Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Direct evidence for a carbon–carbon one-electron σ-bond

Nature volume 634, pages 347–351 (2024)Cite this article

Subjects

Abstract

Covalent bonds share electron pairs between two atoms and make up the skeletons of most organic compounds in single, double and triple bonds. In contrast, examples of one-electron bonds remain scarce, most probably due to their intrinsic weakness1,2,3,4. Although several pioneering studies have reported one-electron bonds between heteroatoms, direct evidence for one-electron bonds between carbon atoms remains elusive. Here we report the isolation of a compound with a one-electron σ-bond between carbon atoms by means of the one-electron oxidation of a hydrocarbon with an elongated C–C single bond5,6. The presence of the C•C one-electron σ-bond (2.921(3) Å at 100 K) was confirmed experimentally by single-crystal X-ray diffraction analysis and Raman spectroscopy, and theoretically by density functional theory calculations. The results of this paper unequivocally demonstrate the existence of a C•C one-electron σ-bond, which was postulated nearly a century ago7, and can thus be expected to pave the way for further development in different areas of chemistry by probing the boundary between bonded and non-bonded states.

Access through your institution
Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Proposed redox mechanisms in HPE derivatives.
Fig. 2: Redox reactions and X-ray structures.
Fig. 3: Experimental evidence of the presence of a C•C one-electron σ-bond in 1•+(I3−).
Fig. 4: Electronic properties of 1•+ with a C•C one-electron σ-bond.

Similar content being viewed by others

Data availability

The X-ray data have been deposited with the Cambridge Crystallographic Data Centre under reference numbers 2301032–2301035 (1•+I3−, main_sample1), 2301036–2301039 (1•+I3−, sub_sample2) and 2301040–2301043 (12+(I3−)2). All other data are presented in the main text or the Supplementary Information.

References

  1. Canac, Y. et al. Isolation of a benzene valence isomer with one-electron phosphorus-phosphorus bonds. Science 279, 2080–2082 (1998).

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Moret, M., Zhang, L. & Peters, J. C. A polar copper–boron one-electron σ-bond. J. Am. Chem. Soc. 135, 3792–3795 (2013).

    Article  CAS  PubMed  Google Scholar 

  3. Hübner, A. et al. Confirmed by X-ray crystallography: the B⋅B one-electron σ bond. Angew. Chem. Int. Ed. 53, 4832–4835 (2014).

    Article  Google Scholar 

  4. Graziano, B. J. et al. One-electron bonds in copper–aluminum and copper–gallium complexes. Chem. Sci. 13, 6525–6531 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  5. Ishigaki, Y., Shimajiri, T., Takeda, T., Katoono, R. & Suzuki, T. Longest C–C single bond among neutral hydrocarbons with a bond length beyond 1.8 Å. Chem 4, 795–806 (2018).

    Article  CAS  Google Scholar 

  6. Shimajiri, T. The Nature of Ultralong C–C Bonds (Springer Nature, 2023).

  7. Pauling, L. The nature of the chemical bond. II. The one-electron bond and the three-electron bond. J. Am. Chem. Soc. 53, 3225–3237 (1931).

    Article  CAS  Google Scholar 

  8. Lewis, G. N. The atom and the molecule. J. Am. Chem. Soc. 38, 762–785 (1916).

    Article  CAS  Google Scholar 

  9. Langmuir, I. The arrangement of electrons in atoms and molecules. J. Franklin Inst. 187, 359–362 (1919).

    Article  Google Scholar 

  10. Clark, T. Odd-electron .sigma. bonds. J. Am. Chem. Soc. 110, 1672–1678 (1988).

    Article  CAS  Google Scholar 

  11. Ioffe, A. & Shaik, S. Ethane cation-radical isomers and their interconversion pathways. Electron shift isomerism in cation radicals. J. Chem. Soc., Perkin Trans. 2 3, 1461 (1993).

    Article  Google Scholar 

  12. Zuilhof, H., Dinnocenzo, J. P., Reddy, C. & Shaik, S. Comparative study of ethane and propane cation radicals by B3LYP density functional and high-level ab initio methods. J. Phys. Chem. 100, 15774–15784 (1996).

    Article  CAS  Google Scholar 

  13. de Sousa, D. W. O. & Nascimento, M. A. C. One-electron bonds are not ‘half-bonds’. Phys. Chem. Chem. Phys. 21, 13319–13336 (2019).

