A 2010 density-functional study (Xu, Li, Xie, King, and Schaefer) predicted that the unsaturated third-row dimetallocenes Cp₂M₂ (Cp = η⁵-C₅H₅; M = Ta, W, Re, Os) adopt bent structures with very short metal–metal distances and exceptional formal bond orders: four for singlet Cp₂Ta₂, five for singlet Cp₂W₂ and Cp₂Os₂, and a formal Re–Re sextuple bond (bond order 6, Re–Re ≈ 2.19–2.25 Å) for a low-lying singlet of Cp₂Re₂ — a candidate for the first sextuple bond in an isolable molecule. None of these species has ever been synthesized, the computed singlet–quintet ordering of Cp₂W₂ flips between density functionals, and the influence of electron correlation, relativity, and multireference character on the assigned bond orders was never established. The problem is to realize these molecules experimentally — or to settle their ground states and bond orders with methods that resolve the functional dependence — and thereby test whether metal–metal bond multiplicity in isolable molecules truly extends to five and six for third-row transition metals.

Background

Metal–metal multiple bonds are described, in the usual molecular-orbital picture, by occupying σ, π, and δ combinations of the metals' valence s and d orbitals; the formal bond order (FBO) conventionally used in this literature is FBO=(nB−nA)/2\mathrm{FBO}=(n_B-n_A)/2, where nBn_B and nAn_A are the numbers of electrons in metal-centered bonding and antibonding orbitals. Quadruple bonds (σ²π⁴δ²) have been part of transition-metal chemistry since the structural characterization of the [Re₂Cl₈]²⁻ ion in the 1960s. Quintuple bonds — one σ, two π, and two δ electron pairs — were long hypothetical: quantum-chemical analyses of model systems such as [PhCrCrPh] (Brynda, Gagliardi, Widmark, Power, and Roos, 2006) preceded the first isolable quintuply bonded compounds, namely Cr(I) dimers stabilized by bulky terphenyl aryl ligands (m-terphenyls, aryl groups carrying two flanking aryl rings that shield the metal–metal axis; Nguyen et al., 2008) and by bridging amidinate ligands (an amidinate, RC(NR′)₂⁻, is a chelating ligand that can span both metals and give lantern-shaped dimers; Tsai et al., 2008), followed by the first Mo–Mo quintuple bond, obtained by reducing a quadruply bonded dimolybdenum amidinate precursor with potassium graphite (Tsai et al., 2009). A sextuple bond — a sixth, s-derived σ pair added to the quintuple manifold — is the maximum covalent bond multiplicity between two equal atoms; high-level computations assign effective bond orders of only about 5.2 to the bare gas-phase dimers Mo₂ and W₂ (Roos, Borin, and Gagliardi, 2007), and no isolable molecule with a sextuple metal–metal bond is known.

A dimetallocene is a compound of stoichiometry Cp₂M₂ in which two metal atoms are each bound to a cyclopentadienyl ring (Cp = η⁵-C₅H₅; the notation η⁵, read 'pentahapto', means the ring coordinates the metal through all five of its carbon atoms). Experimentally realized examples are limited to main-group metals — the Zn–Zn bonded dizincocene Zn₂(η⁵-C₅Me₅)₂ (Resa, Carmona, Gutierrez-Puebla, and Monge, 2004) and related alkaline-earth and zinc bimetallic metallocenes (Gosch and Wilson, 2023) — and none involves a d-block metal. For third-row (5d) transition metals the open question is whether Cp ligation can stabilize the low coordination numbers and low formal oxidation states needed for very high bond orders: with two Cp⁻ ligands, each metal of Cp₂M₂ carries a formal +1 charge, leaving (group number − 1) d electrons per atom, so Ta, W, Re, and Os dimers nominally supply 8, 10, 12, and 14 metal-based electrons — enough, in a bent geometry that preserves metal–metal orbital overlap, for bond orders from four up to six.

