We extend the cage correlation function method for calculating the hopping rate in Zwanzig＇s model of self-diffusion in liquids [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] to liquids composed of polyatomic molecules. We find that the hopping rates defined by the cage correlation function drop to zero below the melting transition and we obtain excellent agreement with the diffusion constants calculated via the Einstein relation in liquids, solids, and supercooled liquids of CS2. We also investigate the vibrational density of states of inherent structures in liquids which have rough potential energy surfaces, and conclude that the normal mode density of states at the local minima are not the correct vibrational frequencies for use in Zwanzig＇s model when it is applied to CS2.