High-throughput screening of metal–organic frameworks for macroscale heteroepitaxial alignment

The ability to align porous metal–organic frameworks (MOFs) on substrate surfaces on a macroscopic scale is a vital step towards integrating MOFs into functional devices. But macroscale surface alignment of MOF crystals has only been demonstrated in a few cases. To accelerate the materials discovery process, we have developed a high-throughput computational screening algorithm to identify MOFs that are likely to undergo macroscale aligned heterepitaxial growth on a substrate. Screening of thou-sands of MOF structures by this process can be achieved in a few days on a desktop workstation. The algorithm ﬁlters MOFs based on surface chemical compatibility, lattice matching with the substrate, and interfacial bonding. Our method presents a simple and computationally eﬃcient measure of the interfacial energy that considers both bond and defect formation at the interface. Further, we show that this novel approach is a better predictor of aligned heteroepitaxial growth than other, established, interface descriptors by testing our screening algorithm on a sample set of copper MOFs that have been grown heteroepitaxially on a copper hydroxide surface. Application of the screening process to several MOF databases, revealed that the top candidates for aligned growth on copper hydroxide comprise mostly MOFs with rectangular lattice symmetry in the plane of the substrate. This result indicates a substrate-directing eﬀect that could be exploited in targeted synthetic strategies. We also identiﬁed that MOFs likely to form aligned heterostructures have broad distributions of in-plane pore sizes and anisotropies. Accordingly, this suggests that aligned MOF thin ﬁlms with a wide range of properties may be experimentally accessible.


Introduction
Metal-organic frameworks (MOFs) are a class of materials formed by connecting metal nodes and organic links into an extended network. During the past two decades, a focus of MOF research has been to develop synthetic strategies for the precise control of pore structure and functionality on the single-crystal scale. 1 However, more recently, extending the design principles of MOF chemistry from single-crystal to the macroscopic dimensions (nm to cm) has garnered significant interest. [2][3][4] Approaches to MOF thin-film fabrication include layer-by-layer synthesis, liquid-phase epitaxy and chemical vapor or atomic layer deposition. 5,6 However, these techniques have yielded partially oriented thin films with out-of-plane alignment only. 2,[7][8][9] To fully realize the potential of crystalline MOF thin films in applications such as optoelectronics, gas separation, and sensing, alignment in both in-plane and out-of-plane directions is required. 3,6 Recently, Falcaro and co-workers developed a one-pot methodology for the fabrication of centimeter-scale MOF films that achieved both in-plane and out-ofplane alignment. 10 In this case, pre-aligned crystalline copper (II) hydroxide (Cu(OH) 2 ) nanobelts were used as a sacrificial substrate for the epitaxial growth 11 of copper-based MOFs and precise pore alignment was confirmed by comprehensive diffraction experiments.
It was found that a necessary condition for epitaxial growth was a close matching between the MOF and Cu(OH) 2 lattice parameters. Such macroscale alignment was demonstrated only for seven MOFs, which represents a very small subset of known MOF structure types and functionalities. To fully exploit this fabrication strategy, an efficient procedure for selecting MOFs that possess lattice parameters that match those of the Cu(OH) 2 substrate from the vast database of known structures is essential.
Materials design through high-throughput computational screening offers a low-cost strategy to efficiently guide experimental endeavors. In recent years, advancements in computer hardware and the development of open databases of experimental and theoretical material properties, which are continually growing, has led to rapid growth in this research area. [12][13][14] Indeed, high-throughput screening of candidate materials for aligned heteroepitaxial growth of MOFs would avoid an arduous and inefficient experimental approach. To this end, we have developed a high-throughput screening process to select and rank MOFs based on their likelihood to form aligned crystallites on a Cu(OH) 2 substrate. Although an atomic-level description of the growth mechanism and interfacial chemistry is necessary to fully characterize the kinetics and thermodynamics of these MOF films, such considerations are not amenable to rapid screening. 4,[15][16][17][18][19] Instead, we have extended established methods for evaluating interfacial lattice matching 17,[20][21][22][23][24] and chemical compatibility 25 to assess MOF-substrate in-teractions in a manner that accounts for framework porosity and allows for high-throughput screening. Geometrical lattice-matching algorithms 20,21 have been employed in many screening studies as they offer an efficient way to exclude incompatible interfacial structures based on lattice mismatches. 17,[22][23][24][25] However, chemical compatibility at the interface is expected to be a more discriminating measure of interfacial stability than lattice matching. 24,25 For example, Walsh and co-workers have reported an efficient screening process for matching contact layers in hybrid perovskites that considered the chemical compatibility at the interface by calculating the overlap of atoms on either side of the interface. 25 Although this approach was demonstrated to be effective for non-porous solids, in this present work we show that the atomic site overlap is not the most suitable measure of interfacial binding for highly porous materials such as MOFs. We identify a simple and easily computed proxy for the interfacial energy that considers the difference between the number of bonds formed and broken as a result of interface formation, which accurately predicts macroscale alignment of MOFs on a Cu(OH) 2 substrate. Application of our screening process to the CORE MOF, 26 hMOF, 27 and TOBACCO 28,29 databases shows that specific MOF topologies are favored for aligned growth from Cu(OH) 2 , but that a wide range of pore network properties can nevertheless be obtained. Such knowledge will underpin design principles that will lead to a significant decrease in the experimental workload to develop precisely aligned MOF films.