    Article  PubMed  Google Scholar 

  14. Claxton, T. A., Overill, R. E. & Symons, M. C. R. Possible structures for C2H6+ and B2H6− E.S.R. evidence and UHF calculations. Mol. Phys. 27, 701–706 (1974).

    Article  ADS  CAS  Google Scholar 

  15. DuPont, T. J. & Mills, J. L. Arylborane anions. Electrochemical study. J. Am. Chem. Soc. 97, 6375–6382 (1975).

    Article  CAS  Google Scholar 

  16. Hudson, R. L. & Williams, F. Electron spin resonance spectrum of trimethyl borate ([(MeO)3B.cntdot.B(OMe)3]−). A novel .sigma. radical with a one-electron bond. J. Am. Chem. Soc. 99, 7714–7716 (1977).

    Article  CAS  Google Scholar 

  17. Kasai, P. H. & McLeod, D. Electron spin resonance study of molecular anions generated in argon matrix at 4°K: ESR spectrum of B2H6−. J. Chem. Phys. 51, 1250–1251 (1969).

    Article  ADS  CAS  Google Scholar 

  18. Iwasaki, M., Toriyama, K. & Nunome, K. Electron spin resonance study of electronic and geometrical structures of C2H6+ and other simple alkane cations at 4.2 K: possible evidence for Jahn–Teller distortion. J. Am. Chem. Soc. 103, 3591–3592 (1981).

    Article  CAS  Google Scholar 

  19. Wang, J. T. & Williams, F. E.S.R. spectra of the hexamethyldisilane and hexamethyldigermane radical cations. J. Chem. Soc. Chem. Commun. 1981, 666–668 (1981).

    Article  Google Scholar 

  20. Shida, T., Kubodera, H. & Egawa, Y. Confirmation of the cation radicals of hexamethylethane and hexamethyldisilane by ESR and other spectroscopy. Chem. Phys. Lett. 79, 179–182 (1981).

    Article  ADS  CAS  Google Scholar 

  21. Hoefelmeyer, J. D. & Gabbaï, F. P. An intramolecular boron–boron one-electron σ-bond. J. Am. Chem. Soc. 122, 9054–9055 (2000).

    Article  CAS  Google Scholar 

  22. Cataldo, L. et al. Formation of a phosphorus–phosphorus bond by successive one-electron reductions of a two-phosphinines-containing macrocycle: crystal structures, EPR, and DFT investigations. J. Am. Chem. Soc. 123, 6654–6661 (2001).

    Article  CAS  PubMed  Google Scholar 

  23. Rao, V. R. & Hixson, S. S. Arylcyclopropane photochemistry. Electron-transfer-mediated photochemical addition of methanol to arylcyclopropanes. J. Am. Chem. Soc. 101, 6458–6459 (1979).

    Article  CAS  Google Scholar 

  24. Dinnocenzo, J. P., Todd, W. P., Simpson, T. R. & Gould, I. R. Nucleophilic cleavage of one-electron .sigma. bonds: stereochemistry and cleavage rates. J. Am. Chem. Soc. 112, 2462–2464 (1990).

    Article  CAS  Google Scholar 

  25. Miyashi, T., Ikeda, H., Konno, A., Okitsu, O. & Takahashi, Y. Photoinduced electron-transfer reactions of the cope and related systems. Pure Appl. Chem. 62, 1531–1538 (1990).

    Article  CAS  Google Scholar 

  26. Ikeda, H. et al. Photoinduced electron-transfer degenerate cope rearrangement of 2,5-diaryl-1,5-hexadienes: a cation-radical cyclization–diradical cleavage mechanism. J. Am. Chem. Soc. 120, 87–95 (1998).

    Article  CAS  Google Scholar 

  27. Ikeda, H. et al. Photoinduced electron-transfer cope rearrangements of 3,6-diaryl-2,6-octadienes and 2,5-diaryl-3,4-dimethyl-1,5-hexadienes: stereospecificity and an unexpected formation of the bicyclo[2.2.0]hexane derivatives. J. Org. Chem. 64, 1640–1649 (1999).

    Article  CAS  PubMed  Google Scholar 

  28. Ikeda, H., Hoshi, Y. & Miyashi, T. 1,3-Bis(4-methoxyphenyl)cyclohexane-1,3-diyl cation radical: divergent reactivity depending upon electron-transfer conditions. Tetrahedron Lett. 42, 8485–8488 (2001).

