Adsorption studies in flexible metal–organic frameworks are challenging and time-consuming. It ismainly because the mechanism of adsorption, defined by structural framework properties, is constantlymodified during the process, as the framework transformation depends on the adsorption uptake. Wepropose here a new approach to investigate adsorption in such complex systems, in which thesimulations of adsorption in a deforming framework are replaced by the analysis of adsorption inintermediate rigid structures. As a proof of concept we analyze carbon dioxide, hexane, and methaneadsorption in MIL-53. 19 intermediate structures were generated using geometrical interpolationbetween the open and the closed MOF forms and optimized with quantum DFT calculations. The grandcanonical Monte Carlo method was applied to calculate adsorption isotherms in all intermediatestructures. The comparison with experimental results enabled the identification of the intermediateadsorption states. The analysis of the microscopic configurations of the adsorbed molecules in thesestructures allowed us to propose a new mechanism of adsorbate evolution over the entire process.

The structural transformations of periodic structures are very often initiated by the dynamicalfluctuation of theequilibrium structure. The natural mechanical excitations in crystals are called phonons. If the energy of thesefluctuations is low, they can easily be transformed into static deformations which define new structural prop-erties of the materials. This is the case in so called gate opening transformations which modify the structure andthe adsorptive properties of porous solids. Using the example of three SOD-type zeolitic imidazolate frameworks(ZIFs) containing linker molecules with different substituents, we show that analysis of low-frequency phononsobtained from density-functional theory (DFT) calculations allows one to model the observed gate opening andto understand the microscopic mechanism of this structural transformation.

Unlike macroscopic objects, any system of nanometric size shows characteristics that strongly depend on its sizeand geometric form. It is mainly because the major part of atoms (or molecules) of nano-object is located at itssurface, and their cohesive energy is smaller than for the atoms in the bulk. Here we show that when a fluid isconfined in nano-volume, delimited by non-attractive pore walls, its density is heterogeneous, in particular closeto the pore wall, and, on average, smaller than the density of bulk fluid. This effect progressively weakens whenthe pore size increases, and totally disappears for pores larger than 5 nm. The reported observation has nontrivialinfluence on evaluation of total and excess amount of fluid adsorbed in nanopores, as these quantities aretraditionally calculated assuming the known – and homogeneous –density of the bulk fluid. Additionally, wepropose a new method of the estimations of the accessible pore volume, based on the analysis of the density ofconfined fluid. The right estimation of both: pore volume and gas density is essential for quantitative interpretationof experimental adsorption isotherms: evaluation of pore size distribution and of the adsorbed amount.Although we analyze these problems taking an example of hydrogen at 77 K, our conclusions are general andapply to any fluid confined in nanopores.

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.