Relativistic quantum chemical calculations show that the uranium molecule U2 has a quadruple bond

Abstract

Understanding the bonding, reactivity and electronic structure of actinides is lagging behind that of the rest of the periodic table. This can be partly explained by the challenges that one faces in experimental studies of such radioactive compounds and also by the need to properly account for relativistic effects in theoretical studies. A further challenge is the very complicated electronic structures encountered in actinide chemistry, as vividly illustrated by the naked diuranium molecule U2. Here we report a computational study of this emblematic molecule using state-of-the-art relativistic quantum chemical methods. Notably, the variational inclusion of spin–orbit interactions leads not only to a different electronic ground state, but also to a lower bond multiplicity compared with those in previous studies.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Frontier atomic valence orbital energies of uranium in non-relativistic, scalar relativistic and fully relativistic molecular orbital theories.
Fig. 2: CASSCF potential energy curves for the lowest electronic states of U2 around the equilibrium structure.

Data availability

All relevant data that are not included in this article and its Supplementary Information are available from the corresponding author upon reasonable request.

References

  1. 1.

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

    CAS  Article  Google Scholar 

  2. 2.

    Neidig, M. L., Clark, D. L. & Martin, R. L. Covalency in f-element complexes. Coord. Chem. Rev. 257, 394–406 (2013).

    CAS  Article  Google Scholar 

  3. 3.

    Kaltsoyannis, N. & Kerridge, A. in The Chemical Bond: Chemical Bonding across the Periodic Table (eds Frenking, G. & Shaik, S.) 337–355 (Wiley, Weinheim, 2014).

  4. 4.

    Cary, S. K. et al. Emergence of californium as the second transitional element in the actinide series. Nat. Commun. 6, 6827 (2015).

    CAS  Article  Google Scholar 

  5. 5.

    Ferrier, M. G. et al. Spectroscopic and computational investigation of actinium coordination chemistry. Nat. Commun. 7, 12312 (2016).

    CAS  Article  Google Scholar 

  6. 6.

    Dutkiewicz, M. S., Apostolidis, C., Walter, O. & Arnold, P. L. Reduction chemistry of neptunium cyclopentadienide complexes: from structure to understanding. Chem. Sci. 8, 2553–2561 (2017).

    CAS  Article  Google Scholar 

  7. 7.

    Windorff, C. J. et al. Identification of the formal +2 oxidation state of plutonium: synthesis and characterization of {Puii[C5H3(SiMe3)2]3}. J. Am. Chem. Soc. 139, 3970–3973 (2017).

    CAS  Article  Google Scholar 

  8. 8.

    Jung, J., Atanasov, M. & Neese, F. Ab initio ligand-field theory analysis and covalency trends in actinide and lanthanide free ions and octahedral complexes. Inorg. Chem. 56, 8802–8816 (2017).

    CAS  Article  Google Scholar 

  9. 9.

    Cross, J. N. et al. Covalency in americium(iii) hexachloride. J. Am. Chem. Soc. 139, 8667–8677 (2017).

    CAS  Article  Google Scholar 

  10. 10.

    Formanuik, A. et al. Actinide covalency measured by pulsed electron paramagnetic resonance spectroscopy. Nat. Chem. 9, 578–583 (2017).

    CAS  Article  Google Scholar 

  11. 11.

    Vitova, T. et al. The role of the 5f valence orbitals of early actinides in chemical bonding. Nat. Commun. 8, 16053 (2017).

    CAS  Article  Google Scholar 

  12. 12.

    Wilson, R. E., De Sio, S. & Vallet, V. Protactinium and the intersection of actinide and transition metal chemistry. Nat. Commun. 9, 622 (2018).

    Article  Google Scholar 

  13. 13.

    The bottom line. Nat. Chem. 9, 831 (2017).

  14. 14.

    Monreal, M. J. & Diaconescu, P. L. The riches of uranium. Nat. Chem. 2, 424 (2010).

    CAS  Article  Google Scholar 

  15. 15.

    Li Manni, G. et al. Assessing metal–metal multiple bonds in Cr–Cr, Mo–Mo, and W–W compounds and a hypothetical U–U compound: a quantum chemical study comparing DFT and multireference methods. Chem. Eur. J. 18, 1737–1749 (2012).

    CAS  Article  Google Scholar 

  16. 16.

    Penchoff, D. A. & Bursten, B. E. Metal–metal bonding in the actinide elements: conceptual synthesis of a pure two-electron U–U f δ single bond in a constrained geometry of U2(OH)10. Inorg. Chim. Acta 424, 267–273 (2015).

    CAS  Article  Google Scholar 

  17. 17.

    Foroutan-Nejad, C., Vicha, J., Marek, R., Patzschke, M. & Straka, M. Unwilling U–U bonding in U2@C80: cage-driven metal–metal bonds in di-uranium fullerenes. Phys. Chem. Chem. Phys. 17, 24182–24192 (2015).

    CAS  Article  Google Scholar 

  18. 18.

