Behavior of the local mode potential in BaTiO3 studied by Effective   Hamiltonian numerical simulations
  The behavior of the local mode potential energy in the unit cell of BaTiO3 is studied by effective Hamiltonian numerical simulations. The study is focused on the evolution of the potential minimum felt by the Ti ion. At the paraelectric phase, the single instantaneous minimum is located at one of eight off-centered regions at the body diagonals of the unit cell. The study shows graphically how the soft mode behavior of the perovskite comes from the average response of the Ti ion to the potential changes in the unit cell, showing that the single minimum of the time-averaged potential is centered at the paraelectric phase and off-centered at the ferroelectric phase. 
Manuel I. Marques, Julio A. Gonzalo