This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of the American Chemical Society, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see: https://dx.doi.org/10.1021/jacs.9b08754. Title: Geometry mismatch and reticular chemistry: strategies to assemble metal-organic frameworks with non-default topologies Authors: Vincent Guillerm†* and Daniel Maspoch†‡* Affiliations: † Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra, 08193 Barcelona, Spain; ‡ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain Keywords: metal-organic frameworks, reticular chemistry, rational design, geometry mismatch, self- assembly, porous materials. TOC image: ABSTRACT The past 20 years have witnessed tremendous advances in the field of porous materials, including the development of novel metal-organic frameworks (MOFs) that show great potential for practical applications aimed at addressing global environmental and industrial challenges. A critical tool enabling this progress has been reticular chemistry, through which researchers can design materials that exhibit highly regular (i.e. edge-transitive) topologies, based on the assembly of geometrically-matched building blocks into specific nets. However, innovation sometimes demands that researchers steer away from default topologies to instead pursue unusual geometries. In this perspective, we cover this aspect and introduce the concept of geometry mismatch, in which seemingly incompatible building blocks are combined to generate non-default structures. We describe diverse MOF assemblies built through geometry mismatch generated by use of ligand bend-angles, twisted functional groups, zigzag ligands and other elements, focusing on carboxylate-based MOFs combined with common inorganic clusters. We aim to provide a fresh perspective on rational design of MOFs and to help readers understand the countless options now available to achieve greater structural complexity in MOFs. 1. Introduction Since the discovery of MOF-51 and HKUST-12 some 20 years ago, great efforts have been dedicated to understanding the basic principles that govern MOF assembly.3 The final structure of a given MOF is now widely understood to be strongly influenced by the geometries of its constituent organic ligands and inorganic moieties (e.g. single metal ions, polynuclear clusters, infinite chains, etc.). Numerous design approaches such as use of molecular building blocks (MBBs) or secondary building units (SBUs) 4-10 have been combined with the mathematic discipline of topology11-13 to synthesize myriad novel porous structures,14 including MOFs that exhibit high performance in crucial environmental and industrial applications such as energy/gas storage separation,15-18 waste/valuables removal,19-20 water harvesting21-25 and smart materials.26-28 Concerted efforts by chemists and materials scientists have given rise to a new subfield of chemistry: reticular chemistry. The dedicated Reticular Chemistry Structure Resource (RCSR) database created in 2008 by O’Keeffe, Yaghi and coworkers now contains roughly 3,000 three-periodic nets (topologies)29 and the ToposPro software has been developed to make topology analysis easily available.30 One might imagine that there would be a limited number of ways to periodically assemble polygons and polyhedra and that all of these topologies would have already been predicted. Surprisingly, this is not the case, even though there are already almost 100,000 MOF structures reported in the MOF subset of the Cambridge structural database.31 Indeed, there are near-monthly reports of MOFs that exhibit topologies described as “novel”, “previously unknown”, “unprecedented” or “unique”. For instance, Eddaoudi and coworkers revealed more than 100 novel topologies,32 based on merged nets.9 However, reticular chemistry is not limited to the discovery of novel 3D periodic nets: in fact, researchers have often discovered MOFs whose constituent clusters have never previously been reported as discrete molecules. Some of these clusters have high connectivity, which is a highly desired asset.33-36 Indeed, the greater the connectivity within the building blocks, the lower number of possible structures attainable upon assembly and consequently, the lesser the chance of obtaining an undesired structure. For example, squares37-38 or tetrahedra can assemble into numerous structures (248 zeolitic nets known),39 whereas triangles and rhombicuboctaedra (rco) can only assemble into one net, the rht topology.40 Accordingly, researchers have been seeking MBBs10, 33, 35, 41-47 or supermolecular building blocks (SBBs)4, 33, 40, 48-49 of high connectivity, with which to rationally construct MOFs. However, whereas most efforts are focused on joining together compatible building blocks to form MOFs of predicable structures and topologies, an opposite strategy would be to combine apparently incompatible building blocks into structures and topologies, which would provide an opportunity to learn about their behavior and access unprecedented materials.33 Along these lines, scientists can employ less-symmetric organic ligands, with bend-angles,35 introduce steric hindrance50 or use zigzag-shaped ligands (transversal reticular chemistry).51 These strategies all induce structural irregularity known as geometry mismatch. Figure 1. Representation of the four common types of clusters studied in this perspective. Vertex figures matching their points of extension are represented in yellow. Theoretically, geometry mismatch could be harnessed for any class of MOFs, such as azolate or phosphonate based MOFs. However, in this perspective, we focus on carboxylate-based MOFs combined with common inorganic MBBs (i.e. those for which the synthetic conditions are well known). Given their abundance in the Cambridge Structural Database,52 we consider the following clusters suitable for reliable analysis: MII (Cu, Zn, Co, etc.) paddle wheels, as in HKUST-1;2 MIII (Fe, Cr, Sc, Ga, Al, etc. ) trimers, as in MIL-100;53 Zn tetramers, as in MOF-5;1 and MIII/IV (rare earths [RE], Zr and Hf) hexamers, as in UiO-66 (Figure 1).54 Thus, here we describe examples of MOFs and synthetic strategies that have pushed the envelope of reticular chemistry, challenged standard assembly rules and enabled high degrees of structural complexity, all thanks to the geometry mismatch generated through assembly of their (apparently incompatible) respective building blocks. 