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A Database of Ultrastable MOFs Reassembled from Stable Fragments with Machine Learning Models

High-throughput screening of large hypothetical databases of metal-organic frameworks (MOFs) can uncover new materials, but their stability in real-world applications is often unknown. We leverage community knowledge and machine learning (ML) models to identify MOFs that are thermally stable and stable upon activation. We separate these MOFs into their building blocks and recombine them to make a new hypothetical MOF database of over 50,000 structures that samples orders of magnitude more connectivity nets and inorganic building blocks than prior databases. This database shows an order of magnitude enrichment of ultrastable MOF structures that are stable upon activation and more than one standard deviation more thermally stable than the average experimentally characterized MOF. For the nearly 10,000 ultrastable MOFs, we compute bulk elastic moduli to confirm these materials have good mechanical stability, and we report methane deliverable capacities. Our work identifies privileged metal nodes in ultrastable MOFs that optimize gas storage and mechanical stability simultaneously.


Introduction.
Metal-organic frameworks (MOFs) have been the target of recent materials discovery efforts 1-3 due to their promise as catalysts 4,5 and functional materials 6 . Reticular MOFs structures are constructed from inorganic secondary building units (SBUs) and organic linkers, making them highly tunable. 7 For example, one may exchange metal atoms while maintaining SBU connectivity to tune catalytic properties 8 or electronic structure. 9,10 One may alternatively change the SBU connectivity while holding metal identity fixed to change MOF properties. [11][12][13] By varying linker identity and holding the SBU fixed, we can tune the pore size to alter gas diffusion and adsorption properties. 14 One may also decorate linkers with functional groups to influence gas adsorption selectivity 15 and catalysis. 16 Although these design knobs enable MOFs to be useful for gas storage 17,18 , separations 3,19 , and catalysis [20][21][22][23][24][25][26] or give them with novel properties that impart unique conductivity [27][28][29][30] and capabilities for sensing 29,[31][32][33] , these materials face limitations stemming from poor stability. 34,35 Many MOFs that are crystalline after synthesis either collapse upon activation or lack the thermal stability needed for practical applications. [36][37][38] In silico databases play a key role in screening to identify promising materials for gas adsorption and separations. 3,39,40 Although lead compounds can be found in these databases, the activation and thermal stability of the MOFs is generally not considered during database construction. Instead, after computational screening has occurred, expert chemists analyze the best MOFs to attempt experimental synthesis. 3,40 There have been some efforts to compute the likely stability of these MOFs from simulations. 41 However, these simulations are expensive, cannot be carried out exhaustively, and may not faithfully describe experimental outcomes. Because it is challenging to predict the impact of including a novel building block in a MOF, in silico databases have been constructed with limited sets of well-studied building blocks. This ad hoc selection of MOF building blocks and nets in hypothetical databases has led to a bias in hypothetical MOF diversity. 42 Despite their relevance in catalysis, many transition metals that appear in experimental MOFs are entirely missing from hypothetical databases. 42,43 The use of data-driven machine learning (ML) models has enabled the prediction of MOF metal oxidation states 44 , band gaps 45 , and gas adsorption 42,[46][47][48] properties from experimental and computational data. We recently obtained measures of experimental stability using natural language processing (NLP) tools to mine the extant experimental literature. 34,49 We trained ML models that predict the experimental thermal and activation stability of MOFs based on their connectivity 42 and pore geometry. 50,51 This choice of features also permits application of the ML models to assess properties of MOFs in hypothetical datasets.
In this work, we use these ML models to identify experimentally known MOFs from an experimentally characterized database (i.e., CoRE MOF) 52 that are ultrastable. We develop a new approach to separate these MOFs into their building blocks and construct an in silico database from fragments of stable MOFs. Our database contains one and two orders of magnitude more building blocks and nets, respectively, than are present in existing in silico databases 3,39,40 , thus enriching the diversity of transition metals in MOF nodes. This procedure enriches the database with MOFs that are likely to be thermally stable and stable upon activation by one order of magnitude. Because our in silico database MOFs contains nets that have not yet been sampled and could influence MOF mechanical stability in unexpected ways, we confirm that thermally stable and activation stable MOFs remain mechanically stable. [53][54][55][56] We demonstrate an application of this database by simulating the methane deliverable capacity of the resulting MOFs and identifying design rules that make a MOF stable (i.e., with respect to activation, thermally, and mechanically) while being suitable for methane adsorption.

