Bond valence in molecular skeletons

Consider a molecular skeleton composed of n main-group atoms, M , which takes the form of a chain, ring, cage, or framework. Let g be the total number of valence electrons of the molecular skeleton. When a covalent bond is formed between two M atoms, each of them effectively gains one electron in its valence shell. In order to satisfy the octet rule for the whole skeleton, 5 (Sn—g) electron pairs must be involved in bonding between the M atoms. The number of these bonding electron pairs is defined as the bond valence b of the molecular skeleton  

When the total number of valence electrons in a molecular skeleton is less than the number of valence orbitals, the formation of normal 2c-2e covalent bonds is insufficient to compensate for the lack of electrons. In this type of electron-deficient compound there are usually found 3c-2e bonds, in which three atoms share an electron pair. Thus one 3c-2e bond serves to compensate for the lack of four electrons and corresponds to a bond valence value of 2, as discussed in 13.2. 

There is an enormous number of compounds that possess metal-metal bonds. A metal cluster may be defined as a polynuclear compound in which there are substantial and directed bonds between the metal atoms. The metal atoms of a cluster are also referred to as skeletal atoms, and the remaining non-metal 

According to the 18-electron rule, the bond valence of a transition metal cluster is 

If the bond valence b calculated from (13.4.1) and (13.4.2) for a cluster M matches the number of connecting lines drawn between pairs of adjacent atoms in a conventional valence bond structural formula, the cluster is termed electron-precise.  

---