Understanding disorder and linker deficiency in porphyrinic zirconium-based metal–organic frameworks by resolving the Zr8O6 cluster conundrum in PCN-221

Porphyrin-based metal–organic frameworks (MOFs), exemplified by MOF-525, PCN-221, and PCN-224, are promising systems for catalysis, optoelectronics, and solar energy conversion. However, subtle differences between synthetic protocols for these three MOFs give rise to vast discrepancies in purported product outcomes and description of framework topologies. Here, based on a comprehensive synthetic and structural analysis spanning local and long-range length scales, we show that PCN-221 consists of Zr6O4(OH)4 clusters in four distinct orientations within the unit cell, rather than Zr8O6 clusters as originally published, and linker vacancies at levels of around 50%, which may form in a locally correlated manner. We propose disordered PCN-224 (dPCN-224) as a unified model to understand PCN-221, MOF-525, and PCN-224 by varying the degree of orientational cluster disorder, linker conformation and vacancies, and cluster–linker binding. Our work thus introduces a new perspective on network topology and disorder in Zr-MOFs and pinpoints the structural variables that direct their functional properties.

In 2013, PCN-221, a MOF similar to MOF-525, was reported featuring Zr 8 O 6 clusters instead of Zr 6 O 4 (OH) 4 clusters ( Fig. 1) 22 . Curiously, the Zr-Zr distance in PCN-221 is only 2.69 Å, much shorter than in all inorganic Zr compounds compiled from the Inorganic Crystal Structure Database and Zr-cluster-based frameworks from the Cambridge Crystallographic Data Centre (Fig. S14). Both MOF-525 and PCN-221 are described with a cubic structure of similar unit cell size and with 12 coordination sites on the SBU. In MOF-525, the reported structure exhibits a completely planar TCPP linker, whereas in PCN-221 the phenyl rings are rotated out-of-plane by 90°1 7,22 .
A difficulty in studying porphyrin-based MOF structures is the synthesis of phase-pure products, due to similar reaction conditions for all seven structures 23 . High-throughput syntheses of MOF-525 have shown the impact of modulator concentration, temperature, and reaction time on the crystallinity and phase purity, demonstrating the complexity in obtaining optimum reaction conditions 24,25 . Although not explicitly stated in the literature, it is discussed in the MOF community that syntheses of porphyrin-based Zr-MOFs are notoriously difficult to reproduce, leading to the co-existence of different MOF-525 and PCN-221 protocols 17,22,[24][25][26][27] . In fact, many studies report the same product for different experimental data 21,[28][29][30][31][32][33][34][35][36][37][38][39][40][41] , suggesting that the synthetic protocols and the resulting structures are still not well understood. This is exacerbated by poor quality and insufficient powder X-ray diffraction (PXRD) data making structure assignment ambiguous. As a consequence, many publications do not reveal differences in the PXRD patterns between MOF-525, PCN-221, and the ordered defect structure PCN-224 21, . However, linker vacancies in MOFs have been found to impact the material's properties due to larger pores (adsorption applications) or open metal sites (e.g., Lewis acid catalyzed reactions), highlighting the importance of being able to reliably distinguish between these MOFs 5,45 .
Zr 6 O 4 (OH) 4 cluster-based MOFs have been found to be remarkably tolerant toward high linker deficiencies, especially in UiO-66 and its analogs [46][47][48][49][50] . The tolerance is a result of large linker coordination numbers and the ability to compensate defects with either modulator molecules, hydroxy groups, or hydroxy water pairs 6,51,52 . The amount of linker vacancies can be tuned synthetically, and the inclusion of defects has been shown to proceed in a correlated manner 47,53,54 . These defect sites can be utilized to introduce functional groups by means of solventassisted ligand incorporation to tune the MOF's properties 55,56 . Only recently, the notion that linker vacancies are prevalent also in the TCPP-based MOF-525 has gained attention, with vacancies reported up to 50% 25,45 .
