Topological aspects of the skeletal bonding in "Isocloso" metallaboranes containing "anomalous" numbers of skeletal electrons

Removal of the transition metal vertex from an "isocloso" metallaborane hav ing 9, 10, or 11 vertices and 2v skeletal electrons leads to a BnHn2- ligan d or isoelectronic derivative thereof having one open hexagonal face for he xahapto bonding to the transition metal and 2v - 7 triangular faces. The nu mbers of available skeletal electrons and orbitals in such isocloso metalla boranes correspond to v 2-electron 3-center bonds in v of the 2v - 4 faces of the original metallaborane deltahedron. This contrasts with the 2-electr on v-center core bond and the v surface bonds in the close metal-free BnHn2 - and C2Bn-2Hn deltahedra with 2v + 2 skeletal electrons. A diamond-square process removing an M-B edge from an isocloso metallaborane to give an "iso nido" metallaborane converts a set of six skeletal orbitals from two 2-elec tron 3-center bonds into three 2-electron 2-center bonds.