3D flexible COFs with dynamics structures. The applicability of enhanced Cryo-cRED was first demonstrated on a flexible 3D COF (FCOF-5), which is formed by the [4 + 4] imine condensation reaction between the molecules of 1,2,4,5-tetrakis[(4-formylphenoxy)methyl] benzene (TFMB) with flexible C-O single bonds in the backbone and the rigid tetra(p-aminophenyl)methane (TAPM) (Figure S1a, S2a and S3a). Due to the bond flexibility, this COF can undergo reversible structural expansion/contraction in response to guest molecular adsorption/desorption, indicating a breathing behavior. Although the simulated structures using PXRD were reported in our recent study38, the dynamic structure at atomic level is still unknown. As the FCOF-5 is sensitive to the environment, the cRED sample preparation should be careful. For the sample preparation of expanded FCOF-5 (E-FCOF-5), a small quantity of micro-crystals was dispersed in ethanol by ultra-sonication for five minutes, and then a suspension droplet was transferred onto a copper grid covered with carbon film. From the grid, thousands of nano-crystals were easily discernible on the grid surface, providing ample nanocrystals for the 3DED data collection (Figure S4a). Prior to being transferred the grid into the transmission electron microscope (TEM), the sample was cooled to ~ 173 K using a cryo-transfer tomography holder to fix the guest molecules within the COF pores. After transferring the grid to electron microscopy, the sample was further cooled down to 96 K for 3DED data collection. To achieve high diffraction resolution, the spot size and exposure time were optimized to 3 and 0.5 s, respectively. Although the E-FCOF-5 nano-crystals could diffract to a high resolution of ~ 0.82 Å, its crystallinity deteriorated quickly and the diffraction resolution dropped to ~ 3 Å at the final stage because of the serious beam damage (Figure S4-S5). From an individual dataset (dataset 1 in table S1), the unit cell parameters can be easily determined to be a = 14.58 Å, b = 8.51 Å, c = 26.49 Å, and β = 92.97° with monoclinic symmetry. The reflections conditions from specific slices were extracted as h0l: l = 2n, 00l: l = 2n, suggesting two possible space groups of P2/c (No. 13) or Pc (No.7) (Figure S5). Due to the completeness and redundancy were as low as 33% and 0.88 for an individual dataset, it failed to solve the E-FCOF-5 structure using ab initial method (direct method, charging flipping, etc.).
To improve the data completeness and redundancy for structure determination and refinement, the enhanced Cryo-cRED method, which is hierarchical cluster analysis43,44 on several cryo-cRED datasets with different orientation of crystals. Twenty-two cRED datasets were collected on the E-FCOF-5 crystals with a large tilt range from 34.5o to 95.2o (detailed information of each dataset is listed in Table S1). The 3D reciprocal lattices reconstructed from the twenty-two datasets are shown in Figure S6, where the reciprocal lattice with a high resolution is in different locations owing to the different crystal orientations. Because E-FCOF-5 belongs to the monoclinic crystal system, none of the cRED datasets can have the completeness greater than 90%, which is necessary for a feasible structure refinement. Therefore, several datasets were carefully selected and merged. Before merging the data sets, all the cRED datasets were processed using an automated data procession method (Details are stated in Method Section). The twenty-two cRED datasets could be indexed with an average lattice parameters of a = 13.7095(2) Å, b = 8.633(6) Å, c = 26.4086(1) Å, and β = 91.393(2)°. The twenty-two datasets were then subjected to the hierarchical cluster analysis (HCA) using a python script developed in-house to determine the optimal datasets for merging44. The distance metric t, which defines the similarity between datasets, is derived from the correlation coefficients of the common reflection intensities (CCI) in dataset pairs, and the “average” linkage method is employed. The clusters can be visualized using a dendrogram, making it easier to find an appropriate cut distance. Clusters with t < 0.40, in our experience with HCA, usually result in usable datasets. But in the E-FCOF-5 case, the distance metric value between each dataset is a little bit larger, which appears to be due to the beam damage. We thus cut the distance metric value with t = 0.5 to balance the completeness and obtained three clusters (Fig. 2a). The largest one (Fig. 2a, in red), consisting of sixteen datasets (Figure S6 and Table S1), possessed the highest data quality with the completeness and redundancy of 91% and 9.22, respectively. The sixteen data sets belonging to the largest cluster were merged. With such high-quality merged dataset (Fig. 2b), all non-hydrogen atoms were located directly from the electrostatic potential map by using ShelxT45, resulting in a six-fold interpenetrated pts topology (Fig. 2f, Figure S7-left). Finally, the structure model was refined isotropically using soft restraints for the geometry of the phenyl ring as well as the C-C and C = N bond lengths. The guest molecular of ethanol can be determined by the difference electron density map (Fig. 2e), benefited from the high data completeness and resolution. With the atomic precision structure, the precise pore size of expanded FCOF-5 was obtained to be 6.2 Å×6.2Å and 4.2 Å×7.2Å (Fig. 2f), which was unknown in previous study. (The details of cryo-cRED experimental parameters, crystallographic data, and structure refinement are in Table S2.)
