]

    & Meyer, G

    Gross, L., Mohn, F., Moll, N., Schuler, B., Criado, A., Guitián, E., Peña, D., Gourdon, A. & Meyer, G. Bond-order discrimination by atomic force microscopy. Science 337, 1326–1329 (2012)

  32. [32]

    M., Kaiser, K., Schulz, F., Sterling, A

    Scriven, L. M., Kaiser, K., Schulz, F., Sterling, A. J., Woltering, S. L., Gawel, P., Christensen, K. E., Anderson, H. L. & Gross, L. Synthesis of cyclo[18]carbon via debromination of C₁₈Br₆. J. Am. Chem. Soc. 142, 12921–12924 (2020)

  33. [33]

    & Repp, J

    Swart, I., Sonnleitner, T., Niedenführ, J. & Repp, J. Controlled lateral manipulation of molecules on insulating films by STM. Nano Lett. 12, 1070–1074 (2012)

  34. [34]

    A., Schirmeisen, A

    Zhong, Q., Ihle, A., Ahles, S., Wegner, H. A., Schirmeisen, A. & Ebeling, D. Constructing covalent organic nanoarchitectures molecule by molecule via scanning probe manipulation. Nat. Chem. 13, 1133–1139 (2021)

  35. [35]

    M., Gourdon, A

    Repp, J., Meyer, G., Stojković, S. M., Gourdon, A. & Joachim, C. Molecules on insulating films: scanning-tunnelling microscopy imaging of individual molecular orbitals. Phys. Rev. Lett. 94, 026803 (2005)

  36. [36]

    E., Paavilainen, M., Persson, M., Repp, J

    Olsson, F. E., Paavilainen, M., Persson, M., Repp, J. & Meyer, G. Multiple charge states of Ag atoms on ultrathin NaCl films. Phys. Rev. Lett. 98, 176803 (2007)

  37. [37]

    & Giovannini, T

    Grillo, S., Pulci, O. & Giovannini, T. Optical response of aromatic cyclocarbons. Chem. Sci. 16, 22465–22472 (2025)

  38. [38]

    J., Caruso, F., Sharifzadeh, S., Ren, X., Scheffler, M., Liu, F., Lischner, J., Lin, L., Deslippe, J

    van Setten, M. J., Caruso, F., Sharifzadeh, S., Ren, X., Scheffler, M., Liu, F., Lischner, J., Lin, L., Deslippe, J. R. & Louie, S. G. et al. GW100: benchmarking G₀W₀ for molecular systems. J. Chem. Theory Comput. 11, 5665–5687 (2015)

  39. [39]

    W., Wang, X., Gallandi, L., Dolgounitcheva, O., Ren, X., Ortiz, J

    Knight, J. W., Wang, X., Gallandi, L., Dolgounitcheva, O., Ren, X., Ortiz, J. V., Rinke, P., Körzdörfer, T. & Marom, N. Accurate ionization potentials and electron affinities of acceptor molecules III. J. Chem. Theory Comput. 12, 615–626 (2016)

  40. [40]

    A., Jeanmairet, G., Alavi, A

    Sharma, S., Holmes, A. A., Jeanmairet, G., Alavi, A. & Umrigar, C. J. Semistochastic heat-bath configuration interaction method. J. Chem. Theory Comput. 13, 1595–1604 (2017)

  41. [41]

    HOMO–LUMO gap as an index of molecular size and structure for polycyclic aromatic hydrocarbons and asphaltenes

    Ruiz-Morales, Y. HOMO–LUMO gap as an index of molecular size and structure for polycyclic aromatic hydrocarbons and asphaltenes. J. Phys. Chem. A 106, 11283– 11308 (2002)

  42. [42]

    C., Tschumper, G

    Rienstra-Kiracofe, J. C., Tschumper, G. S., Schaefer, H. F., Nandi, S. & Ellison, G. B. Atomic and molecular electron affinities. Chem. Rev. 102, 231–282 (2002)

  43. [43]

    Wu, S., Nazin, G., Chen, X., Qiu, X. & Ho, W. Control of relative tunnelling rates in single-molecule bipolar electron transport. Phys. Rev. Lett. 93, 236802 (2004). 13

  44. [44]

    Fernández-Torrente, I., Franke, K. J. & Pascual, J. I. Spectroscopy of C60 single molecules: the role of screening. J. Phys. Condens. Matter 20, 184001 (2008)

  45. [45]

    & Scheffler, M

    Freysoldt, C., Rinke, P. & Scheffler, M. Controlling polarization at insulating surfaces. Phys. Rev. Lett. 103, 056803 (2009)

  46. [46]

    & Persson, M

    Scivetti, I. & Persson, M. Frontier molecular orbitals of a single molecule adsorbed on thin insulating films. J. Phys. Condens. Matter 29, 355002 (2017)

