Modeling proton mobility in acidic zeolite clusters: II. Room temperature tunneling effects from semiclassical rate theory

Abstract

We have developed a novel semiclassical transition state theory (SC-TST) for truncated parabolic barriers, based on the formulation of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)]. Our SC-TST rate coefficient has the form kSC-TST=kTST⋅Γ, where Γ depends on the zero point corrected barrier, ΔE0, and the barrier curvature, |ωF‡|. Our rate expression is stable to arbitrarily low temperatures, as opposed to purely harmonic SC-TST, because we identify the maximum possible semiclassical action in the reaction coordinate. For low temperatures, we derive an analytical approximation for Γ that is proportional to eβ ΔE0. We develop a theory for the tunneling crossover temperature, Tx, yielding kBTx≅ℏ|ωF‡|ΔE0/(2π ΔE0−ℏ|ωF‡|ln 2), which generalizes the harmonic theory for systems with large but finite barriers. We have calculated rate coefficients and crossover temperatures for the O(1)→O(4) jump in H–Y and D–Y zeolites, yielding Tx=368 K and 264 K, respectively. These results suggest that tunneling dominates proton transfer in H–Y up to and slightly above room temperature, and that true proton transfer barriers are being underestimated by neglecting tunneling in the interpretation of experimental mobility data.