Porous Metal–Organic Polyhedra: Morphology, Porosity, and Guest Binding

Designing porous materials which can selectively adsorb CO2 or CH4 is an important environmental and industrial goal which requires an understanding of the host–guest interactions involved at the atomic scale. Metal–organic polyhedra (MOPs) showing permanent porosity upon desolvation are rarely observed. We report a family of MOPs (Cu-1a, Cu-1b, Cu-2), which derive their permanent porosity from cavities between packed cages rather than from within the polyhedra. Thus, for Cu-1a, the void fraction outside the cages totals 56% with only 2% within. The relative stabilities of these MOP structures are rationalized by considering their weak nondirectional packing interactions using Hirshfeld surface analyses. The exceptional stability of Cu-1a enables a detailed structural investigation into the adsorption of CO2 and CH4 using in situ X-ray and neutron diffraction, coupled with DFT calculations. The primary binding sites for adsorbed CO2 and CH4 in Cu-1a are found to be the open metal sites and pockets defined by the faces of phenyl rings. More importantly, the structural analysis of a hydrated sample of Cu-1a reveals a strong hydrogen bond between the adsorbed CO2 molecule and the Cu(II)-bound water molecule, shedding light on previous empirical and theoretical observations that partial hydration of metal−organic framework (MOF) materials containing open metal sites increases their uptake of CO2. The results of the crystallographic study on MOP–gas binding have been rationalized using DFT calculations, yielding individual binding energies for the various pore environments of Cu-1a.


Thermal Gravimetric Analysis
Measurements were performed using a Perkin Elmer TGA 7 Gravimetric Analyser under a flow of air (20 cc/min) at a heating rate of 5 °C/min. Samples of Cu-1a and Cu-1b were solvent exchanged with acetone and dried under a flow of argon before being transferred to the analyser. Figure S1. Plots of TGA data and first derivatives of the slopes for samples of Cu-1a and Cu-1b. Values are reported both in the units in which they were measured (cc/g for volumetric data, wt% for gravimetric data) and converted to mmol/g for comparison.

Gas Adsorption
S4 Figure S2. N 2 isotherms measured volumetrically at 77 K, BET surface area plots and Rouquerol BET plots for samples of Cu-1a, Cu-1b and Cu-2. The vertical blue lines delimit the ranges of data used for calculation of the BET surface are plots.   Figure S4. H 2 isotherms for activated Cu-1a measured at 77 K and 88 K. Figure S5. Sequential CO 2 adsorption isotherms measured at 273 K for a sample of Cu-1a. Between measurement of the isotherms the sample underwent a cycle of rehydration with hot water vapour followed by reactivation.

S7
Isosteric heats of adsorption for Cu-1a were calculated using the virial method. Adsorption data for CO 2 and CH 4 measured at 273 and 298 K were fitted to the virial equation (1).
(1) ln ( ) = 0 + 1 + 2 2 + ⋯ where the p is pressure, n is the amount adsorbed and A 0 , A 1 , etc. are virial coefficients. The enthalpy of adsorption at zero coverage was determined from the relationship: 0 = = 0 ( -1 ) Figure S6. Plots of the isosteric heats of adsorption Q st (kJ/mol) vs gas loading for CH 4 and CO 2 in Cu-1a and CO 2 in Cu-1b determined by the virial method using adsorption data measured at 273 and 298 K. The zero loading heats of adsorption for CO 2 and CH 4 in Cu-1a are -28.5 and -21.0 kJ/mol respectively. The zero loading heat of adsorption for CO 2 in Cu-1b is -20.6 kJ/mol. Figure S7. Plots and statistics for the polynomial fittings of isotherm data used to calculate isosteric heats of adsorption Q st for CO 2 and CH 4 in Cu-1a and Cu-1b.  Single Crystal X-ray Structure Refinement Special Details

