  We formulate a first-principle scheme for structural optimization at finite
temperature ($T$) based on the self-consistent phonon (SCP) theory, which
accurately takes into account the effect of strong 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$_3$ and its pressure-temperature ($p$-$T$) phase diagram 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.

Materials Science