In this context Xu, Li, Xie, King, and Schaefer (2010) systematically examined the unsaturated third-row dimetallocenes Cp₂M₂ (M = Os, Re, W, Ta) with two density functionals (BP86 and MPW1PW91), a Stuttgart–Dresden effective core potential (ECP, a treatment replacing the metal's inner-core electrons by a model potential) and a double-ζ plus polarization basis on C and H. They predicted bent (C₂ or C₂h, i.e., the two Cp rings tilted toward each other rather than coaxial) minima with very short metal–metal distances: for Cp₂Os₂, a bent singlet that is the global minimum at BP86, with the triplet only 0.1–3.6 kcal·mol⁻¹ away depending on the functional (so the Os spin ordering is likewise not settled), with Os–Os = 2.276–2.333 Å and FBO 5 (twelve bonding and two δ* antibonding electrons); for Cp₂Re₂, a low-lying singlet (0.6–8.0 kcal·mol⁻¹ above a triplet global minimum, depending on the functional) with Re–Re = 2.193–2.247 Å and FBO 6 — a formal Re–Re sextuple bond, proposed as a candidate for the first sextuple bond in a stable molecule; for Cp₂W₂, a singlet with W–W ≈ 2.291 Å and FBO 5; and for Cp₂Ta₂, singlets with FBO 4 (of 2σ + 2π type, lacking δ components) near a triplet global minimum of formal order 3. The authors emphasized that the δ components rest on weak d-orbital overlap, that the spin-state ordering of Cp₂W₂ is functional-dependent (BP86 favors the singlet, MPW1PW91 the quintet, by 1.4 kcal·mol⁻¹), and that electron correlation, relativistic effects beyond the ECP, and multireference character were not exhaustively treated. As synthetic entries they suggested dehalogenation of CpMXₙ-type precursors and steric protection of the Cp rings with bulky substituents. None of these species had been synthesized at the time, and the experimental comparison set available then contained only lower-order bonds (e.g., the Re–Re quadruple bond of [Re₂Cl₈]²⁻ at 2.222 Å and carbonyl-ligated W–W triple bonds near 2.51 Å).

Problem Statement

Can the predicted bent dimetallocenes Cp₂M₂ (M = Ta, W, Re, Os) — or their ring-substituted analogues employing the steric protection explicitly suggested in the source work — be synthesized and isolated, and do they possess the predicted high-order metal–metal bonds? A complete answer must establish, for each Cp₂M₂ species: (1) the equilibrium molecular geometry, testing the predicted bent C₂/C₂h minima with short M–M distances (Ta–Ta ≈ 2.37–2.48 Å; W–W ≈ 2.29 Å; Re–Re ≈ 2.19–2.25 Å; Os–Os ≈ 2.28–2.33 Å) against alternatives such as coaxial sandwich or Cp-bridged structures; (2) the electronic ground state, in particular resolving the singlet-versus-quintet ambiguity of Cp₂W₂ that the original BP86/MPW1PW91 computations left functional-dependent (the two orderings differ by ~1.4 kcal·mol⁻¹); (3) the effective metal–metal bond order, testing the assigned formal orders — four (2σ + 2π) for singlet Cp₂Ta₂, five for singlet Cp₂W₂ and Cp₂Os₂, six for the low-lying singlet of Cp₂Re₂ (a formal Re–Re sextuple bond, attained by no isolable molecule to date) — with convergent structural, magnetic, spectroscopic, and quantum-chemical evidence. The theory-side core of the same question — determining the true spin-state ordering, orbital occupations, and bond orders of the Cp₂M₂ series at a level that resolves the density-functional-theory (DFT) functional dependence (multireference treatment of the σ/π/δ manifold with scalar-relativistic effects appropriate to 5d metals) — is independently answerable, and because none of the predicted species has been synthesized, a computational determination of the full Cp₂M₂ series at this level, covering items (1)–(3), is by itself a complete resolution of the task, with the synthesis and isolation of the predicted molecules remaining the outstanding experimental goal.

