Application of ‘molecular’ theories to the structure of the crystalline state
Recent years have seen the development of simple molecular orbital based ideas to view the structures of molecular ring, cage and cluster compounds. The principles of these methods are used here to demonstrate in a new way how the structures of solids depend on electronic configuration.
Cluster molecular orbitals and an orbital symmetry view of solid phase transitions in perovskites
The molecular orbitals, normalization constants and energies of the M8(Oh), M4(Td) and M6(Oh) clusters are derived and tabulated through the d-atomic orbitals. A vector method, adapted to computer application, is devised to compute s, p and d overlap between variously oriented orbitals at atoms that do not have co-directional local axes. Mixing of σ, π and δ orbitals to give the same irreducible representation is also included. As illustrations, the orbitals of Sr8, La8, TiO6 and AlO6 clusters are computed by the Mulliken—Wolfsberg and Helmholz approximations. During solid phase transitions in the perovskite structures of SrTiO3 and LaAlO3, the TiO6 octahedron rotates about the C4 axis whereas the AlO6 octahedron rotates about the C3 axis. This difference is explained qualitatively in terms of the relative symmetries of the cluster HOMOs and LUMOs using the second-order Jahn—Teller effect. Allusions are made to the application of this cluster symmetry approach to other systems.
The crystal structure of ruthenium carbonyl, Ru3(CO)12
An X-ray structural analysis of ruthenium carbonyl, Ru3(CO)12, has been completed using 936 independent reflexions in a least-squares refinement (R= 0·079). The molecule has essentially D3h symmetry with a mean Ru–Ru bond length of 2·848 A. The crystal structure is very similar to that of Os3(CO)12.