Benchmark Data for Interactions in Zeolite Model Complexes and Their Use for Assessment and Validation of Electronic Structure Methods

We present benchmark binding energies for five zeolite model complexes, with four of the adsorbates bound noncovalently and one covalently. The binding energies were determined as the sum of the infinite-basis-set limit of Møller−Plesset second-order perturbation theory (MP2) energies and a CCSD(T) correction term evaluated with the aug-cc-pVDZ basis set. The basis set limit of MP2 energies was determined by two-point extrapolation using the aug-cc-pVXZ basis sets for X = D and T and separate extrapolation of the Hartree−Fock and correlation energies. We found that correlation contributions beyond MP2 to the final binding energies are small; their magnitude is in the range of 0.02−1.0 kcal/mol. For the MP2 method to describe the interactions in these zeolite model systems accurately, one needs to use a basis set at least the size of aug-cc-pVTZ in conjunction with counterpoise corrections. Final binding energies (kcal/mol) of the model complexes are in the range of 3.5−19.5 kcal/mol, and they were used as reference data to test 6 wave function methods and 41 density functionals. Among the tested density functional methods, M06-L/6-31+G(d,p) gives a mean unsigned error (MUE) without counterpoise correction of 0.87 kcal/mol. With counterpoise corrections, the M06-2X and M05-2X functionals give the best performance. The MUE with counterpoise corrections for the M06-2X/6-311+G(2df,2p)//MP2/6-311+G(2df,2p) level of theory is 0.39 kcal/mol. With the DFT/6-31+G(d,p) geometries and the 6-311+G(2df,2p) basis set, M05-2X and M06-2X give MUEs with counterpoise corrections of 0.40 and 0.52 kcal/mol, respectively. Tests against the binding energies of four complexes (two noncovalent and two covalent) of the adsoption of isobutene on a large 16T zeolite model cluster confirmed that M06-L, M06, M05-2X, and M06-2X are very promising quantum mechanical methods for hybrid quantum mechanical/molecular mechanical (QM/MM) simulations of zeolites. In fact the performance of these four Minnesota functionals, as compared to other high-quality functionals, is relatively even better for the larger 16T clusters than for the smaller 3T ones.