Quantum chemical modeling of zeolite-catalyzed methylation reactions: toward chemical accuracy for barriers.

The methylation of ethene, propene, and t-2-butene by methanol over the acidic microporous H-ZSM-5 catalyst has been investigated by a range of computational methods. Density functional theory (DFT) with periodic boundary conditions (PBE functional) fails to describe the experimentally determined decrease of apparent energy barriers with the alkene size due to inadequate description of dispersion forces. Adding a damped dispersion term expressed as a parametrized sum over atom pair C(6) contributions leads to uniformly underestimated barriers due to self-interaction errors. A hybrid MP2:DFT scheme is presented that combines MP2 energy calculations on a series of cluster models of increasing size with periodic DFT calculations, which allows extrapolation to the periodic MP2 limit. Additionally, errors caused by the use of finite basis sets, contributions of higher order correlation effects, zero-point vibrational energy, and thermal contributions to the enthalpy were evaluated and added to the "periodic" MP2 estimate. This multistep approach leads to enthalpy barriers at 623 K of 104, 77, and 48 kJ/mol for ethene, propene, and t-2-butene, respectively, which deviate from the experimentally measured values by 0, +13, and +8 kJ/mol. Hence, enthalpy barriers can be calculated with near chemical accuracy, which constitutes significant progress in the quantum chemical modeling of reactions in heterogeneous catalysis in general and microporous zeolites in particular.