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Substantial π-aromaticity in the anionic heavy-metal cluster [Th@Bi12]4−

Abstract

The concept of aromaticity was originally defined as a property of unsaturated, cyclic planar organic molecules like benzene, which gain stability by the inherent delocalization of 4n + 2 π-electrons over the ring atoms. Since then, π-aromaticity has been observed for a large variety of organic and inorganic non-metal compounds, yet, for molecules consisting only of metal atoms, it has remained restricted to systems with three to five atoms. Here, we present the straightforward synthesis of a metal 12-ring that exhibits 2π-aromaticity and has a ring current much stronger than that of benzene (6π) and equivalent to that of porphine (26π), despite these organic molecules having (much) larger numbers of π-electrons. Highly reducing reaction conditions allowed access to the heterometallic anion [Th@Bi12]4−, with interstitial Th4+ stabilizing a Bi128− moiety. Our results show that it is possible to design and generate substantial π-aromaticity in large metal rings, and we hope that such π-aromatic heavy-metal cycles will eventually find use in cluster-based reactions.

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Fig. 1: Survey of different classes of experimentally secured molecules exhibiting 4n + 2 π-aromaticity.
Fig. 2: Molecular structure of the cluster anion [Th@Bi12]4− in compound 2.
Fig. 3: Frontier orbital region of the molecular orbital schemes of anions based on 12-atomic polybismuthide rings.
Fig. 4: HOMO of the cluster anion [Th@Bi12]4− and localized molecular orbitals (LMOs) from a Boys localization procedure in top and side views.
Fig. 5: Calculated ring currents in [Th@Bi12]4−.

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Data availability

All data generated or analysed during this study are included in this Article and its Supplementary Information files. The structures of compounds 14 were determined by single-crystal X-ray diffraction. The crystallographic data have been deposited with the Cambridge Crystallographic Data Centre under CCDC numbers 1983070 (1), 1983072 (2), 1983073 (3) and 1983071 (4).

The optimized structures of all studied compounds are part of the Supplementary Information (separate zip file ‘Supplementary-Computational-Data.zip’): the coordinates of the optimized structures shown in Fig. 1, as well as their NICS values and ring current strengths, are provided in the Supplementary File ‘Fig1-OptimizedStructures-GIMIC-NICS.txt’. All calculated coordinates of the optimized structures of 2A and the compounds mentioned explicitly in the main text or Supplementary Information are provided in a Supplementary File ‘OptimizedStructures.txt’. The files comprise all necessary data for reproducing the values. All non-default parameters for the computational studies are given in the Supplementary Information together with the corresponding references of the used methods. For the default parameters of TURBOMOLE, such as the convergence criteria for structure optimizations, please see the manual at https://www.turbomole.org (retrieved 29 August 2020).

References

  1. Hückel, E. Quantentheoretische Beiträge zum Benzolproblem. I. Die Elektronenkonfiguration des Benzols und verwandter Beziehungen. Z. Phys. 70, 204–286 (1931).

    Article  Google Scholar 

  2. McNaught, A. D. & Wilkinson, A. IUPAC. Compendium of Chemical Terminology 2nd edn (Blackwell Scientific Publications, 1997); online version (2019) created by S. J. Chalk.

  3. Schleyer, P. V. R. & Jiao, H. What is aromaticity? Pure Appl. Chem. 68, 209–221 (1996).

    Article  CAS  Google Scholar 

  4. Gershoni-Poranne, R. & Stanger, A. Magnetic criteria of aromaticity. Chem. Soc. Rev. 44, 6597–6615 (2015).

    Article  CAS  PubMed  Google Scholar 

  5. Sundholm, D., Fliegl, H. & Berger, R. J. Calculation of magnetically induced current densities: theory and applications. Wiley Interdiscip. Rev. Comput. Mol. Sci. 6, 639–678 (2016).

    Article  CAS  Google Scholar 

  6. Schleyer, P. V. R., Maerker, C., Dransfeld, A., Jiao, H. & Hommes, N. Nucleus-independent chemical shifts: a simple and efficient aromaticity probe. J. Am. Chem. Soc. 118, 6317–6318 (1996).