    Article  CAS  Google Scholar 

  29. Gomberg, M. Triphenylmethyl, ein Fall von dreiwerthigem Kohlenstoff. Ber. Dtsch. Chem. Ges. 33, 3150–3163 (1900).

    Article  CAS  Google Scholar 

  30. Gomberg, M. An instance of trivalent carbon: triphenylmethyl. J. Am. Chem. Soc. 22, 757–771 (1900).

    Article  Google Scholar 

  31. Kahr, B., Van Engen, D. & Mislow, K. Length of the ethane bond in hexaphenylethane and its derivatives. J. Am. Chem. Soc. 108, 8305–8307 (1986).

    Article  CAS  Google Scholar 

  32. Takeda, T. et al. Hexaphenylethanes with an ultralong C–C bond: expandability of the C–C bond in highly strained tetraarylpyracenes. Chem. Lett. 42, 954–962 (2013).

    Article  CAS  Google Scholar 

  33. Suzuki, T. et al. Expandability of ultralong C–C bonds: largely different C1–C2 bond lengths determined by low-temperature X-ray structural analyses on pseudopolymorphs of 1,1-bis(4-fluorophenyl)-2,2-bis(4-methoxyphenyl)pyracene. Chem. Lett. 43, 86–88 (2014).

    Article  CAS  Google Scholar 

  34. Shimajiri, T., Suzuki, T. & Ishigaki, Y. Flexible C–C bonds: reversible expansion, contraction, formation, and scission of extremely elongated single bonds. Angew. Chem. Int. Ed. 59, 22252–22257 (2020).

    Article  CAS  Google Scholar 

  35. Dyker, G., Hagel, M., Henkel, G. & Köckerling, M. Naphthyl-substituted carbocations: from peri interaction to cyclization. Eur. J. Org. Chem. 2008, 3095–3101 (2008).

    Article  Google Scholar 

  36. Cordoneanu, A., Drewitt, M. J., Bavarian, N. & Baird, M. C. Synthesis and characterization of weakly coordinating anion salts of a new, stable carbocationic reagent, the dibenzosuberenyl (dibenzotropylium) ion. New J. Chem. 32, 1890 (2008).

    Article  CAS  Google Scholar 

  37. Nishiuchi, T. et al. Anthracene‐attached persistent tricyclic aromatic hydrocarbon radicals. Chem. Asian J. 14, 1830–1836 (2019).

    Article  CAS  PubMed  Google Scholar 

  38. Sun, D., Rosokha, S. V. & Kochi, J. K. Donor-acceptor (electronic) coupling in the precursor complex to organic electron transfer: intermolecular and intramolecular self-exchange between phenothiazine redox centers. J. Am. Chem. Soc. 126, 1388–1401 (2004).

    Article  CAS  PubMed  Google Scholar 

  39. Small, D. et al. Intermolecular π-to-π bonding between stacked aromatic dyads. Experimental and theoretical binding energies and near-IR optical transitions for phenalenyl radical/radical versus radical/cation dimerizations. J. Am. Chem. Soc. 126, 13850–13858 (2004).

    Article  CAS  PubMed  Google Scholar 

  40. Nojo, W., Ishigaki, Y., Takeda, T., Akutagawa, T. & Suzuki, T. Selective formation of a mixed-valence state from linearly bridged oligo(aromatic diamines): drastic structural change into a folded columnar stack for half-filled polycations. Chem. Eur. J. 25, 7759–7765 (2019).

    Article  CAS  PubMed  Google Scholar 

  41. Casado, J. et al. Evidence for multicenter bonding in dianionic tetracyanoethylene dimers by Raman spectroscopy. Angew. Chem. Int. Ed. 52, 6421–6425 (2013).

    Article  CAS  Google Scholar 

  42. Kubo, T. et al. Long carbon-carbon bonding beyond 2 Å in Tris(9-fluorenylidene)methane. J. Am. Chem. Soc. 143, 14360–14366 (2021).

    Article  CAS  PubMed  Google Scholar 

  43. Dutan, C. et al. Electron transfer between two silyl-substituted phenylene rings: EPR/ENDOR spectra, DFT calculations, and crystal structure of the one-electron reduction compound of a Di(m-silylphenylenedisiloxane). J. Am. Chem. Soc. 125, 4487–4494 (2003).

