Intricate mixed-linker structures

Abstract

Embodiments of the present disclosure describe materials and methods of synthesizing materials comprising a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form an intricate mixed-linker structure with a merged-net. Merged nets may be formed from two 3-periodic edge-transitive parent nets that share a common signature net, wherein at least one parent is an embedded three-dimensional representation of a two-periodic (2p), one-periodic (1p), or zero-periodic (0p) net. The approach enables deliberate construction of multicomponent reticular materials that retain two distinct linker types and realize merged-net topologies from parent nets derived from 2p, 1p, and 0p nets.

Description

INTRICATE MIXED-LINKER STRUCTURESBACKGROUND

[0001] Over the past two decades, metal-organic frameworks (MOFs), a distinctive class of hybrid crystalline materials constructed by linking metal-based units (metal ions or metal clusters) with polytopic organic linkers, have attracted wide interest in academia and industry alike due to their high degree of porosity, unique functionalized structures, and readily modular construction. The MOFs’ readily adjustable pore system metrics and functionality positions MOFs as ideal candidate porous materials to address the enduring challenges pertinent to energy and environmental sustainability such as gas storage, gas separation, catalysis, and chemical sensing.

[0002] The institution of reticular chemistry paved the way for the design, discovery and development of novel functional crystalline solid-state materials including MOFs. Principally, the molecular building block (MBB) approach has emerged as a remarkable pathway toward the design and synthesis of novel functional MOFs. Purposely, prior the assembly process, the desired geometric and connectivity features, functionalities, and properties can be encompassed in preselected MBBs at the design stage. Certainly, the prospective for the effective design is reliant on the ability to access and deploy building blocks with geometrical information and encoded connectivity affording the points of extension to match the vertex figures of the targeted net. Convincingly, edge-transitive nets (all edges are equivalent by symmetry) are regarded as suitable design targets in reticular chemistry and crystal chemistry. The past two decades have witnessed the burgeoning of MOF chemistry with the design and construction of a large myriad of MOF materials based on the reticulation of edge- transitive nets or their derived nets. Indeed, MOFs based on edge-transitive nets are the dominant class of materials in MOF chemistry due to the relative ease of their isoreticulation and functionalization, prompting their exploration in myriad applications.

[0003] Logically, expanding the rational design of MOFs to include multiple distinct linkers based on the reticulation of multi-edge nets is of prime importance as it offers the prospective to deliberately access intricate materials with assorted functionalities needed for prospective applications. Nevertheless, the majority of mixed-linker intricate MOFs encompassing multiple ligands with distinct shapes and dimensions were realized primarily by the tedious trial-and-error approach. Markedly, the practice of isoreticulation for intricate MOF platforms based on multi-4053.277PCT1edges nets remains an ongoing challenge as the connecting polytopic ligands are mathematical correlated and their relative expansion is interrelated and needs to be coordinated / synchronized; i.e. it is critical to elect the appropriate combination of linkers with suitable dimensions to afford the requisite net expansion and construct the looked-for isoreticular MOF. It is to be noted that various relatively simple examples of mixed-linker structures were reported by linking 0-periodic polyhedra or by pillaring 2-periodic layers in an axial-to-axial fashion, or by inserting / placing a second linker into specific MOFs containing “accepting” sites such as open metal or by exchanging terminal coordinating groups (e.g. hydroxide, acetate or benzoate groups). Evidently, despite the notable success in designing MOFs based on edge-transitive nets, the rational design of mixed- linker MOFs with higher complexity, in a purposeful one-pot synthesis, using reticular chemistry has yet to be demonstrated and rationalized.SUMMARY

[0004] Intricate mixed-linker structures, methods of synthesizing intricate mixed-linker structures, and the like are described.

[0005] In one aspect, the present invention is directed to methods of synthesizing an intricate mixed-linker structure comprising:(a) selecting a merged-net to target in a synthesis of the intricate mixed-linker structure, a first 3 -periodic (3p) edge-transitive net, and second 3p edge- transitive net, wherein the first and second 3p edge-transitive nets share a common signature net and are capable of combining to afford the targeted merged-net and wherein one of the first and second 3p edge-transitive nets is an embedded 3 -dimensional representation of a lower-periodicity net selected from 2-periodic (2p), 1-periodic (Ip), and 0-periodic (Op);(b) determining a connectivity and geometrical configuration of each node of the merged-net, wherein the nodes of the merged-net comprise a merged node and unmerged nodes, wherein the unmerged nodes include a first unmerged node and second unmerged node;(c) selecting a first molecular building block (MBB) with identical connectivity and geometrical configuration to the merged node and having two sets of points of extension, wherein each set of points of extension is capable of linking to distinct MBBs;4053.277PCT1(d) selecting a second MBB with the same connectivity and geometrical configuration as the first unmerged node;(e) inputting a length of the selected second MBB into a merged-net equation to calculate a length of a complementary MBB;(f) selecting a third MBB with the same connectivity and geometrical configuration as the second unmerged node, and the same length as the complementary MBB; and(g) reacting precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net.

[0006] The details of one or more examples are set forth in the description below. Other features, objects, and advantages will be apparent net from the description and from the claims.BRIEF DESCRIPTION OF DRAWINGS

[0007] This written disclosure describes illustrative embodiments that are non-limiting and non-exhaustive. In the drawings, which are not necessarily drawn to scale, like numerals describe substantially similar components throughout the several views. Like numerals having different letter suffixes represent different instances of substantially similar components. The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments discussed in the present document.

[0008] Reference is made to illustrative embodiments that are depicted in the figures, in which:

[0009] FIG. 1 illustrates schematics for three embodiments of method 100: extracting signature reo net from the binodal edge-transitive ftw net through the direct transformation method; extracting signature reo net from uninodal edge-transitive nbo net and pcu net through binary transformation and extracting signature reo net from uninodal edge-transitive nbo net and pcu net through edge transformation as well as the resulting merged xbn, xbo, and urk nets, according to some embodiments.

[0010] FIG. 2 illustrates a method 100 of synthesizing an intricate mixed-linker structure, according to some embodiments.

[0011] FIG. 3 illustrates a map showing the signature nets of 3 -periodic edge-transitive nets, with arrows pointing to all the nets sharing the same signature nets, wherein the 33 binodal nets4053.277PCT1are shown in diamonds, the 20 uninodal nets in dark gray squares, and the 2-periodic and 1 -periodic edge-transitive signature nets in light gray squares, according to some embodiments.

[0012] FIG. 4 illustrates a diagram showing the generation of enumerated 143 3p-3p merged nets (53 edge-transitive nets on left; 143 3p-3p merged nets in middle; and 25 signature nets on right), according to some embodiments.

[0013] FIG. 5A illustrates a graph showing the counts of merged nets for each parent net edge-transitive net, according to some embodiments.

[0014] FIG. 5B illustrates a diagram showing representative merging modes of vertex figures in merged nets, according to some embodiments.

[0015] FIG. 5C illustrates a chart showing the percentage of highly-coordinated merged nets in each type of merged nets, according to some embodiments.