Computational Approach
We have applied a three-step screening process: (1) selection of candidate MOFs based on chemistry (in this study, MOF structures were searched for that possess copper-bound carboxylate functionalities); (2) refinement of the data set based on lattice matching; and (3) ranking of MOFs by interfacial bonding (see Figure 1). Step Figure 1: Flow chart of the screening process, in which a database of MOF crystal structures and a target substrate crystal structure act as inputs. The MOF database is filtered toward a smaller list of candidate structures for aligned heteroepitaxial growth. Each step is illustrated schematically on the right.
Step 1 filters the database for MOFs that contain a carboxylate functionality bound to copper atoms and do not contain any metal other than copper.
Step 2 checks if matching supercells (e.g. those outlined in solid lines, with dashed lines the corresponding unit cells; in this example the red supercell is the same size and shape as the unit cell) exist for a given MOF-substrate pair.
Step 3 checks all possible supercells for interfacial bonding, allowing for translations along the supercell vectors. this process: for example, ∼5000 structures were screened in ∼25 hours on six processors.
In general, crystallographic information files (CIFs) are used as the input for the MOF layer (film) and a single crystal structure (also from a CIF) is used as input for the substrate layer (Cu(OH) 2 in the following work). A definition of atom-atom binding across the interface between the two materials is also required. This work focuses on the epitaxial growth of MOFs from a metal-hydroxide surface (specifically carboxylate-bound copper MOFs on Cu(OH) 2 ); however, the screening algorithm is not fundamentally limited to these specific systems.

Identifying Structures with Appropriate Chemistry
Step 1 of the screening process is designed to filter out all MOFs that do not possess the appropriate chemistry to bind to the substrate. This step can be generalized to any binding chemistry. The algorithm uses the Atomic Simulation Environment (ASE) 30 and pymatgen 31 Python libraries (description provided in Supporting Information Section S1). In this study, the search was limited to MOFs containing copper nodes and carboxylate functional groups with both oxygens bound to a copper atom (see Figure 1). This constraint was guided by experiments by Falcaro and co-workers, in which Cu(OH) 2 acted as a sacrificial substrate and metal source for the MOF. However, there is no experimental evidence that heteroepitaxial growth of MOFs is limited to sacrificial substrates or to MOFs of the same metal as the substrate. Walsh and co-workers 22 have suggested that the chemical similarity of both sides of the interface (defined in their work by the difference in Pearson hardness between the metals in the two environments) is a driving force for stability at the interface. According to this criterion, copper-based MOFs on a copper-based substrate are expected to produce stable interfaces.

