Defects in Statically Unstable Solids: The Case for Cubic Perovskite \alpha-CsPbI_3

High-temperature phases of solids are often dynamically stable only. First-principles study of point defects in such solids at 0 K is prohibited by their static instability, which results in random structures of the defect-containing supercell so that the total energy of the supercell is randomly affected by structural distortions far away from the defect. Taking cubic perovskite \alpha-CsPbI_3 as an example, we first present the problem incurred by the static instability and then propose an approach based on molecular dynamics to carry out ensemble average for tackling the problem. Within affordable simulation time, we obtain converged defect ionization energies, which are unattainable by a standard approach and allow us to evaluate its defect tolerance property. Our work paves the way for studying defects in statically unstable solids.