Explicit, mutually orthogonal and normalized molecular orbitals, up to and including d atomic orbitals and four- and five-fold degenerate (Gg,u and Hg,u) irreducible representations in Ih groups, are obtained by computer-adapted methods for M12 clusters of Oh, and Ih symmetry, using B12H122− and [Rh12Sb(CO)27]3− as examples. Similar computer methods are used to obtain the explicit relative orientational-dependent atomic overlaps between various atomic orbitais in terms of differently oriented local coordinates. The overlaps are used to estimate resonance integrals and molecular orbital energies for the B12 and Rh12 complexes. The symmetries of the molecular orbitais of p atomic orbitals are used to derive the symmetries of vibrational modes of the clusters. These vibrations are used to explain the cluster rearrangement/transformation from one isomer to another via vibronic interaction and the second-order Jahn-Teller effect.
Journal of Molecular Structure: Theochem 258(1-2), pp.15-39