References

  1. Bing Xu, Qian-Shu Li, Yaoming Xie, R. Bruce King, Henry F. Schaefer, 'Metal−Metal Quintuple and Sextuple Bonding in Bent Dimetallocenes of the Third Row Transition Metals', Journal of Chemical Theory and Computation 2010, 6, 735–746, DOI 10.1021/ct900564p, https://doi.org/10.1021/ct900564p
  2. Marcin Brynda, Laura Gagliardi, Per-Olof Widmark, Philip P. Power, Björn O. Roos, 'A Quantum Chemical Study of the Quintuple Bond between Two Chromium Centers in [PhCrCrPh]: trans-Bent versus Linear Geometry', Angewandte Chemie International Edition 2006, 45, 3804–3807, DOI 10.1002/anie.200600110, https://doi.org/10.1002/anie.200600110
  3. Tailuan Nguyen, W. Alexander Merrill, Chengbao Ni, Hao Lei, James C. Fettinger, Bobby D. Ellis, Gary J. Long, Marcin Brynda, Philip P. Power, 'Synthesis and Characterization of the Metal(I) Dimers [Ar′MMAr′]: Comparisons with Quintuple-Bonded [Ar′CrCrAr′]', Angewandte Chemie International Edition 2008, 47, 9115–9117, DOI 10.1002/anie.200802657, https://doi.org/10.1002/anie.200802657
  4. Yi-Chou Tsai, Chia-Wei Hsu, Jen-Shiang K. Yu, Gene-Hsiang Lee, Yu Wang, Ting-Shen Kuo, 'Remarkably Short Metal–Metal Bonds: A Lantern-Type Quintuply Bonded Dichromium(I) Complex', Angewandte Chemie International Edition 2008, 47, 7250–7253, DOI 10.1002/anie.200801286, https://doi.org/10.1002/anie.200801286
  5. Yi-Chou Tsai, Hong-Zhang Chen, Chie-Chieh Chang, Jen-Shiang K. Yu, Gene-Hsiang Lee, Yu Wang, Ting-Shen Kuo, 'Journey from Mo−Mo Quadruple Bonds to Quintuple Bonds', Journal of the American Chemical Society 2009, 131, 12534–12535, DOI 10.1021/ja905035f, https://doi.org/10.1021/ja905035f
  6. Björn O. Roos, Antonio C. Borin, Laura Gagliardi, 'Reaching the Maximum Multiplicity of the Covalent Chemical Bond', Angewandte Chemie International Edition 2007, 46, 1469–1472, DOI 10.1002/anie.200603600, https://doi.org/10.1002/anie.200603600
  7. Frank R. Wagner, Awal Noor, Rhett Kempe, 'Ultrashort metal–metal distances and extreme bond orders', Nature Chemistry 2009, 1, 529–536, DOI 10.1038/nchem.359, https://doi.org/10.1038/nchem.359
  8. Zhi Sun, Henry F. Schaefer, Yaoming Xie, Yongdong Liu, Rugang Zhong, 'Does the metal–metal sextuple bond exist in the bimetallic sandwich compounds Cr₂(C₆H₆)₂, Mo₂(C₆H₆)₂, and W₂(C₆H₆)₂?', Molecular Physics 2013, 111, 2523–2535, DOI 10.1080/00268976.2013.798434, https://doi.org/10.1080/00268976.2013.798434
  9. Anokh K. Nair, N. V. Satyachand Harisomayajula, Yi-Chou Tsai, 'Theory, synthesis and reactivity of quintuple bonded complexes', Dalton Transactions 2014, 43, 5618–5638, DOI 10.1039/c3dt53565g, https://doi.org/10.1039/c3dt53565g
  10. N. V. Satyachand Harisomayajula, Anokh K. Nair, Yi-Chou Tsai, 'Discovering complexes containing a metal–metal quintuple bond: from theory to practice', Chemical Communications 2014, 50, 3391–3412, DOI 10.1039/c3cc48203k, https://doi.org/10.1039/c3cc48203k