2a. Fragmenting and Representing Reticular Materials
Inorganic secondary building units (SBUs) and organic linkers are arranged in a net with a specific building block stoichiometry and connectivity to produce a MOF (Figure 1). Redundant definitions of what comprises SBUs make in silico MOF construction challenging. In contrast to organic linkers, which are well-defined, definitions of inorganic SBUs frequently but do not always contain fragments of the linkers ( Figure 1). This "double counting" of the same atoms in both MOF components gives rise to challenges in in silico MOF recombination because one set of atoms from the SBU or linker must be removed. For example, UiO-66 is a commonly studied MOF that comprises a terephthalic acid linker and a Zr metal-oxyhydroxy cluster SBU, where terminal carboxyl groups are counted as part of both the SBU and the terephthalic acid linker (Figure 1).
Developing a recombination strategy that overcomes these limitations is necessary for computational design of other materials, such as covalent organic frameworks (COFs) as well. A less ambiguous way to define a MOF structure from mutually exclusive building blocks (i.e., with no overlap in atoms between building blocks) is to consider the underlying connectivity of the MOF molecular graph. Here, we can think of the MOF as a set of nodes and edges pieced together in a graph. The node can be inorganic or organic, but the edge must be organic and have only two connection points that connect two nodes. From these mutually exclusive building blocks, we can reconstruct MOFs from fragments. Inorganic nodes are analogous to inorganic SBUs and are any building block containing a metal (Figure 1). Similarly, organic nodes are any organic components that have greater than two connection points. In contrast, organic edges are organic fragments that have two connection points. The combination of an inorganic node with an organic edge can give rise to many different linkers when the inorganic node has chemically distinct connection points (see Sec. 2b and Supporting Information Figure S1). In some cases, a MOF can lack an organic edge. The commonly studied HKUST-1 MOF has a benzene-tricarboxylic acid (BTC) linker that can be represented by a single inorganic node and a single organic node ( Figure   1). Because there are no organic building blocks that form two connection points in this case, this MOF has no organic edge. By recombining inorganic nodes, organic nodes, and organic edges, we construct new MOFs from their reticular parts. The recombination strategy we take with nodes and edges is general for other materials, such as COFs, that have defined building blocks that are heuristically chosen. [57][58][59]

2b. Existing Hypothetical Databases Lack Ultrastable MOFs
Hypothetical MOF databases have typically been constructed with "tinker-toy" algorithms that recombine MOF nodes and edges to generate in silico databases for screening. 3,39,40 We assess three hypothetical databases that have previously been studied for gas adsorption and analyzed for their relative chemical diversity 42 : 1) hMOF 40 , 2) BW-DB 3 , and 3) ToBaCCo 39 . The databases are composed of tens-to-hundreds of thousands of structures with a limited number of inorganic nodes: hMOF contains 137,000 structures with five nodes, BW-DB contains 300,000 structures with eight nodes, and ToBaCCo contains 13,000 structures with 12 nodes. ML models trained on literature data 34,49 can be used to identify ultrastable hypothetical MOFs by using connectivity (i.e. revised autocorrelations, or RACs) and geometric features (e.g. pore size and surface area) as inputs. 34,49 We define ultrastability as thermal stability that is one standard deviation (87°C) more stable than the average CoRE MOF 49 (average decomposition temperature, Td = 359°C) while simultaneously retaining activation stability (activation stability prediction > 0.5). If such hypothetical materials are ultrastable, then they would merit follow-up study by experiment or simulation, e.g., for applications in thermal catalysis where such stability is a necessity.
The hMOF database is composed of MOFs that are constructed from five inorganic nodes containing V, Cu, Zn, and Zr (Supporting Information Figure S2). As a consequence of the limited number of inorganic building blocks, this database contains six underlying net topologies (pcu, sra, dia, tbo, nbo, and fcu), where 90% of the structures have the pcu topology. 60 The hMOF set contains a large number (~137,000) of structures, and the MOFs in this database are less thermally stable on average compared to CoRE MOFs as predicted by our models (hMOF average Td = 337°C; CoRE MOF average 49 Td: 359°C, Figure 2 and Supporting Information Figure S3).
Although the majority (60%) of the MOFs are predicted to be stable upon activation, few demonstrate ultrastability (Figure 2 and Supporting Information Table S1). In total, less than 1% (i.e., 416) of the MOFs in the hMOF data set are ultrastable, and this number is further reduced when model uncertainty quantification 34,61 is employed to limit predictions to those that are strongly supported by the existing data (Supporting Information Figure S4).

