Quantum chemical ab initio prediction of proton exchange barriers between CH₄ and different H-zeolites

A hybrid MP2:DFT (second-order Møller–Plesset perturbation theory–density functional theory) method that combines MP2 calculations for cluster models with DFT calculations for the full periodic structure is used to localize minima and transition structures for proton jumps at different Brønsted sites in different frameworks (chabazite, faujasite, ferrierite, and ZSM-5) and at different crystallographic positions of a given framework. The MP2 limit for the periodic structures is obtained by extrapolating the results of a series of cluster models of increasing size. A coupled-cluster (CCSD(T)) correction to MP2 energies is calculated for cluster models consisting of three tetrahedra. For the adsorption energies, this difference is small, between 0.1 and 0.9 kJ/mol, but for the intrinsic proton exchange barriers, this difference makes a significant (10.85 ± 0.25 kJ/mol) and almost constant contribution across different systems. The total values of the adsorption energies vary between 22 and 34 kJ/mol, whereas the total proton exchange energy barriers fall in the narrow range of 152–156 kJ/mol. After adding nuclear motion contributions (harmonic approximation, 298 K), intrinsic enthalpy barriers between 134 and 141 kJ/mol and apparent energy barriers between 105 and 118 kJ/mol are predicted for the different sites examined for the different frameworks. These predictions are consistent with experimental results available for faujasite, ferrierite, and ZSM-5.