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A three-center two-electron (3c–2e) bond is an
electron-deficient Electron deficiency (and electron-deficient) is jargon that is used in two contexts: species that violate the octet rule because they have too few valence electrons and species that happen to follow the octet rule but have electron-acceptor properti ...
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
where three
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s share two
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 n ...
s. The combination of three
atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any ...
s form three
molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of find ...
s: one bonding, one ''non''-bonding, and one ''anti''-bonding. The two electrons go into the bonding orbital, resulting in a net bonding effect and constituting a chemical bond among all three atoms. In many common bonds of this type, the bonding orbital is shifted towards two of the three atoms instead of being spread equally among all three. Example molecules with 3c–2e bonds are the trihydrogen cation () and diborane (). In these two structures, the three atoms in each 3c-2e bond form an angular geometry, leading to a
bent bond In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a ...
.


Boranes and carboranes

An extended version of the 3c–2e bond model features heavily in cluster compounds described by the polyhedral skeletal electron pair theory, such as boranes and
carborane Carboranes are electron-delocalized (non-classically bonded) clusters composed of boron, carbon and hydrogen atoms.Grimes, R. N., ''Carboranes 3rd Ed.'', Elsevier, Amsterdam and New York (2016), . Like many of the related boron hydrides, these c ...
s. These molecules derive their stability from having a completely filled set of bonding molecular orbitals as outlined by
Wade's rules In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by ...
. The monomer BH3 is unstable since the boron atom has an empty p-orbital. A B−H−B 3-center-2-electron bond is formed when a boron atom shares electrons with a B−H bond on another boron atom. The two electrons (corresponding to one bond) in a B−H−B bonding molecular orbital are spread out across three internuclear spaces. In diborane (B2H6), there are two such 3c-2e bonds: two H atoms bridge the two B atoms, leaving two additional H atoms in ordinary B−H bonds on each B. As a result, the molecule achieves stability since each B participates in a total of four bonds and all bonding molecular orbitals are filled, although two of the four bonds are 3-center B−H−B bonds. The reported
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 ...
for each B−H interaction in a bridge is 0.5, F. Albert Cotton,
Geoffrey Wilkinson Sir Geoffrey Wilkinson FRS (14 July 1921 – 26 September 1996) was a Nobel laureate English chemist who pioneered inorganic chemistry and homogeneous transition metal catalysis. Education and early life Wilkinson was born at Springside, Todm ...
and Paul L. Gaus, ''Basic Inorganic Chemistry'', 2nd ed. (Wiley 1987), p.113
so that the bridging B−H−B bonds are weaker and longer than the terminal B−H bonds, as shown by the
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 ...
s in the structural diagram. :


Transition metal complexes

Three-center, two-electron bonding is pervasive in organotransition metal chemistry. A celebrated family of compounds featuring such interactions as called agostic complexes.


Other compounds

This bonding pattern is also seen in
trimethylaluminium Trimethylaluminium is one of the simplest examples of an organoaluminium compound. Despite its name it has the formula Al2( CH3)6 (abbreviated as Al2Me6 or TMA), as it exists as a dimer. This colorless liquid is pyrophoric. It is an industriall ...
, which forms a dimer Al2(CH3)6 with the carbon atoms of two of the
methyl group In organic chemistry, a methyl group is an alkyl derived from methane, containing one carbon atom bonded to three hydrogen atoms, having chemical formula . In formulas, the group is often abbreviated as Me. This hydrocarbon group occurs in ma ...
s in bridging positions. This type of bond also occurs in
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
compounds, where it is sometimes referred to as hyperconjugation; another name for asymmetrical three-center two-electron bonds.


Beryllium

The first stable subvalent Be complex ever observed contains a three-center two-electron π-bond that consists of donor-acceptor interactions over the C-Be-C core of a Be(0)-carbene adduct.


Carbocations

Carbocation A carbocation is an ion with a positively charged carbon atom. Among the simplest examples are the methenium , methanium and vinyl cations. Occasionally, carbocations that bear more than one positively charged carbon atom are also encount ...
rearrangement reaction In organic chemistry, a rearrangement reaction is a broad class of organic reactions where the carbon skeleton of a molecule is rearranged to give a structural isomer of the original molecule. Often a substituent moves from one atom to anothe ...
s occur through three-center bond transition states. Because the three center bond structures have about the same energy as carbocations, there is generally virtually no activation energy for these rearrangements so they occur with extraordinarily high rates.
Carbonium ion In chemistry, a carbonium ion is any cation that has a pentavalent carbon atom. The name carbonium may also be used for the simplest member of the class, properly called methanium (), where the five valences are filled with hydrogen atoms. The ...
s such as
ethanium In chemistry, ethanium or protonated ethane is a highly reactive positive ion with formula . It can be described as a molecule of ethane () with one extra proton ( hydrogen nucleus), that gives it a +1 electric charge. Ethanium is one of th ...
have three-center two-electron bonds. Perhaps the best known and studied structure of this sort is the
2-Norbornyl cation In organic chemistry, the term 2-norbornyl cation (or 2-bicyclo .2.1eptyl cation) describes one of the three carbocations formed from derivatives of norbornane. Though 1-norbornyl and 7-norbornyl cations have been studied, the most extensive studie ...
.


See also

* Three-center four-electron bond *
2-Norbornyl cation In organic chemistry, the term 2-norbornyl cation (or 2-bicyclo .2.1eptyl cation) describes one of the three carbocations formed from derivatives of norbornane. Though 1-norbornyl and 7-norbornyl cations have been studied, the most extensive studie ...
* Dihydrogen complex


References

{{Chemical bonds Chemical bonding