Group Theoretical Investigation of Octahedral and Cuboctahedral Bonding

The behavior of electrons in molecules is governed by quantum mechanical laws – insofar as we can tell. A quantitative check has proved impossible for all except the simplest systems, such as the H2+ and H2 molecules. Generally, severe approximations have to be made. The procedure that is supported by spectral measurements is the molecular orbital method. Indeed, energy levels of many systems can be classified in molecular orbital configurations, while a similar explanation is not possible in terms of valence-bond or hybridization description. In the work reported here, group theoretical methods have been used to obtain symmetry orbitals that are molecular orbital candidates. The symmetric structures considered include an octahedral B6 cage, octahedral Ta6C12+2, and a cuboctahedral B12 cage. The biggest problem arose in combining the symmetry orbitals from multiply occurring irreducible representations to get functions belonging to the same column. Finally, energy levels were found and expressed in parametric form