Multicentre bonding

Multicentre bonding describes a bonding interaction distributed over more than two atomic centers. A two-center localized electron-pair picture may then fail to represent how the occupied molecular orbitals stabilize the structure.

A standard example is a bridging hydrogen in diborane, where a three-centre two-electron bond extends across a boron-hydrogen-boron unit. The electron pair belongs to the whole three-center interaction, rather than to two independent ordinary bonds. This helps explain electron-deficient molecules without requiring each apparent atom-to-atom connection to contain its own pair of electrons.

A hydrogen atom associated with more than one skeletal centre. Removal as a proton must be distinguished from hydride transfer; the cluster charge and electron count change differently in the two operations.

An electron-counting approach relating skeletal electron pairs to a cluster vertex count $n$. A closo deltahedron has $n+1$ pairs; nido and arachno frameworks have $n+2$ and $n+3$. The count excludes electrons in externally directed bonds or lone pairs. It is a structural guide with a defined domain, not a rule that every molecule with the same total valence count has the same shape.

The number of electrons allocated to the connected cluster framework after separating external bonds and appropriate lone pairs. For ${\mathrm{B}}_{\mathrm{n}}{\mathrm{H}}_{\mathrm{m}}^{\mathrm{q}-}$ with one terminal B–H bond per vertex it is $n+m+q$.

A pair of electrons allocated to cluster bonding. closo, nido and arachno counts distinguish the number of missing vertices relative to a closed parent polyhedron.

A three-centre two-electron bond has two bonding electrons shared across three atomic centers. Combining three suitable atomic orbitals gives bonding, nonbonding, and antibonding combinations; occupation of the lowest combination by one electron pair can stabilize the three-center unit.

The bridging boron-hydrogen-boron interactions in diborane are the classic example. Counting each bridge as two ordinary two-center electron-pair bonds would require more electrons than are available. Multicentre bonding resolves the count while preserving a quantum-mechanical description in terms of orbitals extending across the atoms.