Figure 2.
Predicted stability of members of the hMOF (left) and ToBaCCo (right) databases. ANN models from prior work are used to predict activation stability (unstable: 0 and stable: 1) and thermal decomposition temperature (Td, °C). Data are colored by two-dimensional kernel density estimation (KDE) density values, as indicated by color bars. A solid black line on the x-axis indicates a value of 0.5 for activation stability. The solid black line on the y-axis indicates a Td of 359°C which is the average of the CoRE MOF training data. The dashed lines represent one (87°C) and two (174°C) standard deviations above and below the average of the CoRE MOF training data. Marginal histograms are shown in gray for both plots, with count densities on their corresponding axes. A 1D KDE plot of CoRE MOF Td values is shown as a green line for comparison to both thermal stability Td distributions.
In an effort to build a larger and more diverse hypothetical database for CO2 separation materials, BW-DB was constructed from eight distinct inorganic nodes containing Al, V, Cr, Ni, Cu, and Zn (Supporting Information Figure S5). Together, with 12 distinct net topologies, this hypothetical database consists of more than 300,000 MOF structures (Supporting Information   Table S2). Despite the increased number of structures and nodes sampled in this database, an exceedingly small (i.e., 767 or < 1%) number of the BW-DB MOFs are simultaneously stable upon activation and highly thermally stable (Supporting Information Figures S6 and S7). The average BW-DB MOF is less thermally stable than the average CoRE MOF (BW-DB average thermal decomposition temperature, Td = 335°C). As in our prior observations 34 , we find that inorganic nodes influence thermal stability (i.e. average Td: 296°C for a Cu paddlewheel and average Td: 389°C for a V-oxo cluster). Nevertheless, thermal stability ranges (i.e., variation in Td) for a single inorganic node can span over 300°C due to differences in organic edge or MOF net topology, indicating that judicious choice of organic edge should lead to the discovery of more stable MOFs (Supporting Information Figure S8).
In comparison to hMOF and BW-DB databases, ToBaCCo 39 samples a greater number of underlying net topologies (41 in total) to enrich MOF net diversity. ToBaCCo accomplishes this diversity while only sampling a subset of metals in the SBUs, namely Mn, Co, Cu, Zn, and Zr (Supporting Information Figure S9). Nevertheless, even though ToBaCCo is an order of magnitude smaller in size than hMOF or BW-DB (~13,000 structures), it contains both a larger number (i.e., 750) and percentage (i.e., 6.5%) of MOFs that are predicted to be simultaneously stable upon activation and highly thermally stable ( Figure 2). Despite larger tails for the thermal stability distribution, the average MOF in ToBaCCo is also less thermally stable than CoRE MOFs (ToBaCCo average thermal decomposition temperature, Td = 324°C). Indeed, we find that certain MOF topologies absent from the other two hypothetical MOF sets are enriched among the ultrastable ToBaCCo MOF subset. As an example, the csq topology appears in 603 out of 11,754 (5%) MOFs over the full space but is enriched in the ultrastable subset, with 226 out of 750 (30%) MOFs exhibiting this topology. Therefore, the incorporation of novel and less-explored MOF topologies may enable the design of stable MOFs, although it should be noted that the diversity of the ToBaCCo MOFs relative to the CoRE MOF training data results in many fewer of the predictions being strongly supported according to our uncertainty quantification criteria (Supporting Information Figure S10).
When we use our criterion for identifying MOFs that are stable upon activation and highly thermally stable, many of the inorganic nodes that are associated with high stability in CoRE MOF are absent from the current hypothetical databases. The lack of ultrastable MOFs, as especially evident in hMOF and BW-DB, along with their limited metal diversity motivates the construction of new databases that are enriched with stable MOFs. Given the higher diversity of inorganic nodes along with the evidence of their synthetic feasibility and stability, CoRE MOF is an ideal source of building blocks. The improved stability of ToBaCCo MOFs due to increased net diversity demonstrates the need to study and sample a wider range of nets. We thus devise a strategy to recombine building blocks mined from the CoRE MOF database with increased net diversity to access areas of improved MOF stability.

2c. Constructing New MOFs from Building Blocks Mined from Stable MOFs
To use CoRE MOF as a source of inorganic nodes to generate a new dataset, we adapted our previous strategy of mining SBUs 42,49 to ensure that all inorganic nodes can be recombined to construct new MOFs (see Experimental Methods). With the CoRE MOF dataset, we identify the MOFs that have either 1) been identified as highly thermally stable 34,49 (>1 standard deviation above the mean Td) and stable upon activation according to the published article tied to the MOF or 2) predicted by our models with high confidence 34,49,61 to be highly thermally stable and stable upon activation. Then, we mine and recombine their building blocks to construct novel but likely synthesizable MOFs that we re-evaluate with our ML models.
Using our criteria for ground truth or model-predicted stability, we identify a stable subset of 384 CoRE MOFs that we mine for building blocks (Supporting Information Table S3). Analysis of this subset of MOFs demonstrates that metals that are associated with stability (e.g., Zr) are missing ( Figure 3 and Supporting Information Figure S11). This omission could be due to limited literature reports or due to their absence in the original CoRE MOF subset we used (i.e., CoRE MOF 2019 all solvent removed or ASR). To address this limitation, we curated a set of MOFs that was not deposited with the original CoRE 2019 data set, which we call the "extended CoRE 2019 data set" (Supporting Information). This data set contains structures that were not sanitized (i.e., with solvent molecules removed) and thus not deposited with the other CoRE MOFs. By repeating our text mining analysis and applying our models with uncertainty control, we analyzed 2,123 candidate MOFs and identified 90 additional stable MOFs (Supporting Information Table S4 and Figure S12). This additional set increases the diversity of stable building blocks even further by adding 11 new elements (including Zr) that were not present in the original set ( Figure 3 and Supporting Information Figures S11 and S12). The extended CoRE MOF 2019 data set is also a natural test set with unseen MOFs for our ML models. We confirm on this new set aside test set that we achieve ML model prediction errors comparable to that of the original test set (i.e., Td MAE of 44 °C) by making predictions on points with low uncertainty (Supporting Information Figure S13). We combine these two sets together to obtain 474 stable MOFs from which to mine building blocks. (bottom) Stacked bar plots of the 3d, 4d, and 5d metals present within the stable subset of the original and extended CoRE MOF subsets. All y-axes are shown as relative frequencies, and metals labeled by their two-letter abbreviations.
We also identify organic nodes and edges from the stable MOFs to recombine with the inorganic nodes ( Figure 4 and Supporting Information Figure S14). We developed an automated strategy to identify and avoid 1D rod inorganic nodes that cannot easily be truncated and used for MOF construction (Supporting Information Figure S15). A significant fraction (37%) of the mined inorganic nodes from stable MOFs are 1D rods, with the remaining nodes being finite and suitable SBUs for reconstruction ( Figure 4). Analysis of the mined organic building blocks from stable MOFs indicates that edges with non-carbon or hydrogen heteroatoms are uncommon (3 out of 16, 19%) among the stable subset (Supporting Information Figure S14). While identifying organic edges, we avoid cases that would introduce a geometric mismatch 62 when recombining nodes and edges (see Experimental Methods). For each inorganic node identified to be unique by connectivity 63 , we measured the compatibility of the node with each of the possible nets and selected the structure of the building block that was compatible with the most nets (Supporting Information Figure S16). The final set of building blocks corresponds to 88 inorganic nodes, 32 organic nodes, and 16 organic edges to reconstruct new MOFs (Supporting Information). Atoms are colored as follows: white for H, gray for C, blue for N, red for O, yellow for S, pink for Co, purple for Zn, teal for Zr, and black for X, which represents the connection points of the node or edge respectively.
With our de novo strategy, metal diversity, measured by the unique metals used in inorganic nodes, increases 5-fold for our building blocks relative to the building blocks in most diverse hypothetical database considered (e.g., BW-DB). Comparison of unique inorganic node connectivities (i.e., differentiating between a Zn paddlewheel and Zn trimer) reveals a 10-fold increase in inorganic node diversity relative to the building blocks present in existing databases.   Figure S14 and Table S7). Even these edges, however, can lead to unstable MOFs when combined with specific inorganic nodes. Although the organic edge E13 is enriched in stable MOFs overall, when combined with inorganic node N0, it tends to make more unstable MOFs, depending on the net (unstable MOFs with N0 and E13: 80, ultrastable MOFs with N0 and E13: 49). The enriched stability by MOF building block combination type, however, suggests that MOFs with two inorganic nodes and one edge are enriched in stable MOFs ( Figure   5). Therefore, MOFs with more than a single node should be of increased focus to enrich the design of ultrastable MOFs. This finding contrasts with the focus of existing MOF databases on MOF topologies comprising one inorganic node and one organic edge.

2d. Screening Thermally and Activation Stable Hypothetical MOFs for Mechanical Stability and Methane Deliverable Capacity
Because we are constructing an in silico database of MOFs with nets that have not been explored extensively, we sought to confirm that our MOFs are mechanically stable. This evaluation is important because MOFs that are useful for practical applications must not only be thermally stable and amenable to activation but must also retain structural integrity under mechanical force.
During gas adsorption, MOFs must be able to avoid structural distortion arising from hydrostatic compression 64 that can lead to pressure-induced amorphization. 65 Similarly, during catalysis, MOFs must be able to withstand large thermal gradients and fluxes of reactants and products, requiring MOFs to be both thermally and mechanically stable. 64 Previous studies that have focused on MOF mechanical stability have neglected thermal stability and activation stability due to an inability to predict these properties. 54, 55 We use our ML models and hypothetical dataset construction approach to search for MOFs that simultaneously satisfy our ultrastability criteria (i.e., highly thermally stable and stable with respect to activation 34 ) along with mechanical stability. For these MOFs, we study methane adsorption as a value-added property to analyze tradeoffs between different facets of stability and gas adsorption.
We compute the mechanical properties (i.e., bulk elastic and shear moduli) for the set of MOFs that models confidently predict to be highly stable with respect to the other two properties (see Sec. 2b and Supporting Information Table S8 and Text S1). While the intuitive dependence on pore size (i.e., longer edges leading to weaker materials) of mechanical properties has been previously observed 54 , we now find dependence of the elastic and shear moduli on the identity of the inorganic node ( Figure 6 and Supporting Information Figures S17 and S18). In accordance with prior conclusions on edge length, we find that increasing edge length while holding the inorganic node fixed reduces the elastic modulus (shorter E8: 20.2 GPa vs longer E1: 8.4 GPa).
Altering the identity of the node from Co-based N39 to Gd-based N43 increases the elastic modulus 10-fold (N39: 2.6 GPa, N43: 20.2 GPa) even while holding the wir net fixed ( Figure 6).
Despite the overall reduction in mechanical stability with a longer edge, the MOF with the Gdbased N43 node is still four times more mechanically stable than the same MOF with the Co-based N39 node ( Figure 6). Together, these analyses highlight the simultaneous importance of the inorganic node and organic edge in governing mechanical stability. Figure 6. Three representative MOFs in the wir connectivity net showing variation from the Cobased inorganic node N39 to the Gd-based inorganic node N43, and edge E8 to edge E1. The resulting bulk elastic modulus of each combination of inorganic node and organic edge in a wir net is shown. Atoms are colored as follows: white for H, gray for C, blue for N, red for O, pink for Co, blue-green for Gd, and black for X, which represents the connection points of the node or edge. Beyond the roles of individual nodes and edges, we find that MOFs containing an organic node are about 50% less mechanically stable on average relative to MOFs that do not contain one (Supporting Information Figure S19). Similarly, MOFs constructed from two inorganic nodes are not more mechanically stable relative to MOFs constructed from a single inorganic node, suggesting that their promise as ultrastable MOFs would have to be weighed against both lower mechanical stability and the more complex synthesis routes that would be required to achieve these MOF topologies (Supporting Information Figure S19). Conclusions on elastic modulus generally extend to shear modulus because the two properties are correlated (Pearson's r = 0.88, Supporting Information Figure S20). Analysis of a diverse set of MOFs that our models predicted to be thermally unstable and unstable with respect to activation to confirm that our mechanical stability observations were not biased by a focus on high thermal/activation stability MOFs (Supporting Information Figures S21 and S22). Considering only the ultrastable portion of the data set (9,524 out of 54,139 MOFs, or 18%) has minimal influence on the ranges of elastic moduli (Supporting Information Figure S22).
Due to the expected competing influence of linker length (i.e., from the substituent edge and organic nodes) on methane uptake and mechanical stability, we analyze the tradeoff for designing a mechanically stable MOF with reasonable methane deliverable capacities for MOFs that are thermally stable and stable with respect to activation. Among these compounds, MOFs with longer edges have higher methane deliverable capacities, likely due to increased pore sizes (Supporting Information Figure S23). Although many MOFs with two inorganic nodes are simultaneously thermally stable and stable upon activation, they are rarely mechanically stable  Table S9). For the remaining seven MOFs on the Pareto front that also contain an organic node, all have reduced elastic moduli and are at one extreme of the Pareto front ( Figure 7 and Supporting Information Table S9). The most mechanically stable MOFs in this work have bulk elastic moduli that are comparable to mechanically stable MOFs from prior studies. 54 Finding MOFs with bulk elastic moduli of >50 GPa, however, remains a challenge when simultaneously considering methane deliverable capacity, because MOFs with smaller pores tend to be more mechanically stable 54 (Figure 7).