[0016] FIG. 5D illustrates charts showing the edge-ratio of generated merged nets and the distribution of most observed edge-ratio in merged nets, according to some embodiments.

[0017] FIG. 6A illustrates a schematic diagram showing the structure of Tb-sph-MOF-6 merged from 3-p spn parts and 3-p hxg parts, according to some embodiments.

[0018] FIG. 6B illustrates a schematic diagram showing the structure of Y-pch-MOF-1 merged from 3-p pcu part and 2-p hxl part, according to some embodiments.

[0019] FIG. 6C illustrates a schematic diagram showing the structure of Zr-thw-MOF-1 merged from 3-p the part and 1-p lew part, according to some embodiments.

[0020] FIG. 6D illustrates a schematic diagram showing the structure of Fe-nam-MOF-1, which merged from 3-p nbo part and 0-p ada part, according to some embodiments.

[0021] FIG. 7A illustrates a schematic diagram showing the structure design and synthesis of Y-pck-MOF-1 based on the derived net of peu-kgd merged pek MOF, according to some embodiments.

[0022] FIG. 7B illustrates a schematic diagram showing the structure design and synthesis of Tb-nih-MOF-1 based on the related net of nia-hxl merged nih MOF, according to some embodiments.

[0023] FIG. 8 illustrates a schematic diagram showing the discovery of ers signature net as the underlying principle for the merge of spn and hxg-b into sph net, according to some embodiments.4053.277PCT1

[0024] FIG. 9 illustrates a schematic showing the generation of a merged net based on only binary transformation method, according to some embodiments.

[0025] FIG. 10 illustrates a schematic showing the generation of a merged net using only the edge transformation method, according to some embodiments.

[0026] FIG. 11A illustrates a schematic showing the signature nets map of five 2-periodic edge-transitive nets, according to some embodiments.

[0027] FIG. 11B illustrates a signature map of 2-periodic edge-transitive nets, wherein uninodal nets are shown in rectangles, binodal nets are shown in diamonds, and arrows indicate the nets with the same signature nets and are color-coded to indicate different transformation methods: black for direct method, gray for binary transformation, and white for edge transformation.

[0028] FIG. 12 illustrates a schematic showing that the 3 -periodic edge-transitive nets with cubic symmetry can be transformed into their lower symmetry versions, either tetragonal or trigonal, to find their 2-periodic signature nets, according to some embodiments.

[0029] FIG. 13 illustrates a diagram showing the generation of enumerated 135 3p-2p merged nets (3 -periodic parent nets on left; 3p-2p merged nets in middle; and 2-periodic parent nets on right), according to some embodiments.

[0030] FIG. 14 illustrates a signature map of 0-periodic nets, wherein uninodal nets are shown in rectangles, binodal nets are shown in diamonds, and the arrows indicate the nets with the same signature nets and are color-coded to indicate different transformation methods: black for direct method, gray for binary transformation, and white for edge transformation, according to some embodiments.

[0031] FIG. 15 illustrates images of eighteen 3 -periodic edge- transitive nets with 0-periodic edge-transitive tilings, according to some embodiments.

[0032] FIG. 16 illustrates a table showing images of 0-periodic edge-transitive tiling and corresponding 3-periodic edge-transitive nets, according to some embodiments.

[0033] FIG. 17 illustrates a map of the generation of 67 3p-0p merged nets by merging 3- periodic and 0-periodic edge-transitive nets. (3-periodic parent nets on left; merged nets in middle; 0-periodic parent nets on right), according to some embodiments.4053.277PCT1

[0034] FIG. 18A-I illustrate nine representative merged nets with a relatively lower edge ratio, wherein the exact value is shown as a fraction, and the approximate value is shown as a decimal in parentheses, according to some embodiments.

[0035] FIG. 19A-I illustrate nine representative merged nets with a relatively higher edge ratio, wherein the exact value is shown as a fraction, and the approximate value is shown as a decimal in parentheses, according to some embodiments.

[0036] FIG. 20 illustrates a schematic showing an example of pch net showing the variable edge ratio in 3p-2p merged nets, according to some embodiments.

[0037] FIG. 21 illustrates images of proposed merged net structures based on paddlewheel building blocks, according to some embodiments.

[0038] FIG. 22 illustrates images of proposed merged net structures based on trinuclear clusters, according to some embodiments.

[0039] FIG. 23 illustrates images of proposed merged net structures based on tetranuclear clusters, according to some embodiments.

[0040] FIG. 24 illustrates images of proposed merged net structures based on saturated (12- c) hexanuclear clusters, according to some embodiments.

[0041] FIG. 25 illustrates images of proposed merged net structures based on unsaturated (connectivity < 12) hexanuclear clusters, according to some embodiments.

[0042] FIG. 26 illustrates images of proposed merged net structures based on octanuclear clusters, according to some embodiments.

[0043] FIG. 27 illustrates images of proposed merged net structures based on hexapaddlewheel supermolecular building blocks, according to some embodiments.

[0044] FIG. 28 illustrates images of proposed merged net structures based on dodecapaddlewheel supermolecular building blocks, according to some embodiments.

[0045] FIG. 29 illustrates a schematic showing the structural difference between Y-pch- MOF-1 and Y-pch-MOF-2, according to some embodiments.

[0046] FIG. 30 illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-BTPHB-pcu-MOF, according to some embodiments.

[0047] FIG. 31A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Tb-sph-MOF-6, according to some embodiments.4053.277PCT1

[0048] FIG. 31B illustrates a graph showing argon adsorption of Tb-sph-MOF-6 and desorption isotherms measured at 87K, according to some embodiments.

[0049] FIG. 31C illustrates a graph showing pore size distribution analysis of Tb-sph-MOF- 6 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0050] FIG. 31D illustrates a graph showing BET linear fit of Tb-sph-MOF-6, according to some embodiments.

[0051] FIG. 32A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-pch-MOF-1, according to some embodiments.

[0052] FIG. 32B illustrates a graph showing argon adsorption of Y-pch-MOF-1 and desorption isotherms measured at 87K, according to some embodiments.

[0053] FIG. 32C illustrates a graph showing pore size distribution analysis of Y-pch-MOF-1 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0054] FIG. 32D illustrates a graph showing BET linear fit of Y-pch-MOF-1, according to some embodiments.

[0055] FIG. 33A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-pch-MOF-2, according to some embodiments.

[0056] FIG. 33B illustrates a graph showing argon adsorption of Y-pch-MOF-2 and desorption isotherms measured at 87K, according to some embodiments.

[0057] FIG. 33C illustrates a graph showing pore size distribution analysis of Y-pch-MOF-2 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0058] FIG. 33D illustrates a graph showing BET linear fit of Y-pch-MOF-2, according to some embodiments.

[0059] FIG. 34A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Zr-thw-MOF-1, according to some embodiments.

[0060] FIG. 34B illustrates a graph showing argon adsorption of Zr-thw-MOF-1 and desorption isotherms measured at 87K, according to some embodiments.

[0061] FIG. 34C illustrates a graph showing pore size distribution analysis of Zr-thw-MOF- 1 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0062] FIG. 35A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Fe-nam-MOF-1, according to some embodiments.4053.277PCT1

[0063] FIG. 35B illustrates a graph showing argon adsorption of Fe-nam-MOF-1 and desorption isotherms measured at 87K, according to some embodiments.

[0064] FIG. 35C illustrates a graph showing pore size distribution analysis of Fe-nam- MOF-1 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0065] FIG. 35D illustrates a graph showing BET linear fit of Fe-nam-MOF-1, according to some embodiments.

[0066] FIG. 36A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-pck-MOF-1, according to some embodiments.

[0067] FIG. 36B illustrates a graph showing argon adsorption of Y-pck-MOF-1 and desorption isotherms measured at 87K, according to some embodiments.

[0068] FIG. 36C illustrates a graph showing pore size distribution analysis of Y-pck-MOF- 1 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0069] FIG. 36D illustrates a graph showing BET linear fit of Y-pck-MOF-1, according to some embodiments.

[0070] FIG. 37A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Tb-nih-MOF-1, according to some embodiments.

[0071] FIG. 37B illustrates a graph showing argon adsorption of Tb-nih-MOF-1 and desorption isotherms measured at 87K, according to some embodiments.

[0072] FIG. 37C illustrates a graph showing pore size distribution analysis of Tb-nih-MOF- 1 calculated with carbon slit pores model by NLDFT method, according to some embodiments.

[0073] FIG. 37D illustrates a graph showing BET linear fit of Tb-nih-MOF-1 , according to some embodiments.DETAILED DESCRIPTION

[0074] The present disclosure relates to a new class of materials — intricate mixed-linker structures characterized by underlying merged-net topologies. These structures arise from two distinct edge-transitive parent nets that share a common signature net and merge through shared nodes to afford a three-periodic minimal edge-transitive net having two different kinds of linkers (a “merged net” or “merged-net topology”). At least one parent net is made from a two-periodic (2p), one-periodic (Ip), or zero-periodic (Op) structures which has been embedded within a4053.277PCT1compatible three-dimensional crystallographic setting to permit compatibility analysis and merging, called 2p-, Ip-, or Op- derived parent nets, respectively.

[0075] This merged-nets approach formalizes parent net-to-signature transformations (edge, binary, or direct), placement within a common signature-net geometry, and metric compatibility evaluated in the embedding. Using this approach, applicants have identified 210 new merged-net topologies derived from 2p-, Ip-, and Op-derived parent nets: 135 involving embedded 2p parent nets (3p-2p), 8 involving embedded Ip parent nets (3p-lp), and 67 involving embedded Op parent nets (3p-0p). In general, intricate mixed-linker structures can be designed and / or constructed from any two edge-transitive parent nets with

[0011] or

[0021] transitivity that share a common signature net. In some embodiments, the merged-net equation relates the associated edge lengths (measured in the 3D embedding) and effective node sizes of the molecular building blocks, enabling deliberate selection of linker lengths and building units across isoreticular series. FIG. 1 maps representative parent nets to their signature nets and illustrates how these relationships can be applied to design and synthesize the materials disclosed herein.

[0076] The entire disclosure of U.S. Patent No. 11,952,391, filed on June 11, 2019, and entitled “Intricate Mixed-Linker Structures,” is incorporated herein by reference in its entirety for all purposes.Definitions

[0077] The terms recited below have been defined as described below. All other terms and phrases in this disclosure shall be construed according to their ordinary meaning as understood by one of skill in the art.

[0078] As used herein, “intricate mixed-linker structure” refers to any chemical composition having a merged-net as an underlying topology and two different kinds of linkers.

[0079] As used herein, the term “merged-net” refers to an underlying topology of an intricate mixed-linker structure.

[0080] As used herein, the term “node” refers to any component of the intricate mixed-linker structures with two or more connection points.

[0081] As used herein, the term “edge” refers to a linker or ligand between nodes.

[0082] As used herein, the term “metal component” generally refers to metal-containing components.4053.277PCT1

[0083] As used herein, the term “polytopic ligand” refers to any chemical species capable of coordinating to two or more nodes (e.g., metals).

[0084] As used herein, the term “minimal edge-transitive nets” refers to nets with only one or two kinds of edges or linkers.

[0085] As used herein, the term “edge-transitive nets” refers to nets with only one kind of edge or linker.

[0086] As used herein, the term “parent net” refers to a net subjected to a transformation.

[0087] As used herein, the term “signature net” refers to a reduced net that encodes the connectivity and geometric arrangement of shared nodes between two edge-transitive parent nets and thereby indicates their compatibility for merging. Signature nets may be the result of a transformation of a parent net. Examples of transformations include edge transformations, binary transformations, and direct transformations.

[0088] As used herein, the term “coordination number” and “n-c” as in ^-coordinated and / or ^-connected, refers to the number of coordinate sites of a component. The value of n is typically at least 1.

[0089] As used herein, the notation “transitivity [N E]” refers to the number of symmetry- distinct node types, N, and edge types, E, in a net. Thus, a “

[0011] ” net has one vertex kind and one edge kind (uninodal, single edge type), whereas a “

[0012] ” net has one vertex kind and two edge kinds (uninodal, two edge types).

[0090] As used herein, the term “co-subgroup symmetry” refers to a crystallographic symmetry relationship in which the space group of a merged net is determined as a subgroup (or common subgroup) consistent with the space groups of the parent nets when considered under a common embedding.

[0091] As used herein, the terms “three-periodic net” and “3p net” refer to nets that extend periodically in three dimensions and form a fully three-dimensional framework.

[0092] As used herein, the terms “two-periodic net” and “2p net” refer to nets that extend periodically in two dimensions and may be layered or sheet-like in character.

[0093] As used herein, the term “one-periodic net” or “Ip net” refer to nets that extends periodically in one dimension and may form chains, rods, or linear structures.4053.277PCT1

[0094] As used herein, the term “zero-periodic net” or “Op net” refer to discrete or finite structures, such as a molecular or cluster-like entities, that lack translational periodicity in any dimension.

[0095] As used herein, “2p-derived,” “Ip-derived,” and “Op-derived” nets refer to nets derived from parent nets with 2p, Ip, and Op periodicity prior to embedding, respectively.MERGED-NETS APPROACH

[0096] The present disclosure describes the merged-nets approach - an approach that permits the deliberate design and construction of materials with higher complexity. Such materials are referred to herein as intricate mixed-linker structures. The intricate mixed-linker structures are based on two distinct edge-transitive nets that merge through shared nodes to afford a new minimal edge-transitive net with two different kinds of linkers. Edge-transitive nets that are used to make the merged net may be three-periodic (3p) or they may be generated from parent net structures that are zero-, one-, or two-periodic (Op, Ip, 2p) which have been embedded in a compatible three- dimensional crystallographic setting. The merged-nets approach can be used to fabricate intricate mixed-linker structures with assorted functionalities and varied properties suitable for a wide array of applications, ranging from gas storage and gas separations to catalysis, chemical sensing, and beyond.

[0097] The merged-nets approach is based on previously inaccessible relationships / correlations between edge-transitive nets. The coded information embedded in building units is formalized as a signature net that captures node connectivity and geometry and can be extracted from each parent net (e.g., by direct, binary, or edge transformation) to obtain the connectivity and geometrical information required for the design and construction of intricate mixed-linker structures. Once extracted, signature nets can be used to identify pairs of distinct edge-transitive nets that can be merged through shared nodes to afford new minimal edgetransitive nets with two different kinds of linkers. Series of isoreticular intricate mixed-linker structures can be constructed using a merged-net equation which embodies the inherent geometrical features of the resulting merged net. In general, the merged-net equation is based on a correlation between the dimension / length of the associated edges of the two distinct edgetransitive nets from which the merged-net was formed. For parent nets made from Op, Ip, or 2p nets, the associated edge lengths are taken in the 3D embedding. A unique merged-net equation4053.277PCT1can be derived for each merged-net and used to determine the size of a suitable complimentary linker for targeted intricate mixed-linker structures.

[0098] According to the merged-net approach, any two parent nets that share a common signature net can merge through shared nodes (e.g., in a one-pot synthesis) to form intricate mixed- linker structures. A parent net is generally an edge-transitive net selected from nets with

[0011] transitivity and / or

[0021] transitivity. An edge- transitive net with

[0011] transitivity describes a net with one kind of node and one kind of edge. An edge-transitive net with

[0021] transitivity describes a net with two kinds of nodes and one kind of edge.

[0099] A parent net can be transformed to obtain a signature net of the parent net. Parent net transformations involve representing a net as an array of nodes and conducting a transformation operation that involves relinking nodes in a particular manner to yield a parent net’s signature net. Parent nets may be transformed in different ways to yield different signature nets. Examples of parent net transformations include, but are not limited to, direct method transformations, binary transformations, and direct transformations. Direct method transformations involve a binodal parent net being relinked by connecting nearest-neighbor nodes of the same type to yield its signature net (e.g., extracting reo from ftw). Binary transformations involve a uninodal parent net being evenly split into two node sets to create a binodal

[0021] version which are relinked to yield its signature net. In binary transformations, all ring vertex counts must be even to permit an even partitioning of the parent net into two equivalent node sets. Edge transformations involve midpoint nodes being added to every edge to form a pseudo-binodal

[0021] net and relinking those midpoints into an edge-transitive net that serves as the signature net. These three transformations underpin the signature-net map and allow merges of the following nine merge-type classes each corresponding to a distinct pairing of parent net-net transformation types: direct-signature, binarysignature, edge-signature (parent net merged with its signature net) and direct-direct, binarybinary, edge-edge, direct-binary, direct-edge, and binary-edge.

[0100] FIG. 1 demonstrates these three transformation methods being conducted on three parent nets: direct method transformation with ftw net, binary transformation with nbo net, and edge transformation with pcu net. Notably, this figure also demonstrates that different transformation methods on different parent nets can yield the same signature net due to the three transformations all yielding reo net. Using the relationship map shown in FIG. 1, edge-transitive nets having a common signature net were merged and the coded information necessary for the4053.277PCT1design and construction of intricate mixed-linker structures was extracted from the resulting merged- nets and summarized in Table 1. In particular, Table 1 presents a non-exhaustive list of 210 novel merged-net topologies that have heretofore not been available or known. Each merged- net presented in Table 1 is associated with a first parent net (PNi) and a second parent net (PN2), as well as a signature net (SN) shared by the first and second parent nets.Table 1. List of merged nets (3p-2p, 3p-lp, and 3p-0p).4053.277PCT14053.277PCT14053.277PCT14053.277PCT14053.277PCT1

[0101] FIG. 2 is a flowchart of a method of synthesizing intricate mixed-linker structures using the merged-nets approach, according to one or more embodiments of the present disclosure.

[0102] As shown in FIG. 2, the method comprises one or more of the steps (a) through (g):(a) selecting 201 a merged- net to target in a synthesis of the intricate mixed-linker structure, a first 3-periodic (3p) edge-transitive net, and second 3p edge-transitive net, wherein the first and second 3p edge-transitive nets share a common signature net and are capable of combining to afford the targeted merged-net and wherein one of the first and second 3p edge- transitive nets is an embedded 3 -dimensional representation of a lower- periodicity net selected from 2-periodic (2p), 1 -periodic (Ip), and 0-periodic (Op);(b) determining 202 a connectivity and geometrical configuration of each node of the merged-net, wherein the nodes of the merged-net comprise a merged node and unmerged nodes, wherein the unmerged nodes include a first unmerged node and second unmerged node;(c) selecting 203 a first molecular building block (MBB) with identical connectivity and geometrical configuration to the merged node and having two sets of points of extension, wherein each set of points of extension is capable of linking to distinct MBBs;(d) selecting 204 a second MBB with the same connectivity and geometrical configuration as the first unmerged node;(e) inputting 205 a length of the selected second MBB into a merged-net equation to calculate a length of a complementary MBB;4053.277PCT1(f) selecting 206 a third MBB with the same connectivity and geometrical configuration as the second unmerged node, and the same length as the complementary MBB; and(g) reacting 207 precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net.

[0103] In certain embodiments, at least one of the first and second edge-transitive nets is an embedded 3 -dimensional representation of a 2-periodic net.

[0104] In certain embodiments, at least one of the first and second 3p edge-transitive nets is selected from: sql net, kgm net, hcb net, hxl net, and kgd net.

[0105] In certain embodiments, the merged net is selected from: acc net, nia-d net, ack net, aci net, tsn net, acl net, acg net, hep net, acn net, aco net, lon-e net, ali net, alh net, alk net, alj net, bsa net, xal net, bsd net, boh net, bok net, bos net, boq net, csb net, esm net, esg net, die net, ted net, dik net, tsi net, dib net, diq net, epx net, fka net, fuq net, fha net, fhx net, fkm net, flc net, fix net, fll net, flk net, flq net, xak net, pfm net, fib net, fwh net, fwg net, fwk net, fws net, fwl net, fwq net, itx net, itk net, Icq net, mgb net, mgt net, mgx net, mgq net, mgl net, nbh net, nbc net, epa net, nbm net, ats net, nid net, nix net, nih net, nik net, ocb net, ocx net, ock net, ocq net, oev net, ocm net, ocl net, pcc net, peg net, pcs net, pch net, pek net, pem net, ahq net, ptx net, ptl net, ptk net, ptg net, pss net, pst net, urj net, psp net, pyh net, pys net, pyq net, rhh net, rhs net, rhq net, sus net, kty net, shq net, shd net, shm net, shh net, shx net, shk net, shg net, scs net, seq net, sem net, sqq net, ssh net, ssx net, ssg net, ssq net, sti net, stm net, sss net, stn net, eye net, thx net, thk net, tom net, tob net, tox net, tol net, toy net, tow net, tod net, ttk net, ttj net, ttm net, ttn net, twx net, twk net, twq net, and twl net.

[0106] In certain embodiments, at least one of the first and second 3p edge-transitive nets is an embedded 3 -dimensional representation of a 1 -periodic net.

[0107] In certain embodiments, at least one of the first and second 3p edge-transitive nets is lew net.