  47. [47]

    K., Kawai, M

    Imai-Imada, M., Imada, H., Miwa, K., Jung, J., Shimizu, T. K., Kawai, M. & Kim, Y. Energy-level alignment of a single molecule on ultrathin insulating film. Phys. Rev. B 98, 201403 (2018)

  48. [48]

    & Repp, J

    Sellies, L., Eckrich, J., Gross, L., Donarini, A. & Repp, J. Controlled single-electron transfer enables time-resolved excited-state spectroscopy of individual molecules. Nat. Nanotechnol. 20, 27–35 (2025)

  49. [49]

    Giessibl, F. J. High-speed force sensor for force microscopy utilizing a quartz tuning fork. Appl. Phys. Lett. 73, 3956–3958 (1998)

  50. [50]

    R., Grütter, P., Horne, D

    Albrecht, T. R., Grütter, P., Horne, D. & Rugar, D. Frequency modulation detection using high-Q cantilevers. J. Appl. Phys. 69, 668–673 (1991). Acknowledgements: This work was funded by European Research Council grant no. 885606, ARO-MAT (H.L.A. and Y.G.); European Community Horizon 2020, grant project 101019310 CycloCarbonCatenane (Y.G. and H.L.A.); Euro...

  51. [51]

    MgSO4 was used as the drying reagent after the aqueous work-up

    Synthetic general methods: Reagents were purchased reagent-grade from commercial suppliers and used without further purification. MgSO4 was used as the drying reagent after the aqueous work-up. Petroleum ether was used having a boiling point range of 40–60 °C. Thin layer chromatography (TLC) was carried out on aluminium-backed silica gel plates with 0.2 m...

  52. [52]

    1) (80 mg, 0.177 mmol) in THF/H2O (6 mL/0.06 mL) was added tetrabutylammonium fluoride (TBAF , 1.0 M in THF , 390 µL, 0.39 mmol) at 0 °C

    Synthetic protocols: C22-ketal: To a soluƟon of compound S1 (ref. 1) (80 mg, 0.177 mmol) in THF/H2O (6 mL/0.06 mL) was added tetrabutylammonium fluoride (TBAF , 1.0 M in THF , 390 µL, 0.39 mmol) at 0 °C. The soluƟon was sƟrred for 1 h at 0 °C, then water (10 mL) and petroleum ether (20 mL) were added, the layers were separated, and the aqueous phase was ex...

  53. [53]

    NMR comparison: Figure S4. Partial 1H NMR spectra of even CN-ketals (N = 16 – 24) and S2 (400 MHz, CDCl3) showing evidence for an anti-aromatic ring current in compound C20-ketal and an aromatic ring current in C22-ketal. Figure S5. Summary of the shielding and deshielding of the methoxy groups across the five different rings, relative to compound S2. A s...

  54. [54]

    Stability tests: The thermal decomposition of compound C22(CO)8 at 25 °C was monitored by UV-vis spectroscopy, as measured in CHCl3 (Fig. S6b). To perform these experiments, concentrated solutions of C22(CO)8 in CHCl3 were prepared, such that diluting 100 µL of the concentrated solution into 2.5 mL of CHCl3 in a 10-mm pathlength cuvette gave a UV-vis abso...

  55. [55]

    1H NMR (500 MHz) spectra of C22-ketal showing the presence of C24-ketal by- product in CDCl3

    C24 by-product: Figure S7. 1H NMR (500 MHz) spectra of C22-ketal showing the presence of C24-ketal by- product in CDCl3. The top trace shows the 1H NMR (500 MHz) spectrum of the C24-ketal.2 During the synthesis of C22-ketal product, a small amount of the C24-ketal by-product is also formed. Most of this C24-ketal impurity can be removed by silica gel chro...

  56. [56]

    Generation of large cyclocarbons: We formed 172 individual C22 molecules. We determined the yield for the conversion of precursor 1 into C22 from 45 precursor molecules 1 on the NaCl surface, of which we successfully converted 33 into C22, corresponding to a yield of 73%. We formed 15 individual C20 molecules from precursor molecules 3. Note that some pre...

  57. [57]

    Additional AFM data on C20

    AFM characterization of large cyclocarbons: Figure S19. Additional AFM data on C20. (a-d) AFM raw data (top) and Laplace-filtered AFM data (bottom). The molecule is on bilayer NaCl on Au(111). Tip-height offsets Δz with respect to the STM setpoint: V = 0.2 V, I = 0.3 pA. Figure S20. AddiƟonal AFM data on C22. (a-d) AFM raw data (top) and Laplace-filtered A...

