# Sextuple bond

A sextuple bond is a type of covalent bond involving 12 bonding electrons and in which the bond order is 6. The only known molecules with true sextuple bonds are the diatomic dimolybdenum (Mo2) and ditungsten (W2), which exist in the gaseous phase and have boiling points of 4,639 °C (8,382 °F) and 5,930 °C (10,710 °F). There is strong evidence to believe that there is no element with atomic number below about 100 that can form a bond with a greater order than 6 between its atoms,[1] but the question of possibility of such a bond between two atoms of different elements remains open. Bonds between heteronuclear systems with two atoms of different elements may not necessarily have the same limit.[2]

## Dimolybdenum and ditungsten

Dimolybdenum (Mo2) can be observed in the gas phase at low temperatures (7 K) by a laser evaporation technique using molybdenum sheet with, for instance, near-infrared spectroscopy or UV spectroscopy.[3] Like dichromium, a singlet state is expected from dimolybdenum.[4] Higher bond order is reflected in shorter bond length of 194 pm. A singlet 1Σg+ ground state can be expected from ditungsten as well.[5] However, this ground state arises from a combination of either two isolated tungstens' ground 5D0 states or two isolated tungstens' excited 7S3 states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten dimer.[5] Dimolybdenum and dichromium follow much the same mechanism to achieve the stablest ground state of their respective dimers.[6]

## Effective bond order

### Considerations of bond force constants

The formal bond order of a molecule is calculated as the average of electrons occupied in bonding and antibonding orbitals, expressed exclusively in integers. The effective bond order derived from quantum chemistry calculations was defined by Roos et al as

${\displaystyle EBO=\left({\frac {1}{2}}\right)\sum _{p=1}(\eta _{b,p}-\eta _{ab,p})-c}$

where ηb is the formal bonding orbital occupation for an electron pair p and ηab is the formal antibonding orbital occupation for an electron pair p with c as a correction factor accounting or deviations from equilibrium geometry.[1] In a sextuple bond, there would be p=6 different electron pairs. A formal sextuple bond would then have a net total of 12 electrons occupying bonding orbitals. Since effective and formal bond orders (FBO) would only be equivalent if the molecule were in its stablest geometry, the effective bond order (EBO) is usually fractional and less than the formal bond order. Several metal-metal bonds' EBOs are given in the table below, compared to their formal bond orders. The following table lists some effective bond orders of select metal-metal bonds.

Molecule FBO EBO[1]
Cr2 6 3.5
[PhCrCrPh] 5 3.5
Cr2(O2CCH3)4 4 2.0
Mo2 6 5.2
W2 6 5.2
Ac2 3 1.7
Th2 4 3.7
Pa2 5 4.5
U2 6 3.8[7]
[PhUUPh] 5 3.7
[Re2Cl8]2- 4 3.2

Dimolybdenum and ditungsten are the only molecules with effective bond orders above 5, with a quintuple bond and a partially formed sixth covalent bond. Dichromium, while formally described as having a sextuple bond, is best described as a pair of chromium atoms with all electron spins ferromagnetically coupled to each other.[8] Additionally, while diuranium is also formally described as having a sextuple bond, relativistic quantum mechanical calculations have determined it to be a quadruple bond with four electrons ferromagnetically coupled to each other rather than in two formal bonds.[7] Previous calculations on diuranium did not treat the electronic molecular Hamiltonian relativistically and produced higher bond orders of 4.2 with two ferromagnetically coupled electrons.[9] Several metal-metal dimers exist held together by only van der Waals forces, due to poor participation of metal d electrons in bonding.[10] van der Waals metal-metal dimers include the d9 coinage metals Cu, Ag, and Au as well as d10 metals such as Zn, Cd and Hg.[1] Spectroscopic examination of select metal-metal dimers provides a correlation between the measured force constants and calculated bond orders. In general, a higher force constant implies an increasing bond order. Johnston's formula predicts that bond order is proportional to the force constant by the relation n = ke/ke(1) where n is the bond order, ke is the summed force constant of all the bonds between the metal atoms and ke(1) is the force constant of a single bond between the metal atoms.[11] The table below shows some select force constants for metal-metal dimers compared to their EBOs. Thus, molybdenum is determined to have a sextuple bond because its summed