    Article  CAS  PubMed  Google Scholar 

  7. Sekiguchi, A., Matsuo, T. & Watanabe, H. Synthesis and characterization of a cyclobutadiene dianion dilithium salt: evidence for aromaticity. J. Am. Chem. Soc. 122, 5652–5653 (2000).

    Article  CAS  Google Scholar 

  8. Wehrmann, R., Meyer, H. & Berndt, A. Diboriranides and a 1,3-diboraallyl system with B-H-B bridge. Angew. Chem. Int. Ed. 24, 788–790 (1985).

    Article  Google Scholar 

  9. Zhu, Z., Wang, X., Olmstead, M. M. & Power, P. P. Synthesis and characterization of [Ar′GaC(Ph)CH]2 and K2[Ar′GaC(Ph)CH]2·OEt2: from digallene to digallacyclohexadiene to digallatabenzene. Angew. Chem. Int. Ed. 48, 2027–2030 (2009).

    Article  CAS  Google Scholar 

  10. De Proft, F. et al. Ring currents as probes of the aromaticity of inorganic monocycles: P5, As5, S2N2, S3N3, S4N3+, S4N42+, S5N5+, S42+ and Se42+. Chem. Eur. J. 10, 940–950 (2004).

    Article  PubMed  CAS  Google Scholar 

  11. Jin, J. et al. The [B3(NN)3]+ and [B3(CO)3]+ complexes featuring the smallest π-aromatic species B3+. Angew. Chem. Int. Ed. 55, 2078–2082 (2016).

    Article  CAS  Google Scholar 

  12. Unverzagt, M. et al. Carbene analogues of boron stabilized by neighboring B–B moieties: doubly aromatic bishomotriboriranides. Angew. Chem. Int. Ed. 36, 1469–1472 (1997).

    Article  Google Scholar 

  13. Präsang, C., Hofmann, M., Geiseler, G., Massa, W. & Berndt, A. Aromatic boranes with planar-tetracoordinate boron atoms and very short B–B distances. Angew. Chem. Int. Ed. 41, 1526–1529 (2002).

    Article  Google Scholar 

  14. Maier, A., Hofmann, M., Pritzkow, H. & Siebert, W. A planar, aromatic bicyclo‐tetraborane(4). Angew. Chem. Int. Ed. 41, 1529–1532 (2002).

    Article  CAS  Google Scholar 

  15. Takanashi, K., Lee, V. Y. & Sekiguchi, A. Tetrasilacyclobutadiene and cyclobutadiene tricarbonylruthenium complexes: η4-(tBu2MeSi)4Si4]Ru(CO)3 and [η4-(Me3Si)4C4]Ru(CO)3. Organometallics 28, 1248–1251 (2009).

    Article  CAS  Google Scholar 

  16. Gleiter, R. Structure and bonding in cyclic sulfur–nitrogen compounds—molecular orbital considerations. Angew. Chem. Int. Ed. 20, 444–452 (1981).

    Article  Google Scholar 

  17. Bucholz, C. F. Versuche über die Auflösung des Indigs in der Schwefelsäure, als Beytrag zur Ausmittelung des Vorgangs bey Verselben. Gehlen’s Neues J. Chem. 3, 3–29 (1804).

    Google Scholar 

  18. Gillespie, R. J. & Passmore, J. Polycations of group VI. Acc. Chem. Res. 4, 413–419 (1971).

    Article  CAS  Google Scholar 

  19. Kraus, F., Aschenbrenner, J. C. & Korber, N. P42−: a 6π aromatic polyphosphide in dicesium cyclotetraphosphide–ammonia (1/2). Angew. Chem. Int. Ed. 42, 4030–4033 (2003).