  11. Yue Chen, Jun-ya Hasegawa, Kazuya Yamaguchi, Shigeyoshi Sakaki, 'A coordination strategy to realize a sextuply-bonded complex', Physical Chemistry Chemical Physics 2017, 19, 14947–14954, DOI 10.1039/c7cp00871f, https://doi.org/10.1039/c7cp00871f
  12. K. Ventura, J. R. Prat, L. M. Aguirre Quintana, A. Goos, D. Villagran, 'Unprecedented W₂(0) quadruply bonded complex supported by π-donor ligands', Chemical Communications 2016, 52, 3974–3976, DOI 10.1039/c5cc09972b, https://doi.org/10.1039/c5cc09972b
  13. Jing Li, Guoliang Li, Yaoming Xie, R. Bruce King, Henry F. Schaefer, 'Structures of dimetallocenes M₂(C₅H₅)₂ (M = Zn, Cu, Ni, Co, Fe) and their perfluorinated derivatives', New Journal of Chemistry 2017, 41, 5924–5933, DOI 10.1039/C7NJ01105A, https://doi.org/10.1039/C7NJ01105A
  14. Zhihui Zhang, Xuejun Feng, Qun Chen, Mingyang He, Yaoming Xie, R. Bruce King, Henry F. Schaefer, 'Metal–metal bonding in biscycloheptatrienyl dimetal compounds of the second-row transition metals', International Journal of Quantum Chemistry 2017, 117, DOI 10.1002/qua.25374, https://doi.org/10.1002/qua.25374
  15. Shanti G. Patra, Totan Mondal, 'Interplay of Hückel and Möbius Aromaticity in Metal–Metal Quintuple Bonded Complexes of Cr, Mo, and W with Amidinate Ligand: Ab initio DFT and Multireference Analysis', ChemPhysChem 2020, 22, 298–311, DOI 10.1002/cphc.202000923, https://doi.org/10.1002/cphc.202000923
  16. Abhik Ghosh, Jeanet Conradie, 'Theoretical Photoelectron Spectroscopy of Metal–Metal Quintuple Bonds: Relativity-Driven Reordering of Frontier Orbitals', ACS Organic & Inorganic Au 2024, 4, 301–305, DOI 10.1021/acsorginorgau.4c00002, https://doi.org/10.1021/acsorginorgau.4c00002
  17. Fitzerald Hujon, R. H. Duncan Lyngdoh, Henry F. Schaefer, R. Bruce King, 'From no bond to sextuple bond? CrCr distances in binuclear chromium systems', Inorganica Chimica Acta 2026, 602, 123296, DOI 10.1016/j.ica.2026.123296, https://doi.org/10.1016/j.ica.2026.123296
  18. Xingman Liu, Min Zhang, Yingtao Liu, Shuixing Wu, Zhongmin Su, 'A supported Cr–Cr sextuple bond in an all-metal cluster', Dalton Transactions 2022, 51, 2664–2668, DOI 10.1039/d1dt04360a, https://doi.org/10.1039/d1dt04360a
  19. Dan Li, Longjiu Cheng, 'Stabilizing hydrogen-mediated sextuple bonds by quintuple superatomic bonding and a bond', Nanoscale 2023, 15, 9525–9532, DOI 10.1039/d3nr00188a, https://doi.org/10.1039/d3nr00188a
  20. Amlan J. Kalita, Namrata Gohain, Abhik Bordoloi, Kusum K. Bania, Ankur K. Guha, 'Hetero-Polar Sextuple Bond: A Relativistic Quantum Chemical Study', ChemPhysChem 2023, DOI 10.1002/cphc.202200873, https://doi.org/10.1002/cphc.202200873
  21. Irene Resa, Ernesto Carmona, Enrique Gutierrez-Puebla, Angeles Monge, 'Decamethyldizincocene, a Stable Compound of Zn(I) with a Zn–Zn Bond', Science 2004, 305, 1136–1138, DOI 10.1126/science.1101356, https://doi.org/10.1126/science.1101356
  22. Matthew A. Gosch, David J. D. Wilson, 'Heteronuclear and Homonuclear Bimetallic Metallocenes of Alkaline Earths and Zinc', Organometallics 2023, 42, 2185–2196, DOI 10.1021/acs.organomet.3c00157, https://doi.org/10.1021/acs.organomet.3c00157