Dimer Force constant (Å)[10] EBO[10]
Cu2 1.13 1.00
Ag2 1.18 1.00
Au2 2.12 1.00
Zn2 0.01 0.01
Cd2 0.02 0.02
Hg2 0.02 0.02
Mn2 0.09 0.07
Mo2 6.33 5.38

force constant is more than five times the single-bond force constant. However, this relation does not always give the same result as the method applied by Roos et al. For example, using Johnston's formula ditungsten would have a summed force constant of 6.14 but a bond order of 2.90 while dirhenium would have a force constant of 6.26 and a bond order of 2.96, incorrectly implying that dirhenium's bond is stronger than ditungsten's.[12][13] Thus, quantum chemical calculations are usually needed to confirm bond order.

### Considerations of bond length and bond type

Sextuply-bonded dimolybdenum is reported to have an equilibrium bond length of 1.93 Å, significantly lower than quadruply-bonded dimolybdenum species and suggestive of a bond order of higher than 4.[14] Quantum mechanical calculations have revealed that the dimolybdenum bond is formed by a combination of two σ bonds, two π bonds and two δ bonds, in which the σ and π bonds contribute much more significantly to the sextuple bond than the δ bonds.[15] This combination of increased bonding results in a dimer equilibrium internuclear distance that is significantly lower for dimolybdenum than for any neighboring 4d transition metal dimers.[10] Although no φ bonding has been reported for transition metal dimers, it is predicted that if any sextuply-bonded actinides were to exist, at least one of the bonds would likely be a φ bond as in quintuply-bonded diuranium and dineptunium.[16] To date, no sextuple bond has been observed in lanthanides or actinides.[1]

## Ligand effects on sextuple bonding

### Effect of aromatic ligands

Extension beyond the dimer to larger molecules may yield possibilities of true sextuple bonding in other complexes. Calculations on the frontier molecular orbitals of dirhenocene, for example, yielded possible singlet and triplet state geometries for the complex. Although the stabler triplet state is predicted to have a formal bond order of 5, the less stable singlet geometry is predicted to give a sextuple bond with a shorter Re-Re internuclear distance.[17] Among the three types of geometries predicted for dimetallocenes, a bent geometry is predicted to contribute to possible sextuple bonding.

Other large-molecule candidates for sextuple bonding have included the dibenzene sandwich compounds Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2. In the triplet states with geometries of symmetry D6h and D6d, evaluation of the molecular bonding orbitals for all three compounds reveals the possiblity of a sextuple bond between the metal atoms.[18] Quantum chemistry calculations reveal, however, that the corresponding D2h singlet geometry resulting from Jahn-Teller distortion of the D6h triplet state is much stabler than the triplet state itself. In the dichromium dibenzene sandwich, the triplet state is 39 kcal/mol above the singlet state of lower bond order while it lies 19 kcal/mol above the singlet in the molybdenum analog and 3 kcal/mol above the singlet in the tungsten analog.[18] In the sandwich complexes, a triplet state would induce very long Cr-C bond distances so it is concluded that, energetically, strong association of ligands to a metal center is more important than strong bonding between two metal centers.

### Effect of oxygen ligands

Quantum mechanical calculations have revealed that the ditungsten dimer's sextuple bond is predicted to weaken with increasing oxidation state. Taking the simple W2 molecule and increasing the amount of oxo ligands attached to form W2On (n = 1-6) complexes disrupts the sextuple bond and results in a lower bond order.[19] The weak δ bonds break first and result in a quadruply-bonded W2O, which upon further oxidation becomes a ditungsten complex with two bridging oxo ligands and no direct W-W bonds by W2O6. Additionally, the increase in oxidation is accompanied by decreases in the dissociation energy of the already weak W-W sextuple bond and increases in the electron binding energy of the oxo ligands.[19]

