electron-deficient bonding

Most of the bonding you first learn obeys a comfortable rule: pair up two electrons between two atoms and you have a bond, and each atom ends up with a full outer shell (the octet). But some elements simply do not bring enough electrons to play that game. Boron is the classic case: with only three valence electrons, even after forming three bonds it sits at six electrons, two short of an octet. What happens when a molecule has fewer bonding electrons than it seems to need? The answer is electron-deficient bonding, where the few electrons available are made to do extra work.

An atom or molecule is called electron-deficient when it has fewer valence electrons than would be required to fill every bond with a conventional two-electron, two-atom (2c-2e) pair. Boron compounds solve this in two ways. First, BF3 and similar molecules stay hungry: the boron has an empty p orbital and acts as a strong Lewis acid, grabbing a lone pair from anything that will donate one. Second, and more strikingly, the boron hydrides spread their scarce electrons over three atoms at once, forming three-center two-electron (3c-2e) bonds, where one electron pair binds three nuclei, for example two borons and a bridging hydrogen written B-H-B. Counting bonds the ordinary way fails here; you must count delocalized cluster electrons instead.

Electron-deficient bonding matters because it shows the octet rule is a useful habit, not a law of nature, just as hypervalency does at the other extreme. It is the organizing idea behind the whole chemistry of boron, the boranes and carboranes, and the dimeric aluminum chloride Al2Cl6, and it forces a different bookkeeping (Wade's rules) for clusters. Recognizing electron deficiency tells you immediately to expect Lewis acidity, bridging atoms, and cage or cluster structures rather than tidy chains of single bonds.