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Constrained energy minimization, equilibrium and nonequilibrium molecular dynamics calculations, and constrained Monte Carlo simulations were used to determine the influence of the coupling between benzene adsorbed in a NaY zeolite model (Si/Al = 2) and the framework vibrations on benzene site-to-site dynamics. Benzene at an S site is strongly coupled to the nearby Na(II) cation, resulting in a decrease of the external vibrational frequency of the center-of-mass of benzene away from this cation by 60 cm. Despite this coupling, framework vibrations have remarkably little influence on the site-to-site rate constants of benzene. Although with a fixed framework no dissipation of the excess kinetic energy of the adsorbed molecule can take place and thus no thermalization to equilibrium, energy redistribution from the translational motion of benzene into the internal degrees of freedom of the flexible molecule is seen to provide a good thermalization.