Cu-1a_sq
A single crystal was taken directly from the DMF reaction mixture and mounted on a MiTeGen MicroMount under Fomblin oil before being flash frozen under a Cryostream at 120 K.
Copper bound oxygen atom O2 (occupancy 0.5) and water oxygen atoms O3 (occupancy 0.25) and O4 (occupancy 0.5) were refined with partial occupancies. It is likely these atoms are disordered with other bound and free solvent species which could not be located in the electron difference map and modelled. The atoms have been included in the unit cell contents at full occupancy. The hydrogen atoms of both the bound and free water molecules were not included in the model but have been included in the unit cell contents. The atomic displacement parameters of the unbound partial occupancy water molecules O3 and O4 were refined with isotropic displacement parameters.
Geometric constraints (DFIX) were applied to the bond lengths between C37 and surrounding atoms in order to obtain sensible molecular geometry. Target values (C−O 1.26 Å, C−C 1.50 Å) were determined from searches of similar functional groups in the CCDB. 9 Rigid bond restraints (RIGU) were applied to the anisotropic atomic displacement parameters of all atoms in the structure.
The crystal was found to be an inversion twin; the contributions of the two components were refined using a batch scale factor to values of 0.52(16) and 0.48(16). The crystal was weakly diffracting with a strong drop off in diffraction intensity and quality beyond 1.1 Å resolution. Despite multiple attempts at crystallisation and careful crystal selection this problem could not be overcome, it is likely a result of the large regions of disordered solvent present in the porous structure. Consequently, a cut off of 1.1 Å resolution was applied to the data (SHELX). Several large and small voids in the structure contained disordered solvent molecules which could not be sensibly modelled, so the structure was treated with PLATON SQUEEZE. A total of 2320 electrons were accounted from the P1 cell in this, equating to 14 dimethylformamide molecules per asymmetric unit, which have been included in the unit cell contents and calculation of derived parameters.

Cu-1a•(H 2 O)
The degassed structure was measured inside the sealed gas cell under vacuum at 220K. This was the lowest temperature that could be achieved before the formation of ice on the outside of the gas cell. Similar constraints and restraints were applied to the framework geometry and anisotropic displacement parameters of the framework atoms as in the solvated structure Cu-1a_sq. Additionally, the carboxylate functional group and connected carbon C34 and para carbon C31 of the phenyl ring were restrained to lie in a flat plane (FLAT).
The U iso values of all three water oxygen atoms were refined isotropically and fixed at 0.15. The occupancies of these three atoms were allowed to refine freely allowing the extent of desolvation to be assessed (Table S5).
The PLATON SQUEEZE routine was performed for the purpose of assessing the solvent content of the pores (Table S5), however, the structure presented is that of the un-squeezed data.

Cu-1a•(H 2 O-CO 2 )
The carbon dioxide structure was measured at 120 K after removal of the quartz capillary sheath from the cell.
Similar constraints and restraints were applied to the framework geometry and anisotropic displacement parameters of the framework atoms as in the solvated structure Cu-1a.
The atoms of the copper bound water molecules and carbon dioxide molecules were refined with isotropic atomic displacement parameters; the framework atoms were refined anisotropically. The U iso values parameters of the two water oxygen atoms O1 and O2 were fixed at 0.15 and their occupancies allowed to refine freely. The U iso values (0.251 (26)) and occupancies (0.563 (44)) of the atoms of carbon dioxide molecule O1A−C2A−O3A were all constrained to have the same value which was allowed to refine freely. The occupancy of carbon dioxide molecule O1B−C2B disordered over a special position was allowed to refine before being fixed at full occupancy whilst their U iso parameters (0.262 (58)) were constrained to have the same value and allowed to refine.
The geometries of the carbon dioxide molecules were constrained to have linear geometries with C-O bond lengths of 1.16 Å (DFIX). Despite these restraints, carbon dioxide molecule A exhibits a small deviation from linear geometry. Table S4. Occupancies and atomic displacement parameters for water molecules and guest CO 2 from in situ gas loaded single crystal X-ray diffraction experiments on Cu-1a. (6) *U iso values marked with an asterisk were fixed and not freely refined.

PLATON SQUEEZE analysis of in situ single crystal X-ray diffraction experiments.
To assess the extent of desolvation and gas loading of the in situ structures the PLATON SQUEEZE programme was carried out on 'empty' structure models from which all metal bound and free solvent and guest molecules had been removed. These calculations allow assessment and comparison of the sum of electron density in each of the three void spaces in the structure of Cu-1a. A significant observation is the lower electron counts for the intermolecular cavities of the degassed structure Cu-1a compared with the gas-loaded structure confirming the successful removal of scattering guest molecules. The electron counts of the large intermolecular cavities of both gas loaded data sets are indicative of larger numbers of guests than have been refined in the structural model suggesting that further disordered gas molecules are located in this cavity. a The solvent and guest moieties in the formula were omitted from the structure input file for the SQUEEZE calculations; the electron counts are expected to account for both these moieties and any further disordered entities which were not modelled.

