Translational proton motion in zeolite H-ZSM-5. Energy barriers and jump rates from DFT calculations

Abstract

Activation barriers and jump rates for translational proton motion in zeolite H-ZSM-5 are calculated by a combined quantum mechanics–interatomic potential function approach (QM-Pot). The potential energies of the stable intermediate proton positions and the transition structures for proton jumps between two neighboring Brønsted-sites, spatially separated by 14 Å, show an almost symmetrical trend, which reaches a maximum value midway between these sites. The highest barrier is 210 kJ mol⁻¹ above the initial and final state energies. The energy barrier for the initial step of the translational motion (leaving the AlO₄⁻ site) is 127, 119 and 83 kJ mol⁻¹ for Al–Al distances of 14, 8 and 6 Å, respectively. Thus, decreased separation of Brønsted sites leads to decreased energy barriers for proton jumps due to increased interaction of their Coulomb potentials. Proton jump rates calculated by classical transition state theory vary over wide ranges, 10⁻⁵ to 10⁸ s⁻¹ and 10³ to 10¹⁰ s⁻¹, at temperatures of 373 and 673 K, respectively, depending on the particular proton path and the Al–Al distance.