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 and ditungsten, which exist in the gaseous phase and have boiling points of and. 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, 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.
Dimolybdenum and ditungsten
Dimolybdenum can be observed in the gas phase at low temperatures by a laser evaporation technique using molybdenum sheet with, for instance, near-infrared spectroscopy or UV spectroscopy. Like dichromium, a singlet state is expected from dimolybdenum. Higher bond order is reflected in shorter bond length of 194 pm. A singlet 1Σg+ground state can be expected from ditungsten as well. However, this ground state arises from a combination of either two isolated tungstens' ground 5D0 states or two isolated tungstens' excited7S3 states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten dimer. Dimolybdenum and dichromium follow much the same mechanism to achieve the stablest ground state of their respective dimers.
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 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 for deviations from equilibrium geometry. 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 would only be equivalent if the molecule were in its stablest geometry, the effective bond order 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.
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 spinsferromagnetically coupled to each other. 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. 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. Several metal-metal dimers exist held together by only van der Waals forces, due to poor participation of metald electrons in bonding. van der Waals metal-metal dimers include the d9coinage metalsCu, Ag, and Au as well as d10 metals such as Zn, Cd and Hg. 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 where n is the bond order, ke is the summed force constant of all the bonds between the metal atoms and ke is the force constant of a single bond between the metal atoms. 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
EBO
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. 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. 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. 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. 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. To date, no sextuple bond has been observed in lanthanides or actinides.
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 frontiermolecular 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. 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 dibenzenesandwich compounds Cr22, Mo22, and W22. In the triplet states with geometries of symmetry D6h and D6d, evaluation of the molecular bonding orbitals for all three compounds reveals the possibility of a sextuple bond between the metal atoms. 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. 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 complexes disrupts the sextuple bond and results in a lower bond order. 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.
Effect of halogenation
of dimolybdenum and ditungsten with trifluoroiodomethane forms a bisdimolybdenum 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. 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. 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. 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.