Here, we performed a comprehensive synthetic study on PCN-221 and undertook detailed investigations of the resulting structures using total scattering pair distribution function (PDF) analysis, powder and single-crystal X-ray diffraction (PXRD/ SCXRD), solid-state nuclear magnetic resonance (ssNMR) spectroscopy, and quantum chemical calculations. We have determined that PCN-221 forms with orientationally disordered Zr 6 O 4 (OH) 4  recommend a new name, dPCN-224. This study thus highlights the large untapped potential for incorporating correlated orientational disorder of sub-components as a powerful design principle for developing synthetic protocols.
The PXRD patterns of the products MOF_ZrCl 4 , MOF_ZrOCl 2 , and MOF_Zr 6 are all very similar and do not show features that would suggest significantly different structures (Fig. 2). We compared these to calculated PXRD patterns based on the published crystal structures of PCN-221, which is reported with a Zr 8 O 6 cluster and twisted phenyl linker conformation, and MOF-525, reported with a Zr 6 O 4 (OH) 4 cluster and planar linker conformation (for structural details see Fig. 1). At low scattering angles the simulated patterns of the published structure of PCN-221 and MOF-525 are strikingly similar, due to the identical space group Pm 3m and similar lattice parameters (19.51 and 19.39 Å, respectively) 17,22 . This makes structure assignment difficult in the absence of good quality data extending to higher angles. Nevertheless, all sample patterns show better agreement with the simulated structure of PCN-221, including the MOF_Zr 6 sample synthesized from preformed Zr 6 O 4 (OH) 4 Bz 12 clusters. This is surprising, since PCN-221 is published with Zr 8 O 6 clusters. A rearrangement of the pre-synthesized Zr 6 O 4 (OH) 4 cluster is not expected during the synthesis and crystallization of MOF_Zr 6 , raising the question of whether Zr 6 O 4 (OH) 4 or Zr 8 O 6 clusters are actually present. For comparison, we measured PXRD data of experimental PCN-224, with ordered TCPP linker vacancies, showing superstructure reflections at 3.2 and 5.5°2θ (Fig. 2).
Cluster structure. Due to the ambiguity in cluster constitution, based on comparison of measured and calculated PXRD data, we proceeded to use total scattering PDF analysis to investigate the short-range order of the Zr-oxo cluster. For all samples, the PDF data show peaks at the same atom-pair distances, which corroborates similar local Zr environments within the clusters of different samples (Fig. 3a). The experimentally determined Zr-O distances of 2.28 Å and Zr-Zr distances of 3.54 Å are found to match with those expected for a Zr 6 O 4 (OH) 4 cluster, rather than 2.12 and 2.69 Å, respectively, for the Zr 8 O 6 cluster ( Fig. 3b) 22 . The reported structure for MOF-525 gives slightly contracted distances, Zr-O (2.06 Å) and Zr-Zr (3.32 Å) compared to the experimental data, while the structure of PCN-224, with Zr-O (2.15 Å) and Zr-Zr (3.50 Å), gives the best overall agreement to the local structure. These findings are in agreement with quantum chemical calculations on the structure of a Zr 8 O 6 cluster, for which no energetically favorable geometry could be successfully determined. In contrast, an optimized Zr 6 O 4 (OH) 4 cluster shows very good agreement with the Zr-Zr distances from the PDF refinement (Figs. S19-S21 and S33).
