The electronic structure of NaCN and KCN has been investigated by means of the periodic Hartree-Fock method. These calculations reveal a highly ionic character for both compounds. The analysis of the potential energy surfaces in the body-centered orthorhombic phases of both compounds indicates that rotation of the anions is severely hindered. Qualitatively different results were found for the high-temperature cubic structures. In KCN the small barriers allow almost free rotation of the cyanide anions, although shallow minima for the orientation of the CN- ions along the [111] directions of the crystal are found. For NaCN the situation is quite different, with the CN- units fixed in a random fashion in any of the equivalent positions with the molecular axis oriented along the [100] directions of the crystal.