Torsional flexibility in zinc-benzenedicarboxylate metal-organic frameworks

Abstract

We explore the role and nature of torsional flexibility of carboxylate-benzene links in the structural chemistry of metal-organic frameworks (MOFs) based on Zn and benzenedicarboxlyate (bdc) linkers. A particular motivation is to understand the extent to which such flexibility is important in stabilising the unusual topologically aperiodic phase known as TRUMOF-1. We compare the torsion angle distributions of TRUMOF-1 models with those for crystalline Zn/1,3-bdc MOFs, including a number of new materials whose structures we report here. We find that both periodic and aperiodic Zn/1,3-bdc MOFs sample a similar range of torsion angles, and hence the formation of TRUMOF-1 does not require any additional flexibility beyond that already evident in chemically-related crystalline phases. Comparison with Zn/1,4-bdc MOFs does show, however, that the lower symmetry of the 1,3-bdc linker allows access to a broader range of torsion angles, reflecting a greater flexibility of this linker.

Fig. 1. Schematic representations of the topologies of (a) a 2 × 2 × 2 approximant of the TRUMOF-1 structure and (b) MOF-5. In both cases, red circles represent octahedrally-coordinated OZn₄ clusters. The grey sticks indicate the connectivity formed as clusters are connected using (a) 1,3-bdc and (b) 1,4-bdc linkers.

Fig. 2. The two linkers 1,3-bdc and 1,4-bdc and their geometric differences: (a) molecular structures; (b) the resulting bent vs. linear geometries; and (c) their carboxylate–benzene torsion angle flexibility. For both linkers, the dihedral angle corresponding to the torsion angle is indicated in (c) for one of the carboxylates by highlighting the relevant C–C–C–O bonds and atoms in red.

Fig. 3. Distribution of 1,3-bdc torsion angle values observed in TRUMOF-1 DFT supercell configurations. (a) Plot showing the distribution of both average torsion angle magnitude, ϕ_av, and difference in torsion angle magnitudes Δϕ within each 1,3-bdc linker in the various supercells. Linkers with syn and anti conformations are plotted above and below the central dashed line, respectively. All torsion angle values are coloured according to the DFT energy of the supercell to which they correspond. Histograms are given at the bottom of the graph to demonstrate the ratio of syn : anti carboxylates within each 5° interval. (b) Graph showing the average values of ϕ₁ and ϕ₂ for each supercell as a function of its relative DFT energy. Individual data points are represented as pie-charts that reflect the ratio of syn : anti linkers. Note that in order to calculate the average value of ϕ₁ and ϕ₂, the carboxylate with the largest torsion angle was assigned ϕ₁, leaving the smaller torsion angle to be assigned ϕ₂. The standard deviation in torsion angle is represented with error bars.

Fig. 4. Representations of the crystal structures for the new Zn/1,3-bdc MOFs described in this study. (a) MOX-2 basic building block (top), resulting wine-rack structure viewed down the crystallographic b-axis (middle), and topological representation (bottom). Zn coordination environments shown as red polyhedra, and 1,3-bdc linkers shown in ball-and-stick representation. Solvent omitted for clarity. (b) MOX-3 basic building block (top left) and the extended crystal structure viewed down the crystallographic a- (top right) and b-axes (middle). A topological representation is given at the bottom. (c) MOX-4 basic building block (top), representation of the crystal structure, viewed down the crystallographic c axis (middle), and topological representation (bottom). Colour scheme: Zn tetrahedra = red, oxygen = red, carbon = black, nitrogen = blue, Br, Cl, I = brown. Hydrogen atoms are omitted for clarity.

Fig. 5. Distribution of (5-X-)1,3-bdc and (2-X-)1,4-bdc torsion angles in crystalline Zn/bdc MOFs. (a) Plot showing the average torsion angle value, ϕ_av, of each (5-X-)1,3-BDC linker carboxylate extracted from all Zn-(5-X-)1,3-BDC MOFs found in the literature. To demonstrate the independence of the two torsion angles within each 1,3-bdc linker, the difference between the two magnitudes, Δϕ, is given for each torsion angle. Linkers with syn and anti conformations are plotted above and below the dotted line, respectively. Torsion angle values are coloured according to whether the 1,3-bdc linker is substituted (light colours) or not (dark colours). Histograms are given at the top (1,3-bdc) and bottom (5-X-1,3-bdc) to demonstrate the ratio of syn : anti conformations for each 5° interval. (b) Plot showing the equivalent data for (2-X-)1,4-bdc linkers extracted from all Zn-(2-X-)1,4-bdc MOFs in our database. Again, torsion angle values are coloured according to whether the 1,4-bdc linker is substituted (light colours) or unsubstituted (dark colours).