Structural optimization at finite temperature based on self-consistent phonon theory

Ab-initio structural optimization at finite temperatures based on anharmonic phonon theory: Application to the structural phase transitions of BaTiO$_3$

We formulate a first-principle scheme for structural optimization at finitetemperature based on the self-consistent phonon (scp) theory, which nonperturbatively takes into account the effect of phonon anharmonicity.The of the shape of the unit cell and internal atomic configuration is determined by minimizing the variational free energy in the scp theory.We demonstrate that the thermal expansion of silicon and the three-step structural phase transitions in are successfully reproduced.