Boron and Electron-Deficient Clusters
Boron forms a remarkable family of electron-deficient hydrides and clusters whose three-centre bonding and polyhedral shapes are unified by the skeletal-electron-pair counting rules.
Definition
Electron-deficient clusters are species, exemplified by the boranes, in which there are too few valence electrons for conventional two-centre two-electron bonds, so the atoms share electrons over multicentre bonds to form polyhedral cage structures.
Scope
This topic covers electron-deficient main-group cluster chemistry: the boron hydrides (boranes) and their three-centre two-electron bonding, the closo, nido, and arachno structural families, carboranes and metallaboranes, and the Wade–Mingos polyhedral-skeletal-electron-pair rules that predict their shapes from electron counts. It focuses on cluster bonding and structure rather than the general descriptive chemistry of the p-block.
Core questions
- How can boranes be stable despite having too few electrons for classical bonds?
- What is a three-centre two-electron bond?
- How do Wade's rules predict closo, nido, and arachno geometries?
- How do carboranes and metallaboranes extend the borane structural families?
Key concepts
- Boron hydrides (boranes)
- Three-centre two-electron bonds
- closo, nido, and arachno clusters
- Wade's rules
- Carboranes
- Metallaboranes
Key theories
- Three-centre two-electron bonding
- Lipscomb showed that boranes use bonds in which a single electron pair is shared among three atoms, allowing electron-deficient molecules to hold together without enough electrons for ordinary two-centre bonds.
- Wade–Mingos skeletal-electron-pair rules
- Counting the number of skeletal bonding electron pairs predicts whether a cluster adopts a closo, nido, or arachno geometry derived from a parent polyhedron, unifying boranes, carboranes, and many metal clusters.
- Carboranes and isolobal extension
- Replacing borane vertices by carbon or by isolobal metal fragments gives carboranes and metallaboranes that follow the same electron-counting rules, demonstrating the generality of cluster bonding.
Clinical relevance
Boron clusters underpin boron neutron capture therapy for cancer, serve as weakly coordinating anions and ligands in catalysis, and provide models for electron-deficient bonding across chemistry.
History
Alfred Stock first prepared and characterized the boranes in the early twentieth century, and their puzzling electron deficiency was resolved by Lipscomb's three-centre bonding analysis, recognized by the 1976 Nobel Prize. Wade's 1971 electron-counting rules, generalized by Mingos, then provided a unified framework for cluster structures.
Key figures
- Alfred Stock
- William Lipscomb
- Kenneth Wade
- Michael Mingos
Related topics
Seminal works
- wade1971
- lipscomb1963
- greenwood1997
Frequently asked questions
- What does it mean for a molecule to be electron-deficient?
- An electron-deficient molecule has fewer valence electrons than are needed to form the usual two-electron bonds between every pair of bonded atoms, so it must delocalize electrons over multicentre bonds, as the boranes do with three-centre two-electron bonds.
- How do Wade's rules predict a cluster's shape?
- By counting the skeletal bonding electron pairs and comparing that number with the number of vertices, the rules indicate whether the cluster is a complete polyhedron (closo) or one (nido) or two (arachno) vertices short of one, fixing its geometry.