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Three-center two-electron bond

Three-center two-electron bond

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A three-center two-electron bond is an electron-deficient
Electron deficiency
Electron deficiency occurs when a compound has too few valence electrons for the connections between atoms to be described as covalent bonds. Electron deficient bonds are often better described as 3-center-2-electron bonds...

 chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

 where three atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s share two electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s. The combination of three atomic orbital
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

s form three molecular orbital
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the 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 finding an electron in any specific region. The term "orbital" was first...

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. The simplest example of a 3c-2e bond is in the trihydrogen cation, H3+.

Boron compounds


Three-center two-electron bonds are seen in many boron
Boron
Boron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...

 compounds, such as diborane
Diborane
Diborane is the chemical compound consisting of boron and hydrogen with the formula B2H6. It is a colorless gas at room temperature with a repulsively sweet odor. Diborane mixes well with air, easily forming explosive mixtures. Diborane will ignite spontaneously in moist air at room temperature...

 (B2H6). The monomer BH3 is unstable since the boron atom is only surrounded by six valence electron
Valence electron
In chemistry, valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms. Valence electrons are the "own" electrons, present in the free neutral atom, that combine with valence electrons of other atoms to form chemical bonds. In a single...

s, and thus, to form a stable octet
Octet rule
The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low (The octet rule is a chemical rule of thumb that states that atoms of low (...

, shares electrons with a B−H bond on another boron atom, forming a B−H−B 3-center-2-electron bond. In diborane, there are two such bonds: two H atoms bridge the two B atoms, leaving two additional H atoms in ordinary B−H bonds on each B.

This bonding pattern is also seen in trimethylaluminium
Trimethylaluminium
Trimethylaluminium is the chemical compound with the formula Al26, abbreviated as Al2Me6, 2 or the abbreviation TMA. This pyrophoric, colorless liquid is an industrially important organoaluminium compound...

, which forms a dimer Al2(CH3)6 with the carbon atoms of two of the methyl group
Methyl group
Methyl group is a functional group derived from methane, containing one carbon atom bonded to three hydrogen atoms —CH3. The group is often abbreviated Me. Such hydrocarbon groups occur in many organic compounds. The methyl group can be found in three forms: anion, cation and radical. The anion...

s in bridging positions. This type of bond also occurs in carbon
Carbon
Carbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...

 compounds, where it is sometimes referred to as hyperconjugation
Hyperconjugation
In organic chemistry, hyperconjugation is the interaction of the electrons in a sigma bond with an adjacent empty non-bonding p-orbital or antibonding π orbital or filled π orbital, to give an extended molecular orbital that increases the stability of the system...

; another name for asymmetrical three-center two-electron bonds.

Carbocations


Carbocation
Carbocation
A carbocation is an ion with a positively-charged carbon atom. The charged carbon atom in a carbocation is a "sextet", i.e. it has only six electrons in its outer valence shell instead of the eight valence electrons that ensures maximum stability . Therefore carbocations are often reactive,...

 rearrangements 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
Carbonium ion
A carbonium ion is a carbocation of the penta- or tetracoordinated nonclassical type such as an ion of the type R5C+.- Methanium:The parent compound methanium or CH5+ is protonated methane and a superacid. This ion exists as a reactive intermediate in the interstellar medium and can be produced in...

s have three-center two-electron bonds. Perhaps the best known and studied structure of this sort is the norbornyl cation.