Structure model from X-ray data. All three synthetic routes MOF_ZrCl 4 , MOF_ZrOCl 2 , and MOF_Zr 6 yielded a MOF whose structure agrees well with the published structure for PCN-221 with a Zr 8 O 6 cluster in the long range (PXRD), but locally contradicts the presence of Zr 8 O 6 clusters. To elucidate this discrepancy, we studied the structure of the MOF by SCXRD. Several reaction parameters had to be adjusted to grow single crystals of the same MOF with suitable sizes for SCXRD (Fig. S22). Indexing revealed a primitive cubic unit cell with a = 19.315(2) Å, and the initial structure solution gave a Zr 8 O 6 cluster similar to the structure of PCN-221 22 . However, residual electron density arranged in a triangular shape remained around each Zr atom, manifesting itself as extremely flat, disk-shaped thermal ellipsoids of the Zr in the Zr 8 O 6 cluster (Fig. 4a), as previously reported 22 . The corners of the Zr 8 cube point toward all eight triangles of the cuboctahedral cage formed by the carbon atoms of the coordinating linker molecules (Fig. 4). In fact, it is possible to describe such a distribution of electron density by superimposing four different Zr 6 cluster orientations as seen in the 2 × 2 × 2 supercell of PCN-224, so that the corners of any Zr 6 octahedron point to six of the eight cuboctahedron's triangles. The four 4 6 8 10 12 14 16 18 20 22  cubes. For more details on the SC refinement and crystallographic data please refer to the Supplementary Information ("Single-crystal X-ray diffraction"). The crystal structure file is provided in Supplementary Data 1. Our analysis is further consistent with the PDF data that suggest the local environment to be more similar to PCN-224. We found additional evidence for our structural model in the Fourier map of the (111) crystallographic plane through the truncated corners of the cube that show a three-fold symmetry in the electron density map with maxima on the superimposed Zr sites (Fig. 4b).
The tilted Zr 6 O 8 cluster orientations offer 12 simultaneous carboxylate positions coordinating such that six of them bridge two adjacent Zr atoms (bridging ligands) and the other six chelate single Zr atoms (chelating ligands). This building unit shows similarities to the hexagonal TCPP-based PCN-223 16 featuring both bridging and chelating ligands, rather than only bridging as in MOF-525 and PCN-224.
The SCXRD model was solved with a 90°dihedral angle between the porphyrin and the phenyl ring, rather than 0°as reported for MOF-525. The refinement of this angle is prohibited by the symmetry restrictions of the cubic space group Pm 3m. These values are closer to the published structure of PCN-224, in which the phenyl rings of the porphyrin linker are twisted out-ofplane by~78°2 1 . The potential energy surface obtained from quantum chemical calculations of TCPP in the gas phase shows a steep maximum at 0°and a very shallow minimum in the range of 60-90°( Fig. S36 and Table S15). This confirms the preference for a twisted dihedral angle of the phenyl rings.
The occupancy of the linker was further investigated by SCXRD, PDF, Rietveld, and chemical analysis (Supplementary Information "Chemical composition analysis") as well as ssNMR spectroscopy. SCXRD analysis revealed that the porphyrin moiety of the linker is not fully occupied, but rather~50%; therefore, only six out of the 12 sites on the Zr 6 O 8 cluster are coordinated by TCPP, similar to PCN-224. Compared to the porphyrin moiety, the phenyl rings refined to a higher occupancy of~75%. This suggests that besides six TCPP linkers, leftover pore content may occupy the TCPP-vacant sites.
PDF analysis provided further insights into the linker vacancies and cluster orientations (Fig. 5). The intermediate-range atomic density distribution from 5-40 Å suggests a high degree of similarity to experimental PCN-224 with respect to the preferred coordination of linkers around the Zr-oxo clusters, and the relative concentration of linker present, confirmed by comparison to published models (Fig. 5b). The PDFs of all samples thus also indicate 50-60% porphyrin occupancy. Furthermore, slightly increased broadening of features at long distances suggest a more disordered long-range structure compared to the PCN-224 sample (Fig. S17). This could be attributed to more randomly distributed vacancies, in contrast to ordered vacancies in PCN-224. For Rietveld refinements (Fig. S6), accounting for orientationally averaged clusters, nonplanar porphyrin linkers, and random   linker vacancies led to substantially improved agreement with the PXRD data. Additional electron density coordinating cluster surface sites was required to obtain a good fit. This could be primarily accounted for by remaining water content, though contribution from other remaining coordinative species is possible. Multiphase refinements performed found no preference for any ordered domains of MOF-525-like structure.
