Torsional flexibility in zinc–benzenedicarboxylate metal–organic frameworks

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.


Geometry optimisation
Full cell optimisations were carried out using the Quickstep module of the CP2K package S1 .We used the DZVP MOLOPT basis sets for all atoms, the PBE functional S2 and the "D3" van der Waals correction scheme S3 .A 800 Ry cut-off was used in conjunction with a reference cell for smooth optimisation of the cell parameters and atomic coordinates until the forces on the atoms were less than 0.6 kJ mol −1 Å-1 .No atomic constraints were applied during the relaxation and no symmetry was imposed upon the cell parameters or coordinates (in effect the cells are relaxed in P 1).
See Ref. 4 for a more detailed outline of the DFT work, including summaries of the optimised cell parameters and relative energies.

Influence porosity/density
To investigate whether the variety in linker torsion angle may have an influence on the porosity of TRUMOF-1, the data presented in Fig. 3a in the main text was plotted with a colour gradient correlating to the density of the supercell (Fig. S1a).In addition, similar to Fig. 3b in the main text, the average torsion angle of ϕ 1 and ϕ 2 for each supercell was plotted against the density of each supercell (Fig. S1b).Both figures show no correlation between the density and torsion angle distribution of TRUMOF-1, indicating the degree of linker torsion angle has no significant influence on the porosity.

MOX-2
MOX-2 was synthesised by combining solutions of Zn(NO 3 ) 2 • 6 H 2 O (0.33 mmol) and 1,3-bdc (0.33 mmol) in EA (5 mL).The resulting mixture was placed in a Teflon chamber and sealed, which in turn was fitted in an autoclave.The Teflon lined autoclave was placed in an oven and heated to 110 • C.After 14 h at this temperature, the system was slowly cooled to room temperature to afford MOX-2 as colourless, single-crystal rods amidst intergrown clusters.The crystals were isolated by filtration and washed three times with EA.Each washing cycle involved soaking MOX-2 crystals in fresh EA for 24 h, followed by filtration.
By placing the disks in paratone-n oil and leaving them for ca. 2 h, the hexagonal disks turned into oval-shaped crystals (Fig. S2).These crystals belong to the phase of MOX-3.They were kept in oil and therefore not washed nor treated with other solvents for analysis.

MOX-4
MOX-4 was synthesised by combining solutions of Zn(NO 3 ) 2 • 6 H 2 O (0.33 mmol) and 5-X-1,3-bdc (0.33 mmol) in EA (5 mL) for X = Br, Cl, I, F, NO 2 , CH 3 , OH, Br/Cl (1:1) and Br/H (1:1).The resulting mixture was placed in a Teflon chamber and sealed, which in turn was fitted in an autoclave.The Teflon lined autoclave was placed in an oven and heated to 110 • C.After 14 h at this temperature, the system was cooled to room temperature to afford MOX-3 as colourless crystals, most of which intergrown clusters, though some single crystals (Fig. 3.8a).The crystals were isolated by filtration and washed three times with EA.Each washing cycle involved soaking MOX-4 crystals in fresh EA for 24 h, followed by filtration.
Single crystals were obtained for X = Br, Cl, I, and Br/Cl, powders were obtained for X = F, NO 2 , CH 3 and Br/H.For X = OH, no product was obtained.

MOX-2
The single crystal diffraction pattern of MOX-2 was measured using a Rigaku Synergy S diffractometer fitted with a Dectris EIGER2 R 1M detector.The instrument outputted mirrormonochromated Cu-Kα (λ = 1.5406Å) and was equipped with an Oxford Cryosystems Cryostream 700 for temperature control.
A washed crystal of MOX-2 was isolated directly with EA, dried in air, and then mounted onto a 0.2 mm diameter MiTeGen loop using Paratone-N oil as a cryoprotectant.The crystal was then attached to the instrument goniometer before data were collected about ϕ and ω rotations.
Unit cell determination, data integration, frame scaling, and absorption corrections (multiscan implemented in ABSPACK) with beam profile correction) were performed in CRYSAL-ISPRO S5 .A structure solution was obtained using intrinsic phasing methods from SHELXT S6 , followed with refinements using a full-matrix least-squares approach on all unique F 2 values.The refinements were performed using SHELXL S7 as implemented within OLEX2-1.5 S8 .
An initial solution in the non-centrosymmetric orthorhombic space group P 2 1 2 1 2 1 with a = 11.0562(2)Å, b = 12.6155(2) Å, and c = 15.2102(2)Å showed clearly the presence of two Zn atoms directly connected to 1,3-bdc, forming distorted ZnO 4 tetrahedra.The remaining electron density was found to originate from ordered solvent in the pores.All non-hydrogen atoms could be treated by an unrestrained anisotropic refinement unless otherwise stated.The H-atom positions were added in their calculated position and refined using riding thermal parameters.
Final structural parameters are given in Table S6, with the asymmetric unit shown in Fig. S4.The structure has been deposited with the Cambridge crystallographic data centre (CCDC) under the reference number 2302224.