Figure 7.
The relationship between gravimetric methane deliverable capacity (in cm 3 /g) and elastic modulus (KVRH, in GPa) for all thermally and activation stable MOFs. Each connectivity type is shown in a different color: MOFs composed of one inorganic node and one edge in red, one inorganic node, one organic node, and one edge in blue, and two inorganic nodes and one edge in gray.  Table S9).
Longer aromatic edges such as E8 and E13 are enriched in MOFs that are stable upon activation, thermally stable, and mechanically stable (Figure 7 and Supporting Information). This suggests that focusing on these longer aromatic edges during MOF construction in higher connectivity nets can likely produce MOFs that are ultrastable, in contrast to the focus of experimental efforts on smaller linkers such as benzene-dicarboxylic acid. While these identified MOFs represent leads themselves, these combinations of nodes and edges could also provide starting points for subsequent property optimization, e.g., when paired with linker functionalization strategies that could further increase the number of candidate materials with optimal properties with even modest trade-offs in stability expected to still yield stable materials. Beyond MOFs, combinations of edges and organic nodes can also lead to the discovery of other reticular materials, such as zeolites or COFs, with a set of building blocks that rely less on heuristics and thus have enhanced diversity.
Indeed, previous work on COFs has demonstrated that the consideration of increased net diversity leads to novel materials with promising properties, only two of which corresponded to previously synthesized materials. 57 The stability of the structures, however, remained in question, since there were no models to evaluate which compounds are most likely to be stable in that case.

Conclusions
The tailored active sites and pores in MOFs make them promising candidate materials for We developed an approach to fragment MOFs into their building blocks and recombine fragments of stable MOFs to construct a diverse database. With our de novo reconstruction strategy, our database samples two orders of magnitude more connectivity nets than existing databases and an order of magnitude more metals than existing hypothetical databases, thus better reflecting the diversity present in experimental databases. These novel combinations retained the good characteristics of the parent MOFs: we showed an order of magnitude enrichment in ultrastable (i.e., highly thermally and activation stable) MOFs in this database in comparison to prior databases. We observed a strong dependence on linker chemistry for the MOFs that are the most stable, finding that aromatic hydrocarbon edges are enriched in stable MOFs. An analogous approach is applicable to other reticular materials, such as COFs, that are also typically constructed from heuristically chosen building blocks.
From our database, we screened all thermally and activation stable materials for their mechanical stability and found that our MOFs generally retained good mechanical stability. In real-world applications it is common to screen for a target property that is expected to have inherent tradeoffs against common measures of stability. As a demonstration of the use of our database we considered the relationship between methane deliverable capacities and mechanical stabilities, two properties expected to have opposing relationships with porosity, from the set of thermally stable MOFs that are also stable upon activation. MOFs containing Co-porphyrin, lanthanide, or actinide inorganic nodes in combination with more highly connected nets and longer linkers have the best tradeoff for remaining thermally stable, stable upon activation, and mechanically stable while adsorbing methane, counter to expectations of longer linkers universally weakening mechanical stability. By considering experimental stability during in silico database construction, our database of ultrastable MOFs will accelerate the discovery of new, practically usable MOFs that can be used for high temperature applications. This strategy is expected to be beneficial for other porous materials (e.g., COFs) that can be designed from the ground up from their building blocks.

