Bonding patterns in transition metal clusters

Bonding patterns and electron counts of high-symmetry transition metal cluster compounds are discussed using a simplified Tensor Surface Harmonic (TSH) treatment. An n-vertex metal cluster has 9n valence atomic orbitals. From this set orbitals concerned in metal–ligand bonding are eliminated to yield the effective valence orbitals available to cluster bonding. Applying TSH theory to this smaller set gives a clear classification of the cluster MOs and their bonding/antibonding characteristics. Orbital mixing allowed by point group symmetry gives a final, qualitative cluster MO diagram. Results for triangular, tetrahedral and octahedral clusters are compared with other models.