A sextuple bond is a type of
covalent bond
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
involving 12 bonding
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s and in which the
bond order
In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds.
The bond order itself is the number of electron pairs (covalent bonds) between two atoms. For example, in diat ...
is 6. The only known molecules with true sextuple bonds are the diatomic dimolybdenum (
Mo2) and ditungsten (
W2), which exist in the
gaseous phase
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
and have boiling points of and 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
Hybrid may refer to:
Science
* Hybrid (biology), an offspring resulting from cross-breeding
** Hybrid grape, grape varieties produced by cross-breeding two ''Vitis'' species
** Hybridity, the property of a hybrid plant which is a union of two dif ...
of the
''s'' orbital and all five
''d'' orbitals, and
''f'' orbitals contract too close to the
nucleus
Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
*Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA
Nucle ...
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
In chemistry, pi bonds (π bonds) are covalent bond, covalent chemical chemical bond, bonds, in each of which two lobes of an atomic orbital, orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap oc ...
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
actinide
The actinide () or actinoid () series encompasses the 15 metallic chemical elements with atomic numbers from 89 to 103, actinium through lawrencium. The actinide series derives its name from the first element in the series, actinium. The inform ...
s 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
In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds.
The bond order itself is the number of electron pairs (covalent bonds) between two atoms. For example, in diat ...
of a molecule is half the number of
bonding electrons surplus to
antibonding electrons; for a typical molecule, it attains exclusively
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
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 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 could be determined by the formula
where is the proportion of formal bonding orbital occupation for an electron pair , is the proportion of the formal antibonding orbital occupation, and is a correction factor accounting for deviations from
equilibrium geometry.
Several
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
-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
A quintuple bond in chemistry is an unusual type of chemical bond, first reported in 2005 for a dichromium compound. Single bonds, double bonds, and triple bonds are commonplace in chemistry. Quadruple bonds are rarer but are currently known only ...
and a partially formed sixth
covalent bond
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
.
Dichromium
Chromium is a chemical element with the symbol Cr and atomic number 24. It is the first element in group 6. It is a steely-grey, lustrous, hard, and brittle transition metal.
Chromium metal is valued for its high corrosion resistance and hardn ...
, 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
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation p ...
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
Near-infrared spectroscopy (NIRS) is a spectroscopic method that uses the near-infrared region of the electromagnetic spectrum (from 780 nm to 2500 nm). Typical applications include medical and physiological diagnostics and research incl ...
or
UV spectroscopy
Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm (with a corresponding frequency around 30 PHz) to 400 nm (750 THz), shorter than that of visible light, but longer than X-rays. UV radiation i ...
.
Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers.
For example, sextuply-bonded dimolybdenum has an equilibrium
bond length
In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of ...
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.
One empirical technique to determine bond order is
spectroscopic
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
examination of bond
force constant
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of ...
s.
Pauling's formula predicts that bond order is roughly
proportional to the force constant; that is,
where is the bond order, is the force constant of the interatomic interaction and 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
1Σ
g+ singlet ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
.
However, in tungsten, this ground state arises from a
hybrid
Hybrid may refer to:
Science
* Hybrid (biology), an offspring resulting from cross-breeding
** Hybrid grape, grape varieties produced by cross-breeding two ''Vitis'' species
** Hybridity, the property of a hybrid plant which is a union of two dif ...
of either two
5D
0 ground states or two
7S
3 excited states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten
dimer
Dimer may refer to:
* Dimer (chemistry), a chemical structure formed from two similar sub-units
** Protein dimer, a protein quaternary structure
** d-dimer
* Dimer model, an item in statistical mechanics, based on ''domino tiling''
* Julius Dimer ...
.
Ligand effects
Although sextuple bonding in
homodimers
In biochemistry, a protein dimer is a macromolecular complex formed by two protein monomers, or single proteins, which are usually non-covalently bound. Many macromolecules, such as proteins or nucleic acids, form dimers. The word ''dimer'' has ...
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
Schaefer is an alternative spelling and cognate for the German word ''schäfer'', meaning 'shepherd', which itself descends from the Old High German '' scāphare''. Variants "Shaefer", "Schäfer" (a standardized spelling in many German-speaking ...
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
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
should exhibit a formal pentuple bond.
Similarly, for the
dibenzene complexes Cr
2(C
6H
6)
2, Mo
2(C
6H
6)
2, and W
2(C
6H
6)
2, molecular bonding orbitals for the triplet states with
symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
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 , depending on the central metal.
Oxo ligands
Both quantum mechanical calculations and
photoelectron spectroscopy
Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in th ...
of the tungsten oxide clusters W
2O
n (n = 1-6) indicate that increased
oxidation state
In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
reduces the bond order in ditungsten. At first, the weak δ bonds break to yield a quadruply-bonded W
2O; further oxidation generates the ditungsten complex W
2O
6 with two bridging oxo ligands and no direct W-W bonds.
References
Further reading
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{{Chemical bonding theory
Chemical bonding