    Article  CAS  Google Scholar 

  20. Korber, N. & Reil, M. An isolated cyclo-tetraarsendiide: low temperature synthesis and crystal structure of bis-pentaamminesodium tetraarsendiide–ammonia (1/3) [Na(NH3)5]2As4·3NH3. Chem. Commun. 84–85 (2002); https://doi.org/10.1039/b108879c

  21. Cisar, A. & Corbett, J. D. Polybismuth anions. Synthesis and crystal structure of a salt of the tetrabismuthide(2−) ion, Bi42−. A basis for the interpretation of the structure of some complex intermetallic phases. Inorg. Chem. 16, 2482–2487 (1977).

    Article  CAS  Google Scholar 

  22. Critchlow, S. C. & Corbett, J. D. Homopolyatomic anions of the post transition elements. Synthesis and structure of potassium-crypt salts of the tetraantimonide(2−) and heptaantimonide(3−) anions, Sb42− and Sb73−. Inorg. Chem. 23, 770–774 (1984).

    Article  CAS  Google Scholar 

  23. Velian, A. & Cummins, C. C. Synthesis and characterization of P2N3: an aromatic ion composed of phosphorus and nitrogen. Science 348, 1001–1004 (2015).

    Article  CAS  PubMed  Google Scholar 

  24. Scherer, O. J. Complexes with substituent-free acyclic and cyclic phosphorus, arsenic, antimony and bismuth ligands. Angew. Chem. Int. Ed. 29, 1104–1122 (1990).

    Article  Google Scholar 

  25. Li, X.-W., Pennington, W. T. & Robinson, G. H. A metallic system with aromatic character. Synthesis and molecular structure of Na2[(Mes2C6H3)Ga]3 (Mes = 2,4,6-Me3C6H2): the first cyclogallane. J. Am. Chem. Soc. 117, 7578–7579 (1995).

    Article  CAS  Google Scholar 

  26. Li, X.-W. et al. Cyclogallanes and metalloaromaticity. Synthesis and molecular structure of dipotassium tris((2,6-dimesitylphenyl)cyclogallene), K2[(Mes2C6H3)Ga]3 (Mes = 2,4,6-Me3C6H2): a structural and theoretical examination. Organometallics 15, 3798–3803 (1996).

    Article  CAS  Google Scholar 

  27. Wright, R. J., Brynda, M. & Power, P. P. Synthesis and structure of the ‘dialuminyne’ Na2[Ar′AlAlAr′] and Na2[(Ar″Al)3]: Al−Al bonding in Al2Na2 and Al3Na2 clusters. Angew. Chem. Int. Ed. 45, 5953–5956 (2006).

    Article  CAS  Google Scholar 

  28. Li, X. L., Kuznetsov, A. E., Zhang, H.-F., Boldyrev, A. I. & Wang, L.-S. Observation of all-metal aromatic molecules. Science 291, 859–861 (2001).

    Article  CAS  PubMed  Google Scholar 

  29. Kuznetsov, A. E., Boldyrev, A. I., Li, X. & Wang, L.-S. On the aromaticity of square planar Ga42− and In42− in gaseous NaGa4 and NaIn4 clusters. J. Am. Chem. Soc. 123, 8825–8831 (2001).

    Article  CAS  PubMed  Google Scholar 

  30. Boldyrev, A. I. & Wang, L. S. All-metal aromaticity and antiaromaticity. Chem. Rev. 105, 3716–3757 (2005).

    Article  CAS  PubMed  Google Scholar 

  31. Pan, F.-X. et al. An all-metal aromatic sandwich complex [Sb3Au3Sb3]3−. J. Am. Chem. Soc. 137, 10954–10957 (2015).

    Article  CAS  PubMed  Google Scholar 

  32. Twamley, B. & Power, P. P. Synthesis of the square-planar gallium species K2[Ga4(C6H3-2,6-Trip2)2] (Trip = C6H2-2,4,6-iPr3): the role of aryl–alkali metal ion interactions in the structure of gallium clusters. Angew. Chem. Int. Ed. 39, 3500–3503 (2000).

  33. Kuznetsov, A. E., Corbett, J. D., Wang, L. S. & Boldyrev, A. I. Aromatic mercury clusters in ancient amalgams. Angew. Chem. Int. Ed. 40, 3369–3372 (2001).

