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The ability of zero-stress simulations, using Gordon-Kim pair potentials, to describe the structures and transformations of known fluoride-based perovskites is demonstrated for the case of KCaF3. When K+ is replaced by Na+ a new ferroelectric crystal isomorphous with LiNbO3 is predicted. The equivalent relationships of the ferroelectric lithium niobate structure with the perovskite and antiperovskite structures are examined. A polarization of 21 jµC/cm2 at room temperature and a transition temperature of 550 K are predicted for NaCaF3. Surface effects are examined in simulations of a 1080-ion cluster.