4a. MOF Building Blocks and Construction.
We study periodic experimental MOF structures that correspond to previously studied 34,49 MOFs obtained from a subset of the all solvent removed (ASR) portion of the CoRE MOF 2019 dataset. 52 Using this set of MOFs, we break down their structures into constituent inorganic nodes, organic nodes, and organic edges for reconstruction of new MOFs (Supporting Information Figure   S15). We define any metal-containing building block as an inorganic node, any organic building block that forms two connections with other units as an edge, and any organic building block with more than two connection points as an organic node (Supporting Information Figures S15 and   S24). We use molSimplify 67 to separate MOFs into their constituent building blocks, assign building block connectivity within an .XYZ file, and identify connection points between building blocks (Supporting Information Figure S24). In order to place compatible building blocks for each net, we used predefined routines in PORMAKE 48 to measure the root-mean-square deviations (RMSDs) of inorganic and organic node building blocks to MOF net templates. We use a suggested 0.3 Å threshold 48 to determine if a node is compatible with a net. Some organic edges have geometries that make them incompatible with most nets 62 because the vectors of the carbon atom to connection point bonds are not collinear. We selected heuristically a cutoff of 150° for this transverse angle to choose edges compatible with MOF reconstruction (Supporting Information Figure S25).
We append the .XYZ file format with extra records containing the non-periodic building block connectivity to construct and store the periodic graph for the MOF. We also append the periodic graph connectivity in the .CIF file. We use this graph in the LAMMPS interface 68 to prepare all input files for energetic minimization using the UFF4MOF force field. 69, 70 We optimize all MOF structures with this force field using LAMMPS for up to 20 minutes. 71 For this step, we modify a previously reported procedure for structural optimization 57 but allow unit cell angles and lengths to change with all other defaults applied (Supporting Information Figure S26).

4b. Machine Learning Features.
We compute revised autocorrelations 42,72 (RACs) on periodic molecular graphs for all MOFs using molSimplify. 67 RACs are products and differences of five atom-wise properties: nuclear charge (Z), identity (I), topology (T), electronegativity (χ), and covalent radius (S) evaluated over a bond difference, d, with a maximum depth of 3. RACs are centered on the metal (metal-centered RACs), centered on linker coordinating atoms (linker-centered RACs), evaluated over the full linker (full-scope linker RACs), or evaluated over the full unit cell (full-scope RACs).
If a MOF has multiple metal atoms, metal-centered RACs are evaluated over each metal and averaged by the number of sites. Any non-carbon or non-hydrogen heteroatom that is part of the linker but is not metal-coordinating is defined as a functional group. There are 134 RAC features after eliminating constant features (Supporting Information Table S10). For the MOFs constructed using PORMAKE 48 , we use the graph connectivity stored in the .CIF file. For the other hypothetical MOF databases (hMOF 40 , BW-DB 3 , and ToBACCo 39 ), we interpret the graph from the atomic coordinates in the .CIF file using molSimplify. 67 We computed geometric properties (e.g., pore volume) with Zeo++, using a nitrogen probe molecule 50,51 with a 1.86 Å radius, resulting in 14 geometric features (Supporting Information Table S11). All models trained in prior work 34,49 used these RACs and geometric features as inputs. Prior to model predictions, all features were scaled based on the model training data.

4c. Molecular Simulation for Mechanical Properties.
All mechanical properties were calculated using the LAMMPS molecular simulation package. 71 We extracted the moduli of elasticity from the 6x6 stiffness matrix. 73 This tensor contains all information about the mechanical properties of a material in the elastic regime of the stress-strain curve. We calculate the stiffness matrix by applying a maximum strain of 1% and evaluating the relative energy difference between the deformed structure and the initial structure.
The initial structures used for mechanical property calculations had optimized and relaxed cells as described in Sec. 2a. All mechanical property calculations used the UFF4MOF 69,70 force field with conjugate gradient minimization for geometry optimization.

4d. Molecular Simulation for Methane Deliverable Capacity.
We performed grand canonical Monte Carlo (GCMC) simulations using the RASPA simulation package 74 to obtain methane uptake at 298 K and two pressures, 65 bar and 5.8 bar, corresponding the ARPA-E target methane deliverable capacity standard. 17 We assumed rigid frameworks from the optimized hypothetical MOF structures and modeled guest-guest and hostguest interactions using a Lennard-Jones potential truncated and shifted at 12.8 Å. The force-field parameters for all framework atoms were taken from the UFF 69 force field. Methane molecules were represented by the united-atom TraPPE force field. 75 All cross interactions were calculated using Lorentz-Berthelot mixing rules. 76,77 Each unit cell was replicated in all dimensions to achieve a minimum cell length which exceeds twice the Lennard-Jones cutoff in order to avoid periodic effects. GCMC simulations were performed for 5000 initialization cycles and 5000 production cycles.

Lead contact
Further information and requests for resources and materials should be directed to and will be fulfilled by the lead contact, Professor Heather J. Kulik (hjkulik@mit.edu)

Materials availability
This study did not generate new, unique reagents.

Data and code availability
The scripts used for MOF construction can be found in the molSimplify