    Qu, N., Su, D.-M., Wu, Q.-Y., Shi, W.-Q. & Pan, Q.-J. Metal–metal multiple bond in low-valent diuranium porphyrazines and its correlation with metal oxidation state: a relativistic DFT study. Comput. Theor. Chem. 1108, 29–39 (2017).

    CAS  Article  Google Scholar 

  19. 19.

    Zhang, X. et al. U2@Ih(7)-C80: crystallographic characterization of a long-sought dimetallic actinide endohedral fullerene. J. Am. Chem. Soc. 140, 3907–3915 (2018).

    CAS  Article  Google Scholar 

  20. 20.

    Scheibe, B. et al. The [U2F12]2− anion of Sr[U2F12]. Angew. Chem. Int. Ed. 57, 2914–2918 (2018).

    CAS  Article  Google Scholar 

  21. 21.

    Lyon, J. T., Hu, H.-S., Andrews, L. & Li, J. Formation of unprecedented actinide≡carbon triple bonds in uranium methylidyne molecules. Proc. Natl Acad. Sci. USA 104, 18919–18924 (2007).

    CAS  Article  Google Scholar 

  22. 22.

    Hu, H.-S., Qiu, Y.-H., Xiong, X.-G., Schwarz, W. H. E. & Li, J. On the maximum bond multiplicity of carbon: unusual C–U quadruple bonding in molecular CuO. Chem. Sci. 3, 2786–2796 (2012).

    CAS  Article  Google Scholar 

  23. 23.

    Hayton, T. W. Recent developments in actinide-ligand multiple bonding. Chem. Commun. 49, 2956–2973 (2013).

    CAS  Article  Google Scholar 

  24. 24.

    Hlina, J. A., Pankhurst, J. R., Kaltsoyannis, N. & Arnold, P. L. Metal–metal bonding in uranium-group 10 complexes. J. Am. Chem. Soc. 138, 3333–3345 (2016).

    CAS  Article  Google Scholar 

  25. 25.

    Ephritikhine, M. Molecular actinide compounds with soft chalcogen ligands. Coord. Chem. Rev. 319, 35–62 (2016).

    CAS  Article  Google Scholar 

  26. 26.

    Fox, A. R., Bart, S. C., Meyer, K. & Cummins, C. C. Towards uranium catalysts. Nature 455, 341–349 (2008).

    CAS  Article  Google Scholar 

  27. 27.

    Liddle, S. T. The renaissance of non-aqueous uranium chemistry. Angew. Chem. Int. Ed. 54, 8604–8641 (2015).

    CAS  Article  Google Scholar 

  28. 28.

    Halter, D. P., Heinemann, F. W., Bachmann, J. & Meyer, K. Uranium-mediated electrocatalytic dihydrogen production from water. Nature 530, 317–321 (2016).

    CAS  Article  Google Scholar 

  29. 29.

    Arnold, P. L. & Turner, Z. R. Carbon oxygenate transformations by actinide compounds and catalysts. Nat. Rev. Chem. 1, 0002 (2017).

    CAS  Article  Google Scholar 

  30. 30.

    Bursten, B. E. & Ozid, G. A. Xα-SW calculations for naked actinide dimers: on the existence of ϕ bonds between metal atoms. Inorg. Chem. 23, 2910–2911 (1984).

    CAS  Article  Google Scholar 

  31. 31.

    Pepper, M. & Bursten, B. E. Ab initio studies of the electronic structure of the diuranium molecule. J. Am. Chem. Soc. 112, 7803–7804 (1990).

    CAS  Article  Google Scholar 

  32. 32.

    Gagliardi, L. & Roos, B. Quantum chemical calculations show that the uranium molecule U2 has a quintuple bond. Nature 433, 848–851 (2005).

    CAS  Article  Google Scholar 

  33. 33.

    Roos, B. O., Malmqvist, P.-Å. & Gagliardi, L. Exploring the actinide–actinide bond: theoretical studies of the chemical bond in Ac2, Th2, Pa2, and U2. J. Am. Chem. Soc. 128, 17000–17006 (2006).

    CAS  Article  Google Scholar 

  34. 34.

    Gorokhov, L. N., Emelyanov, A. M. & Khodeev, Y. S. Mass-spectroscopic investigation of stability of gaseous U2O2 and U2. High Temp. 12, 1307–1309 (1974).

    CAS  Google Scholar 

  35. 35.

    Pyykkö, P. & Desclaux, J.-P. Relativity and the periodic system of elements. Acc. Chem. Res. 12, 276–281 (1979).

    Article  Google Scholar 

  36. 36.

    Reiher, M. & Wolf, A. Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (Wiley, Weinheim, 2009).

  37. 37.

    Dyall, K. G. & Fægri, K. Introduction to Relativistic Quantum Chemistry (Oxford Univ. Press, Oxford, 2007).

    Google Scholar 

  38. 38.

    Saue, T. Relativistic Hamiltonians for chemistry: a primer. Chem Phys Chem 12, 3077–3094 (2011).

