Orbital interaction and vibrational mode analyses for phase transitions of BaTiO3

Abstract

The phase transitions of ATiO ₃ -type perovskite structures, mainly those of barium titanate (BaTiO ₃ ), are studied theoretically in terms of orbital interactions and vibrational modes. Vibrational analyses for fundamental TiO ₆ clusters, up to Ti ₈ O ₃₆ , are performed with a hybrid (Hartree–Fock/density functional) method. Important structural distortions from the high symmetry cubic phase are rationalized by a second-order perturbational treatment of quantum chemistry. The orbital symmetry argument based on group theory indicates that the transition density around frontier molecular orbitals plays an important role in the motions of ions at the transition temperatures. Our orbital interaction and vibrational mode analyses of the phase transitions are consistent with the soft mode theory of Cochran.