# 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 (Mo$_2$) and ditungsten (W$_2$), which exist in the gaseous phase and have boiling points of 4,639 °C (8,382 °F) and 5,930 °C (10,710 °F) respectively.

## Theoretical analysis

Roos et al argue that no stable element can form bonds of higher order than a sextuple bond, because the latter corresponds to a hybrid of the s orbital and all five d orbitals, and f orbitals contract too close to the nucleus to bond in the lanthan­ides. Indeed, 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. (Also, the σ and π bonds contribute much more significantly to the sextuple bond than the δ bonds.)
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. No sextuple bond has been observed in lanthanides or actinides.
For the majority of elements, even the possibility of a sextuple bond is foreclosed, because the d electrons ferromagnetically couple, instead of bonding. The only known exceptions are dimolybdenum and ditungsten.

### Quantum-mechanical treatment

The formal bond order (FBO) of a molecule is half the number of bonding electrons surplus to antibonding electrons; for a typical molecule, it attains exclusively integer values. A full quantum treatment requires a more nuanced picture, in which electrons may exist in a superposition, contributing fractionally to both bonding and antibonding orbitals. In a formal sextuple bond, there would be P = 6 different electron pairs; an effective sextuple bond would then have all six contributing almost entirely to bonding orbitals.
| Molecule | FBO | EBO |
| Cr$_2$ | 6 | 3.5 |
| [PhCrCrPh] | 5 | 3.5 |
| Cr$_2$(O$_2$CCH$_3$)$_4$ | 4 | 2.0 |
| Mo$_2$ | 6 | 5.2 |
| W$_2$ | 6 | 5.2 |
| Ac$_2$ | 3 | 1.7 |
| Th$_2$ | 4 | 3.7 |
| Pa$_2$ | 5 | 4.5 |
| U$_2$ | 6 | 3.8 |
| [PhUUPh] | 5 | 3.7 |
| [Re$_2$Cl$_8$]$^{2-}$ | 4 | 3.2 |
In Roos et al's calculations, the effective bond order (EBO) could be determined by the formula$EBO=\left({\frac {1}{2}}\right)\sum _{p=1}^{P}(\eta _{b,p}-\eta _{ab,p})-c$ where η$_b$ is the proportion of formal bonding orbital occupation for an electron pair p, η$_{ab}$ is the proportion of the formal antibonding orbital occupation, and c is a correction factor account­ing for deviations from equilibrium geometry. Several metal-metal bonds' EBOs are given in the table at right, compared to their formal bond orders.
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 exchange-coupled to each other.
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. 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.

## Known instances: dimolybdenum and ditungsten

Laser evaporation of a molybdenum sheet at low temperatures (7 K) produces gaseous dimolybdenum (Mo$_2$). The resulting molecules can then be imaged with, for instance, near-infrared spectroscopy or UV spectroscopy.
Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers. For example, sextuply-bonded dimolybdenum has an equilibrium bond length of 1.93 Å. This equi­librium internuclear distance is signi­ficantly lower than in the dimer of any neighboring 4d transition metal, and sug­gestive of higher bond orders. However, the bond dissociation energies of ditungsten and dimolybdenum are rather low, because the short internuclear distance introduces geometric strain.
| Dimer | Force constant (Å) | EBO |
| Cu$_2$ | 1.13 | 1.00 |
| Ag$_2$ | 1.18 | 1.00 |
| Au$_2$ | 2.12 | 1.00 |
| Zn$_2$ | 0.01 | 0.01 |
| Cd$_2$ | 0.02 | 0.02 |
| Hg$_2$ | 0.02 | 0.02 |
| Mn$_2$ | 0.09 | 0.07 |
| Mo$_2$ | 6.33 | 5.38 |
One empirical technique to determine bond order is spectroscopic exami­nation of bond force constants. Linus Pauling investigated the relationships between bonding atoms and developed a formula that predicts that bond order is roughly proportional to the force constant; that is, $k_{e}=n\cdot k_{e}^{(1)}$ where n is the bond order, k$_e$ is the force constant of the interatomic inter­action and k$_e$$^{(1)}$ is the force constant of a single bond between the atoms.
The table at right shows some select force constants for metal-metal dimers com­pared to their EBOs; consistent with a sextuple bond, molybdenum's summed force constant is substantially more than quintuple the single-bond force constant.
Like dichromium, dimolybdenum and ditungsten are expected to exhibit a $^1$Σ$_g$$^+$ singlet ground state. However, in tungsten, this ground state arises from a hybrid of either two $^5$D$_0$ ground states or two $^7$S$_3$ excited states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten dimer.

## Ligand effects

Although sextuple bonding in homodimers is rare, it remains a possibility in larger molecules.

### Aromatics

Theoretical computations suggest that bent dimetallocenes have a higher bond order than their linear counterparts. For this reason, the Schaefer lab has investi­gated dimetallocenes for natural sextuple bonds. However, such com­pounds tend to exhibit Jahn-Teller distortion, rather than a true sextuple bond.
For example, dirhenocene is bent. Calculating its frontier molecular orbitals sug­gests the existence of relatively stable singlet and triplet states, with a sextuple bond in the singlet state. But that state is the excited one; the triplet ground state should exhibit a formal quintuple bond. Similarly, for the dibenzene complexes Cr$_2$(C$_6$H$_6$)$_2$, Mo$_2$(C$_6$H$_6$)$_2$, and W$_2$(C$_6$H$_6$)$_2$, molecular bonding orbitals for the triplet states with symmetries D$_{6h}$ and D$_{6d}$ indicate the possibility of an intermetallic sex­tuple bond. Quantum chemistry calculations reveal, however, that the corre­sponding D$_{2h}$ singlet geometry is stabler than the D$_{6h}$ triplet state by 3–39 kcal/mol, depending on the central metal.

### Oxo ligands

Both quantum mechanical calculations and photoelectron spectroscopy of the tungsten oxide clusters W$_2$O$_n$ (n = 1-6) indicate that increased oxidation state reduces the bond order in ditungsten. At first, the weak δ bonds break to yield a quadruply-bonded W$_2$O; further oxidation generates the ditungsten complex W$_2$O$_6$ with two bridging oxo ligands and no direct W-W bonds.