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

Ryota Masuki, Takuya Nomoto, Ryotaro Arita, Terumasa Tadano

We formulate a first-principle scheme for structural optimization at finite
temperature ($T$) based on the self-consistent phonon (SCP) theory, which
nonperturbatively takes into account the effect of phonon anharmonicity. The
$T$-dependence of the shape of the unit cell and internal atomic configuration
is determined by minimizing the variational free energy in the SCP theory. At
each optimization step, the interatomic force constants in the new structure
are calculated without running additional electronic structure calculations,
which makes the method dramatically efficient. We demonstrate that the thermal
expansion of silicon and the three-step structural phase transitions in
BaTiO$_3$ are successfully reproduced. The present formalism will open the way
to the non-empirical prediction of physical properties at finite $T$ of
materials having a complex structural phase diagram.