4 × P = 4 × 5 = 20 It is a 5n structure with n = 4, so it is tetrahedral Example: P4S3 Electron count 4 × P + 3 × S = 4 × 5 + 3 × 6 = 38 It is a 5n + 3 structure with n = 7. Three vertices are inserted into edges Example: P4O6 Electron count 4 × P + 6 × O = 4 × 5 + 6 × 6 = 56 It is a 5n + 6 structure with n = 10. Six vertices are inserted into edges 6n rules As more electrons are added to a 5n cluster, the number of electrons per vertex approaches 6. Instead of adopting structures based on 4n or 5n rules, the clusters tend to have structures governed by the 6n rules, which are based on rings. The rules for the 6n structures are as follows. Example: S8 Electron count = 8 × S = 8 × 6 = 48 electrons. Since n = 8, 6n = 48, so the cluster is an 8-membered ring. Hexane (C6H14) Electron count = 6 × C + 14 × H = 6 × 4 + 14 × 1 = 38 Since n = 6, 6n = 36 and 6n + 2 = 38, so the cluster is a 6-membered chain. Isolobal vertex units Provided a vertex unit is isolobal with BH then it can, in principle at least, be substituted for a BH unit, even though BH and CH are not isoelectronic. The CH+ unit is isolobal, hence the rules are applicable to carboranes. This can be explained due to a frontier orbital treatment. Additionally there are isolobal transition-metal units. For example, Fe(CO)3 provides 2 electrons. The derivation of this is briefly as follows: Fe has 8 valence electrons. Each carbonyl group is a net 2 electron donor after the internal σ- and π-bonding are taken into account making 14 electrons. 3 pairs are considered to be involved in Fe–CO σ-bonding and 3 pairs are involved in π-backbonding from Fe to CO reducing the 14 to 2. Bonding in cluster compounds closo- The boron atoms lie on each vertex of the octahedron and are sp hybridized. One sp-hybrid radiates away from the structure forming the bond with the hydrogen atom. The other sp-hybrid radiates into the center of the structure forming a large bonding molecular orbital at