2. Topological tools in reticular chemistry: a precious but limited asset 2.1. Nets, nodes, augmented nets and vertex figures Figure 2. a) The three edge-transitive (4,12)-c nets ith, ftw and shp. b) Augmented representation of the three edge-transitive (4,12)-nets ith-a, ftw-a and shp-a. c) Polygonal and polyhedral building units resulting from the deconstruction of augmented nets. d) Topology prediction map for the assembly of a 12-c hexanuclear cluster with 4-c tcpp ligand, leading to the ftw-type structure of MOF-525. In this section, we briefly highlight the role of topology in the standard design strategy for MOF synthesis, endeavoring to help novices understand the potential and limits of topology in structure design and prediction, through the relatively counterintuitive strategies that we describe in this perspective. In fact, reticular chemistry has always been associated with topology, and several articles from Delgado- Friedrich et al. have been a major source of inspiration for molecular architects.11-12, 55-58 Targeting a specific MOF requires selection of at least one organic MBB and one inorganic MBB, each of which will have a specific connectivity (i.e. the number of other MBBs it will be linked to). Ideally, assembly of these building blocks would be limited to only one possible structure. The resultant three-periodic net should be as regular as possible, preferably edge-transitive (i.e. having only one type of edge bridging the nodes of the net), such that the risk of obtaining undesired structures is minimized. As an illustrative example, we consider the ideally 12-connected (12-c) Zr hexanuclear cluster and the 4-c ligand, tetrakis(4-carboxyphenyl)porphyrin (tcpp). The expected topology would be an edge- transitive (4,12)-c net. According to the RCSR database, three such nets exist: ith, ftw and shp (Figure 1a). To differentiate among these three nets and find the expected topology, one must inspect the corresponding augmented nets (net-a, Figure 1b), in which the vertices (nodes) are replaced with the corresponding vertex figures (polygons or polyhedra). Such inspection reveals that ith, ftw and shp differ from each other: thus, ith-a is the combination of icosahedra with tetrahedra; ftw-a comprises cuboctahedra linked by squares; and shp-a comprises hexagonal prisms and squares (Figure 1c). In parallel, the twelve extension points of the Zr cluster together form a cuboctahedron, whereas the four extension points of the tcpp ligand form a square. Therefore, formation of the nets ith or shp can be excluded. Consequently, for a MOF with 12-c Zr cluster and a 4-c tcpp ligand, the expected topology is ftw (MOF-525, Figure 1d).59 2.2. Angles, offset and twists in organic ligands: limitations of topology in MOF design Figure 3. Schematic representation of a) the fcu-a net and how b) twisted, c) bent or d) zigzag ligands would create geometry mismatch. After illustrating the prime importance and power of topology as a design tool in reticular chemistry, we address here its relative weakness. Indeed, the simplification of a structure into its underlying net (topology) reduces MBBs as nodes, or for the case of ligands that are 2-connected, it is simply discarded and corresponds to the edges of the net. For instance, UiO-66 comprises 12-c Zr MBBs bridged by 2-c terephthalates; however, the corresponding fcu topology is uninodal (12-c net). Therefore, it is difficult to gain insight a priori on the possible effects of different ligand geometries (i.e. introducing a twist, an angle or an offset into a 2-c ligand) on the resulting structure or topology, apart from evidence that it might create geometry mismatch and thus, prevent formation of the default structure or topology (Figure 3). In the following sections, we aim to elucidate existing strategies and remaining challenges for the efficient design of MOFs with less regular, non-default topologies. 3. Ditopic ligands 3.1. Linear, twisted ligands with steric hindrance: a cornerstone of MOF design In this section, the default topologies are the edge-transitive sql net (4-c), in the case of 4-c paddle wheels, and fcu net (12-c), in the case of Zr/Hf/RE hexanuclear clusters (“UiO type cluster”). Both types of MOFs assemble by bridging linear ligands with coplanar carboxylate groups. Breaking this coplanarity by introducing steric hindrance creates geometry mismatch (Figure 3b). Figure 4. Assembly of bdc or Br-bdc with paddle wheels leads to a) 2-periodic (MOF-2, sql) or b) 3-periodic (MOF-101, nbo) structures, respectively. Until 2002, the majority of reported structures resulted from either isoreticular expansion of known MOFs, to create isoreticular MOFs (IRMOFs),60 or from exploratory trial-and-error work.2, 61-65 Then, the report of MOF-101, a Cu dicarboxylate, appeared as a cornerstone of rational MOF design in reticular chemistry (Figure 4).50 To modify the orientation of the Cu paddle wheels, the coplanarity between the two carboxylic groups in the linear terephthalate (bdc) was broken, by employing a sterically hindered ligand (Br-bdc). This altered the directionality of the connectivity points by 90º, enabling formation of a 3-periodic structure with the nbo topology (Figure 4b), rather than the sql topology of MOF-2 (Figure 4a).64 However, the twist angle does not need to be as large as 90º to affect the structure and topology of a MOF. For example, smaller twists in the ligands (28o and 47o) will alter the directionality of the paddle wheels to a lesser extent than in MOF-101. Using this approach, Furukawa et al. formed MOF-604, which exhibits the cds topology.37 This strategy has also been applied with longer ligands such as 2,2′-dimethyl biphenyl-4,4′-dicarboxylate (Me2bpdc)37 as well as with zirconium, enabling formation of Zr-based MOFs with the bcu topology,66-68 rather than the fcu topology, which is commonly obtained when linear ligands are used.41, 54, 69-72 Lü et al. described a surprising example along these lines, having assembled the complex, chiral N,N′-di-(4-benzate)-1,2,6,7- tetrachloroperylene-3,4,9,10-tetracarboxylic acid diimide (pdi) with zirconium. 73 The dihedral angle between the two carboxylates (38°), and the unusual length and slight flexibility of the ligand, together generated the dia topology, rather than the fcu or bcu topologies. In this structure, the Zr clusters of Zr- PDI are capped by eight ligands, such that each cluster is connected to four others (i.e. two ligands each bridge two similar clusters). As a concluding example, we consider the zinc tetramer used to produce IRMOFs.60 Interestingly, unlike in the case of MII paddle wheels (Figure 5a) and MIII/IV hexanuclear clusters (Figure 5c), for IRMOFs, introducing a 90º twist into the organic ligands does not have any impact on the resulting connectivity directions of the cluster (Figure 5b). This is due to the octahedral connectivity of the zinc tetramer. To the best of our knowledge, this observation has not been reported elsewhere. Figure 5. Comparison of the ideal orientation and directionality of MBBs with coplanar or 90º-twisted dicarboxylate ligands. Upon a 90º twist, Cu paddle wheels (a) and Zr hexamers (c) undergo a change in directionality, whereas Zn tetramer (b) maintain their directionality. 3.2. Bent ligands: the door to polymorphism In this section, the default topologies are the edge-transitive sql net (4-c), in the case of 4-c paddle wheels, and fcu net (12-c), in the case of Zr/Hf hexanuclear clusters (“UiO type cluster”). Both types of MOFs assemble by bridging linear ligands with coplanar carboxylate groups. Breaking this linearity by introducing a bending angle (Figure 3c), through use of a bent ligand, creates geometry mismatch; consequently, the ligands that surround the same MBB end up having many distinct orientations. Combining paddle wheels with bent ligands of various angles leads mainly to discrete metal-organic polyhedra (MOPs) molecules 74-75 and to 2D MOFs (sql and kgm).38 For MOPs generated with square building units (paddle wheels or single metal ion), the influence of the bend-angle in the ligand is clear, enabling isolation of MOPs of various geometries and distinct organic/inorganic content (i.e. metal/ligand [M/L] content), which has already been well documented elsewhere.4, 76-81 To illustrate the influence of bent ligands on MOF assembly, we have chosen hexanuclear Zr/Hf clusters as the representative inorganic MBB (Figure 6), owing to their