For the contracted FCOF-5 (C-FCOF-5), the crystals were placed directly onto the copper grid without any dispersion. To ensure that the framework is fully contracted, the sample was transferred into the TEM with a high vacuum (< 2×10 − 5 Pa) at room temperature for five minutes to extract the guest molecules. After that, the sample was cooled to 96 K for data collection. Twenty-two cRED datasets (Table S3) were obtained on the C-FCOF-5 crystals, among which sixteen were selected for merging after HCA with the distance metric t of 0.56 (Fig. 2c, Figure S8). The C-FCOF-5 unit cell in the space group P2/c shrinks to a = 10.9511(2) Å, b = 7.7945(1) Å, c = 26.8214(6) Å, and β = 95.247(3)° (Figure S9) with a large volume contraction of ~ 27%, indicating a significant breathing motion. After similar data procession with E-FCOF-5, the completeness and redundancy for the C-FCOF-5 data were increased from 20 ~ 50% and ~ 1.0 (individual dataset) to 90% and 10.0 (merged sixteen datasets after HAC), respectively. The cRED data collected on the C-FCOF-5 crystals had a resolution of up to ~ 0.81 Å (Figure S10), and all the non-hydrogen atoms could be located directly from the electrostatic potential map using the ab initio structure solution with ShelxT45, yielding the same six-fold interpenetrated pts topology with E-FCOF-5 (Fig. 2h, Figure S7-right). The C-FCOF-5 structure was also refined isotropically with soft restraints on the phenyl ring geometry as well as the C-C and C = N bond lengths and the observed peaks also appeared to be spherical with similar peak heights for the same atom types (Fig. 2g). As expected, the building block TFMB in the contracted FCOF-5 structure is twisted with its phenyl ring blocking the pores, thus no solvent void is accessible during the PLATON/SQUEEZE46 procedure. From the atomic precision structure, the width was the pores of contracted FCOF-5 was only 1.7 Å (Fig. 2h), which finally revealed the reason of no N2 and Ar adsorption in our previous study. In addition, the bond angle and geometry of E-FCOF-5 and C-FCOF-5 that obtained from simulation of PXRD data shown a large deviation, comparing the atomic precision structure (Figure S11), atomic level structure determination is very important to understand the dynamics of flexible COFs. To our best knowledge, it is the first time that the structures of a flexible 3D COF at both the expansion and contraction states is resolved with atomic precision. (The details of cryo-cRED experimental parameters, crystallographic data, and structure refinement are in Table S4.)
3D COFs with functional group. The internal functional groups of 3D COF can be used to provide a structurally accurate application platform. Encouraged by the exciting results of FCOF-5, the applicability of enhanced cryo-cRED was employed on three 3D-TPB-COFs with different functional groups of methoxy (OMe), methyl (Me) and hydroxyl (OH), to thoroughly explore the scope and applicability of this powerful ab initial structure determination method. (Figure S1b, S2b, S3b-d). These three 3D-TPB-COFs were synthesized by the [4 + 4] condensation reaction of three 1,2,4,5-tetraphenylbenzene (TPB) derivatives, namely TPB-OMe, TPB-Me and TPB-OH functionalized by the respective methoxy, methyl and hydroxyl groups, with tetra(p-aminophenyl)methane (TAPM). The synthesis condition was described in our previous reports but the single crystal structures with atomic resolution are unclear36,40,41.
For 3D-TPB-COF-OMe, the nano-crystals could diffract to a high resolution of ~ 0.87 Å at the beginning of the cryo-cRED32,47 data collection (Figure S12), but the highest completeness and redundancy from a single dataset were ~ 65.9% and 1.55 (dataset 4# in table S5, Figure S13), respectively, resulting in missing observed peaks, significant variations in peak heights, and severe peak elongation during refinement (Figure S14). Eleven cRED datasets were collected on 3D-TPB-COF-OMe crystals (Table S5). The distance metric value is cut with t = 0.3, equivalent CCI = 0.95, which result in three clusters (Fig. 3b). The largest one consisting of six datasets (Fig. 3a), possessed the highest data quality with the completeness and redundancy of 91.8% and 8.43, respectively. With such high-quality merged dataset (Fig. 3c), all non-hydrogen atoms, including the functional group of OMe, were located directly from the electrostatic potential map by using ShelxT45. The structure refinement was greatly improved, from which the observed peaks appeared to be spherical with similar peak heights for the same atom types (Fig. 4a). The ordered guest molecular of water and ethanol in the pores of 3D-TPB-COF-OMe were observed at the final stage of refinement. In the end, the R1 value was converged to 0.2281. With the same method, the atomic precession structure of 3D-TPB-COF-Me (Fig. 4b) and 3D-TPB-COF-OH (Fig. 4c) were determined directly and precise anisotropic refinement by merging 6 datasets (Table S7, Fig. 3d-3f, Figure S15-S16) and 4 datasets (Table S9, Figure S17-S19) after HAC, respectively. 3D-TPB-COF-OMe, 3D-TPB-COF-Me and 3D-TPB-COF-OH are determined to have a five-fold interpenetrated structure with a reported pts net with the same one-dimensional (1D) straight channels, but offering varied pore size (Fig. 4, Figure S20). In addition, the position of functional groups can be refined without any restraints. The obtained bond length of C-O(-C), (C=)C-C and (C=)C-O in methoxy, methyl and hydroxyl were 1.41Å, 1.55 Å and 1.28 Å, which close to the theoretical value (Fig. 4). (The details of cryo-cRED experimental parameters, crystallographic data, and structure refinement are in Table S6, S8 and S10, respectively.)