[0108] In certain embodiments, the merged net is selected from: ith-d net, thw net, itw net, sww net, rew net, brw net, tbw net, and flw net.

[0109] In certain embodiments, at least one of the first and second 3p edge-transitive nets is an embedded 3 -dimensional representation of a 0-periodic net.

[0110] In certain embodiments, at least one of the first and second 3p edge-transitive nets is selected from: cub net, cuo net, oct net, rdo net, and tet net.4053.277PCT1

[0111] In certain embodiments, the merged net is selected from: boc net, era net, crc net, ere net, erf net, erv net, did net, dig net, dih net, dii net, ffv net, ffe net, ffh net, ffk net, ffl net, fid net, lie net, fwm net, fwn net, fww net, hxa net, hxe net, hxc net, kpl net, mga net, mge net, nam net, nbb net, nbr net, nbu net, neb net, pea net, peb-e net, pee net, pef net, pej net, pcq net, pha net, pyc net, rea net, rec net, ree net, ref net, reg net, reh net, rha net, rhe net, rhg net, rhi net, sej net, scr net, sew net, spa net, spb net, str net, tbm net, tw net, tew net, tex net, tew net, tex net, thi net, thm net, xay net, xbf net, xbh net, and xbi net.

[0112] In certain embodiments, at least one of the first and second 3p edge-transitive nets is a 3-periodic net selected from: acs net, alb net, ana net, bes net, bcu net, bor net, ers net, esq net, ctn net, dia net, feu net, flu net, ftw net, hxg net, ith net, les net, lev net, Icy net, Ivt net, mge net, nbo net, nia net, ocu net, peu net, pth net, pto net, pts net, pyr net, qtz net, reo net, rhr net, rht net, scu net, she net, shp net, soc net, sod net, spn net, sqc net, srs net, ssa net, ssb net, ssc net, stp net, tbo net, the net, thp net, toe net, ttt net, and twf net.

[0113] In certain embodiments, the first MBB and second MBB are different. In certain embodiments, each of the MBB, first MBB, and second MBB is independently selected from an organic MBB or inorganic MBB. In certain embodiments, each of the MBB, first MBB, and second MBB is independently selected from a first polytopic ligand, second polytopic ligand, or metal component. In certain embodiments, at least one of the MBB, first MBB, and second MBB is an inorganic MBB comprising a cluster of metals or metal ions.

[0114] In certain embodiments, the first MBB associates with at least one of the two sets of points of extension to afford the first 3p edge-transitive net. In certain embodiments, the second MBB associates with at least one of the two sets of points of extension to afford the second 3p edge-transitive net.

[0115] In certain embodiments, the merged-net equation is represented by formula (1):where CR is a ratio constant for a merged-net, SBBI is the size of all building blocks for the first 3p edge-transitive net, and SBB2 is the size of all building blocks for the second 3p edge-transitive net. In certain embodiments, the merged-net equation splits building blocks into two parts, organic parts and inorganic parts. In some embodiments, the size of the inorganic building block is4053.277PCT1considered to be a constant and can be measured from reported structures. In some embodiments, the size relation between organic linkers is represented by formulas (2) or (3). In certain embodiments, the merged-net equation is represented by formula (2) or (3):where Soi and S02 are the total size of all organic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively; CR is a ratio constant for a merged-net; and Sn and Sn are the total size of all inorganic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively.

[0116] In certain embodiments, the method further comprises selecting additional pair of first and second MBBs to form an isoreticular intricate mixed-linker structure.

[0117] Embodiments of the present disclosure further describe compositions comprising: an intricate mixed-linker structure with a merged-net topology, the metal-organic framework comprising a molecular building block (MBB) having a first point of extension and second point of extension, wherein the first point of extension is coordinated to a first MBB and the second point of extension is coordinated to a second MBB, wherein the first MBB and second MBB are different.

[0118] In certain embodiments, the first MBB is a first polytopic ligand and the second MBB is a second polytopic ligand.

[0119] In certain embodiments, the coordination of the first MBB with the first point of extension affords a first 3p edge-transitive net.

[0120] In certain embodiments, the coordination of the second MBB with the second point of extension affords a second 3p edge-transitive net.

[0121] While various features have been described, other aspects of the features described above are described elsewhere throughout the present disclosure. Accordingly, embodiments shall be understood to include other such features, even if not explicitly described above, without departing from the scope of the present invention. Such disclosure and descriptions are thus hereby incorporated by reference in their entirety.4053.277PCT1

[0122] Now having described one example of a method of synthesizing the intricate mixed- linker structures, various aspects of the intricate mixed-linker structures are described.INTRICATE MIXED-LINKER STRUCTURES

[0123] In some embodiments, materials comprise a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form an intricate mixed-linker structure with a merged-net topology. The first and second polytopic ligands are distinct. The merged-net topology arises from a first edge-transitive net and a second edge-transitive net that share a common signature net and merge through shared nodes to afford the merged net. In addition to forming a new minimal edge-transitive net, portions of the parent net-net frameworks — corresponding to unmerged nodes and original edges — can, in some embodiments, be retained within the merged net. Parent nets may be three-periodic (3p) or derived from zero-, one-, or two- periodic (Op, 1 p, 2p) structures after embedding in a compatible three-dimensional crystallographic setting.

[0124] The intricate mixed-linker structures can include a variety of material classes. In some embodiments, they are metal-organic frameworks (MOFs), coordination polymers (CPs), porous coordination polymers (PCPs), porous coordination networks (PCNs), or metal-organic materials (MOMs). In other embodiments, they are porous organic polymers (POPs), covalent organic frameworks (COFs), porous aromatic frameworks (PAFs), porous polymer networks (PPNs), conjugated microporous polymers (CMPs), microporous polymer networks (MPNs), polymers with intrinsic microporosity (PIMs), or hyper-cross-linked polymers (HCPs).MERGED-NETS TOPOLOGY

[0125] As described herein, the underlying topology of the intricate mixed-linker structures is a merged-net topology or a merged-net. In general, a merged-net is a 3 -periodic minimal edgetransitive net with two kinds of edges or linkers. In some embodiments, the merged-net has two kinds of edges or linkers, and either two or three kinds of vertices or nodes. For example, in some embodiments, the merged-net is a net with

[0022] transitivity, which describes a net with two kinds of nodes and two kinds of edges. In some embodiments, the merged-net is a net with

[0032] transitivity, which describes a net with three kinds of nodes and two kinds of edges.

