Three-center two-electron bond

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A three-center two-electron (3c–2e) bond is an electron-deficient chemical bond where three atoms share two electrons. The combination of three atomic orbitals form three molecular orbitals: 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. An example of a 3c–2e bond is the trihydrogen cation and diborane H
+ and B
. In some structures, the three atoms form an angular geometry, leading to a bent bond.


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 carboranes. These molecules derive their stability from having a completely filled set of bonding molecular orbitals as outlined by Wade's rules.

Resonance structures of 3c-2e bond in diborane. Diborane resonance.svg
Resonance structures of 3c-2e bond in diborane.

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. [1]

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 for each B−H interaction in a bridge is 0.5, [2] so that the bridging B−H−B bonds are weaker and longer than the terminal B−H bonds, as shown by the bond lengths in the structural diagram.


Transition metal complexes

One of many transition metal silane complexes, examples feature three-center two-electron bonding. Cp'Mn(CO)2(HSiPh3).png
One of many transition metal silane complexes, examples feature three-center two-electron bonding.

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, which forms a dimer Al2(CH3)6 with the carbon atoms of two of the methyl groups in bridging positions. This type of bond also occurs in carbon compounds, where it is sometimes referred to as hyperconjugation; another name for asymmetrical three-center two-electron bonds.


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. [4]


Carbocation rearrangement reactions 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 ions such as ethanium C
have three-center two-electron bonds. Perhaps the best known and studied structure of this sort is the 2-Norbornyl cation.

See also

Related Research Articles

Chemical bond Lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

Covalent bond Chemical bond that involves the sharing of electron pairs between atoms

A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full outer shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonds are much more common than ionic bonds.

Ionic bonding Chemical bonding involving attraction between ions

Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be of a more complex nature, e.g. molecular ions like NH+
or SO2−
. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms.

A coordinate covalent bond, also known as a dative bond, dipolar bond, or coordinate bond is a kind of two-center, two-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. This type of interaction is central to Lewis theory.


Boranes is the name given to the class of synthetic hydrides of boron with generic formula BxHy. In the past, borane molecules were often labeled "electron-deficient" because of their multicenter bonding (in which a pair of bonding electrons links more than two atoms, as in 3-center-2-electron bonds); this was done in order to distinguish such molecules from hydrocarbons and other classically bonded compounds. However, this usage is incorrect, as most boranes and related clusters such as carboranes are actually electron-precise, not electron-deficient. For example, the extremely stable icosahedral B12H122− dianion, whose 26 cluster valence electrons exactly fill the 13 bonding molecular orbitals, is in no actual sense deficient in electrons; indeed it is thermodynamically far more stable than benzene.

Lewis acids and bases Chemical bond theory involving the transfer of an electronic pair from the donor (the base) to the acceptor (the acid)

A Lewis acid is a chemical species that contains an empty orbital which is capable of accepting an electron pair from a Lewis base to form a Lewis adduct. A Lewis base, then, is any species that has a filled orbital containing an electron pair which is not involved in bonding but may form a dative bond with a Lewis acid to form a Lewis adduct. For example, NH3 is a Lewis base, because it can donate its lone pair of electrons. Trimethylborane (Me3B) is a Lewis acid as it is capable of accepting a lone pair. In a Lewis adduct, the Lewis acid and base share an electron pair furnished by the Lewis base, forming a dative bond. In the context of a specific chemical reaction between NH3 and Me3B, the lone pair from NH3 will form a dative bond with the empty orbital of Me3B to form an adduct NH3•BMe3. The terminology refers to the contributions of Gilbert N. Lewis.

Conjugated system

In chemistry, a conjugated system is a system of connected p orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.

Carbocation Ion with a positively charged carbon atom

A carbocation is an ion with a positively charged carbon atom. Among the simplest examples are the methenium CH+
, methanium CH+
and vinyl C
cations. Occasionally, carbocations that bear more than one positively charged carbon atom are also encountered.

Diborane Chemical compound

Diborane(6), generally known as diborane, is the chemical compound consisting of boron and hydrogen with the formula B2H6. It is a colorless, pyrophoric gas with a repulsively sweet odor. Synonyms include boroethane, boron hydride, and diboron hexahydride. Diborane is a key boron compound with a variety of applications. It has attracted wide attention for its electronic structure. Its derivatives are useful reagents.

In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or ions by the combination of several contributing structures into a resonance hybrid in valence bond theory. It has particular value for describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis structure.