    Article  CAS  Google Scholar 

  34. Gausa, M., Kaschner, R., Lutz, H. O., Seifert, G. & Meiwes-Broer, K.-H. Photoelectron and theoretical investigations on bismuth and antimony pentamer anions: evidence for aromatic structure. Chem. Phys. Lett. 230, 99–102 (1994).

    Article  CAS  Google Scholar 

  35. Todorov, I. & Sevov, S. C. Heavy-metal aromatic rings: cyclopentadienyl anion analogues Sn56− and Pb56− in the Zintl phases Na8BaPb6, Na8BaSn6 and Na8EuSn6. Inorg. Chem. 43, 6490–6494 (2004).

    Article  CAS  PubMed  Google Scholar 

  36. Yong, L., Hoffmann, S. D., Fässler, T. F., Riedel, S. & Kaupp, M. [Pb5{Mo(CO)3}2]4−: a complex containing a planar Pb5 unit. Angew. Chem. Int. Ed. 44, 2092–2096 (2005).

    Article  CAS  Google Scholar 

  37. Zubarev, D. Y., Averkiev, B. B., Zhai, H.-J., Wang, L.-S. & Boldyrev, A. I. Aromaticity and antiaromaticity in transition-metal systems. Phys. Chem. Chem. Phys. 10, 257–267 (2008).

    Article  CAS  PubMed  Google Scholar 

  38. Kuznetsov, A. E. & Boldyrev, A. I. A single π-bond captures 3, 4 and 5 atoms. Chem. Phys. Lett. 388, 452–456 (2004).

    Article  CAS  Google Scholar 

  39. Liu, C., Popov, I. A., Chen, Z., Boldyrev, A. I. & Sun, Z.-M. Aromaticity and antiaromaticity in Zintl clusters. Chem. Eur. J. 24, 14583–14597 (2018).

    Article  CAS  PubMed  Google Scholar 

  40. Huang, X., Zhai, H. ‐J., Kiran, B. & Wang, L. ‐S. Observation of d‐orbital aromaticity. Angew. Chem. Int. Ed. 44, 7251–7254 (2005).

    Article  CAS  Google Scholar 

  41. Popov, I. A. et al. Peculiar all-metal σ-aromaticity of the [Au2Sb16]4− anion in the solid. Angew. Chem. Int. Ed. 55, 15344–15346 (2016).

    Article  CAS  Google Scholar 

  42. Liu, C. et al. [Co2@Ge16]4−: localized versus delocalized bonding in two isomeric intermetalloid clusters. Chem. Eur. J. 24, 699–705 (2018).

    Article  CAS  PubMed  Google Scholar 

  43. Jones, C. E. Jr. et al. AlnBi clusters: transitions between aromatic and jellium stability. J. Phys. Chem. 112, 13316–13325 (2008).

    Article  CAS  Google Scholar 

  44. Wilson, R. J., Lichtenberger, N., Weinert, B. & Dehnen, S. Intermetalloid and heterometallic clusters combining p-block (semi)metals with d- or f-block metals. Chem. Rev. 119, 8506–8554 (2019).

    Article  CAS  PubMed  Google Scholar 

  45. Min, X. et al. All‐metal antiaromaticity in Sb4‐type lanthanocene anions. Angew. Chem. Int. Ed. 55, 5531–5535 (2016).

    Article  CAS  Google Scholar 

  46. Lichtenberger, N. et al. Main group metal–actinide magnetic coupling and structural response upon U4+ inclusion into Bi, Tl/Bi or Pb/Bi cages. J. Am. Chem. Soc. 138, 9033–9036 (2016).

    Article  CAS  PubMed  Google Scholar 

  47. Xu, L. & Sevov, S. C. Heteroatomic deltahedral clusters of main-group elements: synthesis and structure of the Zintl ions [In4Bi5]3−, [InBi3]2− and [GaBi3]2−. Inorg. Chem. 39, 5383–5389 (2000).

