Molecular Dynamics Study of Ferroelectric Perovskites based on Effective Hamiltonians: implementation of Nose-Hoover and Parinello-Rahman algorithms

Molecular Dynamics is applied to Ferroelectric Perovskites in the framework of a first-principles derived effective Hamiltonian (Zhong, Vanderbilt, Rabe, Phys. Rev. Lett. {\bf 73} (1994), 1861). The degrees of freedom, that obey the Newton equations of motion, are the local modes and the displacement modes. The Nose-Hoover method is implemented, as well as the Parinello-Rahman scheme to perform fixed temperature and fixed stress tensor simulations. This allows to study the thermodynamics of ferroelectric perovskites and to reproduce successfully the Monte Carlo results on phase transitions, polarization and homogeneous strain evolution with temperature of BaTiO$_3$, taken as an example.