The characterisation of coordination polyhedra by invariants

We have extended the use of the invariants of spherical harmonics for the characterisation of the angular distribution of coordinating atoms about a central atom. These invariants are suitable indices for use in clustering algorithms for automatic crystal chemistry. Invariants for coordination polyhedra in intermetallic compounds and Ca-O silicates are considered. A study of invariants in coordination polyhedra distorted by the Jahn-Teller effect is presented. In addition, Invariants from small clusters and the cuboctahedron-icosahedron transition are analyzed.