  The impact of ordered vacancies on the dynamic stability of perovskites is
investigated under the $\textit{ab initio}$ framework with a focus on cubic
BaFeO$_{3}$ ($Pm\bar{3}m$) and vacancy-ordered monoclinic BaFeO$_{2.67}$
($P2_{1}/m$). The harmonic approximation shows that both structures are
dynamically unstable at 0 K. For the monoclinic structure, the instability is
related to rotational distortions of the Fe coordination tetrahedra near the
ordered vacancies. $\textit{Ab initio}$ molecular dynamics simulations in
combination with the introduced structural descriptor demonstrate that both
structures are stabilized above 130 K. Our results suggest that the ordered
vacancies do not significantly alter the critical temperature at which
Ba$-$Fe$-$O perovskites are dynamically stabilized. Further, strong
anharmonicity for the vacancy-ordered structure above its critical temperature
is revealed by a significant asymmetry of the trajectories of O anions near the
ordered vacancies.