### Effect of halogenation

Halogenation of dimolybdenum and ditungsten with trifluoroiodomethane forms a bis(trifluoroiodomethano)dimolybdenum and ditungsten complexes with paradoxical bond behavior. Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers due to the presence of an effective sextuple bond. However, their bond dissociation energies are rather low.[1] Upon halogenation of the dimolybdenum dimer with trifluoroiodomethane ligands, it was determined that bond order decreased while bond length increased while ditungsten experienced a more regular decrease in bond length along with bond order.[20] Due to the ultra-short bonding distance in dimolybdenum, molybdenum's 5s orbital participating in a σ bond with the second molybdenum had a slightly more repulsive character than expected due to a crowding of electron density near the equilibrium geometry of the dimer, contributing to a lower bond dissociation energy. Tungsten's 6s orbital does not exhibit repulsive character at the W-W equilibrium distance. Trifluoroiodomethane, a well-known electron acceptor, siphons off some of the electron density in the sextuple bond, effectively reducing bond order but also reducing electronic repulsions.[21] The decrease in repulsive electron density results in a strengthening of the Mo-Mo bond by 5.34 kcal/mol and a weakening of the W-W bond by 4.60 kcal/mol, corresponding to a decrease in bond length for the Mo dimer and an increase in bond length for the W dimer.[20]