    Article  CAS  PubMed  Google Scholar 

  44. Frisch, J. M. et al. Gaussian 16, Revision C.01 (Gaussian, Inc., 2019).

  45. Lu, T. & Chen, F. Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33, 580–592 (2012).

    Article  PubMed  Google Scholar 

  46. Glendening, E. D., Reed, A. E., Carpenter, J. E. & Weinhold, F. NBO v.3.1 (Gaussian, Inc., 2001).

  47. Dolomanov, O. V., Bourhis, L. J., Gildea, R. J., Howard, J. A. K. & Puschmann, H. OLEX2: a complete structure solution, refinement and analysis program. J. Appl. Crystallogr. 42, 339–341 (2009).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  PubMed  PubMed Central  Google Scholar 

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

    Article  ADS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

We thank E. Fukushi and Y. Takata (Hokkaido University) for recording mass spectra, H. Hirata (Hokkaido University) for recording electron spin resonance spectra, S. Noro, Y. Saito and A. Yamazaki for recording solid-state UV/Vis/NIR spectra, as well as J. P. Gong and T. Nakajima for recording solid-state IR spectra. Parts of the theoretical calculations were carried out at the Research Center for Computational Science, Okazaki, Japan (Project 23-IMS-C218). We would also like to thank U. F. J. Mayer at www.mayerscientificediting.com for proofreading our manuscript. This work was supported by the Masason Foundation (to S.K.) and by the Research Program ‘Five-star Alliance’ in ‘NJRC Mater. & Dev.’ of MEXT (Japan). Y. I. and T. Shimajiri acknowledge financial support from a Toyota Riken Scholarship. This work was furthermore supported by Grants-in-Aid from MEXT (JSPS Nos. 23K13726 to T. Shimajiri, 23K20275 to T. Suzuki, and 23K21107 and 23H04011 to Y.I.) and JST PRESTO (No. JPMJPR23Q1) to Y.I.

Author information

Author notes

  1. Takuya Shimajiri

    Present address: Department of Chemistry, Graduate School of Science, The University of Tokyo, Tokyo, Japan

Authors and Affiliations

  1. Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Japan

    Takuya Shimajiri, Soki Kawaguchi, Takanori Suzuki & Yusuke Ishigaki

  2. Creative Research Institution, Hokkaido University, Sapporo, Japan

    Takuya Shimajiri

Authors
  1. Takuya Shimajiri
    View author publications

    Search author on:PubMed Google Scholar

  2. Soki Kawaguchi
    View author publications

    Search author on:PubMed Google Scholar

  3. Takanori Suzuki
    View author publications

    Search author on:PubMed Google Scholar

  4. Yusuke Ishigaki
    View author publications

    Search author on:PubMed Google Scholar

Contributions

T. Shimajiri, T. Suzuki and Y.I. developed the concept of this study. T. Shimajiri and S.K. conducted the synthetic and spectroscopic experiments as well as the theoretical calculations. T. Shimajiri, T. Suzuki and Y.I. supervised the project. T. Shimajiri prepared the manuscript with feedback from all authors.

Corresponding authors

Correspondence to Takuya Shimajiri or Yusuke Ishigaki.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Tobias Krämer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shimajiri, T., Kawaguchi, S., Suzuki, T. et al. Direct evidence for a carbon–carbon one-electron σ-bond. Nature 634, 347–351 (2024). https://doi.org/10.1038/s41586-024-07965-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41586-024-07965-1

This article is cited by

Comments

Commenting on this article is now closed.

  1. Henry Rzepa

    In this region of sub two-electron bonds, there is much scope for a continuum of interactions, ranging from "strong" to "weak". The example identified in this article might be classified as of the weak non-covalent interaction type, as revealed by an NCI (non-covalent-interaction) analysis. See DOI: https://doi.org/10.59350/xp5a3-zsa24 for this analysis. Model one-electron bonds formed from e.g. hexafluoroethane and ethane itself have much shorter C-C bonds, down to 1.93A for the latter, and appear to be closer to the covalent bond type than the interaction type. This is supported by the properties of the electron density Laplacian. See DOI: https://doi.org/10.59350/88k04-2x509 Thus the one-electron C-C bond can apparently sustain lengths differing by as much as ~1Å, a much larger variation than any higher electron C-C bonds.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing