Exploring the Solution Formation of UiO Family Hf Metal-Organic Framework clusters with in situ X- Ray Pair Distribution Function Analysis

The structures of Zr and Hf metal-organic frameworks (MOFs) are very sensitive to small changes in synthetic conditions. One key difference affecting the structure of UiO MOF phases is the shape and nuclearity of Zr or Hf metal clusters acting as nodes in the framework; although these clusters are crucial, their evolution during MOF synthesis is not fully understood. In this paper, we explore the nature of Hf metal clusters which form in different reaction solutions, including in a mixture of DMF, formic acid and water. We show that the choice of solvent and reaction temperature in UiO MOF syntheses determines the cluster identity and hence the MOF structure. Using in situ Xray pair distribution function measurements, we demonstrate that the evolution of different Hf cluster species can be tracked during UiO MOF synthesis, from solution stages to the full crystalline framework, and use our understanding to propose a formation mechanism for the hcp UiO-66(Hf) MOF, in which first the metal clusters aggregate from the M6 cluster (as in fcu UiO66) to the hcp-characteristic M12 double cluster, and following this, the crystalline hcp framework forms. These insights pave the way towards rationally designing syntheses of as-yet unknown MOF structures, via tuning the synthesis conditions to select different cluster species. Introduction Metal-organic frameworks (MOFs) are of great interest for a wide variety of applications, including energy storage and carbon capture, and have outstanding chemical tunability. In order to fully exploit the potential of MOFs for real-world applications, however, we must work towards designing syntheses to obtain MOFs with new sorption or catalytic properties, particularly enabled by new or previously inaccessible structures. While to some extent this can be achieved by the use of new geometries and functionalities of organic linker, one of the key components determining the structure of a MOF is the shape and identity of the metal cluster. By increasing our understanding of the inorganic component, we can obtain control over the nuclearity of the cluster, and hence the connectivity of the MOF, which allows us to dramatically change the MOF structure. Zirconium and hafnium are particularly favourable for the design of new MOF structures: in contrast to copper, for example, (which often forms dinuclear “paddlewheel” units), there is a rich variety of known zirconium and hafnium clusters, with a wide range of nuclearities, geometries and coordination denticities. There are in fact over 1300 structures containing between 3 and 21 Zr or Hf ions in their molecular formula – forming either molecular clusters or being part of an extended framework (including MOFs) – in the CCDC (Cambridge Crystallographic Database) alone. From these structures, we can identify a wide variety of Zr and Hf metal-oxide inorganic substructures (derived by removing peripheral ligands), or “core” clusters. The metal ions have high charge density, arising from their +4 oxidation state, and so favour hard donor atoms such as oxygen, to which they coordinate strongly. Therefore, hydroxyl bridges and oxoand hydroxocapped clusters are predominant in the Zr and Hf “core” clusters, and clusters are often found with ligands coordinating through oxygen, such as carboxylate groups. Although the most common cluster motif in Zr and Hf MOFs, e.g. in the UiO family [Error! Reference source not found.], is the M6(μ -O)4(μ -OH)4 cluster based on Zr6O8 octahedra, 8,15,16 the “core” clusters range from small, low-nuclearity molecular clusters through to large structures such as infinite polymeric chains. Just as in other extended metal oxide structures, these metal (hydr)oxide clusters can share vertices, edges, faces and coordination-polyhedra. As these structures increase in nuclearity, they increasingly resemble the structure of high temperature, tetragonal ZrO2. 26 The standard method for synthesising Zr/Hf MOFs is solvothermal synthesis; the choice of solvent affects the MOF metal clusters, the degree of Zr or Hf cluster aggregation being greatly * Cambridge Crystallographic Database, search performed July 2020 affected in particular by the presence of water in the synthesis. In aqueous, and especially aqueous acidic conditions, the distorted-square tetrameric species [M4(OH)8∙16H2O] 8+ is dominant. This cluster is surrounded by a structured coordination sphere of water molecules similar to other nanoparticles in solution. This water coordination sphere is potentially the source of further hydroxide bridges between metal centres during condensation of the clusters. The degree of hydrolysis, and subsequent aggregation, can be modulated by the use of additional reagents, such as acid, which in some MOF syntheses is required to form the crystalline framework, and in others is used to control particle morphology. Monocarboxylic acids are often chosen for this purpose; since they can possess a wide range of metal-ligand binding strengths, a judicious choice of carboxylic acid can “block” coordination sites on the cluster to further nucleophilic attack preventing, in the case of water/hydroxides, cluster aggregation, or for linkers, the formation of multi-cluster framework species. However, while it is now clear that water and modulating ligands are critical to the identity and stability of the resultant metal clusters (from ligand-terminated molecular clusters through to MOFs), the exact interplay of these factors, especially in multi-species reaction mixtures, is not well understood. The degree of cluster aggregation is also directly affected by the temperature and duration of the synthesis. Both heating acidic aqueous zirconium solutions, for example during a solvothermal synthesis, and ageing the reaction mixture, increase the amount of bridging μ-OH between metal centres, and also encourages their conversion to μ-O and μ-OH groups. This therefore favours the formation of higher-nuclearity Zr or Hf clusters. Building on this work, we recently showed that by tuning the synthesis conditions of UiO family MOFs, we can produce MOFs with distinct and different framework topologies, caused by the formation of different nuclearities of different zirconium or hafnium metal clusters. Increasing the temperature, concentration of water and concentration of formic acid modulator allowed us to selectively produce UiO family hafnium MOFs containing larger Hf12 metal clusters [hcp (hexagonal close-packed) UiO-66(Hf), hcp and hns (hexagonal nanosheets) UiO-67(Hf)] instead of Hf6 clusters, which form the fcu (face-centred cubic) topology [Figure 1]. Figure 1 Differences in synthesis conditions of UiO family MOFs lead to the formation of different MOF phases. A synthesis performed with HCl leads to the fcu MOF structure with Hf6(μ O)4(μ -OH)4 ‘single’ clusters, while a synthesis performed with formic acid and water leads to the hcp MOF structure with [Hf6(μ -O)4(μ -OH)4]2(μ -OH)6 ‘double’ clusters: the type and nuclearity of the metal cluster affects the topology via the change in linker coordination site number and geometry. The metal-oxide coordination polyhedra are also shown. Colour scheme: Hf or Zr, blue; O, red; C, black; H, white. Our previous work showed that, due to the similarities between the PXRD patterns of the fcu and hcp MOFs, it is not always immediately obvious that a MOF structure with a different cluster has formed. Despite advances in understanding, including studies on the effects of different variables (including acid modulator and water) on the crystallisation of UiO-66(Zr) (and cerium analogues), a full picture of the formation routes of MOFs – in particular the precrystalline stages of cluster growth – is still far off. In our work on UiO family MOFs, in situ measurements to probe crystallisation of the hcp phase suggested that inorganic (i.e. largely free from organic ligands) pre-crystalline species formed at early stages in the synthesis. Although this inorganic, noncrystalline material is likely to be a key intermediate in the formation and crystallisation of UiO family MOFs, we were unable to determine its identity. Moreover, it is unknown when in the reaction the crucial structural differences between UiO MOF phases emerge (i.e., selectivity of the hcp phase over the fcu); it is unclear whether the different clusters form via different routes, or if they pass through common intermediates; finally, the timing of the cluster interlinking and framework growth, relative to the timing of the formation of the different clusters, has been little explored. Studies on Zr and Hf clusters to track or solve their structures are not straightforward (especially in situ studies of solvothermal syntheses). Bragg diffraction cannot be used to study the critical non-crystalline species. Solution NMR is extremely challenging, as the key nuclei (O, Zr, Hf and Hf, in the absence of organic linker species) all either have large quadrupolar moments (e.g. Q(Hf) = 4.9 b), have low gyromagnetic ratios (e.g. γ(Hf) = -0.682x10 rad/Ts), or are of very low abundance (e.g. O = 0.038 %). While extended X-ray absorption fine structure (EXAFS) methods can identify Zr and Hf species in solution, and are sensitive to species with low abundance, this technique is limited to smaller molecular clusters such as the tetramer and single cluster, due to multiple scattering events reducing the sensitivity required to observe longer-range coordination, such as that seen in the molecular double cluster or in the interlinked MOF. X-ray pair distribution function (XPDF) measurements can acquire structural information on non-crystalline species and are particularly sensitive to heavier elements such as Zr and Hf due to their high electron density. In our previous work, we have shown that ex situ XPDF measurements are sensitive to the identity of the cluster in UiO family MOFs, and can clearly distinguish between isolated Zr atoms, Zr6 clusters, and Zr12 clusters. 16 Ex situ XPDF measurements can detect and differentiate between tetramer and single cluster species in room temperature solutions related to UiO syntheses, and have successfully been used in situ to track the size of interlinked cluster aggregates forming MOF crystallites in solvothermal UiO-66 syntheses, as well as of metal oxido nanoclusters. However, until now, no study has been able to follow both the cluster formation and the coordination of the MOF framework in the same in situ reaction. It is imperative to further explore the in situ formation of Hf and Zr MOFs and their related clusters and precursors, in order to understand their behavior when combined with other species, with different identities and concentrations, which are present under solvothermal conditions. The future of MOF design lies in the rational synthesis of new desired MOF structures, with a range of connectivities and different linkers and subsequently different physical/chemical properties and topologies. In order to do this, through the deliberate design of syntheses to exploit the wide library of possible cluster species, we must improve our understanding of the mechanisms of MOF and MOF-precursor formation. In this work, we bridge the gap between ex situ cluster identification and in situ MOF crystallite growth. We focus our investigation on the UiO-66 family of MOFs, as an archetype of Zr/Hf MOFs. We perform in situ XPDF measurements on reactions of Hfcontaining solutions, under conditions required to form both the hcp UiO-66(Hf) MOF and its molecular cluster precursors. We show that, alongside a careful structure search for plausible cluster models, these XPDF measurements enable us to identify critical cluster intermediates in the materials, including the M6 cluster found in fcu UiO-66(Hf) and the M12 double cluster found in hcp UiO-66(Hf). We also gain insight into the relationship between the cluster formation and the MOF framework coordination. These advances