Cluster molecular orbitals and an orbital symmetry view of solid phase transitions in perovskites

Abstract

The molecular orbitals, normalization constants and energies of the M 8( O h ), M 4( T d ) and M 6( O h ) 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 Sr 8, La 8, TiO 6 and AlO 6 clusters are computed by the Mulliken—Wolfsberg and Helmholz approximations. During solid phase transitions in the perovskite structures of SrTiO 3 and LaAlO 3, the TiO 6 octahedron rotates about the C 4 axis whereas the AlO 6 octahedron rotates about the C 3 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.