Molecular dynamics simulations of individual trajectories that are started in the transition state for cage-to-cage diffusion are presented for benzene and p-xylene in zeolite NaY. Furthermore, diffusion coefficients and the activation energies for the diffusion are determined from a hopping model that considers dynamical corrections. The transmission coefficients for both molecules are small, particularly at low temperatures. The influence of the window adsorption site of benzene on the transmission coefficient is investigated. The hopping model fails for the treatment of the diffusion of benzene at high temperatures T > 700 K, because the diffusion cannot be divided into different jump events at such temperatures. The results for the diffusion coefficient of p-xylene are in very good agreement with experimental results, whereas for benzene an activation energy results that is slightly too high. This fact is related to the possibility of a dependence of the activation energy on the exact positions of the sodium ions.