in understanding the stages of growth of UiO family MOFs, including the formation of clusters as precursors, provide routes towards the deliberate and efficient design of MOF syntheses, exploiting the wide library of possible metal cluster species for new and unrealised members of this important class of materials. Experimental Methods No unexpected or unusually high safety hazards were encountered in the course of this work. Synthesis Reaction mixtures were carried out in a 2.5 mm fused-quartz capillary, sealed with a Teflon cap before being loaded into the in situ cell. An aqueous solution of HfCl4 (30 wt%) was prepared through dissolution of HfCl4 (Acros Organics, 99 %) in deionised water and sonication for 10 minutes. The conditions for the synthesis of the hcp UiO-66(Hf) MOF were adapted from Ref. 54, with quantities reduced to account for the smaller in situ reaction volume. The concentrations of HfCl4 and, where relevant, organic linker, were increased to improve signal to noise. The compositions of the reaction mixtures are described below. HfCl4 (4.8 mg, 0.015 mmol) and terephthalic acid (H2BDC) (Alfa Aesar, 98 %, 2.5 mg, 0.015 mmol) were added to a capillary, followed by dry N,N-dimethylformamide (Sigma Aldrich, 99.85 % anhydrous DMF) (65 μL), formic acid (Fisher, 98/100 %) (25 μL) and water (10 μL), then sonicated for 10 minutes. We also carried out reactions without the terephthalic acid ligand, to assess its importance in cluster formation. HfCl4 (116 mg, 0.362 mmol) was sonicated for 10 minutes with dry DMF (6.5 mL), formic acid (2.5 mL) and water (1.0 mL). 0.1 mL of the resulting solution was measured into the capillary. In situ measurements Total scattering X-ray diffraction patterns were collected at beamline i15-1 at the Diamond Light Source using an X-ray energy of 76.7 keV (λ = 0.161669 Å). Initial calibration measurements were performed on a silicon standard. In situ measurements were carried out using a heated steel sample holder with openings for the X-ray beam to pass through the sample. The capillary was positioned so that the beam passed through it close to the base, so that any solid formed during the reaction would not precipitate out of the path of the beam. Once the capillary was loaded, heating was started with a fast ramp, then scattering detection and temperature measurements proceeded at a rate of one scan per minute. Two separate thermocouples measured the temperature of the capillary and of the sample holder. The experimental setup of the hydrothermal cell is shown in Figure S1. Diffraction measurements of capillaries containing pure water and the 65:25:10 DMF : formic acid : water solvent were taken at room temperature and at 150°C for use as backgrounds. In situ experiments were performed at room temperature, 120°C and 150°C. Analysis The diffraction data were integrated using DAWN and processed, with corrections applied for background, meaningful instrument intensity cutoff and polynomial smoothing using the PDFgetX3 software package using the following parameters: qmin = 1 Å , qmax = 22.5 Å , rpoly = 1.24 Å. Structural models were quantitatively refined against XPDF data using the DiffPy-CMI software package. The resolution peak dampening term Qdamp was constrained to Qdamp = 0.035 Å, this value derived from refinement against a Si standard. The delta1 parameter, corresponding to atomic-motion-derived peak broadening in the “high temperature limit” (with a 1/r dependence) was set to 2 Å following an initial refinement and the isotropic displacement parameters (Uiso) were derived from the reported values for Hf clusters, determined from single-crystal data, and set to 0.18 Å for H, 0.075 Å for C and 0.06 Å for O. Uiso for Hf was obtained from refinement of an ex situ sample of hcp UiO-66(Hf) [Figure S2] and subsequently fixed at 0.0069 Å. Refinement of isolated cluster models and the optimised full structure model of hcp UiO-66(Hf) was carried out with refinement parameters set to qmin = 1 Å , qmax = 22.5 Å , rpoly = 1.24 Å and rmin = 1.5 Å. XPDF patterns were simulated using the DiffPy-CMI software package, with the optimised parameters as detailed above. Peak tracking and analysis of processed XPDF and powder X-ray diffraction (PXRD) data was performed using the NumPy and SciPy packages. Results In order to study the in situ formation of UiO-66 family MOFs, we designed a series of experiments based on the conditions used in our lab syntheses of these materials, as summarised in Table 1. While UiO family MOFs are typically synthesised from zirconium salts, in this (as with our previous) work we have used hafnium chloride, due to the chemical similarity of Hf compared to Zr but greater scattering power. While a variety of solvents and conditions have been used across the literature, the majority of our work has focussed on reactions in DMF with formic acid and water. Our XPDF experiments, therefore, used these same reagents. We initially observed the behaviour of our HfCl4 metal salt in water alone as a baseline, since the behaviour of ZrCl4 in water is well-established. We then focussed on a 65:25:10 (by volume) DMF : formic acid : water mixture (referred to below as “DFW 65:25:10”) as a solvent, setting out to elucidate the behaviour of the UiO-related system throughout the reaction at different temperatures. We also investigated whether the stages and rate of cluster formation are affected by the presence of additional coordinating linkers, and explored the timing of the framework growth and crystallinity relative to the cluster formation, by performing reactions at the two different temperatures both with and without terephthalic acid (H2BDC) linker, i.e. reactions with the potential to form UiO-66-type structures (containing BDC, at 150 and 120°C), and molecularcluster-only reactions (no BDC, at 150 and 120°C) [Table 1]. Table 1 Summary of experimental conditions used in the XPDF studies, listing the solvent, nature of linkers (if any) and temperatures used. Experiment Solvent Linker Temperature