[0126] In embodiments wherein at least one of the first and second edge-transitive nets is an embedded 3 -dimensional representation of a 2-periodic net, examples of merged-nets include nets selected from: acc net, nia-d net, ack net, aci net, tsn net, acl net, acg net, hep net, acn net, aco4053.277PCT1net, lon-e net, ali net, alh net, alk net, alj net, bsa net, xal net, bsd net, boh net, bok net, bos net, boq net, csb net, csm net, csg net, die net, ted net, dik net, tsi net, dib net, diq net, epx net, fka net, fuq net, fha net, fhx net, fkm net, flc net, fix net, fll net, flk net, flq net, xak net, pfm net, fib net, fwh net, fwg net, fwk net, fws net, fwl net, fwq net, itx net, itk net, Icq net, mgb net, mgt net, mgx net, mgq net, mgl net, nbh net, nbc net, epa net, nbm net, ats net, nid net, nix net, nih net, nik net, ocb net, ocx net, ock net, ocq net, oev net, ocm net, ocl net, pcc net, peg net, pcs net, pch net, pek net, pem net, ahq net, ptx net, ptl net, ptk net, ptg net, pss net, pst net, urj net, psp net, pyh net, pys net, pyq net, rhh net, rhs net, rhq net, sus net, kty net, shq net, shd net, shm net, shh net, shx net, shk net, shg net, scs net, seq net, sem net, sqq net, ssh net, ssx net, ssg net, ssq net, sti net, stm net, sss net, stn net, eye net, thx net, thk net, tom net, tob net, tox net, tol net, toy net, tow net, tod net, ttk net, ttj net, ttm net, ttn net, twx net, twk net, twq net, and twl net.

[0127] In embodiments wherein at least one of the first and second edge-transitive nets is an embedded 3 -dimensional representation of a 1 -periodic net, examples of merged-nets include nets selected from: ith-d net, thw net, itw net, sww net, rew net, brw net, tbw net, and flw net.

[0128] In embodiments wherein at least one of the first and second edge-transitive nets is an embedded 3 -dimensional representation of a 0-periodic net, examples of merged-nets include nets selected from: boc net, era net, crc net, ere net, erf net, erv net, did net, dig net, dih net, dii net, ffv net, ffe net, ffh net, ffk net, ffl net, fid net, fie net, fwm net, fwn net, fww net, hxa net, hxe net, hxe net, kpl net, mga net, mge net, nam net, nbb net, nbr net, nbu net, neb net, pea net, peb- e net, pee net, pef net, pej net, pcq net, pha net, pyc net, rea net, rec net, ree net, ref net, reg net, reh net, rha net, rhe net, rhg net, rhi net, sej net, scr net, sew net, spa net, spb net, str net, tbm net, tw net, tew net, tex net, tew net, tex net, thi net, thm net, xay net, xbf net, xbh net, and xbi net.

[0129] In some embodiments, each edge or linker of the merged-net corresponds with or can be assigned to a 3-periodic edge-transitive net (e.g., the first 3p edge-transitive net and second 3p edge-transitive net). For example, in some embodiments, the merged-net comprises two edgetransitive nets, such as a first edge-transitive net and a second edge-transitive net. In some embodiments, the merged-net comprises a first edge-transitive net and a second edge-transitive net that share nodes. In embodiments where the first edge-transitive net and second edge-transitive net share nodes (e.g., inorganic, organic, and / or organic- inorganic MBBs), the first edge-transitive net and second edge-transitive net are said to have merged. For example, in some embodiments, the4053.277PCT1merged-net comprises a first edge-transitive net and second edge-transitive net that have merged through shared nodes.

[0130] In some embodiments, the merged-net is a novel minimal edge-transitive net with two different kinds of linkers. In some embodiments, the merged-net encompasses and / or retains each of the edge- transitive nets that merged. For example, in some embodiments, the merged-net encompasses and / or retains the structural properties of the first edge-transitive net, second edgetransitive net, or both the first edge-transitive net and second edge-transitive net.

[0131] In some embodiments, each of the first edge-transitive net and second edge-transitive net are nets with only one kind of edge or linker. For example, in some embodiments, the first edge-transitive net and / or second edge-transitive net have one kind of edge or linker, and either one or two kinds of vertices or nodes. In some embodiments, the first edge-transitive net and / or second edge-transitive net is a net with

[0011] transitivity, which describes a net with one kind of node and one kind of edge. In some embodiments, the first edge-transitive net and / or second edgetransitive net is a net with

[0021] transitivity, which describes a net with two kinds of nodes and one kind of edge. Accordingly, in some embodiments, the first and second edge-transitive nets are nets with

[0011] transitivity. In some embodiments, the first edge-transitive net is a net with

[0011] transitivity and the second edge-transitive net is a net with

[0021] transitivity. In some embodiments, the first edge-transitive net is a net with

[0021] transitivity and the second edge-transitive net is a net with

[0011] transitivity. In some embodiments, the first and second edge-transitive nets are nets with

[0021] transitivity.

[0132] Examples of nets with

[0011] transitivity (e.g., first edge-transitive net with

[0011] transitivity, second edge-transitive nets with

[0011] transitivity, or both) are selected from a hxg net, lew net, hxl net, kgm net, heb net, dia net, ers net, nbo net, sod net, rhr net, acs net, sql net, Ivt net, bcu net, peu net, feu net, reo net, qtz net, srs net, lev net, ley net, bes net, les net, ana net, and thp net.

[0133] Examples of nets with

[0021] transitivity (e.g., first edge-transitive net with

[0021] transitivity, second edge-transitive nets with

[0021] transitivity, or both) are selected from a shp net, alb net, stp net, mge net, spn net, toe net, nia net, ssa net, esq net, ith net, twf net, ocu net, she net, pto net, pth net, ssb net, pts net, soc net, ttt net, rht net, bor net, the net, scu net, sqc net, flu net, pyr net, ftw net, tbo net, ifi net, ssc net, iac net, gar net, and ctn net.4053.277PCT1

[0134] In some embodiments, the merged-net comprises a first edge-transitive net and a second edge-transitive net, wherein the first and second edge-transitive nets share a common signature net. As used herein, the term “signature net” generally refers to any net resulting from a transformation of an edge-transitive net. In such embodiments, the first and second edge-transitive nets can be described or referred to as “parent nets.” As used herein, the term “parent nets” generally refers to the edge-transitive nets subjected to the transformation. In some embodiments, edge-transitive nets with a common signature net can combine or merge to afford intricate mixed- linker structures with merged-nets. Accordingly, in some embodiments, the identification of a common signature net among parent nets is an approach that can be used to design the intricate mixed-linker structures of the present disclosure.

[0135] Examples of signature nets include nets selected from a kgm net, ana net, feu net, reo net, bes net, pen net, ers net, nbo net, thp net, lew net, les net, sod net, hxg net, lev net, srs net, bcu net, ley net, dia net, acs net, qtz net, feu net, o-p net, rhr net, hxl net, Ivt net, and thp net.

[0136] In some embodiments, to identify a signature net, the parent net, an edge-transitive net, is transformed to a net with

[0021] transitivity. For example, in some embodiments, edgetransitive nets with

[0011] transitivity (e.g., parent nets with

[0011] transitivity) are transformed into nets with

[0021] transitivity by edge transformation, wherein edge transformation involves the addition of nodes (e.g., 2-c nodes) to the middle point of edges of the parent net. In some embodiments, edge-transitive nets with

[0011] transitivity (e.g., parent nets with

[0021] transitivity) are transformed to nets with

[0021] transitivity by binary transformation, wherein binary transformation involves the separation of nodes of a parent net into two groups of nodes. In some embodiments, edge-transitive nets with

[0021] transitivity (e.g., parent nets with

[0021] transitivity) are transformed into nets with

[0021] transitivity by direct transformation, wherein direct transformation involves the linking the same types of nodes.