Powder X-Ray Diffraction
High resolution in situ synchrotron X-ray powder diffraction (PXRD) data were collected at Beamline I11 of Diamond Light Source using multi-analysing crystal-detectors (MACs) and monochromated radiation (λ = 0.825582 Å). These in situ diffraction measurements were carried out in capillary mode and the temperature controlled by an Oxford Cryosystems open-flow N 2 gas cryostat. An acetone-exchanged powder sample of Cu-1a was dried in air and ground briefly (grinding provides a uniform small (~20 micron) particle size essential for obtaining high-quality X-ray patterns) before loading into a capillary tube (0.7 mm diameter) and a powder pattern collected at 293 K. The capillary tube was connected to high vacuum (10 −5 mbar) and a powder pattern collected at 293 K. The sample was then sequentially heated to temperatures of 333, 373, 423 and 473 K and cooled to 293 K between each temperature in order to measure a powder pattern. The degassed sample was cooled to 195 K and an X-ray pattern collected before the tube was charged with CO 2 at pressures of 504 and 1000 mbar at 293 K and then after each loading cooled to 195 K for subsequent data collection. Le Bail refinements were carried out using the Topas software package. The unit cell was found to contract by 0.6% upon degassing the sample with a subsequent 0.1% expansion upon loading the sample with 1000 mbar of CO 2 (Table S6).  Figure S10. Powder X-ray diffraction pattern (blue) and Le Bail analysis fitting (red) of acetone-exchanged    .5 13 12.5 12 11.5 11 10.5 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 Counts 16,000 15,000 14,000 13,000 12,000 11,000 10,000 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 -1,000 -2,000 -3,000 -4,000 hkl_Phase 0.00 % Figure S16. Powder X-ray diffraction pattern (blue) and Le Bail analysis fitting (red) Figure S17. Powder X-ray diffraction pattern (blue) and Le Bail analysis fitting (red) of Cu-1a loaded with CO 2 (504 mbar) measured at 195 K.  Figure S18. Powder X-ray diffraction pattern (blue) and Le Bail analysis fitting (red) of Cu-1a loaded with CO 2 (1000 mbar) measured at 195 K.  Figure S19. Powder X-ray diffraction pattern (blue) and Le Bail analysis fitting (red) of Cu-1a after removal of CO 2 under vacuum measured at 195 K.

Neutron Powder Diffraction
Neutron powder diffraction (NPD) experiments were undertaken on the WISH diffractometer at the ISIS facility. The lack of dependence of neutron scattering power on atomic number Z means in many light atoms have comparable prominence in the nuclear density map to heavier metal atoms. This property of neutron scattering permits facile identification of light guest molecules in Cu-1a since the nuclear density map is not dominated by the heavy copper nuclei. The polychromatic neutron beam profile and time-of-flight data collection method used on the WISH beamline beneficially result in enhanced intensity for high-resolution diffraction data which is often problematically absent or weak in porous structures. Table S7. Unit cell dimensions, Rietveld refinement statistics and CCDC deposition numbers for in situ NPD structures.

Cu-1a
Cu-1a•6.7(CO 2 ) Cu-1a•18.2(CO 2 ) Cu-1a•6.1(CD 4 ) Three guest sites CO 2 A , CO 2 B and CO 2 C are found in Cu-1a•6.7(CO 2 ), coordinated to Cu1, adjacent to phenyl ring C21-C26 and located at the centre of the tetrahedral void, respectively. Guest CO 2 A is coordinated to Cu1 via O1A in an η 1 fashion (Cu1a•••O1A distance = 2.46(6) Å). The coordinated oxygen atom O1A is offset by 1.53 Å from the Cu-Cu axis coincident with the four-fold symmetry axis running through the Cu(II) paddlewheel. CO 2 A makes an angle of 79(3)° with the plane perpendicular to the four-fold symmetry axis. The four-fold symmetry axis results in four CO 2 A sites each located equidistant from Cu1, which lies directly on the axis. The intermolecular distance between adjacent symmetry-related coordinated oxygen atoms O1A•••O1A' is 2.16(6) Å. The intermolecular distance between diagonally opposite symmetry-related coordinated oxygen atoms O1A•••O1A'' is 3.06(8) Å, but simultaneous coordination of two CO 2 guests to the same copper centre is electrostatically and sterically unfavourable and hence unlikely. These distances preclude simultaneous occupancy of any of the symmetry related O1A sites, and, as a consequence, the maximum permissible chemical occupancy of each site is 0.25. To reflect this symmetry-imposed restriction, for the purpose of discussion and comparison with other sites, the crystallographic occupancy of CO 2 A , 0.126(4), is multiplied by four to give a chemical site occupancy 0.504(16). The crystallographic site occupancy and multiplicity are used for the purpose of calculating the total number of CO 2 guests per cage.
Guest site CO 2 B is adjacent to both site CO 2 A and a phenyl ring C21-C26. The closest oxygen atom to the phenyl ring, O1B, is 3.07(6) Å from the ring centroid and 3.01(6) Å from the mean-plane of the ring. The linear molecule CO 2 B is oriented parallel to the mean plnce of the phenyl ring, making an angle of 89(2)° with the axis normal to the plane. The site has a crystallographic and chemical occupancy of 0.121(4). The closest contact between adjacent guests CO 2 A and CO 2 B is 1.03(1) Å (between oxygen atoms O3A and O1B) precluding simultaneous occupancy of the adjacent sites. The four-fold symmetry axis running through the paddlewheel generates four equivalent CO 2 B sites around the edge of the binding pocket. The closest contact between symmetry equivalent CO 2 B sites is 3.62 (6)

