Hirshfeld atom refinement of metal-organic frameworks for accurate positioning of hydrogen atoms and disorder analysis

The application of Hirshfeld atom refinement (HAR) fragmentation is demonstrated for the refinement of metal-organic framework (MOF) crystal structures. The presented method enables anisotropic refinement of imidazolate hydrogen atoms, as well as complex analysis of solvent disorder within MOF pores. The data used were derived from standard resolution in-house single crystal X-ray diffraction measurements, demonstrating that high quality structural analysis of MOFs no longer requires access to neutron or synchrotron facilities.


Preparation of single crystals of ZIF-2
1 mmol (68.1 mg) of imidazole 1 was dissolved in 3 mL of N,N-dimethylformamide (DMF) and the solution was placed in a 10 mL glass vial.After that, a solution of 0.5 mmol (110.7 mg) zinc acetate dihydrate dissolved in 2 mL of propylamine was carefully layered over the imidazole-DMF solution.Single crystals of zinc imidazolate, suitable for X-ray diffraction, were obtained by liquid diffusion after several days of storing the vial at room temperature.

Single crystal X-ray diffraction measurement
A good quality single-crystal of investigated compound was selected for X-ray diffraction experiments at 100(2) K.The crystal was mounted on a MiTeGen micro-mount using paratone-N-oil (Figure S1).Diffraction data were collected on an Agilent Technologies SuperNova Dual Source diffractometer equipped with an HyPix-6000HE hybrid pixel 2-dimensional detector with CuKα radiation (λ = 1.54184Å) using CrysAlis Pro software. 2During the measurement the crystal was positioned 55 mm from the detector.A total number of 882, 4112 and 8798 frames were collected at 0.5° intervals with a counting time of 0.05, 0.10 and 0.50 s, respectively.The analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by R.C. Clark & J.S. Reid was applied. 3The lattice parameters were obtained by least-squares fit to the optimized setting angles of the reflections collected by using the CrysAlis CCD software 2 .Data were reduced using the CrysAlis RED program.

Details of fragmentation-based Hirshfeld atom refinement method
The refinement procedure starts by the fragmentation of ZIF-2 crystal structure into separate molecular fragments.In this case, seven distinct molecular fragments were defined, one representing the ZIF structure (shown in Figure 1 from main text).The remaining six fragments represent the three DMF molecules in the asymmetric unit, each present in two disordered configurations.The QM calculations were performed in Orca 5.03.Electron densities were computed for each fragment, initially using the PBE functional with cc-pVDZ basis set.The effect of the crystal field from the atoms surrounding the molecular fragments was simulated by adding multipole functions within a distance of 6 Å from every atom within the molecular fragment.To initially test the HAR method, PBE functional with cc-pVDZ basis set were used.After each molecular wavefunction calculation, the resulting electron density was used by DiSCaMB 4 to obtain aspherical atomic scattering factors for a standard least squares refinement in OLEX2, 5 so that the atomic positional and thermal parameters are improved.All non-hydrogen atoms, as well as hydrogen atoms on the imidazolate rings were refined anisotropically, while the hydrogen atoms belonging to the DMF molecules were refined isotropically.Positions of imidazolate hydrogens were refined without restraints, while C-H bond lengths for the DMF hydrogens were restrained to 1.088 Å.
The QM-refinement steps were repeated in a loop until geometry convergence had been reached.Finally, the effect of using different QM methods (ie.Hartree-Fock or density functional theory with B3LYP and PBE) and four basis sets (6-31G, 6-311g, cc-pVDZ and cc-pVTZ) was tested via additional 11 structure refinements (Tables S2-S8).

