three-center two-electron bond
/ three-CEN-ter two-electron; 3c-2e /
An ordinary covalent bond is a handshake between two atoms: one shared pair of electrons glues two nuclei together. But what if a molecule does not have enough electron pairs to glue every neighbor pairwise? Boron's hydrides face exactly this shortage. Their elegant escape is to let a single pair of electrons hold three atoms at once, like one rope tied around three poles instead of two.
A three-center two-electron (3c-2e) bond is a single bonding molecular orbital that spreads over three atoms and is filled by just two electrons (one pair). In diborane, B2H6, the two boron atoms are bridged by two hydrogens; each bridge is a B-H-B unit where one electron pair occupies an orbital built from one boron orbital, the hydrogen 1s, and the other boron orbital. The electron density piles up in the middle, off the straight line between the borons, which is why such bridges are sometimes drawn as bent or banana bonds. Larger boranes and carboranes also use central B-B-B 3c-2e bonds, where the shared pair binds three boron atoms in a triangle. The key feature is that two electrons do the binding work of what would naively look like two separate bonds.
This idea rescues electron-deficient chemistry from paradox and is the structural heart of the boranes, carboranes, and many metal clusters. It also appears in protonated species like H3+ (a triangle of three protons sharing one pair) and in some organometallic bridges and agostic interactions. Recognizing a 3c-2e bond is the moment a confusing electron-deficient formula suddenly makes sense: you stop trying to draw too many lines and instead delocalize one pair over three centers.
In B2H6 the four terminal B-H bonds are ordinary 2c-2e bonds, but the two bridging hydrogens sit in B-H-B 3c-2e bonds. That is why the bridging B-H distances are longer and the bridge angle is bent, not linear.
One pair of electrons holding three atoms is the trick that lets electron-poor molecules exist.
A 3c-2e bond is not a weak or partial bond; it is a perfectly real bond whose single occupied orbital simply happens to span three nuclei rather than two. It is the bookkeeping (one pair, three atoms) that differs, not the reality of the binding.