[0137] In some embodiments, the merged-net comprises an edge-transformed net and the edge-transformed net’s signature net (e.g., “e-s” merged-net). In some embodiments, the coordination of a “e-s” merged-net is (2, ve, vs+ 2)-c, where veis the coordination of the edge- transformed parent net and vsis the coordination of the edge-transformed net’s signature net.

[0138] In some embodiments, the merged-net comprises a binary-transformed net and the binary-transformed net’s signature net (e.g., “b-s” merged-net). In some embodiments, the4053.277PCT1coordination of a “b-s” merged-net is (2, vb, Vb + vs)-c, where Vb is the coordination of the binary- transformed parent net and vsis the coordination of the binary -transformed net’s signature net.

[0139] In some embodiments, the merged net comprises a direct-transformed net and the direct-transformed net’s signature net (e.g., “d-s” merged-net). In some embodiments, the coordination of a “d-s” merged-net is (2, va, vam + vs)-c, where va is the coordination of the direct- transformed parent net (exclusive), vam is the coordination of the direct-transformed parent net (shared), and vsis the coordination of the direct-transformed net’s signature net.

[0140] In some embodiments, the merged-net comprises a first edge-transformed net and a second edge-transformed net (e.g., “e-e” merged-net). In some embodiments, the coordination of the “e-e” merged-net is (vei, ve2, 4)-c, where veiis the coordination of the first edge-transformed net and ve2 is the coordination of the second edge-transformed net.

[0141] In some embodiments, the merged-net comprises a first binary-transformed net and a second binary-transformed net (e.g., “b-b” merged-net). In some embodiments, the coordination of the “b-b” merged-net is (vbi, Vb2, Vbi + Vb2)-c, where vbi is the coordination of the first binary- transformed net and Vb2 is the coordination of the second binary-transformed net.

[0142] In some embodiments, the merged-net comprises a first direct-transformed net and a second direct-transformed net (e.g., “d-d” merged-net). In some embodiments, the coordination of the “d-d” merged-net is (vai, va2, vami + Vdm2)-c, where vai is the coordination of the first direct- transformed net (exclusive), Vd2 is the coordination of the second direct-transformed net (exclusive), Vdmi is the coordination of the first direct-transformed net (shared), and Vdm2 is the coordination of the second direct-transformed net (shared).

[0143] In some embodiments, the merged-net comprises an edge-transformed net and a binary-transformed net (e.g., “e-b” merged-net). In some embodiments, the coordination of the “e- b” merged-net is (ve, vb, vb + 2)-c, where veis the coordination of the edge-transformed net and vb is the coordination of the binary-transformed net.

[0144] In some embodiments, the merged-net comprises an edge-transformed net and a direct-transformed net (e.g., “e-d” merged-net). In some embodiments, the coordination of the “e- d” merged-net is (ve, va, vam + 2)-c, where veis the coordination of the edge-transformed net, va is the coordination of the direct-transformed net (exclusive), and vam is the coordination of the direct- transformed net (shared).4053.277PCT1

[0145] In some embodiments, the merged-net comprises a binary-transformed net and a direct-transformed net (e.g., “b-d” merged-net). In some embodiments, the coordination of the “b- d” merged-net is (vb, va, Vb + Vdm)-c, where Vb is the coordination of the binary-transformed net, va is the coordination of the direct-transformed net (exclusive), and Vdm is the coordination of the direct- transformed net (shared).

[0146] Enumeration of 3p-2p merged nets. There are five 2-periodic edge-transitive nets: uninodal nets sql, kgm, hcb, hxl, and binodal net kgd. The kgm and kgd are duals of each other, and the hxl and hcb are duals of each other. As used herein, the term “dual net” refers to the net obtained from a given embedded net or tiling by placing a vertex at the center of each tile (for three-dimensional tilings) or each face (for two-dimensional tilings) and joining two such vertices when the corresponding tiles (or faces) share a face (or edge), respectively. The edges of the dual net therefore cross the faces / edges of the original, and the construction is reversible in that taking the dual a second time yields a net isomorphic to the original. This duality construction is topological and independent of chemical composition.

[0147] The four uninodal nets could be used as signature nets to enumerate 3p-2p merged nets. The signature nets map of 2-periodic nets is simpler than the map of 3-periodic nets. The hxl net is the signature net of hcb and kgd. The hcb net is the signature net of kgd net. The kgm net is the signature net of hxl and hcb nets. The sql net is a signature net of itself through the binary method or edge method. The 2p parent net may be embedded within a compatible three- dimensional setting suitable for compatibility analysis (another term for transformation yielding a signature net), and any edge lengths used in merged-net equations are taken in this 3D embedding. A 3p parent net and an embedded 2p parent net may be merged if they share a common signature net obtained by edge, binary, or direct transformation.

[0148] Among the 53 3-periodic edge-transitive nets, 39 nets are based on cubic symmetry, and 14 nets are based on non-cubic symmetry. The non-cubic symmetry nets are pillared nets by themselves, and the 2-periodic signature nets can be directly isolated from the layer information of the 3-periodic pillared nets. In some embodiments, when a 2p layer is isolated from a pillared 3p net, the layer is treated as placed (embedded) in the parent net’s 3D setting so that node geometry and inter-edge angles are preserved for compatibility analysis. For parent net selection and placement, the following guardrails are applied after embedding: (i) distances between non-4053.277PCT1connected vertices are at least as long as edge lengths, and (ii) multiple edges (parallel edges sharing both end nodes) are excluded.

[0149] The 39 cubic-symmetry edge- transitive nets were observed not to exhibit 2-periodic signature nets directly, as the layers would be interconnected through isotropy. Therefore, a transformation is required to convert them into their non-cubic version. Two methods were found to achieve this transformation. The first method involves elongation along an axis of the unit cell, which results in a change in symmetry to tetragonal. (See FIG. 12) Upon transformation, the net has the potential to be merged with the sql net. The second method involves elongation through the body diagonal of the cubic unit cell, resulting in trigonal symmetry. (See FIG. 12) Upon transformation, the net has the potential to be merged with hxl, hcb, kgm, or kgd net. These elongations select a compatible embedding for the 3p parent net; merging still requires a common signature net with the embedded 2p parent net. In some embodiments, the nine merge-type classes apply to 3p-2p merges: direct-signature, binary-signature, edge-signature (parent net merged with its signature net) and direct-direct, binary-binary, edge-edge, direct-binary, direct-edge, and binary-edge. In some embodiments, the resulting merged-net transitivity follows the same outcomes observed generally:

[0022] for parent net + signature net (-signature merge type classes) cases, and

[0032] for the same-method and mixed-method pairs.

[0150] In some embodiments, a single 3p-2p parent net pair that shares a signature net can yield more than one merged net due to symmetry-equivalent placements (e.g., origin shifts or layer-orientation choices) that change vertex figures while preserving connectivity, resulting in distinct coordination sequences.