Increasing the temperature, concentration of water and concentration of formic acid modulator allowed us to selectively produce UiO family hafnium MOFs containing larger Hf12 metal clusters [hcp (hexagonal close-packed) UiO-66(Hf), hcp and hns (hexagonal nanosheets) UiO-67 (Hf)] instead of Hf6 clusters, which form the fcu (face-centred cubic) topology [ Figure 1]. Our previous work showed that, due to the similarities between the PXRD patterns of the fcu and hcp MOFs, 16,54 it is not always immediately obvious that a MOF structure with a different cluster has formed. Despite advances in understanding, [56][57][58] including studies on the effects of different variables (including acid modulator and water) on the crystallisation of UiO-66(Zr) 41 (and   cerium analogues 59 ), a full picture of the formation routes of MOFs -in particular the precrystalline stages of cluster growth -is still far off. In our work on UiO family MOFs, in situ measurements to probe crystallisation of the hcp phase suggested that inorganic (i.e. largely free from organic ligands) pre-crystalline species formed at early stages in the synthesis. 16 Although this inorganic, noncrystalline material is likely to be a key intermediate in the formation and crystallisation of UiO family MOFs, we were unable to determine its identity. Moreover, it is unknown when in the reaction the crucial structural differences between UiO MOF phases emerge (i.e., selectivity of the hcp phase over the fcu); it is unclear whether the different clusters form via different routes, or if they pass through common intermediates; finally, the timing of the cluster interlinking and framework growth, relative to the timing of the formation of the different clusters, has been little explored.
Studies on Zr and Hf clusters to track or solve their structures are not straightforward (especially in situ studies of solvothermal syntheses). Bragg diffraction cannot be used to study the critical non-crystalline species. Solution NMR is extremely challenging, as the key nuclei ( 17 O, 91 Zr, 177 Hf and 179 Hf, in the absence of organic linker species 60,61 ) all either have large quadrupolar moments (e.g. Q( 177 Hf) = 4.9 b), 62 have low gyromagnetic ratios (e.g. γ( 179 Hf) = -0.682x10 7 rad/Ts), or are of very low abundance (e.g. 17 O = 0.038 %). While extended X-ray absorption fine structure (EXAFS) methods can identify Zr and Hf species in solution, and are sensitive to species with low abundance, this technique is limited to smaller molecular clusters such as the tetramer and single cluster, 30 due to multiple scattering events reducing the sensitivity required to observe longer-range coordination, such as that seen in the molecular double cluster or in the interlinked MOF.
X-ray pair distribution function (XPDF) measurements can acquire structural information on non-crystalline species and are particularly sensitive to heavier elements such as Zr and Hf due to their high electron density. In our previous work, we have shown that ex situ XPDF measurements are sensitive to the identity of the cluster in UiO family MOFs, and can clearly distinguish between isolated Zr atoms, Zr6 clusters, and Zr12 clusters. 16 Ex situ XPDF measurements can detect and differentiate between tetramer and single cluster species in room temperature solutions related to UiO syntheses, 56 and have successfully been used in situ to track the size of interlinked cluster aggregates forming MOF crystallites in solvothermal UiO-66 syntheses, 56 as well as of metal oxido nanoclusters. 63 However, until now, no study has been able to follow both the cluster formation and the coordination of the MOF framework in the same in situ reaction.
It is imperative to further explore the in situ formation of Hf and Zr MOFs and their related clusters and precursors, in order to understand their behavior when combined with other species, with different identities and concentrations, which are present under solvothermal conditions. The future of MOF design lies in the rational synthesis of new desired MOF structures, with a range of connectivities and different linkers and subsequently different physical/chemical properties and topologies. In order to do this, through the deliberate design of syntheses to exploit the wide library of possible cluster species, we must improve our understanding of the mechanisms of MOF and MOF-precursor formation. In this work, we bridge the gap between ex situ cluster identification and in situ MOF crystallite growth. We focus our investigation on the UiO-66 family of MOFs, as an archetype of Zr/Hf MOFs. We perform in situ XPDF measurements on reactions of Hfcontaining solutions, under conditions required to form both the hcp UiO-66(Hf) MOF and its molecular cluster precursors. We show that, alongside a careful structure search for plausible cluster models, these XPDF measurements enable us to identify critical cluster intermediates in the materials, including the M6 cluster found in fcu UiO-66(Hf) and the M12 double cluster found in hcp UiO-66(Hf). We also gain insight into the relationship between the cluster formation and the MOF framework coordination. These advances in understanding the stages of growth of UiO family MOFs, including the formation of clusters as precursors, provide routes towards the deliberate and efficient design of MOF syntheses, exploiting the wide library of possible metal cluster species for new and unrealised members of this important class of materials.