Powder X-ray diffraction
To verify the phase purity of the MOX-2 sample, a powder X-ray diffraction experiment was performed at ambient conditions using a high-intensity Bruker D8 Advance Eco diffractometer equipped with a Cu-Kα source (λ = 1.54 Å) and a fluorescence-filtering LYNXEYE XE-T detector.
The observed additional phases likely arise from unreacted starting material; both the Zn(NO 3 ) 2 • H 2 O salt and 1,3-bdc linker did not dissolve in the EA solvent at room temperature.Whilst heating in the oven, the solution may become saturated, in turn leaving some of the starting material undissolved.

MOX-3
The SCXRD patterns of both crystals were measured using a Rigaku Synergy S diffractometer fitted with a Dectris EIGER2 R 1M detector.The instrument outputted mirror-monochromated Cu-Kα (λ = 1.5406Å) and was equipped with an Oxford Cryosystems Cryostream 700 for temperature control.
Crystals of both MOX-3α and MOX-5 were isolated directly with DMF and mounted onto a 0.2 mm diameter MiTeGen loop using Paratone-N oil as a cryoprotectant.The crystals were then attached to the instrument goniometer before data were collected about ϕ and ω rotations.
Unit cell determination, data integration, frame scaling, and absorption corrections (multiscan implemented in ABSPACK) were performed in CRYSALISPRO S5 .A structure solution was obtained using intrinsic phasing methods from SHELXT S6 , followed with refinements using a full-matrix least-squares approach on all unique F 2 values.The refinements were performed using SHELXL S7 as implemented within OLEX2-1.5 S8 .
For the crystalline phase of MOX-3, an initial solution in the centrosymmetric monoclinic space group P 2 1 /n (no.14) with a = 12.7970(2) Å, b = 9.5085(1) Å, c = 16.9103(2)Å, and β = 111.969(2)• showed clearly the presence of a Zn atom on the 4e Wyckoff position directly connected to a 4,6-Br 2 -1,3-bdc linker, forming distorted ZnO 4 tetrahedra.The remaining electron density was found to originate from ordered DMF solvent, of which the O atom is coordinated to the Zn atom.All non-H atoms could be treated by an unrestrained anisotropic refinement unless otherwise stated.The H-atom positions were added in their calculated position and refined using riding thermal parameters.
Final structural parameters are given in Table S7, with the asymmetric unit shown in Fig. S6.The structure has been deposited with the Cambridge crystallographic data centre (CCDC) under the reference number 2302220.

Powder X-ray diffraction
Due to both the low quality and instability of the MOX-3 crystals, it was not possible to perform PXRD to confirm the phase purity of the sample.