Periodic DFT calculations
Periodic DFT calculations were performed in plane-wave DFT code CASTEP20. 6The input structure files were prepared using cif2cell software. 7Given that DMF molecules are disordered in the experimental crystal structure, and the periodic DFT calculation requires the structural model to be fully ordered, we prepared two separate models: one containing all DMF molecules in the orientation from the major disorder component, and the other corresponding to the minor disordered component.These two structural models were then geometry-optimized and the final geometries were compared with the experimental structures refined by HAR method (see Table S1).
The crystal structures were optimized with respect to atom positions, subject to the symmetry constraints of the Pbca space group.The unit cell parameters were fixed at their experimental values.The calculations were performed using the PBE 8 functional, combined with Grimme D3 9 dispersion correction.The plane-wave basis set was truncated at 800 eV cutoff.The 1 st electronic Brillouin zone was sampled with a 2πx0.05Å -1 k-point grid.Convergence criteria were set with respect to maximum energy change per atom (2x10 -5 eV), maximum force on atom (0.05 eV Å -1 ) and maximum atom displacement (0.001 Å).The energies of the optimized structures corresponding to the major and minor disorder component are shown in Table S1.
Table S1.Comparison of the energies for the periodic DFT-optimized structures representing the major and minor components of the disorder of DMF molecules.The energy difference between two configurations is 5.818 kJ mol -1 per formula unit, which contains three DMF molecules, or 1.939 kJ mol -

Independent reflections 6081
Table S4.General refinement statistics of using a given QM method and basis set are summarized here (PBE method with cc-pVTZ is used as a reference), where R1(I>2 sigma) is the regression coefficient of the least squares fit for the atomic positions to the experimental electron density, R1(all I) and wR2 is the discrepancy factor, gof is the goodness of fit and max/min peak is the maximum/minimum atomic peak heights.

Figure S1 .
Figure S1.Selected single-crystal of investigated compound mounted on a MiTeGen micro-mount.

Comparison of Hirshfeld atom refinement parameters with different QM methods.Table S2 .
1per DMF molecule.Summary of all refined imidazolate C-H bond lengths at each given QM method and basis set, as well as those calculated by periodic DFT.The population standard deviation values are shown in the brackets.

Table S3 .
Crystal data and structure refinement details, shared for all HAR calculations.For geometry analysis and refinement statistics for different QM methods and basis sets see Tables S4-S8.

Table S5 .
Statistics for comparison of imidazolate C-H bond lengths, using various QM methods and basis sets using PBE method with cc-pVTZ refinement as the reference for bond lengths.|Rx -Rr|is the average absolute bond length difference compared to the reference bond length; sd is the population standard deviation; wRMSD(ΔR) is the weighted root mean squared deviant of the imidazolate C-H bond lengths; Rx -Rr is the average bond length difference compared to the reference bond length; Rx / Rr is the average bond length ratio compared to the reference bond length and finally Rx are the averaged bond lengths.

Table S6 .
Statistics for comparison of anistropic imidazolate hydrogen atoms with different QM methods and basis sets (using PBE method with cc-pVTZ as a reference for ADP values).|ΔUij| is the average absolute difference of ADP tensor components; wRSMD(ΔUij) is the weighted root mean square deviation for components of ADP tensor; Uijx/Uijr is the average ration of ADP tensor components; S12 is the ADP similarity index; Vx/Vr is the ratio of X-ray to reference thermal ellipsoids; sigma is the population standard deviation of the averaged ADP tensor components; and |ΔUij|/|Uij|is the ration of average absolute difference of ADP tensor components to average absolute value of ADP tensor components.

Table S7 .
Statistics for averaged non-hydrogen atom ADP comparisons using various QM methods and basis sets (PBE method with cc-pVTZ refinement is the reference for ADP values).|Uijx -Uijr| is the average absolute difference of ADP tensor components; wRSMD(ΔUij) is the weighted root mean square deviation for components of ADP tensor and Uijx/Uijr is the average ration of ADP tensor components.

Table S8 .
Maximum discrepancies of anisotropic imidazolate hydrogen atoms for each QM method and basis set, using PBE method with cc-pVTZ refinement as the reference ADPs.|Ux -Ur| is the average absolute difference of ADP tensor components; S12 is the ADP similarity index and min/max Vx/Vr is the maximum/minimum ratio of X-ray thermal ellipsoids to reference thermal ellipsoids.