Identifying Structures with Matching Lattices
Step 2 of the screening process determines whether at least one Miller plane of a given MOF matches the lattice dimensions of the target substrate. In this work, the (010) Miller plane of Cu(OH) 2 32 was selected as it is known from experiments that this plane is exposed at the surface of this material. 10 Zur and McGill 20,21 have developed an efficient geometrical latticematching algorithm that has been widely adopted and shown to predict heteroepitaxial interfaces consistent with experimental data. 17,[23][24][25] The lattice-matching algorithm requires that the translational symmetry of each lattice matches at the interface within a specified tolerance. Although lattice matching is not a sufficient condition for growth, poor lattice matching can impact interfacial growth and can be used to rule out candidate structures for aligned MOF films. For example, large lattice mismatches have been found to anisotropically limit the size of hybrid perovskite crystals/grains in the direction of high mismatch. 25,33 Given a set of primitive vectors for a specified lattice on one side of the interface (the unit cell), the algorithm (implemented using the pymatgen Python library 31,34 ) produces a series of supercells made up of an integer multiple of contiguous unit cells. A supercell is defined by two lattice vectors, which are reduced such that the supercell is unique. 20,21 A pair of supercells on either side of the interface, with match areas m times the MOF unit cell area and n times the substrate unit cell area, are deemed to match based on four criteria: (1) the supercell match areas are below a defined threshold (set to the smaller of 90× the substrate unit cell area or 9× the film unit cell area), (2) the area ratio,

Identifying Interfaces with Favorable Binding
Even if MOF and substrate lattices are found to match, chemical compatibility at the interface is expected to be the major factor in determining interfacial stability. 20 where S A and S B are the number of binding atoms in the substrate and film binding planes, respectively, and S C is the number of coincident atom pairs at the interface. Throughout this work, two atoms on either side of the interface were defined as coincident (bonded) if their separation in the 2D binding plane was less than the mean of their ionic radii (0.96Å for copper (0.57Å) and oxygen (1.35Å)). 37,38 This definition for the ASO has previously been applied to determine the chemical stability of contact layers in hybrid perovskites; 25 however, for interactions involving porous structures, such as MOFs, it yields low ASOs in general due to the disparity between the number of binding sites per unit area in the MOF and substrate layers as a result of the porous MOF structure. 22 Therefore, we have redefined the ASO to be a function of the coordination of the MOF binding sites only as where S C is the number of MOF (film) binding atoms that form bonds with the substrate and S B remains the number of film binding atoms, as defined above. Thus, the ASO describes the proportion of MOF binding atoms that can form bonds with the substrate.
The atom positions in a given supercell are not uniquely specified, but can be varied by rigid translations of the lattice along the supercell vectors without changing the supercell itself. We use a Metropolis Monte Carlo (MC) algorithm to apply random rigid translations along the MOF supercell vectors with respect to the fixed substrate to find the maximum ASO (see Supporting Information Section S4 for details). For computational simplicity, we assumed rigid MOF and substrate structures (we also did not consider the possibility of surface reconstruction); however, flexibility is implicitly taken into account by the latticematching and binding tolerances used in screening steps 2 and 3. Rigid frameworks could lead to false negatives in the screening process as structural relaxation could enhance interfacial binding. Nevertheless, we found that the rigid approximation yields sufficient agreement with experimental results while allowing efficient screening (see Section 3.1). Structural distortions of the MOF framework 10,16 and in-plane rotations that afford improved epitaxial matching 39 have previously been shown to relieve interfacial stress in MOF heterostructures.
Accordingly, our screening process accounts-either explicitly or implicitly-for mechanisms by which interfacial stress can be reduced by considering multiple interface orientations and inherent MOF flexibility.
As MOFs are formed from metal nodes and organic linkers, slicing their crystal structures without breaking strong covalent bonds (that may be part of the organic linkers) is non-trivial. 22 We use a bond network approach to determine appropriate binding planes when slicing a MOF crystal at a particular Miller plane (see Supporting Information Section S3), which introduces missing linker defects (i.e. removes the entire linker) when covalent bonds of the linker are broken by the slicing process. This approach is similar to that used in recent work that applied a graph network analysis to determine the most stable way to slice a crystal structure based on the assumption that the most stable slice minimizes the number of broken bonds. 40 A missing linker defect results in coordinatively unsaturated metal centers in the MOF near the binding plane, which is likely to be energetically unfavorable with respect to the pristine structure. 41 However, we note that a number of MOFs possessing defect sites are known to retain their structural integrity. 16,[41][42][43] As the ASO does not account for the number of dangling or non-coordinated MOF atoms that are not carboxylate oxygens, thermodynamically unstable interfaces with a large proportion of dangling bonds can potentially have high ASOs and thus falsely predict macroscale aligned heteroepitaxial growth.
Therefore, we propose a novel geometric measure of interfacial binding that is similar to the ASO, but also considers the number of dangling MOF bonds at the interface and thus is expected to be a better proxy for the interfacial energy. We call this quantity the change in interfacial bonds or ∆IB and define it to be where n formed is the number of MOF binding atoms that make bonds with substrate binding atoms and n broken is the number of bonds broken when building the interface that do not form bonds at the interface, S C and S B are as defined earlier, and S D is the number of MOF non-binding atoms with dangling bonds. ∆IB is identical to the ASO if no missing linker defects (broken bonds) are introduced when building the binding interface, but decreases relative to the ASO with increasing numbers of missing linker defects. We contend that considering the energetic cost of forming the interface using ∆IB provides a more accurate measure of interface stability than previously used geometric descriptors. Indeed, in Section 3.1.2 we demonstrate the superiority of the ∆IB over the ASO as a predictor for aligned heteroepitaxial growth of MOFs.