usually high and adaptable connectivity (from 4 to 12). Introducing an angle into a dicarboxylic ligand (i.e. changing the directionality of its connectivity) can, depending on the bending angle, prevent the formation of the ubiquitous fcu-type framework (Figure 3c). Interestingly, at an angle of 160º, such as that in the ligand 9-fluoreneone- 2,7dicarboxylate (fldc), found in BUT-10, the topology remains fcu (Figure 6a). Figure 6. Varying the angle, and/or the orientation around Zr based clusters, of bent ligands leads to MOFs with a) the fcu (BUT-10), b) reo (DUT-67), c) bon (DUT-68), d) bct (DUT-69), e) hbr (DUT-126), f) kag (CAU-28) or g) pcu (BUT-66) topologies, as well as to 1D coordination polymers (DUT-80). Some organic rings are filled in yellow to better distinguish the ligand orientations around the clusters. However, to offset the effects of the bend-angle, the clusters exhibit an overall inclination of ca. 14º from their ideal orientation.82 At smaller angles, such as ca. 150º, as in the case of the ligands dithienothiophene dicarboxylate (dttdc) and 4,4'-(2 H-1,2,4-triazole-3,5-diyl) dibenzoate (tadiba), the angle has a large influence on the outcome, leading to the reo-MOFs DUT-5183 and JLU-MOF58,84 respectively. Interestingly, using a shorter ligand of comparable angle, 2,5-thiophenedicarboxylate (tdc), leads to four distinct structures: three 8-c nets (the reo-MOF DUT-6785 [Figure 6b] and its two polymorphs, the bon-MOF DUT-68 [Figure 6c]85 and the hbr-MOF DUT-126 [Figure 6e]86), and one 10-c net (the bct-MOF DUT-69 [Figure 6d]85), whose rare topology is also found in MOF-802, which is based on the ligand 3,5-pyrazoledicarboxylate (pzdc).25 These examples highlight the great potential of bent ligands to promote structural diversity, by conferring the bent ligands around the Zr clusters with different orientations without necessarily altering the connectivity of the binding groups (Figure 6). An intriguing case is CAU-28 (Figure 6f),87 which comprises two crystallographically distinct 2,5-furane dicarboxylate (fdc) ligands, one of which exhibits a 124º angle, four of them surrounding the Zr/Ce clusters and bridging them into a Kagomé lattice. The other ligands (four per cluster), which have a markedly smaller angle (ca. 103º), act as “pillars” between the layers along the z axis, to form an overall kag topology. No section on bend-angles would be complete without mentioning a bent ligand with a 120º angle. Surprisingly, and to the best of our knowledge, no one has yet reported assembly of a MOF from Zr clusters and the ubiquitous 120o bent isophthalate ligand (m-bdc). However, Xie et al. did recently report combination of Zr clusters with either 4,4’-(benzene-1,3-diyl)dibenzoate (bdb) or 4,4’-(naphthalene- 2,7-diyl)dibenzoate (ndb) to form the pcu-MOFs BUT-66 (Figure 6g) or BUT-67, respectively.88 Although their clusters are 12-connected, these MOFs exhibit the same topology as in MOF-5: each Zr cluster is bridged to six others by pairs of ligands. Similarly to Xie et al., Wei et al. subsequently reported that combination of Gd hexanuclear clusters and tetrafluoroisophthalate (m-bdc-F4) generates a pcu-MOF.89 Finally, Krause et al. evaluated an even smaller angle, of 90º, in their assembly of a MOF from Zr clusters and the ligand 9h-carbazole-3,6-dicarboxylate (cdc) into the 1D coordination polymer DUT-80 (Figure 6h). In this structure, the 8-c Zr clusters are quadruple-bridged to each other by cdc ligands to form “chains” of clusters, which can be connected together to yield the flexible MOF DUT-98 (vide infra).90 Overall, the case of MOFs assembly with bent ligands still represents a major challenge in terms of net predictability. The many possibilities of varying angles and the numerous ways of orienting the ligands around the clusters prevents for easy rationalization. We anticipate recent and future advances in computational chemistry will permit a better understanding of these systems in a near future. 3.3. Zigzag ligands: transversal reticular chemistry In this section, the default topology is the edge-transitive fcu net (12-c) with Zr/Hf hexanuclear clusters (“UiO type cluster”). Such MOFs assemble by bridging linear ligands with coplanar carboxylate groups. Breaking this linearity by introducing a transversal offset creates geometry mismatch (Figure 3d). In addition to linear, twisted or bent ligands, another type of ditopic bridge, zigzag ligands (Figure 3d), is currently gaining attention in MOF assembly.91 Examples of MOFs built with such ligands, in which the collinearity between chelating groups is broken, have been reported.92-94 However, before the advent of transversal reticular chemistry, no clear focus had been made on the potential of their unique shape (Figure 7a).51 By adding the transversal parameter of width (w) to the height (h) of the ligands, Guillerm et al. demonstrated that, along with making ligands taller or shorter, they could also stretch them transversally, thus breaking the collinearity of the binding carboxylates. In the case of Zr-based MOFs, this effect is reflected by generation of geometry mismatch (Figure 7b), as zigzag ligands do not match the perfect alignment of Zr clusters. Thus, assembling Zr clusters with zigzag ligands leads to bcu-MOFs, which can be regarded as fcu-MOFs with systematic, ordered defects — namely, four missing ligands on each MBB (Figure 7c).51 Guillerm et al. reported Zr-bcu-MOFs (Figure 7e-h) with trans, trans muconate (tmuc), 2,6-naphthalene dicarboxylate (26ndc), 2,2'-bipyridine-4 4'-dicarboxylate (22bipy44dc) or azobenzene-3 3'-dicarboxylate (azo33).51 Additionally, Maurin, Serre and co-workers used simulations to predict that Zr clusters and zigzag succinate (suc) ligand would combine to form another MOF, Zr-bcu-suc (MIP-204, Figure 7d), whose assembly they subsequently confirmed experimentally.95 Figure 7. a) Comparison of the characteristic distances and angle in bdc (linear) and tmuc (zigzag) ligands. b) schematic of the geometry mismatch in Zr-bcu-tmuc. c) comparison between the fcu-a and bcu-a nets. A family of isoreticular Zr-bcu-MOFs based on d) suc, e) tmuc, f) 26ndc, g) 22bipy44dc or h) azo33 ligands. Shortly after, by introducing steric hindrance by the mean of a sulfonic group on a 26ndc ligand, Nguyen et al. showed the possibility to not only deviate from the 12-c fcu net to the 8-c bcu net, but also to assemble its polymorphic analog, the 8-c reo net.96 As in the case of bent ligands, the many possibilities of orienting zigzag ligands around a cluster is a great challenge to tackle in order to achieve rational design of such MOFs. The help of computation tools will surely be crucial to understand and predict the assembly of MOFs with such complex ligands. The case of ligands with small widths, such as 26ndc and azobenzene-4 4'-dicarboxylate (azo44), is worth mentioning. Some of these act as linear ligands, as their disorder in the framework compensates for their small width values without affecting the cluster orientation or reducing the overall symmetry (Figure 8).85, 97 Figure 8. Detail of the 26ndc ligand disordered in Zr-fcu-26ndc (DUT-52-Zr) and ordered Zr-bcu-26ndc. Multi-functionality has recently become a highly-desired property for MOFs, as it facilitates their selective post-synthetic modification.98-99 Many multivariate MOFs have been reported,9, 100-106 most of which contain randomly distributed ligands having similar shapes