Pi bond Type of chemical bond

In chemistry, pi bonds are covalent chemical bonds where two lobes of an orbital on one atom overlap two lobes of an orbital on another atom and this overlap occurs laterally. Each of these atomic orbitals has zero electron density at a shared nodal plane, passing through the two bonded nuclei. The same plane is also a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases.

Electron deficiency is a term describing atoms or molecules having fewer than the number of electrons required for maximum stability. For each atom in a molecule, main group atoms having less than 8 electrons or transition metal atoms having less than 18 electrons are described as electron-deficient. For a whole molecule, molecules which have an incompletely filled set of bonding molecular orbitals are considered to be electron-deficient. Thus, CH3 and BH3 are electron-deficient, while methane (CH4) and diborane (B2H6) are not. Not surprisingly, electron-deficient molecules are typically strongly electron-attracting (electrophilic). As the most extreme form of electron deficiency one can consider the metallic bond.

Organoboron chemistry

Organoborane or organoboron compounds are chemical compounds of boron and carbon that are organic derivatives of BH3, for example trialkyl boranes. Organoboron chemistry or organoborane chemistry is the chemistry of these compounds.

Magic acid Chemical compound

Magic acid (FSO3H·SbF5) is a superacid consisting of a mixture, most commonly in a 1:1 molar ratio, of fluorosulfuric acid (HSO3F) and antimony pentafluoride (SbF5). This conjugate Brønsted–Lewis superacid system was developed in the 1960s by the George Olah lab at Case Western Reserve University, and has been used to stabilize carbocations and hypercoordinated carbonium ions in liquid media. Magic acid and other superacids are also used to catalyze isomerization of saturated hydrocarbons, and have been shown to protonate even weak bases, including methane, xenon, halogens, and molecular hydrogen.

The 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogen compounds, sulfur tetrafluoride, the xenon fluorides, and the bifluoride ion. It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. An extended version of this model is used to describe the whole class of hypervalent molecules such as phosphorus pentafluoride and sulfur hexafluoride as well as multi-center π-bonding such as ozone and sulfur trioxide.

In organic chemistry, the term 2-norbornyl 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 studies and vigorous debates have been centered on the exact structure of the 2-norbornyl cation.

Homoaromaticity Special case of aromaticity in which conjugation is interrupted by a single sp³ hybridized carbon atom

Homoaromaticity, in organic chemistry, refers to a special case of aromaticity in which conjugation is interrupted by a single sp3 hybridized carbon atom. Although this sp3 center disrupts the continuous overlap of p-orbitals, traditionally thought to be a requirement for aromaticity, considerable thermodynamic stability and many of the spectroscopic, magnetic, and chemical properties associated with aromatic compounds are still observed for such compounds. This formal discontinuity is apparently bridged by p-orbital overlap, maintaining a contiguous cycle of π electrons that is responsible for this preserved chemical stability.

Diborane(4) Chemical compound

Diborane(4) is a transient inorganic compound with the chemical formula B
. Stable derivatives are known.

Hydrogen-bridged cations are a type of charged species in which a hydrogen atom is simultaneously bonded to two atoms through partial sigma bonds. While best observable in the presence of superacids at room temperature, spectroscopic evidence has suggested that hydrogen-bridged cations exist in ordinary solvents. These ions have been the subject of debate as they constitute a type of charged species of uncertain electronic structure.


The triboracyclopropenyl fragment is a cyclic structural motif in boron chemistry, named for its geometric similarity to cyclopropene. In contrast to nonplanar borane clusters that exhibit higher coordination numbers at boron (e.g., through 3-center 2-electron bonds to bridging hydrides or cations), triboracyclopropenyl-type structures are rings of three boron atoms where substituents at each boron are also coplanar to the ring. Triboracyclopropenyl-containing compounds are extreme cases of inorganic aromaticity. They are the lightest and smallest cyclic structures known to display the bonding and magnetic properties that originate from fully delocalized electrons in orbitals of σ and π symmetry. Although three-membered rings of boron are frequently so highly strained as to be experimentally inaccessible, academic interest in their distinctive aromaticity and possible role as intermediates of borane pyrolysis motivated extensive computational studies by theoretical chemists. Beginning in the late 1980s with mass spectrometry work by Anderson et al. on all-boron clusters, experimental studies of triboracyclopropenyls were for decades exclusively limited to gas-phase investigations of the simplest rings (ions of B3). However, more recent work has stabilized the triboracyclopropenyl moiety via coordination to donor ligands or transition metals, dramatically expanding the scope of its chemistry.


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