The models discussed still could not explain weak, diffuse features consistently observed at the superstructure reflection positions of PCN-224 (Figs. 5c and S9), which were also observed by SCXRD (Fig. S24). We built a 2 × 2 × 2 supercell and refined separate occupancy factors for each individual linker and cluster orientations for each cluster site, allowing for different local vacancy-orientation environments. This gave a good fit over the entire angular range and reproduced the weak features; however, it is not sufficient to identify a distinct local structure patterning of orientations and vacancies, as other supercell models can also produce similar diffuse features. Altogether, the findings suggest that these structures form more as a frustrated network than as a simple crystal, though the average structure can be described by orientationally disordered Zr 6 O 4 (OH) 4 clusters and linker vacancies distributed more randomly than in PCN-224. As such, we propose disordered PCN-224 (dPCN-224) as a more systematic description of PCN-221. The crystal structure models from refinement using a single unit cell and with a 2 × 2 × 2 supercell, as presented in Fig. 5a models 5 and 6, are given in Supplementary Data 2 and 3, respectively.
Local environment of the cluster. To obtain insights into the local coordination of the Zr-oxo cluster in PCN-221 (dPCN-224), a comprehensive set of solid-state NMR measurements was carried out. High-resolution 1 H, 13  The aromatic regions (7-9 ppm) of the 1 H NMR spectra show significantly more intensity than expected for TCPP linkers alone. Combined with the small amount of modulator molecules, as determined from the 1 H and 13 C cross polarized magic angle spinning spectra (Figs. 6a and S25 and S26), we conclude that the remaining six (dPCN-224) to seven (PCN-224) coordinatively unsaturated sites at the Zr 6 O 4 (OH) 4 clusters are mainly saturated by hydroxy water pairs (for details see Supplementary Information "Solid-state NMR spectroscopy"). A similar situation was recently reported for the same cluster type in NU-1000 51,58 . The strong downfield shift for the protons within such pairs translates into comparably short O-O distances between 2.6 and 2.7 Å (Fig. 6), characteristic for strong hydrogen bonds 52,58,59 . The additional spectral intensity between 6 and 4 ppm was attributed to mobile water in the neighborhood of the Zr clusters. Both the hydroxy water pairs at the coordinatively unsaturated sites of the clusters, as well as the mobile water may account for the additional electron density close to the cluster surface sites, which is required for the Rietveld refinement of the PXRD data.
The carboxylic region of the 13 C MAS NMR spectra for dPCN-224 and PCN-224 contains several signals between 167.3 and 177.2 ppm centered around a main peak at ≈171.9 ppm (Fig. 6b). Such a broad spread reflects different binding modes between the Zr 6 O 4 (OH) 4 clusters and the carboxylate units of the TCPP linkers and residual modulator molecules, in combination with a configurational variance from cluster to cluster. Based on DFT calculations ( Fig. S30 and ref. 60 ) we assigned the central resonance and its high-field region (165-173 ppm) to carboxylates in a bridging motif and the low-field region (173-176 ppm) to a chelating motif. As such, the primary coordination motif consists in bridging TCPP linkers for both dPCN-224 and PCN-224, in accordance with the published structure model of PCN-224 21 and reported calculations showing that bridging carboxylate groups are favorable over chelating ones 60 . A small part of carboxylate groups is found in a chelating motif reflecting the local disorder of the clusters in both dPCN-224 and PCN-224.
The distribution of different binding modes is also reflected in the lineshapes of the 91 Zr wideline NMR spectra (Fig. 6d). They consist of at least four different quadrupolar shapes with nonaxial symmetric coupling tensors and coupling constants (C Q ) between 10 and 25 MHz. This proves a markedly more diverse coordination for the individual Zr atoms compared to a free Zr 6 O 4 (OH) 4 Bz 12 cluster with 12-fold Bz coordination 61 (Fig. S31). Compared to the free cluster, the broader variance for dPCN-224 and PCN-224 reflects the disorder induced by attached hydroxy water pairs, residual modulator molecules, and the strain on the Zr clusters imposed by the framework.
