Anharmonic Adsorption Free Energies and Apparent Activation Barriers for Mobile Reactants Based on Molecular Dynamics Simulations

For zeolites, an approach is tested to compute adsorption free energies by using molecular dynamics (MD) simulations based on density functional theory (DFT) at the PBE-D3 level of theory. The interaction free energy between zeolite and adsorbate is computed with Bennett's acceptance ratio method (BAR). An intermediate hard-sphere model is introduced to improve overlap between interacting and noninteracting systems. Using this intermediate model also allows one to alternatively evaluate the interaction reliably with both backward and forward free energy perturbation theory (FEPT). This approach works for weakly adsorbed systems and is applied to compute adsorption free energies of CO, propene, and ketene at a surface methoxy species (SMS) in H-SSZ-13 at 200 and 400 °C. Intrinsic activation barriers for methylation of the adsorbed species are determined using constrained MD simulations. Apparent activation free energies are then obtained as the sum of the adsorption free energies and the intrinsic activation barriers. The anharmonicity of the apparent activation free energies is negligible for CO and is in the range -20 to -10 kJ/mol for propene and ketene. To address the limited accuracy of PBE-D3, calculations with the random phase approximation (RPA) are performed both as single points for stationary points and using FEPT based on the MD simulations. Both approaches agree to be better than 5 kJ/mol and predict that PBE-D3 apparent activation barriers are too low by 20 to 30 kJ/mol.