The adequate choice of the interaction model is essential to reproduce qualitatively and estimate quantitatively the experimentally observed characteristics of materials or phenomena in computer simulations. Here we present the results of a benchmarking of density-functional theory calculations of rigid and flexible metal-organic frameworks (MOFs). The stability of these systems depends on the dispersion interactions. We compare the performance of two functionals, Perdew-Burke-Ernzerhof (PBE) and PBE designed for solids, with and without the dispersion corrections (D2 and TS), in reproducing the high-accuracy low-temperature X-ray and neutron diffraction data for both groups of MOFs. We focus our analysis on the key structural parameters: the lattice parameters, bond lengths, and angles. We show that the dispersion long range correction is essential to stabilize the structures and, in some cases, to converge the system to a geometry that is in line with the experimentally observed structure, especially for breathing MIL-53 structures or zeolitic imidazolate frameworks. We find that for all structures and all analyzed parameters, the D2-corrected PBE functional performs the best, except for bonds involving the metal ions; however, even for these bonds the difference between the experimentally observed and calculated lengths is small. Therefore, we recommend the use of the PBE-D2 functional in further numerical analyses of rigid and flexible nanoporous MOFs.

Structural transformations of nano-systems show properties different from their 3D bulk analogs. The mechanism of transformation is different due to the nano-object size or nanometric confinement. This field has not yet been fully explored and requires more fundamental studies which may lead to future application, e.g., in nanoporous systems characterization. Properties of methane adsorbed in confined geometries are interesting from both fundamental and practical points of view. At ambient temperatures supercritical adsorption is studied for possible methane storage applications. At the same time, the analysis of methane’s low temperature adsorption properties is essential for understanding the mechanism of adsorption as a function of temperature, pore size, pore topology and heterogeneity. The temperature dependence of structures of adsorbed phases allows one to understand evolution of confined phases in nano-space. In this work we compare the mechanism of adsorption and structural transformations of methane confined in (i) homogeneous carbon slit pores of widths between 1nm and 4nm and (ii) heterogeneous MOF pores. We discuss the mechanism of layering transition, melting and capillary condensation in subcritical conditions, for temperatures between 80 K and 180 K. The mechanism of layer formation is strongly temperature dependent. At the same time, a commensurability between the methane and the pore sizes is important factor. In slit pores it evolves from a sharp layers formation at 80 K to continuous adsorption at higher temperatures. The capillary condensation is observed clearly in slit pores bigger than 2 nm. The melting transition of methane in slit pores shows complicated mechanism where the interior of the pore melts at lower temperature than the layers adsorbed closer the pore wall. We compare this behavior with the mechanism of adsorption in MOF porous structures where the adsorbing walls are strongly heterogeneous both structurally and energetically. The comparison between the slit pores and the MOFs will allow us to discuss an influence of the heterogeneous wall topology and intermolecular interactions on the thermodynamic properties of nano-confined structures.