Activated diffusion of benzene in NaY zeolite: Rate constants from transition state theory with dynamical corrections

Abstract

We calculated transition state theory and exact rate coefficients for benzene jumps in Na-Y zeolite between 150 and 500 K. This is the first exact flux correlation function rate calculation for a non-spherical molecule inside a zeolite. We calculated rates for jumps between SII and W sites, located near Na ions in 6-rings and in 12-rings windows, respectively. Partition function ratios were calculated using Voter’s displacement vector method. A general Arrhenius behavior is observed over the whole temperature range for all processes. The activation energies are close to the difference between the minimum energies in the sites, and between the sites and the transition states. The calculated prefactors present reasonable values around 1012–1013 s−1, in good agreement with nuclear magnetic resonance relaxation experiments. We were not able to decompose the prefactors into simple vibrational and entropic components, and therefore a complete calculation of the rate constant seems necessary to obtain reliable values. In three of the four types of motions investigated, the transition state theory rate constant is approximately equal to the more exact correlation function rate constant. However, in the case of the W→W jump, transition state theory is qualitatively wrong. This is due to the fact that the minimum energy path from one W site to another is very unstable and intersects the SII→SII minimum energy pathway, so a slight perturbation sends the molecule to a SII site instead of the W site. As a consequence, the prefactor for the W→W jump is found to be almost one order of magnitude smaller than the prefactor for the W→ SII jump, although the activation energies are similar.