Department of Chemistry and Center for Biomolecular Simulation,
Columbia University, 3000 Broadway, New York, New York 10027

We present a method for estimating the hopping rate for Zwanzig's model of self-diffusion in liquids [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)]. To obtain this estimate, we introduce the cage correlation function which measures the rate of change of atomic surroundings, and associate the long-time decay of this function with the basin hopping rate for diffusion. Results from a set of simulations on Lennard-Jones particles are presented. A simple analytic model for the diffusion constant in supercooled and normal liquids that is based on estimates of the activation energy obtained via the cage correlation function is derived. We discuss the breakdown of Zwanzig's hopping mechanism for mass transport as well as the low temperature behavior of the self-diffusion constant on rough potential energy surfaces.