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, H+
3.  Another example of a 3c-2e bond is in dihydrogen complexes.
Boron compounds 
Three-center two-electron bonds are 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 electron configuration closer to an 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.
The two electrons (corresponding to one bond) in a B−H−B bonding molecular orbital are spread out across three internuclear spaces. The reported bond order for each B−H interaction is 0.5, so that the bridging B−H bonds are weaker and longer than the terminal B−H bonds, as shown by the bond lengths in the structural diagram.
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.
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.
See also 
- IUPAC Gold Book
- I. Mayer (1989). "Bond orders in three-centre bonds: an analytical investigation into the electronic structure of diborane and the three-centre four-electron bonds of hypervalent sulphur". Journal of Molecular Structure 186: 43–52. doi:10.1016/0166-1280(89)87037-X.
- F. Albert Cotton, Geoffrey Wilkinson and Paul L. Gaus, Basic Inorganic Chemistry, 2nd ed. (Wiley 1987), p.113