MOX-4
All MOX-4 single crystal diffraction patterns were measured using a Rigaku Synergy S diffractometer fitted with a Dectris EIGER2 R 1M detector.The instrument produced mirror-monochromated Cu-Kα (λ = 1.5406Å) and was equipped with an Oxford Cryosystems Cryostream 700 for temperature control.
A washed crystal of MOX-4 was isolated directly with EA, dried in air, and then mounted onto a 0.2 mm diameter MiTeGen loop using Paratone-N oil as a cryoprotectant.The crystal was then attached to the instrument goniometer before data were collected about ϕ and ω rotations, using an exposure time of 0.1 s.
Unit cell determination, data integration, frame scaling, and absorption corrections (multiscan implemented in ABSPACK) were performed in CRYSALISPRO S5 .A structure solution was obtained using intrinsic phasing methods from SHELXT S6 , followed with refinements using a full-matrix least-squares approach on all unique F 2 values.The refinements were performed using SHELXL S7 as implemented within OLEX2-1.5 S8 .
An initial solution in the non-centrosymmetric rhombohedral space group R 3m (lattice parameters given in Table 3.1) showed clearly the presence of distorted ZnO 4 tetrahedra centred on the 18f Wyckoff position, connected by 5-X-1,3-bdc linkers.The remaining electron density was determined to originate from disordered EA solvent molecules in the pores.Their exact positions and orientation was not able to be solved.Since the remaining electron density was quite low, no solvent masking was used to account for this.
All non-hydrogen atoms could be treated by an unrestrained anisotropic refinement unless otherwise stated.The H-atom positions were added in their calculated position and refined using riding thermal parameters.
Final structural parameters are given in Tables S8, S9, S10, and S11, with the asymmetric unit shown in Fig. S7.The structures have been deposited with the Cambridge crystallographic data centre (CCDC) under the reference numbers 2302221-2302223, and 2302225.

Powder X-ray diffraction
To verify the phase purity of the MOX-4 samples, powder X-ray diffraction experiment were performed at ambient conditions using a high-intensity Bruker D8 Advance Eco diffractometer equipped with a Cu-Kα source (λ = 1.54 Å) and a fluorescence-filtering LYNXEYE XE-T detector.The obtained diffraction patterns were subsequently compared to patterns calculated from the single-crystal models, as the unit cells appeared to large to perform an accurate Pawley fit (Fig. S8).Interestingly, the phase purity of the samples -as derived from comparison of the experimental and simulated patterns -seems to decrease as the size of the linker functional group becomes smaller.This could imply that the functional group has a structure directing role, ultimately lining the large hexagonal channels and keeping them apart through e.g.steric hindrance.

Figure S1 :
Figure S1: 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 ∆ϕ within each 1,3-bdc linker in the various supercells.Linkers with syn and anti conformations are plotted above and below the dotted line, respectively.All torsion angle values are coloured according to the density of the supercell to which they correspond.(b) Graph showing the average values of ϕ 1 (pink) and ϕ 2 (grey) foreach supercell as a function of its density.Note that in order to calculate the average value of ϕ 1 and ϕ 2 , the carboxylate with the largest torsion angle was assigned ϕ 1 , leaving the smaller torsion angle to be assigned ϕ 2 .The standard deviation in torsion angle is represented with error bars.

Figure S2 :
Figure S2: Batch of MOX-5 crystals, indicating both oval-and hexagonal-shaped crystals with blue and red arrows, respectively.Scale bar given in the top left corner for reference (100 µm)

Figure S4 :
Figure S4: Asymmetric unit of MOX-2 at 298 K. Ellipsoids are drawn at 50% probability.Colour scheme: C atoms are shown in black, O atoms in red, Zn atoms in grey and H atoms in pink.

Figure S6 :
Figure S6: Asymmetric unit of MOX-3 at 298 K. Ellipsoids are drawn at 50% probability.Colour scheme is as follows: C = black spheres, O = red spheres, N = blue spheres, Zn = grey spheres, Br = brown spheres and H = pink spheres.

Figure S7 :
Figure S7: Asymmetric unit of MOX-4 at 298 K. Ellipsoids are drawn at 50% probability.Colour scheme is as follows: C = black spheres, O = red spheres, Zn = grey spheres and H = pink spheres.

Figure S8 :
Figure S8: PXRD patterns of all MOX-4 samples (i.e. with X = Br/Cl, I, Br and Cl).For all samples, the experimental pattern is given at the top (dark colour), with the simulated pattern given at the bottom (light colour).Each pattern is labelled at the top right corner.

Table S6 :
Crystal data and structure refinement for MOX-2.

Table S7 :
Crystal data and structure refinement for MOX-5.

Table S8 :
Crystal data and structure refinement for MOX-4 for X = Br.

Table S9 :
Crystal data and structure refinement for MOX-4 for X = Cl.

Table S10 :
Crystal data and structure refinement for MOX-4 for X = Cl/Br.

Table S11 :
Crystal data and structure refinement for MOX-4 for X = I.