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.

Ewald summation is used to apply semiempirical long-range dispersion corrections (Grimme, J Comput Chem 2006, 27, 1787; 2004, 25, 1463) to periodic systems in density functional theory. Using the parameters determined before for molecules and the Perdew-Burke-Ernzerhof functional, structure parameters and binding energies for solid methane, graphite, and vanadium pentoxide are determined in close agreement with observed values. For methane, a lattice constant a of 580 pm and a sublimation energy of 11 kJ mol(-1) are calculated. For the layered solids graphite and vanadia, the interlayer distances are 320 pm and 450 pm, respectively, whereas the graphite interlayer energy is -5.5 kJ mol(-1) per carbon atom and layer. Only when adding the semiempirical dispersion corrections, realistic values are obtained for the energies of adsorption of C(4) alkenes in microporous silica (-66 to -73 kJ mol(-1)) and the adsorption and chemisorption (alkoxide formation) of isobutene on acidic sites in the micropores of zeolite ferrierite (-78 to -94 kJ mol(-1)). As expected, errors due to missing self-interaction correction as in the energy for the proton transfer from the acidic site to the alkene forming a carbenium ion are not affected by the dispersion term. The adsorption and reaction energies are compared with the results from Møller-Plesset second-order perturbation theory with basis set extrapolation.

All experimental attempts to identify the tert‐butyl carbenium ion in zeolites have been unsuccessful. Calculations with the hybrid MP2:DFT method predict that this ion is less stable than the isomeric surface species isobutene, isobutoxide, and tert‐butoxide, but once it has been formed as an intermediate it will survive long enough (59 μs) to be detected by laser spectroscopy (see picture; O red, Si yellow, Al magenta, C green).

The alkylation of benzene by ethene over H-ZSM-5 is analyzed by means of a hybrid MP2:DFT scheme. Density functional calculations applying periodic boundary conditions (PBE functional) are combined with MP2 energy calculations on a series of cluster models of increasing size which allows extrapolation to the periodic MP2 limit. Basis set truncation errors are estimated by extrapolation of the MP2 energy to the complete basis set limit. Contributions from higher-order correlation effects are accounted for by CCSD(T) coupled cluster calculations. The sum of all contributions provides the "final estimates" for adsorption energies and energy barriers. Dispersion contributes significantly to the potential energy surface. As a result, the MP2:DFT potential energy profile is shifted downward compared to the PBE profile. More importantly, this shift is not the same for reactants and transition structures due to different self-interaction correction errors. The final enthalpies for ethene, benzene, and ethylbenzene adsorption on the Brønsted acid site at 298 K are -46, -78, and -110 kJ/mol, respectively. The intrinsic enthalpy barriers at 653 K are 117 and 119/94 kJ/mol for the one- and two-step alkylation, respectively. Intrinsic rate coefficients calculated by means of transition state theory are converted to apparent Arrhenius parameters by means of the multicomponent adsorption equilibrium. The simulated apparent activation energy (66 kJ/mol) agrees with experimental data (58-76 kJ/mol) within the uncertainty limit of the calculations. Adsorption energies obtained by adding a damped dispersion term to the PBE energies (PBE+D), agree within +/-7 kJ/mol, with the "final estimates", except for physisorption (pi-complex formation) and chemisorption of ethene (ethoxide formation) for which the PBE+D energies are 12.4 and 26.0 kJ/mol, respectively larger than the "final estimates". For intrinsic energy barriers, the PBE+D approach does not improve pure PBE results.