Modeling Proton Mobility in Acidic Zeolite Clusters. 3. A Sudden Approximation via Semiclassical Rate Theory

Abstract

We have developed and applied an angular sudden approximation for modeling proton transfer in zeolites, using Miller’s semiclassical transition state theory. We have parametrized the rate theory by performing B3LYP/ 6-311G(d,p) density functional theory calculations for paths with fixed O-Al-O angle in a cluster model of H-Y zeolite. We find that both the barrier height and barrier curvature increase with O -Al-O angle. We also find that the classical barrier height increases with angle more rapidly than does the curvature, forcing the tunneling probability to decrease strongly with angle. The range of important angles for proton transfer, the so-called dynamical distribution, involves angles far from the saddle point angle at low temperatures (i.e., large curvature paths), and broadens significantly at higher temperatures, encompassing the saddle point region. The final temperature dependence of the proton jump rate within the sudden approximation shows surprisingly good agreement with that from conventional semiclassical transition state theory, which is based on the minimum energy path. We attribute this in part to a coincidence that occurs in the temperature regime of interest, namely 200-1000 K, a coincidence that we do not expect will occur in other systems.