Declaration of Interests
The authors declare no competing financial interests. Figure S1 Nodes and edges that lead to multiple linkers Page S3 Figure S2 Inorganic nodes used in the hMOF database Page S3 Table S1 Counts for hMOFs that can be featurized and are stable Page S4 Figure S3 Distribution of thermal stability for the hMOF database Page S4 Figure S4 Stability predictions for hMOF while accounting for UQ Page S5 Figure S5 Inorganic nodes used in the BW-DB database Page S5 Table S2 Counts for BW-DB MOFs that can be featurized and are stable Page S6 Figure S6 Stability predictions for BW-DB Page S6 Figure S7 Stability predictions for BW-DB while accounting for UQ Page S7 Figure S8 Thermal stability predictions by node in hMOF and BW-DB Page S8 Figure S9 Inorganic nodes used in the ToBaCCo database Page S9  Figure S10 Stability predictions for ToBaCCo while accounting for UQ Page S10 Figure S11 Metals present in the stable subset of CoRE MOFs Page S10 Table S4 Stable MOFs within extended CoRE MOF Page S11 Figure S12 Metals present in the stable subset of extended CoRE Page S11 Figure S13 Set aside test set for thermal stability of extended CoRE Page S12 Figure S14 Edges mined for use in our ultrastable database Page S13 Figure S15 Logic for algorithm to extract MOF building blocks Page S14 Figure S16 Comparison of RMSD distributions for a given node Page S15 Table S5 Attrition rate for MOFs constructed in PORMAKE Page S16 Table S6 Relative frequencies of linkers that appear in ultrastable set Page S16 Table S7 Relative frequencies of linkers that appear in ultrastable set Page S16 Table S8 Convergence statistics for mechanical properties Page S17 Text S1 Details of mechanical property calculations Page S17 Figure S17 Box and whisker plots of mechanical stability edge dependence Page S18 Figure S18 Box and whisker plots of mechanical stability node dependence Page S19 Figure S19 Box and whisker plots of elastic modulus for different connectivities Page S20

Figure S20
Comparison of bulk elastic and shear moduli Page S20 Figure S21 PCA plot of KMedoids sampling for unstable MOFs Page S21 Figure S22 Distributions of properties for stable and unstable sets Page S21 Figure S23 Box and whisker plots of CH4 deliverable capacity edge dependence Page S22 Table S9 Pareto optimal cases for methane deliverable capacity and elastic modulus Page S23 Figure S24 Representative building blocks for MOF reconstructions Page S24 Figure S25 Distribution of angles used to select edges for MOF reconstruction Page S25 Figure S26 Methodology for optimizing MOFs in the database Page S26 Table S10 Details about revised autocorrelation features for MOFs Page S27 Table S11 Details for geometric features of MOFs Page S28

