Systematics of Atomic Orbital Hybridization of Coordination Polyhedra: Role of f Orbitals.

The combination of atomic orbitals to form hybrid orbitals of special symmetries can be related to the individual orbital polynomials. Using this approach, 8-orbital cubic hybridization can be shown to be spdf requiring an f orbital, and 12-orbital hexagonal prismatic hybridization can be shown to be spdfg requiring a g orbital. The twists to convert a cube to a square antiprism and a hexagonal prism to a hexagonal antiprism eliminate the need for the highest nodality orbitals in the resulting hybrids. A trigonal twist of an octahedron into a trigonal prism can involve a gradual change of the pair of d orbitals in the corresponding spd hybrids. A similar trigonal twist of an cuboctahedron into a anticuboctahedron can likewise involve a gradual change in the three f orbitals in the corresponding spdf hybrids.