(670d) Entropy Predictions in Zeolites and the Impact of Acid-Site Pairing on Adsorption Entropies.

Quantifying thermodynamic properties is essential for predicting reaction rates and equilibrium constants from transition state theory. While reasonable enthalpy predictions are achievable, there remains no definitive way to calculate the entropy of a system from ab initio calculations, with the treatment of anharmonic modes posing the greatest challenge. For rigid crystalline systems, anharmonic contributions can be ignored with reasonable results. Zeolites are nonrigid crystalline structures; therefore, anharmonicity contributes significantly to the entropy and, thus, the free energy of a zeolite system and cannot be ignored. Consequently, many ab initio entropy calculations invoke the quasi-harmonic approximation, which assumes the harmonic approximation is valid for all independent harmonic and anharmonic oscillators. In this work, we examine the applicability of the quasi-harmonic approximation for detecting small entropy differences between reactions at isolated and paired Brønsted acid sites in zeolites using DFT-based ab initio molecular dynamics (AIMD) simulations. Rates of propane and butane cracking are higher in CHA at paired Brønsted acid sites (two Al in a single 6-MR) than at isolated sites. These rate differences occur despite small differences in measured activation energies, indicating that they are caused by differences in activation entropies instead. This suggests that interactions between paired Brønsted acid sites confer greater entropy to nearby cationic transition states than for isolated sites. These cationic transition states, however, are too unstable for AIMD simulation, and thus we examined the adsorption enthalpy and entropy of a dimethylammonium cation as a proxy. In this contribution, we compare entropy estimates from different methods, including the integration of the vibrational density of states (VDOS, Fig. 1), and contrast those ab initio estimates to measured values.