$A$ Priori Predictions of Phase Transitions in KCa${\mathrm{F}}_3$ and RbCa${\mathrm{F}}_3$: Existence of a New Ground State

We have made an $a$ priori theoretical study of the potential-energy surfaces for KCa${\mathrm{F}}_3$ and RbCa${\mathrm{F}}_3$, and have examined the relative stability of the various lower-symmetry structures generated from the cubic perovskite phase by "rotations" of the Ca${\mathrm{F}}_6$ octahedra. A completely new ground state was discovered which, when included in the sequence of energy levels, allows us to give a full account both qualitatively and, in the case of RbCa${\mathrm{F}}_3$, quantitatively of the phase transition sequences in both systems.