Accurate calculations of phonon dispersion in CaF₂ and CeO ₂

We report the lattice dynamic properties of CaF₂ and CeO ₂ obtained using a direct method in combination of a mixed-space approach accounting for the vibration-induced dipole-dipole interactions. We overcame the overestimation of T_1u TO mode shown in prior calculations using the linear response theory. For CaF₂, we employed the Perdew-Burke-Ernzerhof functional and achieved a significant improvement over previous linear response calculations by comparing the results with experimentally measured phonon dispersion curves. For CeO₂, we adopted the Heyd-Scuseria-Ernzerhof hybrid functional and an elongated supercell and obtained results in excellent agreement with experimental measurements. We attributed the improved calculation results to the convenience of the direct method in implementing new exchange-correlation functionals and use of the mixed-space approach for treating the long-range dipole-dipole interactions.