Theory of Skeletal Electron Pairs

Historically, the structural theory of borane and carborane clusters was developed first. This theory was later expanded to include clusters of the main group elements as well as those of the transition metals.This approach allowed the anticipation, in many cases, of the structure and the number of valence electrons of a given cluster as well as its mode of transformation during oxidation and reduction reactions. 

The nido and arachno structures may formally be obtained from hypothetical and anions, respectively, by addition of protons to the terminal B —H 

Each boron or carbon atom has sp hybridization. One of the hybridized orbitals of each atom forms a bond with the terminal hydrogen atom, and the remaining three orbitals (one sp and two p orbitals) give multicenter orbitals of the cluster grouping. The molecular orbital theory shows that borane polyhedra having n vertices have such symmetry that 3n atomic orbitals of the cluster possessing n skeletal atoms form +1 bonding molecular orbitals.  

The atoms residing inside the cluster donate all their valence electrons for the formation of the skeletal bonds. For example, the compound [Ru6(CO)i7C] has 86 valence electrons and therefore represents a closo cluster. The placement of an atom of the main group elements or the transition metals in the cluster hole does not change the number of valence electrons. The value of x is zero for clusters in which the group M(CO) is added to one face of a regular polyhedron such as an octahedron, or x is — 1 if two groups are added, etc. 

Geometry of the cluster Formula of the compound Number of edges E Number of valence electrons N Sidgwick s rule 18F-2F Wade s rule 4V + 2X 

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