but carrying diverse functional groups.104 Strategies to achieve ordered multi-functionality include ligand insertion/pore partition,66-67, 107 use of programmed pores108 and assembly of merged nets.9 Transversal reticular chemistry is taking crystal engineering to the next level, by enabling selective postsynthetic placement of ligands (i.e. functional groups) to create materials that mimic natural structures such as proteins and nucleic acids. For instance, Kim et al. reported ready functionalization of the MOF Zr-bcu-26ndc (Figure 9a) with tagged terephthalates to produce ordered, multivariate fcu-MOFs.109 To complete the coordination of the Zr clusters in Zr-bcu-26ndc assembled through transversal reticular chemistry (vide supra), they filled the resultant unoccupied positions with their desired ligand (Figure 9b). Figure 9. Transversal reticular chemistry enables precise insertion of additional ligands to transform a) Zr-bcu-26ndc into b) Zr-fcu-26ndc/x-bdc, by completing the coordination of the Zr hexamer (from 8-c to 12-c). Consequently, the channels in Zr- bcu-26ndc are transformed into the tetrahedral cages in Zr-fcu-26ndc/x-bdc. Introducing a zigzag ligand into a MOF can influence the MOF’s geometry without impacting its overall topology (Figure 10). For example, Chevreau et al. described the case of MIL-142B (Figure 10a), an Fe-nht-MOF constructed with 4,4’-biphenyldicarboxylate (44bpdc) and 4,4’,4’’,-benzene- 1,3,5-triyl-trisbenzoate (btb),100 whose framework is interpenetrated, yet whose transversal reticular analog, MOF-909 (Figure 10b), which contains azo33 instead of 44bpdc, comprises a single nht net. This is due to the distortion of the framework, preventing intergrowth of a second nht net.110 Interestingly, Nguyen et al. reported that introduction of 50% of azo33 is sufficient to prevent its interpenetration (MOF-908). Figure 10. a) In nht-MOF MIL-142B, substituting linear 44bpdc with b) zigzag azo33 in MOF-909 prevents interpenetration. 4. Polytopic ligands with various angles and/or twists 4.1. Triangular ligands and cuboctahedral building blocks: geometry mismatch par excellence In this section, there is no edge-transitive net to assemble regular triangles (equilateral, coplanar carboxylates) with 12-c Zr/Hf/RE hexanuclear clusters (“UiO type cluster”). Therefore, all existing structures arise from geometry mismatch, which explains the high variety of topologies (Figure 11). Figure 11. a-f) Summary of the RE-based MOFs and g-l) Zr-based MOFs resulting from assembly of RE/Zr with triangular ligands in the appropriate conditions to form RE/Zr hexanuclear clusters. 4.1.1. The rare earths example In 2014, upon noticing the apparent incompatibility of 3-c ligands with 12-c (cuboctahedra) clusters (which lacks a corresponding edge-transitive net), Guillerm et al. envisioned the possibility of unveiling novel clusters and topologies, which had yet to be discovered in rare-earth and MOF chemistries.33 After determining the conditions to form the desired rare-earth hexanuclear cluster as a discrete entity, they used similar conditions, in combination with btb. Their system was highly versatile, as additional metal ions and carboxylates caused the hexanuclear cluster to spontaneously evolve into an 18-c, nonanuclear cluster, which was compatible with 3-c btb and gave rise to an unprecedented, minimal transitive, (3,18)- c net with gea topology (Figure 11a). Further studies on this net revealed its suitability for rational design of MOFs using supermolecular building blocks (SBBs),4 which we discuss later in this perspective.33 Subsequently, Eddaoudi and co-workers also studied the effects of varying the angles of 3-c ligands.35 Using the 90° angle provided by the ligand 9-(4-carboxyphenyl)-9H-carbazole-3,6-dicarboxylate (bcdc), they were able to unveil yet another nonanuclear cluster, a 12-c one that differs slightly from that observed in gea-MOF-1 (Figure 11a) and which led to formation of a MOF with a novel (3,12,12)- c net, aea topology (Figure 11b). In parallel, they demonstrated that reducing two branches of the btb ligands (e.g. by using the [1,1'-biphenyl]-3,4',5-tricarboxylate ligand [bptc]) generated another previously unknown topology, pek, and that in the resulting pek-MOFs (Figure 11c), a 12-c nonanuclear cluster coexisted with the classical hexanuclear cluster (albeit, with connectivity reduced to eight). Finally, by using the extended ligand 5-(4-carboxybenzyloxy)isophthalate (obi), they prepared the isoreticular analog pek-MOF-2. Inspired by these reports, Wang et al. recently discovered three novel MOFs in the RE/3-c ligand system: PCN-912 (Figure 11d), PCN-918 (Figure 11e) and PCN-909 (Figure 11f). They obtained these MOFs by reducing one branch of the btb ligand and introducing various levels of steric hindrance (using functionalized [1,1':3',1''-terphenyl]-4,4'',5'-tricarboxylate ligands [R-tptc]).44 They unveiled two novel highly-connected nets: the (3,3,12)-c net, flg (PCN-912); the (3,3,18)-c net, ytw (PCN-918); and also isolated a sep-MOF (PCN-909), with the same (3,9)-c net as in the previously reported Zr based MOF, BUT-39 (vide infra).111 4.1.2. The zirconium example Under many synthetic conditions, zirconium can produce a similar hexanuclear cluster to that of rare earths (vide supra).112-113 Since the first report of UiO-66 in 2008,54 and given the success achieved by forcing competition between monotopic acids (as modulators) and polytopic acids in their crystallization,41, 71-72, 114 Zr-MOFs have become some of the best-studied MOFs.34, 115-117 These findings paved the way towards construction of MOFs with topologies other than fcu. For instance, in 2012, Morris et al. described assembly of Zr-MOFs with square ligands. They obtained the expected MOF- 525 and MOF-535, which exhibit the edge-transitive ftw topology, and surprisingly, also obtained MOF- 545, which shows another edge-transitive net, csq, whose hexanuclear cluster exhibits a connectivity reduced to eight (the first-ever reported example of this in a MOF).59 Regarding equilateral triangular ligands with coplanar carboxylate groups, since they cannot be assembled with 12-connected cuboctahedral shapes, the clusters instead reduce their connectivity to eight, to fit to edge-transitive nets having lower connectivity. This adaptability of the Zr clusters explains the generation of the two spn-MOFs MOF-80825 (ligand: trimesate [btc]) and PCN-777 (ligand: 4,4′,4″- s-Triazine-2,4,6-triyl-tribenzoate [tatb], Figure 11g),118 whose Zr clusters are six-connected with octahedral directionality. Similarly, Wang et al. reported that in presence of btb, Zr clusters also exhibit six-connectivity, albeit in hexagonal directionality, leading to formation of a kgd-MOF based on edge- transitive kgd layers that interpenetrate to form an overall 3D framework (Figure 11h). In this MOF, the carboxylates are slightly twisted (38º and 46º) relative to the ligand plane.119 An example of a MOF in which the carboxylates show a greater twist angle (90º) was given by Wang and co-workers, who reported that Zr clusters reacted with 4,4’,4’’-(2,4,6-trimethyl-benzene-1,3,5-triyl)tribenzoate (Me3btb) adopt a connectivity of eight, with cubic directionality, to yield BUT-12 (Figure 11i), a MOF with the edge-transitive the topology.120 Likewise, the use of other ligands sharing the geometry of Me3btb, 6,6′,6″-(2,4,6-trimethylbenzene-1,3,5-triyl)tris(2-naphthoate)) (tnna) or 