Experimental Methods
No unexpected or unusually high safety hazards were encountered in the course of this work.

Synthesis
Reaction mixtures were carried out in a 2.5 mm fused-quartz capillary, sealed with a Teflon cap before being loaded into the in situ cell.
The conditions for the synthesis of the hcp UiO-66(Hf) MOF were adapted from Ref. 54, with quantities reduced to account for the smaller in situ reaction volume. The concentrations of HfCl4 and, where relevant, organic linker, were increased to improve signal to noise. The compositions of the reaction mixtures are described below.

In situ measurements
Total scattering X-ray diffraction patterns were collected at beamline i15-1 at the Diamond Light Source using an X-ray energy of 76.7 keV (λ = 0.161669 Å). Initial calibration measurements were performed on a silicon standard. In situ measurements were carried out using a heated steel sample holder with openings for the X-ray beam to pass through the sample. The capillary was positioned so that the beam passed through it close to the base, so that any solid formed during the reaction would not precipitate out of the path of the beam. Once the capillary was loaded, heating was started with a fast ramp, then scattering detection and temperature measurements proceeded at a rate of one scan per minute. Two separate thermocouples measured the temperature of the capillary and of the sample holder. The experimental setup of the hydrothermal cell is shown in Figure S1.
Diffraction measurements of capillaries containing pure water and the 65:25:10 DMF : formic acid : water solvent were taken at room temperature and at 150°C for use as backgrounds. In situ experiments were performed at room temperature, 120°C and 150°C.

Analysis
The diffraction data were integrated using DAWN 64 and processed, with corrections applied for background, meaningful instrument intensity cutoff and polynomial smoothing using the PDFgetX3 software package 65 using the following parameters: qmin = 1 Å -1 , qmax = 22.5 Å -1 , rpoly = 1.24 Å. Structural models were quantitatively refined against XPDF data using the DiffPy-CMI software package 66 . The resolution peak dampening term Qdamp was constrained to Qdamp = 0.035 Å −1 , this value derived from refinement against a Si standard. The delta1 parameter, corresponding to atomic-motion-derived peak broadening in the "high temperature limit" (with a 1/r dependence) was set to 2 Å following an initial refinement and the isotropic displacement parameters (Uiso) were derived from the reported values for Hf clusters, determined from single-crystal data, and set to 0.18 Å 2 for H, 0.075 Å 2 for C and 0.06 Å 2 for O. Uiso for Hf was obtained from refinement of an ex situ sample of hcp UiO-66(Hf) [ Figure S2] and subsequently fixed at 0.0069 Å 2 . Refinement of isolated cluster models and the optimised full structure model of hcp UiO-66(Hf) was carried out with refinement parameters set to qmin = 1 Å -1 , qmax = 22.5 Å -1 , rpoly = 1.24 Å and rmin = 1.5 Å.
XPDF patterns were simulated using the DiffPy-CMI software package, 66 with the optimised parameters as detailed above. Peak tracking and analysis of processed XPDF and powder X-ray diffraction (PXRD) data was performed using the NumPy and SciPy packages. 67,68

Results
In order to study the in situ formation of UiO-66 family MOFs, we designed a series of experiments based on the conditions used in our lab syntheses of these materials, as summarised in Table 1. While UiO family MOFs are typically synthesised from zirconium salts, in this (as with our previous) work we have used hafnium chloride, due to the chemical similarity of Hf compared to Zr but greater scattering power. 54 While a variety of solvents and conditions have been used across the literature, the majority of our work has focussed on reactions in DMF with formic acid and water. 16,54 Our XPDF experiments, therefore, used these same reagents.
We initially observed the behaviour of our HfCl4 metal salt in water alone as a baseline, since the behaviour of ZrCl4 in water is well-established. We then focussed on a 65:25:10 (by volume) DMF : formic acid : water mixture (referred to below as "DFW 65:25:10") as a solvent, setting out to elucidate the behaviour of the UiO-related system throughout the reaction at different temperatures. We also investigated whether the stages and rate of cluster formation are affected by the presence of additional coordinating linkers, and explored the timing of the framework growth and crystallinity relative to the cluster formation, by performing reactions at the two different temperatures both with and without terephthalic acid (H2BDC) linker, i.e. reactions with the potential to form UiO-66-type structures (containing BDC, at 150 and 120°C), and molecularcluster-only reactions (no BDC, at 150 and 120°C) [ Table 1]. We start by detailing our approach to model the different clusters present, beginning with the aqueous solution of HfCl4. We then consider the effect of changing the solvent and temperature, and the effect of adding linkers, on the type and evolution of the clusters in these UiO-related systems.