## References

1. Roos, Björn O.; Borin, Antonio C.; Laura Gagliardi (2007). "Reaching the Maximum Multiplicity of the Covalent Chemical Bond". Angew. Chem. Int. Ed. 46 (9): 1469–72. doi:10.1002/anie.200603600. PMID 17225237.
2. Frenking, Gernot; Tonner, Ralf (March 2007). "The six-bond bound". Nature. 446 (7133): 276–277. doi:10.1038/446276a. ISSN 0028-0836.
3. Kraus, D.; Lorenz, M.; Bondybey, V. E. (2001). "On the dimers of the VIB group: a new NIR electronic state of Mo2". PhysChemComm. 4 (10): 44–48. doi:10.1039/b104063b.
4. Merino, Gabriel; Donald, Kelling J.; D’Acchioli, Jason S.; Hoffmann, Roald (2007). "The Many Ways To Have a Quintuple Bond". J. Am. Chem. Soc. 129 (49): 15295–15302. doi:10.1021/ja075454b. PMID 18004851.
5. Borin, Antonio Carlos; Gobbo, João Paulo; Roos, Björn O. (April 2010). "Electronic structure and chemical bonding in W2 molecule". Chemical Physics Letters. 490 (1–3): 24–28. doi:10.1016/j.cplett.2010.03.022. ISSN 0009-2614.
6. Borin, Antonio Carlos; Gobbo, João Paulo; Roos, Björn O. (January 2008). "A theoretical study of the binding and electronic spectrum of the Mo2 molecule". Chemical Physics. 343 (2–3): 210–216. doi:10.1016/j.chemphys.2007.05.028. ISSN 0301-0104.
7. Knecht, Stefan; Jensen, Hans Jørgen Aa.; Saue, Trond (January 2019). "Relativistic quantum chemical calculations show that the uranium molecule U2 has a quadruple bond". Nature Chemistry. 11 (1): 40–44. doi:10.1038/s41557-018-0158-9. ISSN 1755-4330.
8. Goodgame, Marvin M.; Goddard, William A. (February 1981). "The "sextuple" bond of chromium dimer". The Journal of Physical Chemistry. 85 (3): 215–217. doi:10.1021/j150603a001. ISSN 0022-3654.
9. Gagliardi, Laura; Roos, Bjoern O. (2005-05-17). "Quantum Chemical Calculations Show that the Uranium Molecule U2 Has a Quintuple Bond". ChemInform. 36 (20). doi:10.1002/chin.200520001. ISSN 0931-7597.
10. Jules, Joseph L.; Lombardi, John R. (March 2003). "Transition Metal Dimer Internuclear Distances from Measured Force Constants". The Journal of Physical Chemistry A. 107 (9): 1268–1273. doi:10.1021/jp027493+. ISSN 1089-5639.
11. Eyring, E. M. (1967-08-04). "Gas Phase Reaction Rate Theory. Harold S. Johnston. Ronald, New York, 1966. 372 pp., illus. \$10". Science. 157 (3788): 535–536. doi:10.1126/science.157.3788.535-a. ISSN 0036-8075.
12. Hu, Zhendong; Dong, Jian‐Guo; Lombardi, John R.; Lindsay, D. M.; Harbich, W. (July 1994). "Absorption, fluorescence, and Raman spectra of mass‐selected rhenium dimers in argon matrices". The Journal of Chemical Physics. 101 (1): 95–103. doi:10.1063/1.468092. ISSN 0021-9606.
13. Hu, Zhendong; Dong, Jian Guo; Lombardi, John R.; Lindsay, D. M. (September 1993). "Raman spectra of mass-selected dihafnium in argon matrixes". The Journal of Physical Chemistry. 97 (37): 9263–9265. doi:10.1021/j100139a001. ISSN 0022-3654.
14. Efremov, Yu.M; Samoilova, A.N; Kozhukhovsky, V.B; Gurvich, L.V (December 1978). "On the electronic spectrum of the Mo2 molecule observed after flash photolysis of Mo(CO)6". Journal of Molecular Spectroscopy. 73 (3): 430–440. doi:10.1016/0022-2852(78)90109-1. ISSN 0022-2852.
15. Bursten, Bruce E.; Cotton, F. Albert; Hall, Michael B. (September 1980). "Dimolybdenum: nature of the sextuple bond". Journal of the American Chemical Society. 102 (20): 6348–6349. doi:10.1021/ja00540a034. ISSN 0002-7863.
16. Bursten, Bruce E.; Ozin, Geoffrey A. (August 1984). "X.alpha.-SW calculations for naked actinide dimers: existence of .vphi. bonds between metal atoms". Inorganic Chemistry. 23 (18): 2910–2911. doi:10.1021/ic00186a039. ISSN 0020-1669.
17. Xu, Bing; Li, Qian-Shu; Xie, Yaoming; King, R. Bruce; Schaefer, Henry F. (2010-02-17). "Metal−Metal Quintuple and Sextuple Bonding in Bent Dimetallocenes of the Third Row Transition Metals". Journal of Chemical Theory and Computation. 6 (3): 735–746. doi:10.1021/ct900564p. ISSN 1549-9618.
18. Sun, Zhi; Schaefer, Henry F.; Xie, Yaoming; Liu, Yongdong; Zhong, Rugang (September 2013). "Does the metal–metal sextuple bond exist in the bimetallic sandwich compounds Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2?†". Molecular Physics. 111 (16–17): 2523–2535. doi:10.1080/00268976.2013.798434. ISSN 0026-8976.
19. Zhai, Hua-Jin; Huang, Xin; Cui, Li-Feng; Li, Xi; Li, Jun; Wang, Lai-Sheng (July 2005). "Electronic and Structural Evolution and Chemical Bonding in Ditungsten Oxide Clusters:  W2On-and W2On(n= 1−6)". The Journal of Physical Chemistry A. 109 (27): 6019–6030. doi:10.1021/jp051496f. ISSN 1089-5639.
20. Joy, Jyothish; Jemmis, Eluvathingal D. (2017). "A halogen bond route to shorten the ultrashort sextuple bonds in Cr2 and Mo2". Chemical Communications. 53 (58): 8168–8171. doi:10.1039/c7cc04653g. ISSN 1359-7345.
21. Henkel, Stefan; Costa, Paolo; Klute, Linda; Sokkar, Pandian; Fernandez-Oliva, Miguel; Thiel, Walter; Sanchez-Garcia, Elsa; Sander, Wolfram (2016-02-02). "Switching the Spin State of Diphenylcarbene via Halogen Bonding". Journal of the American Chemical Society. 138 (5): 1689–1697. doi:10.1021/jacs.5b12726. ISSN 0002-7863.