    CAS  Article  Google Scholar 

  39. 39.

    Christiansen, P. A. & Pitzer, K. S. Electronic structure and dissociation curves for the ground states of Tl2 and T12 + from relativistic effective potential calculations. J. Chem. Phys. 74, 1162–1165 (1981).

    CAS  Article  Google Scholar 

  40. 40.

    Saue, T., Fægri, K. & Gropen, O. Relativistic effects on the bonding of heavy and superheavy hydrogen halides. Chem. Phys. Lett. 263, 360–366 (1996).

    CAS  Article  Google Scholar 

  41. 41.

    Blaise, J. & Wyart, J. F. Selected Constants Energy Levels and Atomic Spectra of Actinides (Centre National de la Recherche Scientifique, 1992); http://web2.lac.u-psud.fr/lac/Database/Contents.html

  42. 42.

    Herzberg, G. Zum Aufbau der zweiatomigen Moleküle. Z. Phys. 57, 601–630 (1929).

    CAS  Article  Google Scholar 

  43. 43.

    Roos, B. O., Borin, A. C. & Gagliardi, L. Reaching the maximum multiplicity of the covalent chemical bond. Angew. Chem. Int. Ed. 46, 1469–1472 (2007).

    CAS  Article  Google Scholar 

  44. 44.

    Shaik, S. et al. Quadruple bonding in C2 and analogous eight-valence electron species. Nat. Chem. 4, 195–200 (2012).

    CAS  Article  Google Scholar 

  45. 45.

    Shaik, S., Rzepa, H. S. & Hoffmann, R. One molecule, two atoms, three views, four bonds? Angew. Chem. Int. Ed. 52, 3020–3033 (2013).

    CAS  Article  Google Scholar 

  46. 46.

    Schwerdtfeger, P. in The Chemical Bond: Fundamental Aspects of Chemical Bonding (eds Frenking, G. & Shaik, S.) 383–404 (Wiley, Weinheim, 2014).

  47. 47.

    Demissie, T. B., Garabato, B. D., Ruud, K. & Kozlowski, P. M. Mercury methylation by cobalt corrinoids: relativistic effects dictate the reaction mechanism. Angew. Chem. Int. Ed. 55, 11503–11506 (2016).

    CAS  Article  Google Scholar 

  48. 48.

    Gaggioli, C. A. et al. Dioxygen insertion into the gold(i)–hydride bond: spin orbit coupling effects in the spotlight for oxidative addition. Chem. Sci. 7, 7034–7039 (2016).

    CAS  Article  Google Scholar 

  49. 49.

    Visscher, L. et al. DIRAC, a relativistic ab initio electronic structure program Release DIRAC17 (2017); http://www.diracprogram.org

  50. 50.

    Balasubramanian, K. Relativity and chemical bonding. J. Phys. Chem. 93, 6585–6596 (1989).

    CAS  Article  Google Scholar 

  51. 51.

    Maurice, R. et al. Effective bond orders from two-step spin–orbit coupling approaches: the I2, At2, IO+, and AtO+ case studies. J. Chem. Phys. 142, 094305 (2015).

    Article  Google Scholar 

  52. 52.

    Gagliardi, L., Pyykkö, P. & Roos, B. O. A very short uranium–uranium bond: the predicted metastable U2 2+. Phys. Chem. Chem. Phys. 7, 2415–2417 (2005).

    CAS  Article  Google Scholar 

  53. 53.

    Jong, W. A. D., Visscher, L. & Nieuwpoort, W. C. On the bonding and the electric field gradient of the uranyl ion. J. Mol. Struct. THEOCHEM 458, 41–52 (1999); corrigendum 581, 259 (2002).

  54. 54.

    Dyall, K. G. Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the actinides Ac–Lr. Theor. Chem. Acc. 117, 491–500 (2007).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank the Danish Center for Scientific Computing for ample computational resources. We thank T. Helgaker and E. Uggerud (University of Oslo) for help with Gorokhov et al.34. We thank C. K. Elmar for preparing the graphical abstract. S.K. acknowledges fruitful discussions with P. Pyykkö (University of Helsinki) on numerous occasions. S.K. thanks M. Reiher (ETH Zürich) for his continuous support. We dedicate this paper to the memory of B. Roos, an outstanding quantum chemist.

Author information

Affiliations

Authors

Contributions

S.K. ran all calculations reported in this paper, whereas the interpretation of the results and the preparation of the manuscript was a joint effort by all three authors. The generalized EBO (equation (2)) was developed by S.K. and T.S.

Corresponding author

Correspondence to Stefan Knecht.

Ethics declarations

Competing interests

The Authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Methods, Supplementary Figures, Supplementary Tables, Sample Input Files

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Knecht, S., Jensen, H.J.A. & Saue, T. Relativistic quantum chemical calculations show that the uranium molecule U2 has a quadruple bond. Nature Chem 11, 40–44 (2019). https://doi.org/10.1038/s41557-018-0158-9

Download citation

Further reading

Search

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