Treating dispersion effects in extended systems by hybrid MP2:DFT calculations—protonation of isobutene in zeolite ferrierite‡§

We propose use of a hybrid method to study problems that involve both bond rearrangements and van-der-Waals interactions. The method combines second-order Møller–Plesset perturbation theory (MP2) calculations for the reaction site with density functional theory (DFT) calculations for a large system under periodic boundary conditions. Hybrid MP2:DFT structure optimisation for a cluster embedded in the periodic model is the first of three steps in a multi-level approach. The second step is extrapolation of the MP2 energy to the complete basis set limit. The third step is extrapolating the high-level (MP2) correction to the limiting case of the full periodic structure. This is done by calculating the MP2 correction for a series of cluster models of increasing size, fitting an analytic expression to these energy corrections, and applying the fitted expression to the full periodic structure. We assume that, up to a constant, the high-level correction is described by a damped dispersion expression. Combining the results of all three steps yields an estimate of the MP2 reaction energy for the full periodic system at the complete basis set level. The method is designed for a reaction between a small or medium sized substrate molecule and a very large chemical system. For adsorption of isobutene in zeolite H-ferrierite, the energies obtained for the formation of different structures, the π-complex, the isobutoxide, the tert-butoxide, and the tert-butyl carbenium ion, are −78, −73, −48, and −21 kJ mol−1, respectively. This corresponds to corrections of the pure DFT (PBE functional) results by −62, −70, −67, and −29 kJ mol−1, respectively. Hence, the MP2 corrections are substantial and, perhaps more importantly, not the same for the different hydrocarbon species in the zeolite. Coupled-cluster (CCSD(T)) calculations change the MP2 energies by −4 kJ mol−1 (tert-butyl cation) or less (below ±1 kJ mol−1 for the other species).