Three-center two-electron bond

A three-center two-electron 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. The simplest example of a 3c-2e bond is in the trihydrogen cation, H3+. [1]
Diborane. The two central hydrogen atoms are simultaneously bonded to both boron atoms in 3c-2e bonds.

This type of bond is seen in many boron compounds, such as diborane, B2H6; the monomer BH3 is unstable since the boron atom is only surrounded by six valence electrons, and thus, to form a stable octet, 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 (Al(CH3)3), where the carbon atom of a methyl group is bridging. 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.

Carbocation 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.

The so-called non-classical carbocations have three-center two-electron bonds. Perhaps the best known and studied structure of this sort is the norbornyl cation.