4,4’,4’’-[benzene-1,3,5-triyl- tris(benzene-4,1-diyl)]tribenzoate (bbc), leads to two other the-MOFs: BUT-13120 and MOF-1005, respectively.121 Despite the adaptability of the connectivity of the Zr clusters, which helps to form MOFs of highly regular structure and edge-transitive nets, He et al. found that use of the highly original T- shaped ligand 4,4′,4″-(1H-benzo[d]imidazole-2,4,7-triyl)tribenzoate (btba) led to a novel, (3,9)-c topology (sep) within the Zr/3-c ligand system, as illustrated in their discovery of BUT-39 (Figure 11l).111 As we mentioned above, DUT-80 is a unidimensional structure constructed from 8-c Zr clusters and cdc, a ligand with a bend-angle of 90º. Krause et al. discovered that using this 1D motif with such an angle implemented in the bcdc ligand leads to an unprecedented (3,12)-c net: they obtained the llj-MOF DUT-98 (Figure 11j), which exhibits high structural flexibility.90 Another possibility to obtain a novel (3,12)-c net was reported by Lee et al. in their construction of MOF-1004, which exhibits the sky topology, in which the geometry of the 12-c node is cuboctahedral.121 To generate this net, they used the wide and slightly flexible ligand 4,4’,4’’-[benzene-1,3,5- triyltris(ethyne-2,1-diyl)]tribenzoate (bte), in which the angle between two branches is only 94º (compared to 120º in the ideal geometry of the ligand). Interestingly, Sun and co-workers followed this prerequisite in the design of their ligand 4,4’,4’’-(1H-imidazole-2,4,5-triyl)tribenzoate (ittc), which they subsequently used to assemble UPC-158 (Figure 11k), an isoreticular analog with the sky topology.122 Their work demonstrates that even such unexpected topologies can be rationally targeted, provided that the geometrical requirements are known. 4.2. Triangular ligands with square paddle wheel building blocks In this section, the default topology to assemble regular triangles (equilateral, coplanar carboxylates) with paddle wheels (4-c) is the (3,4)-c edge-transitive tbo net. Modifying the coplanarity of the carboxylates, the angles or using ligands with unequal edge-lengths creates geometry mismatch (Figure 12). Figure 12. Summary of the Cu-based MOFs resulting from assembly of paddle wheels with triangular ligands. The geometric differences among 3-c ligands strongly influence the resulting MOF structures, leading to the a) tbo (PCN-6), b) pto (MOF- 143), c) fmj (UMCM-150), d) agw (UMCM-151) or e) ftw/gee (DUT-75) topologies. Although the structural and topological variety of MOFs based on paddle wheels and triangular ligands is not as rich as that for hexanuclear clusters and these ligands (vide supra), we do consider some examples worthy of discussing here. Combination of a regular planar ligand such as trimesate (btc) with paddle wheels leads to HKUST-1, which exhibits the tbo topology;2 however, obtaining extended reticular analogs is not trivial. Interestingly, using 4,4’,4’’-benzene-1,3,5-triyl-tris(benzoate) (btb) instead of btc leads to two MOFs that exhibit the pto topology, another edge-transitive net: MOF-1465 (interwoven) and MOF-143123 (single net, Figure 12b). This is due to the natural twist of the carboxylates in btb. Alternatively, using a fully planar and regular ligand such as 4,4',4"-s-triazine-2,4,6-triyl- tribenzoate (tatb) or 4,4’,4’’-(benzene-1,3,5-triyl-tris)benzene-4,1-diyltrisbenzoate (bbc), affords the expected tbo-MOFs PCN-6 (Figure 12a)124 or MOF-399,123 respectively. Another approach to access unusual topologies from paddle wheels and triangular ligands is simply to elongate one or more ligand branches. For instance, Wong-Foy et al. employed biphenyl-3,4,5- tricarboxylate (bptc) to elongate one branch of btc, enabling them to assemble UMCM-150 (Figure 12c), a MOF resulting from the pillaring of Kagomé layers (kgl) by a rare Cu trimer to generate the agw topology. The layers are constructed from paddle wheels bridged by the isophthalic moieties of the bptc ligands, whereas the remaining benzoic moieties alternately point up or down from the layers, such that another paddle wheel cannot be incorporated, thus “forcing” formation of a 6-c Cu trimer.125 Lim et al. reported that this Cu trimer could be substituted with other metal trimers (Co, Fe, Ni),126 and Lu et al. found that the ligand could be further extended to obtain greater porosity.127 Similarly, Schnobrich et al. used terphenyl tricarboxylate (tptc) to elongate two branches of the btc ligand, ultimately obtaining a UMCM-151 structure that contains paddle wheels only, albeit in an unpredictable, complex, pentanodal (3,3,4,4,4)-c net, fmj topology (Figure 12d).128 In addition to varying the carboxylate orientation and/or elongating the ligand branches, another approach to obtain dramatically different topologies is to introduce a 90º angle between two branches of the ligand by using carbazole groups, such as those in 4,4′-(9-(4′-carboxy-[1,1′-biphenyl]-4-yl)-9H- carbazole-3,6-diyl)dibenzoate (bpcdc). For example, Stoeck and co-workers rationally designed DUT- 75 (Figure 12e) and DUT-76 (gee topology) by using the SBB approach to adopt overall ftw-type structures.129 Exploiting the possibility to form carbazole-based MOPs with cuboctahedral shapes,130 they simply linked the 12-extremities together through a paddle wheel. 4.3. Triangular ligands with 6-c trigonal prismatic building blocks In this section, there is no edge-transitive net with which to assemble regular triangles (equilateral, coplanar carboxylates) with 6-c MIII (Fe, Al, Cr, Ga, In, etc.) trimers. Given the high incidence of the moo net, which derives from the zeolitic mtn net, we can consider it to be the default net for these assemblies. Modifying the coplanarity of the carboxylates, the angles using ligands with unequal edge- lengths leads to geometry mismatch (Figure 13). Figure 13. a) Equilateral triangle ligands with coplanar carboxylates assemble with trimers to form supertetrahedra, that further assemble into an underlying zeolitic mtn type network (moo-MOFs). Breaking the coplanarity leads to other types of MOFs, b) Sc-btb, c) PCN-260 and d) PCN-261), whereas e) using tbab yields the Fe-fmz-tbab structure. Although assembly of regular triangular ligands with 6-c trigonal prismatic MBBs cannot generate an edge-transitive net, various compatible nets with only two types of edges have been reported, including the ceq, dag, hwx, sit and ydq topologies. Surprisingly, most MOFs in this system adopt the extremely complex, decanodal moo topology of MIL-100.53 This assembly had first been predicted by simulations131-132 and can be explained by formation of super-tetrahedra that favor further self-assembly of MOFs into an overall zeolitic (mtn type) topology, as observed in the examples of MIL-100,53 MIL- 100-btb,133 PCN-332,134 PCN-333134 and PCN-888 (Figure 13a).135 Intriguingly, and similarly to other systems that we discuss in this perspective, not all assemblies of regular triangular ligands with 6-c trigonal prisms lead to the moo topology. For example, when Ibarra and co-workers assembled btb, which can yield moo MOFs,133 with scandium trimers, they instead obtained the MOF Sc-btb (Figure 13b), 136 which exhibits a different topology, (3,6)-c (not described in the RCSR database).137 This is not surprising, given that the carboxylates from btb are naturally out of plane, as has been observed in other systems.33, 65, 119, 138 Additional examples of MOFs constructed from btb (PCN-260, (3,3,3,6,6)-c, not described in the RCSR database,139 Figure 13c), or amino- (PCN-261, (3,3,6)-c, not described in the RCSR database,140 Figure 13d) or hydroxyl- (PCN-262) functionalized btb, also derive from the moo net. In these MOFs, geometry mismatch again resides in the natural twist, for PCN-260 or forced twist, for PCN-261 and PCN-262, of the carboxylates.141 Although it is difficult to know if it is a parameter governing the topology, or resulting from it, the angles formed by the ligands around the clusters vary significantly from one structure to another, and are far from the ca. 115° angle required to form the supertetrahedra necessary for the assembly of mtn/moo type MOFs (Figure 13). Another example of geometry mismatch in these systems is to replace btb with a ligand that has one shorter branch (e.g. tbab), such that upon assembly of the ligand with the metal trimer, the shorter branch length precludes formation of super-tetrahedra. In this sense, the assembly of tbab with Fe, Ga, In or Al trimers to yield Fe-MOF (Fe-fmz-tbab, Figure 13e) and SNNU-5, which exhibit a (3,6)-c net, fmz topology.142-143 4.4. Triangular ligands with 6-c octahedral building blocks In this section, pyr is the edge-transitive net to assemble regular triangles with 6-c Zn tetramers (“MOF-5 type” cluster). They require equilateral ligands with highly twisted carboxylate groups of the ligand (i.e. relatively flexible branches). Non-equilateral ligands, ligands with lower coplanarity and ligands with less-twisted carboxylates all generate geometry mismatch (Figure 14). Figure 13. a) Equilateral triangle ligands with coplanar carboxylates assemble with trimers to form supertetrahedra, that further assemble into an underlying zeolitic mtn type network (moo-MOFs). Breaking the coplanarity leads to other types of MOFs, b) Sc-btb, c) PCN-260 and d) PCN-261), whereas e) using tbab yields the Fe-fmz-tbab structure. There are several examples of regular triangular ligands being assembled with 6-c octahedral Zn tetramers to form pyr-MOFs, including MOF-150, constructed with 4,4',4"-tricarboxylate triphenylamine (tca) (Figure 14a);144 MOF-155-J, built with 1-(3-amino-4-carboxyphenyl)-3-(4- carboxyphenyl)-5-(4-carboxynaphthalen-1-yl)-benzene (btb-mNH2);145 and MOF-950, made from benzene-1,3,5-tri-β-acryate (btac).146 However, MOF-177 (Figure 14b),138 built from btb, and its many (> 20) functionalized145 or extended analogs,147 are all based on the “queen of MOFs”, the qom net. In these cases, preferential generation of qom over pyr is due to the weaker twisting of the carboxylates in the ligands used in the qom MOFs. However, contrary to a common assumption138 – and as we explained in the previous paragraph – the carboxylates in the constituent btb ligands of MOF-177 are not coplanar. Another MOF based on different carboxylate twists induced by the use of btb ligand with steric hindrance is MOF-156-J, which exhibits the rtl topology (Figure 14c).145 In addition to modifying the level of twisting in the ligand carboxylates, other methods to confer systems with geometry mismatch might include altering either the ligand length148-149 or the angle between the ligand branches150 (i.e. using non-equilateral ligands). The fact that no structure built this way has yet been reported could be explained by the idea that these approaches would likely prevent formation of the Zn tetramer; however, their possible assembly cannot be ruled out. 4.5. Square/rectangle ligands with 4-c paddle wheels building blocks In this section, the default topology to assemble square/rectangle ligands with 4-c paddle wheels, is the (3,3,4)-c fof net, derived from the edge-transitive nbo net (4-c). fof MOFs assemble by linking rectangle ligands with two coplanar dicarboxylate groups with a 120° angle (i.e. isophthalate). Breaking this coplanarity or modifying the dicarboxylate angle creates geometry mismatch (Figure 15). Note: this section does not cover examples with ligands based on “naturally tetrahedral” ligands (i.e. containing sp3 carbon, adamantane central core, etc.). Figure 15. Assembly of paddle wheels with square/rectangular ligands mainly affords a) pillared kgl layers in nbo/fof-type MOFs (MOF-505). b) Introducing bending into the ligand yields a different type of pillaring, leading to the ssa/sty topology (PCN-12). c) Steric hindrance leads to pillaring sql into ssb/stx MOFs (NOTT-109). d) Reducing the bend-angle from 120º to 90º by replacing isophthalate moieties with carbazoles enables assembly of SBB-based tfb-MOF (PCN-81), whose underlying topology is fcu. Numerous MOFs constructed from di-isophthalic-based ligands and paddle wheels have been reported, including MOF-505 (Figure 15a),151 and their default nbo/fof topology is widely described in the literature.4, 152-153 Their structures can be considered as ligand-to-ligand (L-L) pillaring of supermolecular building layers (SBLs).4 The default SBLs are kgl, which are staggered in the fof net. Interesting non-default examples include PCN-12 (Figure 15b)154 and ZJU-25,155 in which bending of the central core of their respective ligands prevents staggered packing and instead, generates eclipsed pillaring to yield an ssa/sty topology. Another noteworthy example is NOTT-109 (Figure 15c),156 in which a bulky naphthalene core precludes formation of the main cage characteristic of nbo/fof MOFs and instead, leads to formation of sql SBLs, which are pillared in an eclipsed fashion to form the ssb/stx topology. Researchers have built other pillared sql MOFs by using highly flexible ligands.4, 157 Expectedly, such MOFs may be subject to polymorphism, depending on the ligand conformation. 158-159 Thus, planar (rectangular) ligands lead to an overall lvt/lil topology, as in DUT-10,157 whereas tetrahedral analogs of the same ligands (e.g. obtained by twisting of the dicarboxylate moieties) lead to the pts/tfk topology, as in DUT-11.157 Pillaring of SBLs is not the only way to achieve non-default topologies in MOFs assembled from di- isophthalic-based ligands and paddle wheels. As we have discussed above for other MOF families, ligand bend-angles can be chosen to dictate topology. For example, researchers have reported that in SBB assembly with paddle wheels, substituting isophthalate (120º bend) with carbazole dicarboxylate (90º bend) yields PCN-81 (Figure 15d)160 and DUT-49 with tfb topology.49, 161 In these structures, the dicarboxylate moieties combine with the paddle wheels to form cuboctahedral cages that are bridged by the central core of the ligands to generate the underlying fcu topology. 