(307d) Free Energies of Adsorption Calculated through Potential of Mean Force Ab Initio Molecular Dynamics in Metal-Exchanged Zeolites

Dynamic adsorption and desorption of small molecules from catalytic active sites, such as exchanged metal ions in zeolites, is important in heterogeneous catalysis. Accurate calculation of free energies of adsorption (â??G_ads) is critical for estimating reaction rates and condition-dependent site speciation [1]. Adsorbate free energies calculated by harmonic approximation (HA) are commonly used in addition to 0K energies calculated by density functional theory (DFT) to estimate â??G_ads at finite temperatures. However this approximation becomes inaccurate when anharmonicity is present in adsorbate-site interactions [2] and when the adsorbate-site complex becomes very mobile [1,3]. In this work we show the inadequacy of HA for chemisorption of molecules on zeolite-supported exchanged metal cations. We demonstrate alternative computational methods that more reliably compute â??G_ads, and develop an empirical model for quick estimation of adsorption entropy.

The reactions studied are the adsorption of small molecules (X) on the zeolite Cu-SSZ-13. We consider several small molecules, such as NH₃ and H₂O, chemically adsorbing to exchanged metal cation active sites (*) as represented by equation * + X - > *X. Ab initio molecular dynamics (AIMD) simulations are performed on zeolite-adsorbate complexes to explore their finite temperature behavior. Cu is mobilized within the zeolite after adsorption, resulting in a vibrational spectrum that significantly deviates from that obtained using HA.

The potential of mean force (PMF) method is thus implemented which includes anharmonic entropy in the AIMD simulations. In the PMF simulations one selected reaction coordinate (RC) is constrained. â??G_ads is then calculated by integration of the average constraint force over the range of RC from the adsorbed state to the state where no interaction exists between the adsorbate and Cu site. Metadynamics is also used to explore the free energy of the system where Gaussian potential hills are added to the free energy surface. After both the product and reactant wells are sampled the added Gaussian hills are used to reconstruct the real free energy landscape. These two methods give the same â??G_ads, which are significantly more exergonic than those obtained by HA. Lastly we propose an empirical correlation between adsorbate gas phase entropies and adsorption entropies backed out from â??G_ads=â??H_ads-Tâ??S_ads. This allows a quick estimation of â??G_ads using only reaction energies from static DFT calculations and gas phase entropies of the adsorbates from statistical mechanical calculations.

 [1] C. Paolucci, A. A. Parekh, I. Khurana, J. R. Di Iorio, H. Li, J. D. Albarracin Caballero, A. Shih, T. Anggara, W. N. Delgass, J. T. Miller, F. H. Ribeiro, R. Gounder and W. F. Schneider, Journal of the American Chemical Society, (2016) DOI: 10.1021/jacs.6b02651.

[2] G. Piccini, J. Sauer, Journal of Chemical Theory and Computation, (2014) 10, 2479-2487.

[3] C. Paolucci, A. A. Verma, S. A. Bates, V. F. Kispersky, J. T. Miller, R. Gounder, W. N. Delgass, F. H. Ribeiro, W. F. Schneider, Angewandte Chemie International Edition, (2014) 53, 11828â??11833.