    Article  CAS  PubMed  Google Scholar 

  48. Turbomole version 7.4.1 2019 and version 7.5 2020 (University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH since 2007); https://www.turbomole.org

  49. Balasubramani, S. G. et al. TURBOMOLE: modular program suite for ab initio quantum-chemical and condensed-matter simulations. J. Chem. Phys. 152, 184107 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996); erratum 78, 1396 (1997).

    Article  CAS  PubMed  Google Scholar 

  51. Cao, X., Dolg, M. & Stoll, H. Valence basis sets for relativistic energy consistent small-core actinide pseudopotentials. J. Chem. Phys. 118, 487–496 (2003).

    Article  CAS  Google Scholar 

  52. Metz, B., Stoll, H. & Dolg, M. Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: application to PbH and PbO. J. Chem. Phys. 113, 2563–2569 (2000).

    Article  CAS  Google Scholar 

  53. Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7, 3297–3305 (2005).

    Article  CAS  PubMed  Google Scholar 

  54. Schäfer, A., Klamt, A., Sattel, D., Lohrenz, J. C. W. & Eckert, F. COSMO Implementation in TURBOMOLE: extension of an efficient quantum chemical code towards liquid systems. Phys. Chem. Chem. Phys. 2, 2187–2193 (2000).

    Article  Google Scholar 

  55. Mulliken, R. S. Electronic population analysis on LCAO–MO molecular wave functions. I. J. Chem. Phys. 23, 1833–1840 (1955).

    Article  CAS  Google Scholar 

  56. Boys, S. F. Construction of some molecular orbitals to be approximately invariant for changes from one molecule to another. Rev. Mod. Phys. 32, 296–299 (1960).

    Article  CAS  Google Scholar 

  57. Knizia, G. Intrinsic atomic orbitals: an unbiased bridge between quantum theory and chemical concepts. J. Chem. Theory Comput. 9, 4834–4843 (2013).

    Article  CAS  PubMed  Google Scholar 

  58. Becke, A. D. & Edgecombe, K. E. A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 92, 5397–5403 (1990).

    Article  CAS  Google Scholar 

  59. Jusélius, J., Sundholm, D. & Gauss, J. Calculation of current densities using gauge-including atomic orbitals. J. Chem. Phys. 121, 3952–3963 (2004); https://github.com/qmcurrents/gimic

  60. Peng, D., Middendorf, N., Weigend, F. & Reiher, M. An efficient implementation of two-component relativistic exact-decoupling methods for large molecules. J. Chem. Phys. 138, 184105 (2013).

    Article  PubMed  CAS  Google Scholar 

  61. Franzke, Y. J., Middendorf, N. & Weigend, F. Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory. J. Chem. Phys. 148, 104110 (2018).

    Article  PubMed  CAS  Google Scholar 

  62. Franzke, Y. J. & Weigend, F. NMR shielding tensors and chemical shifts in scalar-relativistic local exact two-component theory. J. Chem. Theory Comput. 15, 1028–1043 (2019).

    Article  PubMed  CAS  Google Scholar 

  63. Franzke, Y. J., Treß, R., Pazdera, T. M. & Weigend, F. Error-consistent segmented contracted all-electron relativistic basis sets of double- and triple-zeta quality for NMR shielding constants. Phys. Chem. Chem. Phys. 21, 16658–16664 (2019).

    Article  CAS  PubMed  Google Scholar 

  64. Franzke, Y. J., Sundholm, D. & Weigend, F. Calculations of current densities and aromatic pathways in cyclic porphyrin and isoporphyrin arrays. Phys. Chem. Chem. Phys. 19, 12794–12803 (2017).

    Article  CAS  PubMed  Google Scholar 

  65. Lichtenberger, N., Spang, N., Eichhöfer, A. & Dehnen, S. Between localization and delocalization: Ru(cod)2+ units in the Zintl clusters [Bi9{Ru(cod)}2]3− and [Tl2Bi6{Ru(cod)}]2−. Angew. Chem. Int. Ed. 56, 13253–13258 (2017).

    Article  CAS  Google Scholar 

  66. Ababei, R. et al. Making practical use of the pseudo-element concept: an efficient way to ternary intermetalloid clusters by an isoelectronic Pb–Bi combination. Chem. Commun. 48, 11295–11297 (2012).

