Van der Waals interactions between hydrocarbon molecules and zeolites: Periodic calculations at different levels of theory, from density functional theory to the random phase approximation and Møller-Plesset perturbation theory

Abstract

The adsorption of small alkane molecules in purely siliceous and protonated chabazite has been investigated at different levels of theory: (i) density-functional (DFT) calculations with a gradient-corrected exchange-correlation functional; DFT calculations using the Perdew-Burke-Ernzerhof (PBE) functional with corrections for the missing dispersion forces in the form of C(6)∕R(6) pair potentials with (ii) C(6) parameters and vdW radii determined by fitting accurate energies for a large molecular data base (PBE-d) or (iii) derived from "atoms in a solid" calculations; (iv) DFT calculations using a non-local correlation functional constructed such as to account for dispersion forces (vdW-DF); (v) calculations based on the random phase approximation (RPA) combined with the adiabatic-coupling fluctuation-dissipation theorem; and (vi) using Hartree-Fock (HF) calculations together with correlation energies calculated using second-order Møller-Plesset (MP2) perturbation theory. All calculations have been performed for periodic models of the zeolite and using a plane-wave basis and the projector-augmented wave method. The simpler and computationally less demanding approaches (i)-(iv) permit a calculation of the forces acting on the atoms using the Hellmann-Feynman theorem and further a structural optimization of the adsorbate-zeolite complex, while RPA and MP2 calculations can be performed only for a fixed geometry optimized at a lower level of theory. The influence of elevated temperature has been taken into account by averaging the adsorption energies calculated for purely siliceous and protonated chabazite, with weighting factors determined by molecular dynamics calculations with dispersion-corrected forces from DFT. Compared to experiment, the RPA underestimates the adsorption energies by about 5 kJ/mol while MP2 leads to an overestimation by about 6 kJ/Mol (averaged over methane, ethane, and propane). The most accurate results have been found for the "hybrid" RPA-HF method with an average error of less than 2 kJ/mol only, while RPA underestimates the adsorption energies by about 8 kJ/mol on average. MP2 overestimates the adsorption energies slightly, with an average error of 5 kJ/mol. The more approximate and computationally less demanding methods such as the vdW-DF density functional or the C(6)∕R(6) pair potentials with C(6) parameters from "atoms in a solid" calculations overestimate the adsorption energies quite strongly. Relatively good agreement with experiment is achieved with the empirical PBE+d method with an average error of about 5 kJ/mol.