4.6. Square/rectangle ligands with Zr hexanuclear cluster building blocks In this section, the default topology to assemble square/rectangle ligands with Zr/Hf/RE hexanuclear clusters (“UiO type cluster”) is the edge-transitive (4,12)-c ftw. MOFs assemble by linking square ligands with coplanar carboxylate groups. Breaking this coplanarity or deviating from the ideal square shape of the ligand creates geometry mismatch (Figure 16). Note: this section does not cover examples with ligands based on “naturally tetrahedral” ligands (i.e. containing sp3 carbon, adamantane central core, etc.). Beyond the expected ftw topology, various other edge-transitive nets have been obtained upon assembly of 4-c ligands with Zr/Hf/RE hexanuclear clusters, including csq,59 she,162 scu,163 shp,164 flu,25 ith,25 sqc,165 stp166 and lvt.167 This is not surprising, given the capacity of such clusters to adapt to lower connectivities (vide supra). Many of these topologies resulted when researchers changed the synthetic conditions or the amount of modulator previously used for ftw MOFs. Although Chen et al. described most of these in their recent review of Zr-MOFs based on edge-transitive nets,116 we have chosen to highlight a few examples below (Figure 16). Intriguingly, the ftw and scu nets are related. The main cage in ftw-MOFs can be represented as a cube, in which the clusters lying on the vertices are connected through the 4-c ligands that occupy the faces. Accordingly, elongation of the ligand in a single direction (i.e. by using a longer ligand) creates geometry mismatch, as only four of the six faces in the initial cage can accommodate a ligand, leaving the other two free. This scenario favors the scu/tty topology, in which 1D channels exist and the connectivity of the MBBs is reduced to eight (Figure 16). Moreover, if the length of the longer ligand is moderate compared to its width, as in the case of biphenyl-3,3′,5,5′-tetracarboxylate, bptet,167 then an ftw related MOFs with kle topology can still be formed (Figure 16b), as first reported for RE clusters by Luebke et al.168 Along these lines, Wang et al., in their work on replacing the ligand bptet with the longer ligand 3,3′,5,5′-azobenzene-tetracarboxylate (azotet), obtained a rare, scu-derived net that is not reported in the RCSR database,169 in which the ligand orientation alternates and the clusters are tilted from their ideal alignment to balance the ligand length/width ratio (Figure 16c).167 Interestingly, when they evaluated an even longer ligand, [1,1′:4′,1″]terphenyl- 3,3″,5,5″-tetracarboxylate (tptet), they obtained the first-ever Zr based lvt/lim-MOF, in which the connectivity of the Zr cluster is reduced to 4 (Figure 16d). Figure 16. Although assembly of square building blocks with the ideally 12-c connected Zr hexanuclear clusters should lead to the edge-transitive ftw net (MOF-525), elongation of the ligand in one direction can yield kle, scu/3,3,8T132 or lvt/lim- MOFs. By introducing steric hindrance into a rectangular ligand, the topology can be selectively controlled among scu/tty (PCN-606), csq/xly (PCN-608) or, in some cases, flu/flt (PCN-605). In most cases, if a ligand’s shape deviates significantly from the ideal square shape required for forming an ftw-MOF, then the resulting topology will be derived from csq (xly or xlz) or from scu (tty or cut). In some cases, the final geometry of the ligand, and ultimately, the resulting topology, can be controlled by introducing steric hindrance or by using ligands with a less rigid core. Indeed, Pang et al. reported selective control among flu/flt (PCN-605, Figure 16g), scu/tty (PCN-606, Figure 16e) and csq/xly (PCN-608, Figure 16f) MOFs, via selective functionalization of a set of 4-c ligands based on 3,3’,5,5’-tetra(ethyl-4-carboxyphenyl)-1,1’biphenyl (tpcb).170 Similarly, Lyu et al., were able to switch from the scu net in CAU-24171 to either the shp net in NU-904172 or the csq net in NU-1008,172 by simply introducing one or two bulky functional groups, respectively, onto the 4,4',4'',4'''-benzene-1,2,4,5- tetrayl-tetrabenzoate (tcpb) ligand. These groups directly influence the twisting of the carboxylates and therefore, dictate the resulting topology. 4.7. Hexacarboxylate ligands with 4-c square paddle wheel building blocks: not another rht-MOF In this section, the default topology is ntt, derived from the edge-transitive (3,24)-c net rht. Dicarboxylate bent (120o) extremities of trefoil ligands construct externally functionalized MOPs (24- c), that act as SBBs, and are linked together by the central core of the ligand (3-c). Breaking the planarity of the ligand, or preventing the formation of a 24-c MOP by modifying the angles between carboxylates, each introduces geometry mismatch that precludes formation of rht/ntt-MOFs (Figure 17). Figure 17. In addition to a) the many rht/ntt-based MOFs (NU-108-Cu) based on planar hexacarboxylate ligands, one can obtain b) zyg-MOF (UTSA-20), by breaking the planarity of the ligand, or c) an SBB-based gea/gwe-MOF (gea-MOF-2), by decreasing (from 120o to 90o) one of the angles in one of the three dicarboxylate moieties, via introduction of carbazole moieties. The latter change leads to an 18-c MOP instead of a 24-c MOP (which would be required to form rht/ntt-MOFs). In 2008, Nouar et al. described use of externally-functionalized MOPs as SBBs, which they assembled with copper trimers to form rht-MOF-1.40 Interestingly, this trimer can be substituted with 3-connected organic cores173-174 to afford overall planar hexacarboxylate ligands, which have been used to assemble various rht-MOFs (also known as ntt-MOFs, Figure 17a) 40, 48, 173, 175-176. In parallel, Guo et al. reported UTSA-20 (Figure 17b), which they built with a similar type of ligand, 3,3’,3’’,5,5’,5’’-benzene-1,3,5- triyl-hexabenzoate (bhb), showing that the geometry of this ligand was too intricate and resulted in broken planarity.177 UTSA-20 exhibits a zyg topology and represents one of the rare MOFs based on paddle wheels and hexacarboxylate ligands that does not exhibit the ubiquitous rht/ntt topology. Another example of a paddle wheel hexacarboxylate MOF that does not exhibit the rht topology is gea-MOF-2 (formally: gwe topology), a representative case to the scope of this perspective, as the gea topology was discovered by employing a geometry mismatch strategy.33 Indeed, gea-MOF-2 (Figure 17c) was rationally designed using the SBB approach, to specifically adopt an overall gea topology. Guillerm et al. identified a suitable MOP with 18 vertices178 matching the geometry of a triangular orthobicupola (eto/ebc), corresponding to the points of extension of a newly discovered RE nonanuclear cluster with 18 points of extension in gea-MOF-1. By incorporating this geometric information to build the eto-MOP in a trefoil hexacarboxylic ligand (i.e. two 120º angles for one 90º angle), they were able to use the ligand 5′,5⁗-((5-((4-(3,6-dicarboxylato-9H-carbazol-9-yl)phenyl)ethynyl)-1,3- phenylene)bis(ethyne-2,1-diyl))bis((1,1′:3′,1″-terphenyl]-4,4″-dicarboxylate (lgea2) as a net-coded building unit4 to replicate the underlying gea net, enabling its use as a blueprint for rational assembly of gea-MOF-2. In this sense, the 90º angle provided geometry mismatch to preclude formation of an rht- MOF (for which the 120º angles are crucial). 