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) 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.[1] 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.)[2]
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.[3] No sextuple bond has been observed in lanthanides or actinides.[1]
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.[1]
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.
In Roos et al's calculations, the effective bond order (EBO) could be determined by the formula
where ηb is the proportion of formal bonding orbital occupation for an electron pair p, ηab is the proportion of the formal antibonding orbital occupation, and c is a correction factor accounting for deviations from
equilibrium geometry.[1] 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 spinsexchange-coupled to each other.[5]
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.[4] 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.[6]
Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers.[1] 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.[8][9][10] However, the bond dissociation energies of ditungsten and dimolybdenum are rather low, because the short internuclear distance introduces geometric strain.[1][11]
One empirical technique to determine bond order is
spectroscopic examination of bond
force constants.
Linus Pauling investigated the relationships between bonding atoms[12] and developed a formula that predicts that bond order is roughly[13] proportional to the force constant; that is,
where n is the bond order, ke is the force constant of the interatomic interaction and ke(1) is the force constant of a single bond between the atoms.[14]
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 1Σg+singletground state.[15][16] However, in tungsten, this ground state arises from a
hybrid of either two 5D0 ground states or two 7S3excited states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten
dimer.[8]
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.[17] 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.[17] Similarly, for the
dibenzene complexes Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2, molecular bonding orbitals for the triplet states with
symmetries D6h and D6d indicate the possibility of an intermetallic sextuple bond. Quantum chemistry calculations reveal, however, that the corresponding D2h singlet geometry is stabler than the D6h triplet state by 3–39 kcal/mol, depending on the central metal.[18]
Oxo ligands
Both quantum mechanical calculations and
photoelectron spectroscopy of the tungsten oxide clusters W2On (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 W2O; further oxidation generates the ditungsten complex W2O6 with two bridging oxo ligands and no direct W-W bonds.[19]
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^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.
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^Goodgame, Marvin M.; Goddard, William A. (February 1981). "The "sextuple" bond of chromium dimer". The Journal of Physical Chemistry. 85 (3): 215–217.
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^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.
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^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.
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^
abcJules, 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.
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^Lombardi, John R.; Davis, Benjamin (2002-06-01).
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^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.
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abXu, 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.
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^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.
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