 
Summary: Modeling Proton Mobility in Acidic Zeolite Clusters. 3. A Sudden Approximation via
Semiclassical Rate Theory
Justin T. Fermann and Scott M. Auerbach*,,§
Departments of Chemistry and of Chemical Engineering, UniVersity of Massachusetts,
Amherst, Massachusetts 01003
ReceiVed: October 17, 2000; In Final Form: January 30, 2001
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/
6311G(d,p) density functional theory calculations for paths with fixed OAlO angle in a cluster model of
HY zeolite. We find that both the barrier height and barrier curvature increase with OAlO 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 socalled 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 2001000 K, a coincidence that we do not expect will occur in other systems.
I. Introduction
Zeolites are nanoporous, shapeselective catalysts widely
