Three-Centre Bonding Explained: Diborane and Beyond

Three-centre bonding is a bond in which a single pair of electrons is shared by three atoms instead of two. It appears in electron-deficient molecules like diborane (B2H6), where there are too few electrons for every pair of atoms to have its own bond.

It matters because it explains the strange bridge structure of diborane, the chemistry of boranes and carboranes, and how molecules cope when the octet rule cannot be satisfied with ordinary two-centre bonds.

Key Concepts

• Electron deficiency: boron has only 3 valence electrons, so BH3 holds just 6 electrons around boron, two short of an octet.
• 3-centre-2-electron (3c-2e) bond: one electron pair shared by three atoms, written B-H-B. Also called a banana bond for its curved shape.
• Terminal vs bridging hydrogens: diborane has 4 normal terminal B-H bonds and 2 bridging hydrogens, each between the two boron atoms.
• sp3 hybridization: each boron is roughly tetrahedral, using two sp3 orbitals for terminal bonds and two for the bridges.
• Beyond diborane: higher boranes (B4H10, B5H9, B10H14) contain more B-H-B and B-B-B bridges; the idea also appears in Al2Cl6 bridges.

How It Works

• Step 1 - count electrons: B2H6 has 2x3 + 6x1 = 12 valence electrons, but 7 atom pairs would need 14 for full two-centre bonds.
• Step 2 - place terminal bonds first: four normal B-H two-centre bonds use 8 electrons, leaving 4 for the two bridges.
• Step 3 - form the bridges: each bridge merges one sp3 orbital from each boron with the 1s orbital of hydrogen into one orbital holding 2 electrons.
• Step 4 - check the geometry: the B-H-B angle is about 83 degrees and the bridging B-H length is 133 pm, longer and weaker than the 119 pm terminal bonds.

Worked Example

Question: Show by electron counting that diborane must contain 3c-2e bonds.

Step 1: Total valence electrons: 2 boron x 3 + 6 hydrogen x 1 = 12 electrons, i.e. 6 pairs.

Step 2: A simple structure with only two-centre bonds would need: 1 B-B bond + 6 B-H bonds = 7 bonds = 14 electrons. Only 12 are available, so at least one bond must be shared.

Step 3: Put 4 pairs into the 4 terminal B-H bonds (8 electrons). The remaining 2 pairs (4 electrons) must cover the connections between the borons and the 2 bridging hydrogens.

Step 4: Two B-H-B 3c-2e bridges use exactly those 4 electrons, completing every hydrogen's duet and giving each boron 8 shared electrons.

Common Misconceptions

• "Diborane is just two BH3 molecules stuck together." The bridges are real chemical bonds with measurable length and vibrational spectra, not weak contacts; B2H6 does not fall apart into BH3 at room temperature.
• "The bridging hydrogens are negatively charged hydrides." They are covalently shared in the 3c-2e orbital; diborane is a neutral covalent molecule, not an ionic hydride.
• "3c-2e bonds break the octet rule." Each boron still shares 8 electrons (4 terminal + 4 from two bridges); the octet is satisfied through sharing, not exceeded.

Real-World Applications

• Diborane is a precursor for semiconductor doping and a high-energy rocket fuel component, where its electron deficiency makes it a strong reducing agent.
• Hydroboration: diborane adds across C=C double bonds, a Nobel-winning reaction used to make alcohols with precise stereochemistry.
• Carboranes (boron-carbon clusters built on 3c-2e bonding) are used in cancer therapy agents and ultra-stable polymers.
• Recognizing 3c-2e bridges helps interpret structures of aluminium alkyls and transition-metal hydrides in catalysis.

Three-centre bonding shares one electron pair among three atoms when electrons run short, as in diborane's two B-H-B bridges. Electron counting proves the bridges are necessary, and their longer, weaker bonds match measurement.