Understanding CO$_{2}$/N$_{2}$ Selectivity and Binding in MOFs Using Dispersion-Corrected DFT*

Metal-organic frameworks (MOFs) are a class of highly ordered, highly customizable nanoporous materials that are attractive for use in energy-relevant gas separations. MOF-253 (AlOH)(bpydc) can be post-synthetically modified by introduction of metal cations and charge-stabilizing anions [1]. Post-synthetically modified MOF-253 samples have been shown to exhibit enhanced CO$_{2}$/N$_{2}$ selectivity over the unmodified framework [1]. Here we focus on the following series of post-synthetic modifications: ~CoCl$_{2}$, CuCl$_{2}$, FeCl$_{2}$, NiCl$_{2}$, PdCl$_{2}$. We use the vdW-DF, vdW-DF2, and DFT-D2 dispersion-corrected density functional theory (DFT) methods to study CO$_{2}$ and N$_{2}$ binding trends in this series of modified frameworks. Particular focus is paid to examining the predictive power of our calculations on both the modified framework and modified bipyridine clusters as a proxy for the full framework. Additionally, we examine the suitability of an approximate Henry coefficient model to predict measured gas selectivity trends [1]. \\[4pt] [1] E. Bloch, et. al, J. Am. Chem. Soc., 132, 14382-14384, 2010.