5. Conclusions We have provided an overview of geometry mismatch-based approaches to assemble MOFs that exhibit non-default topologies, which in some cases, have enabled discovery of novel clusters that remain to be studied. These approaches obviate classical MOF assembly strategies, in which pre- designed building blocks are used to form specific, edge-transitive or highly regular topologies. Instead, they rely on methods such as transversal reticular chemistry; use of zigzag ligands; introduction of twisting into the ligand carboxylate groups; alteration of ligand bending angles; and changing of the length/width ratio in branched ligands. Thus, by combining classical topology with these strategies to create non-default geometry, researchers are gradually elucidating the pre-requisites for designing MOFs with complex topologies. As researchers have come to understand the basic rules for assembly of some of the topologies previously discovered serendipitously (e.g. gea, sky, agw, pek, etc.), they have been able to exploit these topologies to further rationally design isoreticular materials. In several cases, the MBBs are left unsaturated, such that the aforementioned approaches to non- default topologies can be harnessed to construct multivariate MOFs with precisely-positioned functional groups, with the aim of creating functional sequences that mimicking natural structures such as enzymes or DNA. Finally, given the potential of geometry mismatch to generate countless new MOF topologies and the numerous ways to orient non-linear ligands around a cluster (Figure 6), we consider that human efforts to predict MOF topology are about to reach their limit. Accordingly, we believe that if the MOF research community truly wants to attain the next level of structural complexity in rational design, we must now turn to computational approaches to complement our human efforts. Clearly, such computational tools should be openly available and accessible to theoretical but also experimental scientists in materials science, chemistry and related fields. ASSOCIATED CONTENT Supporting information. Summary table of the main structures discussed in this perspective, with topologies, crystallographic information (CCDC codes), corresponding DOI, etc. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * vincent.guillerm@icn2.cat, daniel.maspoch@icn2.cat Author Contributions All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT Prof. Davide M. Proserpio is gratefully acknowledged for fruitful discussion and his help in identifying the net codes of topologies not registered in the RCSR database. Dr. Volodymyr Bon and Dr. Feng Liang are acknowledged for their help regarding the signification of some topology acronyms. Borja Ortín-Rubio is acknowledged for his helpful comments on a preliminary version of the perspective. The authors acknowledge the reviewers for their critical and constructive comments, they helped to improve this perspective. NOTES In this perspective, we consider the default net to be the one with edge transitivity or minimal transitivity, and the node corresponding to the inorganic cluster matching its ideal connectivity. In case several edge- transitive exist for assembling similar building blocks (sql vs nbo; tbo vs pto, etc.), the net chosen as default is the one for which the ligands have higher symmetry in the corresponding structures. In various cases, the topology used to design specific MOFs, or the reported topology, do not match those obtained by following the recommendations of O’Keeffe and coworkers, on using derived nets. For such cases, we have denoted both topologies in the text (e.g. rht/ntt, ftw/gee, fcu/tfb, nbo/fof, etc.). Figure S1 represents several examples of such MOFs described in two different ways. There are several occurrences of MOFs discussed in this perspective that do not have their topology registered in the RCSR database. They have been identified using ToposPro30 and we refer to them using the TopCryst codes (https://topcryst.com/). In the case several crystallographically independent ligands are present in a structure, ranges of bend angle or average twist/torsion angle are reported in this perspective. ABBREVIATIONS General acronyms (order of appearance): MOF, metal-organic framework; MBB, molecular building block; SBU, secondary building unit; IRMOF, isoreticular MOF; RCSR, reticular chemistry structure resource; SBB, supermolecular building block; RE, rare earth; MOP, metal-organic polyhedra; L-L, ligand-to-ligand; SBL, supermolecular building layer; DNA, deoxyribonucleic acid. Materials acronyms (order of appearance): HKUST, Hong Kong University of Science and Technology; MOF, Metal-Organic Framework; MIL, Material Institute Lavoisier; UiO, Universitetet i Oslo; DUT, Dresden University of Technology; JLU, Jilin University; CAU, Christian Albrechts University; BUT, Beijing University of Technology; MIP, Materials from Institute of porous materials of Paris; PCN, porous coordination network; UPC, University of Petroleum, Qingdao, China; UMCM, University of Michigan crystalline material; SNNU, Shangqiu Normal University; ZJU, Zhejiang University; NOTT, Nottingham; NU, Northwestern University; UTSA, the University of Texas at San Antonio. Ligands acronyms (order of appearance): tcpp, tetrakis(4-carboxyphenyl)porphyrin; bdc, terephthalate; Br-bdc, bromo-terephthalate; Me2bpdc, 2,2′-dimethyl biphenyl-4,4′-dicarboxylate; pdi, N,N′-di-(4- benzate)-1,2,6,7-tetrachloroperylene-3,4,9,10-tetracarboxylic acid diimide; fldc, 9⁗fluoreneone⁗2,7⁗ dicarboxylate; dttdc, dithienothiophene dicarboxylate; tadiba, 4,4'-(2 H-1,2,4-triazole-3,5-diyl) dibenzoate; tdc, 2,5-thiophenedicarboxylate; pzdc, 3,5-pyrazoledicarboxylate; fdc, 2,5- furandicarboxylic; m-bdc, isophthalate; bdb, 4,4’-(benzene-1,3-diyl)dibenzoate; ndb, 4,4’-(naphthalene- 2,7-diyl)dibenzoate; m-bdc-F4, tetrafluoroisophthalate; cdc, 9h-Carbazole-3,6-dicarboxylate; tmuc, trans, trans muconate; 26ndc, 2,6-naphthalene dicarboxylate; 22bipy44dc, 2 2'-bipyridine-4 4'- dicarboxylate; azo33, azobenzene-3 3'-dicarboxylate; suc, succinate; azo44, azobenzene-4 4'- dicarboxylate; 44bpdc, 4,4’-biphenyldicarboxylate; btb, 4,4′,4′′,-benzene-1,3,5-triyl-trisbenzoate; bcdc, 9-(4-carboxyphenyl)-9H-carbazole-3,6-dicarboxylate; bptc, [1,1'-biphenyl]-3,4',5-tricarboxylate; obi, 5-(4-carboxybenzyloxy)isophthalate; tptc, [1,1':3',1''-terphenyl]-4,4'',5'-tricarboxylate; btc, trimesate; tatb, 4,4′,4″-s-Triazine-2,4,6-triyl-tribenzoate; Me3btb, 4,4’,4’’-(2,4,6-trimethyl-benzene-1,3,5- triyl)tribenzoate; tnna, 6,6′,6″-(2,4,6-trimethylbenzene-1,3,5-triyl)tris(2-naphthoate)); bbc, 4,4’,4’’- [benzene-1,3,5-triyl-tris(benzene-4,1-diyl)]tribenzoate; btba, 4,4′,4″-(1H-benzo[d]imidazole-2,4,7- triyl)tribenzoate; bte, 4,4’,4’’-[benzene-1,3,5-triyltris(ethyne-2,1-diyl)]tribenzoate; ittc, 4,4’,4’’-(1H- imidazole-2,4,5-triyl)tribenzoate; bpcdc, 4,4′-(9-(4′-carboxy-[1,1′-biphenyl]-4-yl)-9H-carbazole-3,6- diyl)dibenzoate; tca, 4,4',4"- tricarboxylate triphenylamine; btb-mNH2, 1-(3-amino-4-carboxyphenyl)- 3-(4-carboxyphenyl)-5-(4-carboxynaphthalen-1-yl)-benzene; btac, benzene-1,3,5-tri-β-acryate; bptet, biphenyl-3,3′,5,5′-tetracarboxylate; azotet, 3,3′,5,5′-azobenzene-tetracarboxylate; tptet, [1,1′:4′,1″]terphenyl- 3,3″,5,5″-tetracarboxylate; tpcb, 3,3’,5,5’-tetra(ethyl-4-carboxyphenyl)- 1,1’biphenyl; tcpb, 4,4',4'',4'''-benzene-1,2,4,5-tetrayl-tetrabenzoate; bhb, ,3’,3’’,5,5’,5’’-benzene-1,3,5- triyl-hexabenzoate; lnu108, 1,3,5-tris[(1,3-di(4'-carboxylate-phenyl)-phenyl)-5-ethynyl]benzene; lgea2, 5′,5⁗-((5-((4-(3,6-dicarboxylato-9H-carbazol-9-yl)phenyl)ethynyl)-1,3-phenylene)bis(ethyne-2,1- diyl))bis((1,1′:3′,1″-terphenyl]-4,4″-dicarboxylate) Topology acronyms (order of appearance): rht, rhombicuboctahedron, triangle; ith, icosahedron, tetrahedron; ftw, four, twelve; shp, square, hexagonal prism; fcu, face centered cubic; sql, square lattice; nbo, Nb2O5; cds, CdSO4; bcu, body centered cubic; dia, diamond; kgm, Kagomé lattice; reo, ReO3; bon, Volodymyr Bon; bct, body centered tetragonal; kag, Kagomé net; pcu, primitive cubic; gea, Guillerm, Eddaoudi, net A; aea, Alezi, Eddaoudi, net A; pek, Puthan Peedikakkal, Eddaoudi, Kaust; flg, Feng Liang; ytw, Yutong Wang; sep, september; csq, cube, square; spn, spinel; kgd, Kagomé dual; the, three, eight; tbo, twisted boracite; agw, Antek G. 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