Cluster models
Since there are many possible cluster structures adopted by Zr and Hf in solution, we first identified all the relevant clusters that could be present in our system via a systematic search of the Cambridge Structural Database (CSD). This search yielded over 1300 structures containing 3 to 21 Zr or Hf atoms † (including "infinite" structures with repeating subunits) [ Figure 2 (a)]. We then discarded all structures containing heterometallic clusters and extracted the metal (hydr)oxo core clusters by stripping out the peripheral ligands, giving us more than 170 unique results. Our candidates were then reduced to 25 core clusters by considering only those feasible in typical MOF reaction conditions and within the constraints of our experimental conditions [ Figure 2 (b)]. We then discarded core clusters appearing only once, those with syntheses reported to be irreproducible, and those from syntheses requiring more than a few days (i.e. with reaction times more than two orders of magnitude longer than used in our experiments) or temperatures below 0°C, and further only considered clusters reported to form in reaction mixtures containing water.
The remaining 25 clusters included the classic (fcu) UiO M6 single cluster and hcp UiO M12 double cluster [shown in Figure 1]. † The majority of n<3 search results contained higher-nuclearity clusters, but with the molecular formula reduced to an empirical formula; very few clusters with n>21 are observed.   [18][19][20]79 Initial examination of an in situ XPDF dataset of a linker-free reaction in DFW 65:25:10 solvent [Error! Reference source not found. (c)] revealed that low-r peaks were only experimentally observed in six regions (as illustrated in Figure 3c). We therefore used this constraint to narrow down the 25 chemically feasible core clusters to five [ Figure 3], removing those core clusters with peaks outside these regions. We edited all five core cluster models to obtain the Hf (rather than Zr) analogues, in keeping with the composition of our reaction mixtures. In order to obtain our cluster models, we removed peripheral ligands from the original structures.
However, in our reactions, it is likely that the clusters are coordinated by a combination of carboxylate groups 30 (formate and/or BDC, where present in the synthesis), and water/hydroxide 54 (the tetramer is predominantly coordinated by water only). 25,30 We therefore added coordinating oxygen atoms to the five core cluster models, to allow for the presence of non-specific peripheral ligands while avoiding chemically-unrealistic undercoordinated metal centres.

Hf behaviour in water
Due to the similarity between the calculated XPDF patterns of the five core clusters, we turned to quantitative refinement of the structures against the experimental data with Diffpy-CMI, 66 to determine the composition of our reaction mixtures. To validate our approach, we carried out a refinement, our model ("the five-cluster model") including all five core clusters (as in Figure 3) and allowed their relative concentrations to vary, against an XPDF measurement of our "baseline" solution of aqueous HfCl4 (30 wt%, room temperature). Our refinement converged to give a contribution from the tetramer only [ Figure 4 (a)], as expected, 25,29,32 confirming the viability of this approach, even for structurally closely-related clusters.
A significant misfit in the region around 4.5 Å was found in this initial refinement [ Figure 4 (a)] that was not well fit by the isolated tetramer cluster model. This initial model did not take account of the likely structuring of water as a coordination sphere around the cluster. 33, 34 We therefore augmented our tetramer model by including an additional coordination shell of 24 water molecules, with the oxygens placed using the locations of water and chloride in the crystal structure of zirconyl chloride octahydrate [ Figure S3]. 25,31 The simulated XPDF of this augmented tetramer