  58. [58]

    For large rings (C46, C66 and C88) we oŌen observe that segments of the ring appear doubled in AFM images, see Figs

    Doubling of ring segments of large cyclocarbons and intensity modulaƟon of STM orbital density maps: In AFM images, the Cl sites of NaCl are observed as bright features, from which we can deduce the crystallographic orientaƟon of the NaCl surface and the adsorpƟon site of the molecule. For large rings (C46, C66 and C88) we oŌen observe that segments of th...

  59. [59]

    The NIR and PIR densiƟes for both N = 4n (Figs

    STM characterization of large cyclocarbons: For each cyclocarbon formed in this study, we mapped by STM the negaƟve (NIR) and posiƟve (PIR) ion resonances, which reflect the orbital densiƟes associated with electron aƩachment (NIR) and detachment (PIR)5,6. The NIR and PIR densiƟes for both N = 4n (Figs. S27, S30 and S33) and N = 4n+2 cyclocarbons (Figs. S2...

  60. [60]

    Input cards for OX-BLYP30: GAUSSIAN 16: # Single point energy calculaƟon with OX-BLYP30 (=0.025, EXHF: 30% => 100%) in Gaussian16 %nproc=36 %mem=72GB #p def2tzvp cam-b3lyp IOp(3/107=0025000000,3/108=0025000000,3/119=0700000000,3/120=0700000000,3/130=03000,3/131=03000) ORCA 6.1: # Single point energy calculaƟon with OX-BLYP30 (=0.025, EXHF: 30% => 100%) ...

  61. [61]

    Computational Methods: All geometry optimizations were performed using the def2-TZVP basis set8 within GAUSSIAN 16.9 For functional tuning, geometry optimizations were carried out using the smaller def2- SVP basis set.8 Harmonic frequency calculations were performed to confirm that the optimized geometries correspond to either minima (all positive frequen...

  62. [62]

    A geometry optimization with an ideal DFA will yield the correct equilibrium geometry and exact ground state energy at equilibrium, Eexact,eq

    Functional tuning: This work follows our recently introduced strategy for fine-tuning DFAs.18 Briefly, a single- point calculation with the ideal DFA will give the exact ground state energy Eexact. A geometry optimization with an ideal DFA will yield the correct equilibrium geometry and exact ground state energy at equilibrium, Eexact,eq. If we assume tha...

  63. [63]

    Bond-length alternation in cyclocarbons: To compute the BLA in the optimized cyclo[N]carbon geometries, we identified all carbon– carbon bonds and sorted the bond lengths in ascending order. BLA was defined as the difference between the average of the longer half and the shorter half of these sorted bond lengths: BLA=ൻ𝑑longൿ−⟨𝑑short⟩ (1) where the average...

  64. [64]

    The cyclization energy of cyclo[N]carbon (CN) was evaluated relative to linear polyynic precursors using the isodesmic reaction in Scheme S1

    Aromatic stabilization energies: Cyclization. The cyclization energy of cyclo[N]carbon (CN) was evaluated relative to linear polyynic precursors using the isodesmic reaction in Scheme S1. Scheme S1. Isodesmic reaction used to compute cyclocarbon cyclisation energies. Strain and Aromatic stabilization energy. The cyclization energy Ecyc can be written as a...

  65. [65]

    Transport gaps Δ calculated at OX-BLYP30/def2-TZVP (a) and G0W0@OX- BLYP30/def2-QZVP (b) level of theory for even-N cyclocarbons with N = 6–100

    Other supplementary figures: Figure S39. Transport gaps Δ calculated at OX-BLYP30/def2-TZVP (a) and G0W0@OX- BLYP30/def2-QZVP (b) level of theory for even-N cyclocarbons with N = 6–100. Figure S40. Linear regression between G0W0@OX-BLYP30/def2-QZVP gaps and OX- BLYP30/def2-TZVP IPEA gaps for even-N cyclocarbons with N = 6–100. The dashed line indicates th...

  66. [66]

    These calculaƟons were done using OpenMolcas24 and the cc-pVDZ25 basis set

    Quantum compuƟng To invesƟgate electron correlaƟon, we performed single-point calculaƟons on BLYP30/def2- TZVP-opƟmized geometries of C20 and C22 at the Hartree-Fock (HF) and the complete acƟve space self-consistent field (CASSCF) levels of theory. These calculaƟons were done using OpenMolcas24 and the cc-pVDZ25 basis set. AcƟve space consideraƟons. As eve...

  67. [67]

    References of Supplementary InformaƟon 1 Kaiser, K. et al. An sp-hybridized molecular carbon allotrope, cyclo[18]carbon. Science 365, 1299-1301 (2019). https://doi.org/10.1126/science.aay1914 2 Gao, Y. et al. On-surface synthesis of a doubly anti-aromatic carbon allotrope. Nature (2023). https://doi.org/10.1038/s41586-023-06566-8 3 Lie, Y., Baryshnikov, G...