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The Gordon-Kim theory of interionic interactions between closed-shell ions, which has had considerable success for existing alkali halide systems, has been applied to the determination of the structure, phonon dispersion, and room-temperature dielectric properties of a proposed superlattice, RbF(NaC1)2, of alkali halides. The dielectric properties of such a hypothetical material can have an unusually strong low-frequency dependence because of the presence of Brillouin-zonefolded "infrared”-active modes. In evaluating the standard expressions for the dielectric properties, in the rigid-ion approximation, we make use of standard cubic and quartic anharmonic terms in addition to the instantaneous-phonon cubic anharmonic term, which is needed because of the lack of a center of inversion. Our procedure for numerically calculating the absorption for complex materials is described in detail. Effects of off-diagonal terms in the Green's function and of the long-range ionic Coulomb interactions are examined. In particular, an absorption peak at 30 cm-1 is found to be especially sensitive to these contributions. This paper demonstrates (a) the theoretical existence of metastable phases of an alkali halide superlattice and (b) the application of anharmonic perturbation theory to determine the dielectric response in the infrared and millimeter-wave region for such complex materials. The particular structure studied is just one of many possibilities in this class of materials, which offers the opportunity for joint theoretical and experimental research to fabricate structures with properties tailored for specific applications.