CO 2 Guest Sites in Cu-1a•18.2(CO 2 )
Three guests CO 2 A , CO 2 B and CO 2 C are found in Cu-1a•18.2(CO 2 ) with broadly similar positions to those found in Cu-1a•6.7(CO 2 ) ( Figure S20). Differences between the geometries of sites CO 2 A-C between structures Cu-1a•6.7(CO 2 ) and Cu-1a•18.2(CO 2 ) are not significant with respect to the resolution of the data and resulting uncertainties in positions. The same consideration was given the crystallographic versus chemical site occupancies of CO 2 A in Cu-1a•18.2(CO 2 ) as is discussed above for Cu-1a•6.7(CO 2 ). The total number of CO 2 guests refined per cage molecule (18.16) shows good agreement with the expected number based on the volume of CO 2 dosed into the sample (18.0). Figure S20. Guest binding sites and selected intermolecular distances for CO 2 A−C in Cu-1a•18.2(CO 2 ) determined by NPD. Guest occupancies and colour key inset. Atom colours: carbon, black; hydrogen, white;

DFT Calculations
All calculations in the present work were performed within the DFT formalism using the B3LYP 1,2 exchange and correlation functional corrected to account for the dispersion interactions within the DFT-D3 3 as implemented in Q-Chem software package. 4 We have used the modified m6-31G* basis set 5 for Cu atoms and standard 6-31+G* Pople basis sets for C, O, and H atoms. A set of test calculations have been performed to evaluate the accuracy for the described level of theory (Table S10 and Figure S25). It has been found that for the test systems the results of B3LYP-D3/6-31+G* calculations agree very well with the CCSD(T) data from literature for both geometries and binding energies. Also, the binding energies calculated with the use of 6-31+G* basis set are very close to those obtained with def2-QZVPD/def2-TZVPD 6-8 basis sets. It is, therefore, concluded that 6-31+G* basis set can be used to describe intermolecular interactions with a reasonable level of accuracy, while for the larger systems studied in the present work it provides a significant gain in computational time compared to calculations with def2-QZVPD/def2-TZVPD basis sets.
The atomic coordinates for the MOF fragments and initial positions of the guest molecules have been taken from the NPD and SCXRD experiments. During geometry optimisation, the Cu, C and O atoms of the fragments have been kept at the experimentally determined positions. For the cases of CO 2 Ph and CH 4 Ph configurations the initial positions that correspond to the DFT optimised geometries of C 6 H 6 •••CO 2 and C 6 H 6 •••CH 4 molecular systems have been also considered. It was found that geometry optimisation converges to the same potential energy surface minima as in the case of the experimentally determined initial configurations. For the pairwise guest optimisation calculations, the initial configuration of a molecule at the Cu site has been taken from the single guest geometry optimisation while initial coordinates of the second molecule have been set to the experimental values.
The binding energies, E b , of the adsorbed molecules were calculated as where E F+M is the total energy the MOP fragment with an adsorbed molecule, E F and E M are the total energies of the separate fragment and molecule, respectively. In calculations of binding energies, the three-body dispersion contributions were added using the stand-alone DFT-D3 (V3.2) code. 3 All binding energies were corrected for the basis set superposition error (BSSE) using the counterpoise method of Boys and Bernardi. 9 Table S9 shows the calculated binding energies with and without the three-body interaction term. DFT-D3-3body -22.9 -20.5 -21.6 -31.5 Table S10. Binding energies, E b , in kJ/mol and interatomic distances R (Å) for the test systems shown in Figure S25.   DFT: CH 4 Tet (pink) a DFT Optimised positions for single occupancy guest sites CH 4 Cu and CH 4 Ph (pink) are overlaid with the analogous sites CD 4 A and CD 4 B determined by NPD (blue and yellow). No overlay is present for CH 4 Tet , as the DFT optimised site is identical to the NPD determined site CD 4 C . b For pairwise optimisation, geometries of both guests (pink and blue) were optimised. c For single guest sites, binding energies are calculated for the optimised guest positions (pink). d For the pairwise sites, binding energies are calculated for the guest site coloured pink.