    Article  CAS  Google Scholar 

  67. Deubner, H. L., Rudel, S. S. & Kraus, F. A simple access to pure thorium(iv) halides (ThCl4, ThBr4 & ThI4). Z. Anorg. Allg. Chem. 643, 2005–2010 (2017).

    Article  CAS  Google Scholar 

  68. Sheldrick, G. M. SHELXT—integrated space-group and crystal-structure determination. Acta Crystallogr. A Found. Adv. 71, 3–8 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  69. Sheldrick, G. M. Crystal structure refinement with SHELXL. Acta Crystallogr. C Struct. Chem. 71, 3–8 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  70. Reiter, K., Mack, F. & Weigend, F. Calculation of magnetic shielding constants with meta-GGA functionals employing the multipole-accelerated resolution of the identity: implementation and assessment of accuracy and efficiency. J. Chem. Theory Comput. 14, 191–197 (2018).

    Article  PubMed  CAS  Google Scholar 

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Acknowledgements

We thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for financial support within the framework of GRK 1782. We thank J.L. Vasco and M. Pyschik for help with the synthesis, S. Ivlev, B. Weinert, M. Marsch and R. Riedel for help with the diffraction experiments, and M. Hellwig for measuring the EDX spectra of 1. We also thank K. Reiter and F. Dehnen for discussions. N.L. acknowledges a grant from Marburg University Research Academy (MARA). Y.J.F. is grateful to Fonds der Chemischen Industrie for general support of his PhD. studies (Kekulé fellowship), to the German Academic Exchange Service (Deutscher Akademischer Austauschdienst, DAAD) for a fellowship (grant no. 57438025) and to F. Furche for hosting. R.C. acknowledges support from the University of Bordeaux, the CNRS, the Region Nouvelle Aquitaine, the MOLSPIN COST action CA15128 and the GdR MCM-2.

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Contributions

A.R.E., N.L., R.J.W. and H.L.D. conceived and performed the synthetic experiments, collected single-crystal X-ray crystallographic data, solved and refined the structures, performed ESI-MS and prepared samples for further analyses. R.C. performed and analysed the magnetic measurements. F.W. performed the computational structure optimization and orbital analysis, and Y.J.F. studied the aromaticity and performed the TD-DFT calculations as well as the structure optimizations for Fig. 1. S.D., F.K. and F.W. supervised the work. All authors co-wrote the paper.

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Correspondence to Florian Weigend or Stefanie Dehnen.

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Supplementary information

Supplementary Information

Supplementary discussion on the formation of compound 2, supplementary information on X-ray diffraction (including Supplementary Table 1 and Supplementary Figs. 1–5), supplementary information on micro-X-ray fluorescence spectroscopy (µ-XFS) (including Supplementary Table 2 and Supplementary Figs. 6–8), supplementary information on electrospray ionization (ESI) mass spectrometry (including Supplementary Figs. 9–11), supplementary information on magnetic measurements of compound 2 (including Supplementary Fig. 12), supplementary details on quantum chemical investigations (including Supplementary Figs. 13–16 and Supplementary Tables 3–12).

Supplementary Data

Crystallographic information file for compound 1.

Supplementary Data

Crystallographic information file for compound 2.

Supplementary Data

Crystallographic information file for compound 3.

Supplementary Data

Crystallographic information file for compound 4.

Supplementary Data

The zip archive comprises two ASCII files entitled ‘Fig01-OptimizedStructures-GIMIC-NICS.txt’ (providing the coordinates of the optimized structures shown in Fig. 1, as well as their NICs values and ring currents) and ‘OptimizedStructures.txt’ (providing all coordinates of the optimized structures of 2A and the compounds mentioned explicitly in the manuscript or the Supplementary Information.pdf file).

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Eulenstein, A.R., Franzke, Y.J., Lichtenberger, N. et al. Substantial π-aromaticity in the anionic heavy-metal cluster [Th@Bi12]4−. Nat. Chem. 13, 149–155 (2021). https://doi.org/10.1038/s41557-020-00592-z

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