Linker vacancies. We revisit the implications of linker vacancies at~50% occupation as consistently derived from SCXRD, Rietveld, PDF, and ssNMR. Recently, highly defective MOF-525 structures with up to 50% linker vacancies were reported, further supporting the observation of high vacancy concentrations in our proposed structure of PCN-221 (dPCN-224) 25,45 . The favorable coordination of bridging ligands 60 , as implied by ssNMR, suggests that TCPP vacancies should preferentially occur where chelating coordination would otherwise be required, similar to the reported PCN-224 structure. The presence of diffuse superstructure features in both PXRD and SCXRD further suggest that small domains of vacancy ordering may occur. Both dPCN-224 and MOF-525 are built from Zr 6 clusters, however, MOF-525 only has one cluster orientation, where the primary axes of the octahedron are aligned with the unit cell axes. This straight orientation imposes a more energetically demanding conformation of the TCPP molecules with either fully planar TCPP molecules, or with the carboxylate groups oriented unfavorably perpendicular to the twisted phenyl groups (Fig. S35 and S36). Unlike the MOF-525 models, the six bridging TCPP linkers in dPCN-224 both have twisted phenyl rings and coplanar carboxylate groups, which represents an energetically more favorable situation. We thus conjecture that the formation of MOF-525 with only straight cluster orientations may be hindered by a combination of kinetic limitations and configurational entropy considerations. If TCPP initially attaches to one of the six discussed bridging sites between differently tilted clusters, the 12fold bridging-only coordination of MOF-525 can no longer form. The bridging sites with respect to the tilted cluster are shown in Fig. S37. This may well explain why we consistently obtained dPCN-224 as the dominant structure. While we cannot exclude the possibility of site-isolated MOF-525-like cluster orientations in dPCN-224, possibly in regions of higher coordination, we found no evidence for the formation of ordered domains of the reported MOF-525 structure.
In conclusion, we have resolved the long-standing question regarding the formation of a Zr 8 O 6 SBU within the MOF PCN-221. Based on a combination of local and long-range sensitive structural techniques, we have revealed that the superposition of four statically disordered Zr 6 O 4 (OH) 4 clusters appears on average as a truncated cube, which can easily be misinterpreted as a Zr 8 O 6 cluster. The orientations of the clusters, linker vacancies up to 50%, and the conformation of the TCPP linker are all reminiscent of PCN-224; however, PCN-224 is distinct in that it forms an ordered 3D checkerboard arrangement of linker vacancies and ordered relative cluster orientations. We therefore recommend to describe the structure of PCN-221 as a disordered variant of PCN-224: dPCN-224. The remaining coordination sites at the Zr 6 O 4 (OH) 4 clusters are completed by hydroxy water pairs and modulator molecules. The origin of the linker vacancies was traced back to two different coordination environments in PCN-221 (dPCN-224)-bridging and chelating. While the former is energetically more favorable according to quantum chemical calculations, the relatively flat energy landscape for the different coordination modes and linker conformations, and the high configurational entropy associated with the 12 coordination sites of the Zr 6 O 4 (OH) 4 clusters rationalizes the defect-prone nature of these MOFs. This work thus sheds light on the interplay between network topology, defects, and disorder in Zr-MOFs, and opens up a unique design space by invoking additional degrees of freedom such as correlated cluster orientation, cluster disorder, and cluster-linker binding modes. In the context of these parameters, it may be useful to look for similar phenomena in other MOF systems displaying ordered defect variants and investigate the corresponding differences in properties. Once controlled, these design criteria could unleash a huge untapped potential for directing the functional properties of MOFs.

Data availability
The data supporting the findings of this study are presented within the article and its Supplementary Information files. Datasets are available from the corresponding authors upon request.