The generation of suitable interaction potentials with which to study the coordination chemistry of Al³⁺ ions in Na_xAlF_3+x mixtures by computer simulation is described. The potentials reflect an ‘extended ionic’ model of the interactions in this system, with formal ionic charges and many-body polarization effects included. The parameters are derived from a mixture of abinitio and empirical information. For the Al–F interactions, the structure and energetics of crystalline and molecular AlF₃ form the database. This potential is then combined with an NaF potential and used to predict the crystal structures of three Na_xAlF_3+x crystalline compounds and also the vibrational frequencies of the NaAlF₄ molecule, which have been obtained experimentally. Excellent agreement is found. The potentials will be used in simulations of the spectroscopic and structural properties of Na_xAlF_3+x melts.