Hf behaviour in DMF : formic acid : water solvent
Once we had confirmed the viability of our method to differentiate between structurally closelyrelated clusters, we set out to elucidate the behaviour of the system throughout the reaction in DFW However, the correlations were reduced, and the fit improved, when the tetramer•H2O was used instead of the tetramer in the five-cluster model [ Figure S4 (b)], suggesting that, rather than extra species being present, the refinement was using contributions from the 11-mer to fit the weak signals arising from the solvent restructuring at 7-9 Å [these signals can be seen in Figure S4 (b)].
The refinement was then repeated with the tetramer•H2O and the single cluster only [ Figure 4 ( showing a good fit with a 58:42 ratio of scale factors (albeit correlated), which was an improvement on that obtained from refinement of a mixture of the tetramer (without water) and the single cluster [ Figure S4 (c)], again suggesting some solvent restructuring remains.
Additional refinements were performed to explore the contributions by the tetramer and single cluster separately, and the extent of solvent reorganisation [ Figure S5 (a,b)]. These results overall indicated that the solvent structuring due to water is less obvious than that seen in the XPDF pattern of the tetramer•H2O in water, even though water is in large excess compared to Hf in our sample  16 We also investigated the effect of the presence of additional coordinating linkers by performing reactions at the two different temperatures both with and without terephthalic acid (H2BDC) linker.
For our analysis of these four in situ datasets, we tracked the change in area of specific key peaks in the XPDF [ Figure 5]. Based on our analysis of the room-temperature DFW 65:25:10 dataset [see Figures S4, S5], we established that the area under the peak at 3.5 Å (the nearest neighbour Hf-Hf) is larger for the hexamer than for the tetramer. In all our in situ reactions the area under this peak initially increases, corresponding to a reduction in the proportion of tetramer. This is further corroborated by the increase in the area under the peak at 4.9 Å at the start of the reaction, corresponding to an increase in the amount of next-nearest neighbour Hf-Hf interactions, which also indicates the formation of clusters other than the tetramer. The growth of the peaks at 3.5 and 4.9 Å indicates species of higher nuclearity than the tetramer are forming, but cannot distinguish between the growth of single cluster and the Hf12 double cluster. However, these peaks generally precede the growth of the peak at 9.2 Å, which is only seen in the Hf12 double cluster [ Figure 3], allowing us to distinguish the appearance of the double cluster separate from the single cluster.
While in our room temperature experiments the tetramer is found alongside the single cluster, the elevated-temperature data suggests that once the temperature is raised, higher nuclearity clusters are favoured (as expected 34 ) over the tetramer. As a complementary analysis, we also performed refinements in the same manner as for the room temperature reactions, using the five-cluster model for refinements of each time step in the datasets. These initial refinements [ Figure S6] showed no significant contribution from the nonamer and 11-mer throughout the reactions, meaning that only the tetramer, single cluster and double cluster are present in measurable concentrations. A second analysis was then performed with only these three clusters (i.e. omitting the nonamer and 11-mer) [ Figure S7]. In these refinements of the heated in situ reactions, we always observe the single cluster first, with the double cluster emerging at later stages; this agrees with our analysis from the peak-tracking data.
Due to the high correlation between the proportions of these remaining cluster species, the exact ratios of these species as the reactions progressed could not be confidently determined using this method. However, from the cluster proportions obtained from this refinement [ Figure S7], in all of the in situ reactions, the growth in the concentration of the double cluster occurs alongside a reduction in the amount of single cluster, and there is no delay between the loss of single cluster and the formation of the double cluster. This suggests that the double cluster forms by the direct combination of single clusters, rather than forming directly from the tetramer (a pathway not involving the single cluster) or requiring the breakdown of single clusters into lower nuclearity clusters prior to the formation of the double cluster.
Peaks beyond 11 Å, when considered against our five-cluster model, only arise from intercluster distances in an interlinked framework [ Figure 3]; in our systems, these peaks, such as that at 13.2 Å, correspond to clusters joined by BDC linkers. In the BDC-containing reactions at both temperatures-, the growth of these inter-cluster peaks occurs both following, and at a slower rate than, the intra-cluster peaks. This shows that intercluster coordination occurs following, rather than simultaneously with, the cluster formation, in keeping with our previous work which suggested that the non-crystalline precursor of the framework (i.e. the cluster material) is in large excess prior to the framework coordination and growth. 16 To further understand the behaviour of the linker-containing systems (i.e. with the potential to form a crystalline MOF framework), we also examined the reciprocal-space structure factor, F(Q) [ Figure S8], and tracked the changes at 3.01 Å -1 [shown in Figure 5 for predominantly the single cluster. 56 Although the hydrolysis reactions necessary for cluster interconversion are known to be kinetically hindered, 39 that study employed neither heating nor ageing to overcome these kinetic limitations, so it is surprising that a mixture of single cluster and tetramer was not observed, especially given the lower concentrations of acid and water relative to metal in that study. 56 Our observation in this work of the importance of acid to the formation of the single cluster is corroborated by an EXAFS study, 30 which revealed that the addition of acetic acid to the tetramer in aqueous solution triggers a rearrangement via a (too short-lived to be identifiable) intermediate to form the single cluster. In the EXAFS study, a mixture of the two clusters (as we observed here) was only seen with modulator : metal ratios below 10:1, which is a far smaller ratio than in our work, despite acetic acid being less reactive than the formic acid modulator we use. 39 This difference is likely because the reaction solutions in the EXAFS study were aged for weeks prior to measurement in order to obtain equilibrium, which will greatly affect the degree of cluster hydrolysis and conversion.

