The crystal structure of $\mathrm{Al}{\mathrm{F}}_3$ at high temperatures has a simple cubic lattice. Below $\sim 730\mathrm{K}$, the structure transforms to a rhombohedral ($\alpha$-phase) structure with $R\overline{3}c$ symmetry due to an unstable $R_5^{-}$ phonon. Density-functional based methods, from the least accurate rigid-ion model to highly accurate all-electron Kohn-Sham models, yield the triply degenerate $R_5^{-}$ phonon that becomes unstable with decreasing volume at some critical volume $V_c$. Significant variations for $V_c$ and the equilibrium volume $V_0$ among the models lead to large uncertainties for the energy differences between the cubic and rhombohedral structures, indicating that present density-functional models are not reliable for accurate quantitative results in this case.

• Received 25 September 2006

DOI:https://doi.org/10.1103/PhysRevB.75.132103