Ab initio Study of Valley Line on a Total-Energy Surface for Zone-Center   Distortions of Ferroelectric Perovskite Oxides BaTiO3 and PbTiO3
  An ab initio structure optimization technique is newly developed to determine the valley line on a total-energy surface for zone-center distortions of ferroelectric perovskite oxides and is applied to barium titanate BaTiO3 and lead titanate PbTiO3. The proposed technique is an improvement over King-Smith and Vanderbilt's scheme [Phys. Rev. B 49, p.5828 (1994)] of evaluating total energy as a function of the amplitude of atomic displacements. The results of numerical calculations show that total energy can be expressed as a fourth-order function of the amplitude of atomic displacements in BaTiO3 but not in PbTiO3. 
Takeshi Nishimatsu, Takatoshi Hashimoto, Hiroshi Mizuseki, Yoshiyuki   Kawazoe, Atsushi Sasaki, Yoshiaki Ikeda