We discuss whether or not local information on the potential energy surface embodied by the distribution of unstable instantaneous normal modes can be used to predict the hopping rates and barrier heights for Zwanzig's model of self-diffusion [R. Zwanzig, J. Chem. Phys. 79, 4507 (1983)] in simple liquids, Results from a set of simulations of Lennard-Jones particles done at multiple temperatures and densities are presented. These simulations show that the theories which predict diffusive barrier heights from the distribution of imaginary frequencies are questionable. This discrepancy is due to the presence of imaginary frequency instantaneous normal modes which persist into the solid phase. Model systems are used to show that imaginary frequency instantaneous normal modes (and even those at the top of the barrier along that mode) are not necessarily indicators of diffusive barrier crossing as used in Zwanzig's model. These false barriers are shown to be the cause of all of the imaginary frequency zero-force modes in the solid as a ell as many of the imaginary frequency modes in the high-density super-cooled liquid. We therefore dispute their utility as predictors of barrier heights or hopping rates in related Liquid systems. We also show that attempts to separate the modes that are truly diffusive from those with false barriers using a frequency cutoff or local information on the potential energy surface are not successful at removing all of the non-barrier modes. (C) 1997 American Institute of Physics.