Structural Characterization
We measured crystal structure porosity using Zeo++, 44 which applies a Voronoi decomposition to model the void space in a crystal structure and, due to its efficiency, has been widely employed for high-throughput screening processes. 12,[45][46][47] Where applicable, all Zeo++ calculations used a probe radius of 1.82Å to represent N 2 . The pore-limiting diameter (or largest free sphere) was calculated along each of the three crystallographic axes using the resex command in Zeo++. All structures were rendered with OVITO. 48 3 Results and Discussion

Validation of Screening Methodology
We validated our screening algorithm and determined an optimal set of parameters for each step and substep by comparing the results to experimental data obtained for a series of aligned MOFs heteroepitaxially grown through a one-pot synthetic method on a Cu(OH) 2 (010) surface. 10 The experimental MOF data set (given in Supporting Information or for MOF-on-metal-oxide or MOF-on-metal interfaces (20× the unit cell area for the MOF or metal/metal-oxide). 22 A limit on the number of unit cells in the supercell was imposed because large-area interfaces are unlikely to form without defects. Thus, comparison of computed results for very large match areas with experiment is not expected to be meaningful.
An analysis of the effect of varying the tolerances and maximum area constraints on the final results for a test database found that the chosen parameters provide robust results (see Supporting Information Section S2).     (Table S3). Screening of materials, including MOFs, for heteroepitaxial growth using the lattice-matching algorithm 20,21 has previously shown that top candidates can be determined by ranking matching lattices by their minimal coincident match area (or the smallest unit-cell multiple that yields a matching lattice). 17,22,23 This is because interfaces with smaller match areas (and smaller mismatch) are expected to have fewer defects. 20,21,25 Figure 2a shows that the minimum coincident match area does not distinguish between MOFs that undergo aligned heteroepitaxial growth and those that do not; furthermore, in some cases for which such growth occurs, the MOF interface that grows on the substrate is not the one with the minimum match area. On the other hand, Figure 2b shows that the minimum ratio of the MOF and substrate unit-cell areas for all Miller planes successfully categorizes almost all the MOFs in the experimental data set and suggests that a small ratio of MOF and substrate unit-cell areas is correlated with aligned heteroepitaxial growth.
Both the minimum coincident match area and unit-cell area ratio are geometrical descriptors that do not consider the chemistry at the interface and are significantly faster to calculate than the ASO or ∆IB. But the neglect of interface chemistry misses crucial features of interface formation. For example, in each of the cases in Figure 2a for which the lowest match-area interface is not one that is known to exhibit heteroepitaxial growth, the MOF binding interface comprises pairs of carboxylate groups bound to the same copper paddlewheel that are each at approximately a 45 • angle to the plane of the interface. Such binding configurations would require significant distortion of the MOF and/or substrate structures to avoid steric clashes and form stable interfaces, which is exemplified by their low ASOs and ∆IB (not shown in Figure 2). Figure 2b suggests that aligned heteroepitaxial growth occurs for a unit-cell area ratio below about 10. However, several MOFs in the validation data set have Miller planes that satisfy this criterion but are not observed to undergo aligned growth on Cu(OH) 2 . By contrast, the ∆IB descriptor, which does account for bonding between atoms at the interface, correctly categorizes almost all of the MOF interfaces that grow aligned on Cu(OH) 2 , as shown in Figure 2d, without predicting aligned growth for Miller planes that have not been observed. On the other hand, the ASO, which also considers interfacial binding between atoms and has previously been used to categorize heteroepitaxial growth, 25 does not appear to be as good a predictor of aligned heteroepitaxy as ∆IB, as indicated by the lack of any obvious trend in Figure 2c.   Figure 3a). Second, small changes to the unit-cell vectors modify the spacing between atoms in the supercell, which can impact the coincidence of atoms at the interface. Figure 3f shows the orientation and lattice spacing that gives rise to the ASO of 1 for CuBTC-g and an example interface with a maximum ASO ≈0.33 for the other CuBTC crystal structures.
These issues could potentially be partially resolved by using less stringent interface bonding criteria, but large tolerances required to yield comparable ASOs for all crystal structures for the interface in Figure 3b would likely lead to spurious lattice and binding matches for other MOFs. On the other hand, the maximum ∆IB is comparable and low for all CuBTC crystal structures (Figure 2d). Thus, ∆IB does not show the same sensitivity to the crystal structure lattice parameters as the ASO and so appears to be a more robust descriptor for aligned heteroepitaxial growth.   Topos-specific codes). 56 The cluster representation separates the atomic net into building blocks (such as the metal clusters and organic linkers), which are then treated as nodes to determine the underlying network topology. Structures listed as unknown did not have cluster representation topology entries in the database. Similar to what was found for the limited experimental data set in Figure 2, there is no clear correlation between the maximum ∆IB and the ratio of the unit-cell areas for the MOF structures in the CORE MOF database. Although all structures with high ∆IB values correspond to low unit-cell area ratios, the converse is not true, with structures with low ∆IB exhibiting a wide range of unit-cell area ratios. Therefore, the data suggests that a low ratio of unit cell areas does lead to favorable interfaces, as has previously been suggested, 22  shown experimentally to grow aligned from Cu(OH) 2 (one of these structures, NEJRUR, was in the parameterization data set). 10 Top candidate CEHPIP (Figure 6b) corresponds to an interpenetrated MOF that is isoreticular to CuBDC-BPY, in which the BDC linker has been replaced with 1,4-cyclohexanedicarboxylic acid. CEHPIP also has an underlying pcu topology. Top candidate ZAZBUZ (tfc topology) is made up of BDC linkers bound to chain-like copper nodes, rather then the paddle-wheel in CuBDC (Figure 6e) and the top candidate ZECKID has a dia topology (Figure 6d). Two binding planes (equivalent within a 90 • rotation) for the same Miller plane of ZECKID were found with the same maximum ∆IB, one of which was excluded manually upon visual inspection of all top candidates.

Cost of Interface Formation on Chemical Compatibility
Finally, one of the top candidates corresponds to an interpenetrated MOF (UNABUH, Figure 6e), which has an unknown topology by the cluster representation (using the standard unsimplified representation, it has a tfs topology).  Figure 5a). Furthermore, the Miller planes that meet the ∆IB criteria for top candidates for aligned heteroepitaxial growth have approximate rectangular symmetry, as indicated by their in-plane unit-cell lattice vectors (Supporting Information Figure S10a).
These findings suggest that the rectangular symmetry of the (010) plane of Cu(OH) 2 selects out top candidates for aligned heteroepitaxial growth with similar symmetry. Note that MOFs with pcu and other similar topologies that commonly have at least one lattice plane with rectangular symmetry have been shown previously to exhibit in-plane alignment when grown via heteroepitaxy; 39,57 importantly, the pcu topology has been shown to produce superior internal surface areas compared with other MOF topologies, suggesting that the ability to target pcu MOFs with heteroepitaxy could be beneficial for developing useful MOF heterostructures. 58 The top candidate structures comprise mostly interfaces with one carboxylate binding site per unit cell (or two oxygen binding sites per unit cell), similar to the experimental data set ( Figure 6). Note that MOFs with topologies other than pcu have high maximum ASOs, while their maximum ∆IB is significantly diminished due to the number of missing linker defects required to form the interface. This result suggests that certain topologies may not grow heteroepitaxially due to the difficulty of cleaving the crystal structure at a planar interface without breaking a large number of bonds.

Selective MOF Growth by Topology
Experimental data 10 as well as the top candidates found using our screening process on the CORE MOF database suggest that the rectangular symmetry of the (010) Miller plane of Cu(OH) 2 preferentially selects MOFs with at least one Miller plane with rectangular symmetry. The majority of selected MOFs were found to also have pcu topology, a topology that often corresponds to structures having lattice planes of rectangular symmetry. The ability to select a specific MOF topology could greatly aid the development of MOF heterostructures and provides a design principle for further experimental study. To investigate whether selectivity by MOF topology is expected to occur generally for Cu(OH) 2 , we applied our screening process to two other MOF databases, the TOBACCO database 28,29 and the hMOF database, 27 which contain hypothetical MOF structures that were built using in silico structure generation. The TOBACCO database contains approximately 13 000 noninterpenetrated MOF structures constructed from a diverse range of metal nodes, organic linkers, and underlying network topologies. 28,29 Figure 7a   which supports the assertion that the pcu topology is favorable for aligned growth on the Cu(OH) 2 substrate. As observed for the other two MOF databases, these top candidates for aligned growth also have binding planes with approximate rectangular symmetry (see Supporting Information Figure S10c). Figure 7b also

Templating pore architecture through epitaxial growth
Intuitively, aligned heteroepitaxially grown MOF crystals could lead to anisotropy in the pores along the different directions with respect to the substrate. To test this hypothesis, we calculated the pore-limiting diameters in the a, b, and c crystallographic dimensions for all pcu MOFs in the hMOF database whose maximum ∆IB occurs for a Miller plane with h + k + l = 1 (a subset of those in Figure 7b). This subset of MOFs was chosen because, for the pcu topology, it can reasonably be assumed that the pore windows align with the three crystallographic axes of the MOF for these Miller planes, for which the pore-limiting diameter was calculated. Supporting Information Figures S12 and S13 show that the distribution of the maximum in-plane pore-limiting diameters does not differ substantially from the distribution of the maximum overall pore-limiting diameters of their crystals. High ∆IB MOFs that are predicted to have aligned heteroepitaxial growth have a similar distribution of in-plane pore-limiting diameters to low ∆IB MOFs, which suggests that epitaxial growth does not constrain the in-plane pore-limiting diameters as a result of the registry with the substrate lattice. This suggests that a broad range of possible pore sizes can be achieved for a given substrate and, therefore, MOFs with precise pore sizes can be chosen for target applications.
Falcaro and co-workers 10 showed that macroscale alignment of the CuBPDC MOF on a Cu(OH) 2 substrate could be employed to align fluorescent molecules within the MOF and yield anisotropic fluorescence from the MOF film. It follows that anisotropy of the pore network is an important design aspect for MOF thin films that could be controlled through in-plane heteroepitaxial alignment. Furthermore, the directionality of the pores with respect to the surface due to a preferred crystal orientation has been shown to impact adsorption properties of porous-coordination polymers, 59 and such properties can be predicted once the in-plane orientation is determined. To investigate this concept further, we calculated the pore network anisotropies from the pore-limiting diameters along the three crystallographic axes (described above) for each pcu MOF in the hMOF database with a maximum ∆IB ≥ 0.67 associated with a Miller plane with h + k + l = 1. Pore network anisotropies were calculated as either the ratio or the absolute difference between the maximum in-plane pore-limiting diameter (PLD in-plane,max ) and the pore-limiting diameters in the other two crystallographic dimensions (the minimum in-plane pore-limiting diameter (PLD in-plane,min ) or the out-ofplane pore-limiting diameter (PLD out-of-plane )). Figure 8 shows that the top candidates from our screening process for the hMOF database cover a broad range of anisotropies and pore shapes (using either definition), including some very anisotropic pore networks. While this allows for the selection of the desired pore properties for a target application, we note that the definition of anisotropy that matters will be different for certain applications. For example, a MOF in which all three pores are large may have high anisotropy with respect to the difference between the pore sizes, but low anisotropy with respect to their ratios. This type of pore network would not provide any noticeable anisotropic effect for the adsorption of relatively small molecules, but may be useful for some other application, such as alignment of large guests.  Figure 8: Pore network anisotropy for all MOF structures in the hMOF database predicted to grow aligned on Cu(OH) 2 whose maximum ∆IB is associated with a Miller plane where h + k + l = 1: (a) ratio and (b) absolute difference of the largest in-plane pore-limiting diameter (PLD in-plane,max ) and minimum in-plane pore-limiting diameter (PLD in-plane,min ) versus that of the largest in-plane pore-limiting diameter and out-of-plane pore-limiting diameter (PLD out-of-plane ). Points are colored by the value of the maximum ∆IB and only those with a second highest ∆IB < 0.67 are shown.