References
Page S29 Figure S1. A representative example of an inorganic node and an organic edge that can lead to multiple different linkers when combined. In this example, we have a node (N0) combined with an edge (E1). Because the inorganic node has both an O-and N-coordinating moiety, it forms linkers with both of these metal-coordinating motifs. Figure S2. The five inorganic nodes used for all MOFs in the hMOF database. The atoms are colored as follows: red for O, gray for C, brown for Cu, purple for Zn, light blue for Zr, and light gray for V. Table S1. Counts for the structures in the hMOF database that can be featurized and are predicted to be in the ultrastable set. We define the ultrastable set as MOFs that have a predicted activation stability value >0.5 and a predicted thermal stability that is one standard deviation (87°C) above average (359°C). Stability predictions are made on the featurizable subset of MOFs.   Figure S5. The seven inorganic nodes used for the MOFs in the BW-DB set. The atoms are colored as follows: red for O, gray for C, blue for N, orange for P, brown for Cu, dark purple for Zn, light blue for Zr, light gray for V, light purple for Cr, dark green for Ba, and light green for Ni. Table S2. Counts for the structures in the BW-DB database that can be featurized and are predicted to be in the ultrastable set. We define the ultrastable set as MOFs that have a predicted activation stability value >0.5 and a predicted thermal stability that is one standard deviation (87°C) above average (359°C). Stability predictions are made on the featurizable subset of MOFs.        Table S4. Summary of the MOFs from the "extended" CoRE MOF internal set that are in the stable subset of MOFs. When a ground truth is available, the ground truth (GT) is used. In other cases, a model prediction (MP) with UQ bounds from previous work (scaled LSD ≤ 0.21 for thermal stability, LSE ≤ 0.19 for activation stability) is used. [4][5] Thermal stability is assigned for MOFs with a predicted or actual Td one standard deviation (87°C) above the training data mean (359°C). Activation stability is assigned for MOFs with a predicted value above 0.5 or an actual stable assignment.  Figure S13. Organic edges used throughout this work. Connection points are shown as "X" atoms and the numbering for edges are given inset. For each edge, the 6-letter CSD refcode is provided along with an underscore and the number for the edge to account for multiple edges in the same MOF.  Figure S14. Algorithm for mutually exclusive building block extraction from existing MOFs. Every step in the process is shown in the workflow as follows: extract organic nodes, inorganic nodes, and organic edges from existing MOFs, and nodes and edges are recombined with a choice of net to construct new MOFs. All steps are shown outlined by blue boxes with arrows connecting each sequential step. For the step of splitting the MOF apart into mutually exclusive blocks, we break that step down further in the red-outlined boxes surrounded by a matching red dashed outline. For the step of detecting and eliminating 1D rod inorganic nodes, we also expand this step out into the steps in green-outlined boxes surrounded by a matching green dashed line. Figure S15. A representative example of net compatibility with a 6-connected building block. Two inorganic nodes that are the same by their molecular graph determinant are compared via their geometry to all of the 223 possible 6-connected (6-c) nets present in PORMAKE 1 . Using the 0.3-Å RMSD cutoff suggested in PORMAKE, we select the node that is compatible with more nets. The number of nets that fall within the RMSD cutoff are indicated inset as a fraction for each inorganic node.    Text S1. Mechanical properties were computed using the formalism outlined in prior work. [8][9][10] We obtained the stress tensor following methods described in the main text (see Methods). Upon calculation of the stress tensor, we obtained both the bulk elastic and shear moduli using the Voight (V) and Reuss (R) methods to get upper and lower bounds. We then obtained the Hill (H) modulus by averaging the Voight and Reuss moduli. After obtaining the stress tensor (C), we computed the Voight and Reuss elastic (K) and shear (G) moduli as follows. We compute the inverse of the stress tensor as the stiffness tensor S: 15 (4 * ( "" + $$ + %% ) − 4 * ( "$ + "% + $% ) + 3 * ( (( + )) + ** )) & = ( "" + $$ + %% ) − ( "$ + "% + $% ) + 3 * ( (( + )) + ** ) 15 Figure S16. Box and whisker plots of the edge dependence of the bulk elastic modulus. We order the edges by the distance between X atoms, which indicates edge length. E11 and E12 do not have any converged results, and E6 (marked with an asterisk) only contains two converged results. The box represents quartile 1 (lower) and quartile 3 (upper) with the median marked in orange. The whiskers extend to 1.5 times the interquartile range above quartile 3 and below quartile 1. Dots represent all points outside of the whiskers. The y-axis is truncated at 50 GPa, eliminating five outlier points for the "none" category that are not shown.  Figure S17. Box and whisker plots of the node dependence of the bulk elastic modulus. We group the nodes by metal identity in the periodic table as indicated in inset labels between each set of vertical lines. The box represents quartile 1 (lower) and quartile 3 (upper) with the median marked in orange. The whiskers extend to 1.5 times the interquartile range above quartile 3 and below quartile 1. Dots represent all points outside of the whiskers. The y-axis is truncated at 50 GPa, which truncates the plot and leads to one outlier point omitted for each of the following nodes: N49, N41, N47, N48, and N45.  Figure S18. Box and whisker plots of the elastic modulus for different MOF connectivities. We label MOFs constructed from 1 inorganic node and 1 edge as 1i1e; 1 inorganic node, 1 organic node, and 1 edge as 1i1o1e; and 2 inorganic nodes and 1 edge as 2i1e. The same data with a truncated y-axis range is shown on the right. The box represents quartile 1 (lower) and quartile 3 (upper) with the median marked in orange. The whiskers extend to 1.5 times the interquartile range above quartile 3 and below quartile 1. Dots represent all points outside of the whiskers.   We order the edges by distance between X atoms, which indicates edge length. E11 and E12 do not have any converged results, and E6 (marked with an asterisk) only contains two converged results. The box represents quartile 1 (lower) and quartile 3 (upper) with the median marked in orange. The whiskers extend to 1.5 times the interquartile range above quartile 3 and below quartile 1. Dots represent all points outside of the whiskers.  Table S9. Deliverable capacities and mechanical properties for Pareto-optimal MOFs from the stable subset for which all properties were computed. The type of MOF (1 inorganic node-1 edge: 1i1e, 1 inorganic node-1 organic node-1 edge: 1i1o1e, 2 inorganic nodes-1 edge: 2i1e), the net, the inorganic node, the organic node, the edge, and the corresponding properties are also listed in the  Figure S23. Representative building blocks extracted from existing experimental MOFs labeled by their refcode in the CSD and whether they are an SBU or linker. One MOF may have multiple building blocks extracted. The final number in the label identifies which building block number (zero indexed) was extracted from the MOF. Inorganic and organic nodes refer to building blocks with > 2 connection points, where the former contains metals while the latter contains only main group elements. Edges are exclusively organic and contain only two connection points. All connection points are shown as black "X" atoms. Atoms are colored as follows: blue for Co, gray for Zn, purple for Tb, brown for C, red for O, light blue for N, yellow for S, white for H, and black for X. All extracted and utilized building blocks are reported in the Supporting Information. Figure S24. The X atom angle (in degrees), which is the angle between the connection angle vectors (e.g. vectors of the C-X bonds), versus the transverse angle (in degrees), which represents the angle between a vector along the C-X bond of one X-connection with the angle between the C of the neighboring X atom, as shown at top. A cutoff of 150° for the X-atom angles selected by trial and error is shown as a dotted black vertical line. This also in practice bounds the transverse angle. Example edges are shown inset, with C in brown, N in light blue, O in red, H in white, and X in black.

Figure S25.
Step-by-step workflow for optimizing MOFs after constructing them from PORMAKE. 1 After construction, MOFs are iteratively optimized using the steepest descent and FIRE algorithms as implemented in LAMMPS. 2 All convergence criteria are shown for each step. This workflow follows a previously proposed workflow to optimize covalent organic framework (COF) structures. 3 "Cell relaxed" corresponds to steps in which both cell angles and cell lengths can change. Atomic coordinates are permitted to relax at all steps in the process. gravimetric pore accessible volume cm 3 /g GPONAV gravimetric pore non-accessible volume cm 3 /g GPOV gravimetric pore volume cm 3 /g GSA gravimetric surface area m 2 /g POAV pore accessible volume Å 3 PONAV pore non-accessible volume Å 3 POAVF pore accessible volume fraction unitless PONAVF pore non-accessible volume fraction unitless VPOV volumetric pore volume cm 3 /cm 3 VSA volumetric surface area m 2 /cm 3 r crystal density g/cm 3