van der Waals Corrected Density Functional Theory Calculations on Zeolitic Imidazolate Frameworks

The van der Waals force is ubiquitous in nature, however, first principles calculations of this interaction for large systems, i.e., around 1000 atoms, have been performed only recently. In the following are presented results on the application of the van der Waals density functional (vdW-DF) to gas adsorption and transport in zeolitic imidazolate frameworks (ZIFs).Carbon dioxide and methane binding energies and positions are calculated with the vdW-DF in three distinct binding sites in a series of five rho topology ZIFs. The isostructural set of ZIFs was selected in order to isolate the effect of framework functionalization. Gas molecules are found to bind in locations with high coordination to framework atoms at distances of around 3 A. Contributions to the binding energy from induced polarization and dispersion are quantified in order to elucidate the origins of strong CO2 adsorption and selectivity over CH4. The dispersion energy is found to dominate the interactions, however, CO2 adsorption is also enhanced by electrostatic interactions with asymmetrically functionalized linkers. Steric constraints for methane molecules, that do not impede carbon dioxide binding, further contribute to selectivity.Binding energy landscapes for CO2 and CH4 are calculated using classical force fields for the same set of rho ZIFs and several other ZIFs that differ in functionalization and topology. Quantities extracted from these landscapes are used to explain the effect of framework topology on gas adsorption at low and high pressure as well as how the positions of adsorbed gas molecules evolve as a function of pressure. Materials with large surface areas have greater gas uptake at high pressure, while smaller pores, which are associated with stronger binding, adsorb more gas at low pressure.Finally, the effect of framework flexibility on CO2 transport through the double 8-ring channel of ZIF-97 is investigated with computationally intensive climbing-nudged elastic band calculations utilizing two versions of the vdW-DF. The results are largely consistent between the two versions and show a small decrease (12-33 meV) in the transport barrier with flexibility.In addition, several versions of the vdW-DF are applied to the Kr dimer, graphite, and H2, Al, and Li on graphene. For these systems experimental binding energies and separations are available, such that they provide useful benchmarks for the accuracy of the vdW-DF type methods. The vdW-DF2 and vdW-optB88 methods are found to both produce accurate results for dispersion dominated binding. Analyses of mixed ionic-dispersion binding highlight the importance of further study of these functionals at short-range