Conclusions
We have developed a robust and efficient screening process of metal-organic frameworks (MOFs) for aligned heteroepitaxial growth on metal-hydroxide substrates, which we have validated by comparison with experimental measurements. 10 This process applies a geomet-rical lattice-matching algorithm 20,21 and extends previous methodologies for determining chemical compatibility at an interface 25 to filter and categorize MOF structures. We have proposed a novel metric for the favorability of interfacial binding, ∆IB, which is simple and efficient to compute and accounts for both the energetic gain of bond formation and the energetic cost of broken and dangling bonds. Importantly, our screening process can be generalized to cases other than those studied in this work. The MOF in the experimental data set made from the TDC linker was found to be an outlier in the validation of the screening process, which we suggest could be due to experimental difficulties associated with the solubility of that linker. This finding highlights the need to consider the chemistry of the MOF building blocks of any top candidates generated by computational screening before further experimental evaluation. Our screening process does not consider the kinetics or thermodynamics of MOF growth from the substrate or the possibility of competing binding modes of the ligands used to form the MOF (for example, the nitrogen donors of bipyridine ligands may coordinate to copper species and compete with carboxylate groups). More computationally intensive simulations that quantitatively model different interfacial interactions could be used after initial high-throughput screening in the final selection of MOF candidates. Nonetheless, the criteria we have implemented allows for an efficient screening process that considers the necessary conditions for aligned heteroepitaxial growth of MOF crystallites on the macroscale.
We used the screening process to compile a list of top candidates for aligned heteroepitaxial growth from the CORE MOF, 26 hMOF, 27 and TOBACCO 28,29 databases, which equated to screening approximately 20 000 structures in a few days on a desktop workstation. The screening results showed that MOFs that have at least one lattice plane with rectangular symmetry have the greatest propensity for aligned heteroepitaxial growth on Cu(OH) 2 , a condition that is commonly satisfied only for certain MOF topologies. (The pcu, nbo-b and lvt-b topologies were found to make up the majority of top candidates). This finding indicates a substrate-directing effect, whereby the symmetry of the substrate surface determines the preferential symmetry of MOF binding sites at the interface and, hence, the symmetry of the MOF binding plane. Knowledge of substrate-dependent design principles like this allows for topologically targeted synthetic strategies, which offers an efficient route to viable experimental targets. 58,60,61 We identified six, experimentally realized MOF structures (REFCODES: ZAZBUZ, CEHPIP, NEJRUR, NEJSAY, NEJSEC, and UNABUH) that are likely to form aligned heteroepitaxial structures on Cu(OH) 2 .
Furthermore, we used the hypothetical MOF database (hMOF), which comprises mostly pcu MOF structures, to show that the dimensions of the substrate lattice, which determine the registry and alignment of the MOF, do not constrain the available range of pore diameters and the anisotropy of the pore networks. A broad range of possible pore architectures means that the design of MOF thin films can be tailored toward target applications. The screening algorithm we have described offers a fast and robust way to find MOF candidates for further experimental analysis in the growing field of MOF thin films and device development. In addition, the categorization of vast MOF databases afforded the determination of design principles and structure-property relationships.

Supporting Information Available
Detailed description of screening algorithm, parameter selection, list of MOFs in experimental data set and corresponding crystallographic information files (CIFs), and additional screening results.
This material is available free of charge via the Internet at http://pubs.acs.org/.