The role of water
This paper shows for the first time the formation of the Hf12 double cluster from the Hf6 single cluster. This conversion could be achieved via the hydrolysis reactions common to these Hf and Zr species, via terminal hydroxide groups on the single clusters 54 joining clusters together to give the 12-mer, with its characteristic 'belt' of six μ 2 -OH groups.
The single cluster has the formula [Hf6O4(OH)4]L24 and the double cluster releasing six metal-coordinated water molecules. The joining of clusters alone would give an entropy penalty when considering ΔG for the reaction -this release of water molecules could alleviate the entropy penalty or even make the cluster-joining entropically favourable. While this release of water may seem counterintuitive to our previous observation that water in the synthesis is required for the formation of hcp UiO frameworks, 16,54 we note that this cluster joining reaction requires at least 3 L = (OH) and 3 L = (H2O)} groups on each single cluster (that is, a maximum of 18/24 L sites being coordinated by carboxylate groups); potentially, with less water in the synthesis, insufficient water is present, either in solution or as terminating groups on the clusters, to permit this cluster-joining.
These two observations in this work, of the formation conditions of the single cluster and of the double cluster, therefore help to explain why both water and formic acid are necessary in forming hcp UiO frameworks: formic acid is crucial for the formation of the single clusters, while water is also necessary in order for these single clusters to join to form the double clusters of the hcp framework.

The role of temperature
This paper also shows that the double cluster requires elevated temperatures to form. Compared with studies which did not show any interconversion between pre-synthesised single and double molecular clusters at room temperature, 60  Elevated temperatures also thermodynamically favour processes which result in an increase in entropy. From our discussion of the role of water, the formation of the double cluster is one such process, due to the increase in entropy from the release of structured water upon cluster joining.
As well as the metal-coordinated water released as single clusters join to form double clusters, there is also strong evidence for coordination shells of water -including hydrogen-bonded water -around clusters, 54,82 some which would also be released upon cluster joining. This indicates that higher temperatures favour the formation of the double cluster for thermodynamic, as well as kinetic, reasons.

Framework growth and temperature
Perhaps surprisingly, in this work we observed that that reactions at both 120 and 150°C produced the hcp UiO-66(Hf) framework. This contrasts with our previous work, in which we observed that hcp UiO-67(Hf) required a temperature of 150°C to form (and not 120°C), 16 and also with literature, in which fcu UiO-67(Hf) is usually synthesised at lower temperatures including 120°C. 83 This further suggests that, by adjusting the temperature of the reaction to take advantage of the different rates of cluster condensation and of framework growth, it may be possible to allow more time for the clusters to join together prior to coordination by inter-cluster linkers, and so obtain "multi-cluster" species intermediate between the double cluster and previously-observed infinite 1-D chains, all based on the M6 single cluster unit. 8 Alongside the previous studies, our work with formic acid corroborates that cluster formation in these UiO systems is determined by a complex interplay of temperature, ageing, concentration of metal salt and the type, concentration and pH of acid (which can act as a modulator and as directing groups 43,71,75 ). The complex processes discussed in this work motivate further exploration to enable understanding in greater detail, and hence improved exploitation. With careful control over the timing of linker addition, and consideration of the coordination-site-preferential exchange between linkers and terminating ligands known to occur with molecular double clusters 60 (particularly involving the ligands at the "narrow" ends of the cluster), 16 this enhanced understanding of cluster formation in UiO systems could lead to intentional control of the framework growth, potentially providing routes to ordered mixed-linker frameworks, double-cluster-containing nanosheets such as those we previously reported, 16,54 or as-yet-unknown "multi-cluster" MOFs.

Conclusions
In this work, we have demonstrated that XPDF data can successfully capture the pre-crystalline stages of Hf MOF formation during in situ solvothermal reactions, including distinguishing between different metal clusters in solution. We have used this technique to explore the response of HfCl4 to different reaction temperatures and solvents, in particular those used to synthesise the hcp UiO-66(Hf) MOF, using a combination of refinement and peak area calculations to track subtle changes in the XPDF between different systems and over the course of in situ reactions. In water the dominant cluster form is the tetramer, but in a mixture of DMF, formic acid and water, it quickly begins to convert to the hexanuclear single cluster form even at room temperature; the formic acid is likely to act as a directing group, but we were not able to identify any intermediates in the transition from tetramer to single cluster. Heating this reaction mixture results in an initial decrease in the proportion of tetramer, followed by the growth of the double cluster alongside a reduction in the amount of single clusters. This provides strong support for a mechanism for double cluster formation directly from pairs of single clusters with μ 2 -OH bridges created between them, rather than forming directly from the tetramer or requiring the single clusters to break down and reform larger clusters. No double clusters were observed at room temperature, suggesting that aggregation to form higher-nuclearity clusters is favoured by higher temperatures and the rate of double cluster formation increases with temperature. Once the double clusters form, they then undergo ligand exchange to link together in a framework, with BDC in place of terminating ligands; this framework appears to form directly as a crystalline MOF, with no evidence of a transformation from amorphous to crystalline. Via this analysis we propose a mechanism for the formation of hcp UiO-66(Hf) [outlined in Figure 6].

Associated Content
Supporting Information: Schematic of experimental setup, additional simulations and refinements and in situ F(Q) data.

Author Information
Corresponding Author Matthew J. Cliffe -School of Chemistry, University of Nottingham, Nottingham NG7 2RD, UK; Email: Matthew.Cliffe@nottingham.ac.uk

Conflicts of Interest
There are no conflicts to declare.