[0151] In some embodiments, positional conflicts among unmerged nodes in the placed parent nets can preclude a valid 3p-2p merge even when a common signature net exists; such collisions are identified and excluded during the compatibility analysis in the 3D embedding.

[0152] In some embodiments, a 3p-2p merge may degenerate to a known edge-transitive net rather than produce a distinct merged-net topology (for example, certain 3p+sql layer merges reproduce ftw) when the combined relinking matches the adjacency of a known net.

[0153] In some embodiments, the merged-net equation is used to select linker lengths for the 3p and embedded 2p parent nets; the edge-length ratio condition is evaluated in the 3D embedding and may include effective node half-sizes contributed by molecular building blocks to account for sterics, with a realizability tolerance.4053.277PCT1

[0154] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an acc merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c acc merged-net.

[0155] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an acg merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c acs net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c acg merged-net.

[0156] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an aci merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c acs net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c aci merged-net.

[0157] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ack merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge- transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,12)-c ack merged-net.

[0158] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an aci merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c acs net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c aci merged-net.

[0159] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an acn merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c acn merged-net.4053.277PCT1

[0160] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an aco merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (4,6,6)-c aco merged-net.

[0161] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ahq merged-net. In some embodiments, the first edge- transitive net is a (6)-c pcu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (4,6,6)-c ahq merged-net.

[0162] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an alh merged-net. In some embodiments, the first edge- transitive net is a (6,12)-c alb net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,18)-c alh merged-net.

[0163] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ali merged-net. In some embodiments, the first edge- transitive net is a (6,12)-c alb net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,9,12)-c ali merged-net.

[0164] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an alj merged-net. In some embodiments, the first edge-transitive net is a (6,12)-c alb net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (6,9,12)-c alj merged-net.

[0165] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an alk merged-net. In some embodiments, the first edge-transitive net is a (6,12)-c alb net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,18)-c alk merged-net.4053.277PCT1

[0166] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ats merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c nia net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c ats merged-net.

[0167] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a boh merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c boh merged-net.

[0168] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a bok merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,8)-c bok merged-net.

[0169] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a boq merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c boq merged-net.

[0170] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a bos merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,3,8)-c bos merged-net.

[0171] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a bsa merged-net. In some embodiments, the first edge-transitive net is a (8)-c bcu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c bsa merged-net.4053.277PCT1

[0172] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a bsd merged-net. In some embodiments, the first edge-transitive net is a (8,8)-c bcu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,12)-c bsd merged-net.

[0173] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a csb merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c esq net and the second edge-transitive net is a (3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,10)-c csb merged-net.

[0174] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a esg merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c esq net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c esg merged-net.

[0175] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a esm merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c esq net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,10)-c esm merged-net.

[0176] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a dib merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c dib merged-net.

[0177] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a die merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (3,3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,7)-c die merged-net.4053.277PCT1

[0178] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a dik merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,10)-c dik merged-net.

[0179] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a diq merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c dia net and the second edge- transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c diq merged-net.

[0180] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an epa merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c nbo net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,6)-c epa merged-net.

[0181] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an epx merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c dia net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,8)-c epx merged-net.

[0182] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an eye merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c stp net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,8)-c eye merged-net.

[0183] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fha merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,12)-c fha merged-net.4053.277PCT1

[0184] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fhx merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,12)-c fhx merged-net.

[0185] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fka merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,18)-c fka merged-net.

[0186] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fkm merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c fkm merged-net.

[0187] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fib merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,8)-c fib merged-net.

[0188] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an flc merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (3,3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,7,8)-c flc merged-net.

[0189] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an flk merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,14)-c flk merged-net.4053.277PCT1

[0190] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fll merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,8,10)-c fll merged-net.

[0191] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an flq merged-net. In some embodiments, the first edge- transitive net is a (4,8)-c flu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c flq merged-net.

[0192] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fix merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,14)-c fix merged-net.

[0193] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fuq merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,16)-c fuq merged-net.

[0194] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwg merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,18)-c fwg merged-net.

[0195] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwh merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c fwh merged-net.4053.277PCT1

[0196] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwk merged- net. In some embodiments, the first edge- transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,12)-c fwk merged-net.

[0197] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwl merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,16)-c fwl merged-net.

[0198] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwq merged-net. In some embodiments, the first edge- transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,12)-c fwq merged-net.

[0199] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fws merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,12)-c fws merged-net.

[0200] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an hep merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,12)-c hep merged-net.

[0201] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an itk merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ith net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,18)-c itk merged-net.4053.277PCT1

[0202] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an itx merged-net. In some embodiments, the first edge- transitive net is a (4,12)-c ith net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,18)-c itx merged-net.

[0203] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a kty merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c scu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (4,6,8)-c kty merged-net.

[0204] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an Icq merged-net. In some embodiments, the first edge-transitive net is a (6)-c Icy net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,10)-c Icq merged-net.

[0205] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an lon-e merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,6)-c lon-e merged-net.

[0206] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mgb merged-net. In some embodiments, the first edge- transitive net is a (6, 12)- c mgc net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (3,6,15)-c mgb merged-net.

[0207] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mgl merged-net. In some embodiments, the first edge-transitive net is a (6,12)-c mgc net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,16)-c mgl merged-net.4053.277PCT1

[0208] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mgq merged- net. In some embodiments, the first edge-transitive net is a (6,12)- c mgc net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,16)-c mgq merged- net.

[0209] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mgt merged- net. In some embodiments, the first edge-transitive net is a (6,12)-c mgc net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,15)-c mgt merged-net.

[0210] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mgx merged-net. In some embodiments, the first edge-transitive net is a (6,12)- c mgc net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,18)-c mgx merged-net.

[0211] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nbc merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c nbo net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c nbc merged-net.

[0212] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nbh merged-net. In some embodiments, the first edge-transitive net is a (4)-c nbo net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,6)-c nbh merged-net.

[0213] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nbm merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c nbo net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c nbm merged-net.4053.277PCT1

[0214] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nia-d merged-net. In some embodiments, the first edge-transitive net is a (6)-c acs net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c nia-d merged-net.

[0215] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nid merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c nia net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c nid merged-net.

[0216] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nih merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c nia net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c nih merged-net.

[0217] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nik merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c nia net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c nik merged-net.

[0218] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nix merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c nia net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c nix merged-net.

[0219] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocb merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge- transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,10)-c ocb merged-net.4053.277PCT1

[0220] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ock merged-net. In some embodiments, the first edge- transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c ock merged-net.

[0221] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocl merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,8)-c ocl merged-net.

[0222] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocm merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,8)-c ocm merged-net.

[0223] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocq merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,10)-c ocq merged-net.

[0224] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocv merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,8,10)-c ocv merged-net.

[0225] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ocx merged-net. In some embodiments, the first edge-transitive net is a (6,8)-c ocu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (6,6,10)-c ocx merged-net.4053.277PCT1

[0226] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pcc merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (3,3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c pcc merged-net.

[0227] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a peg merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,12)-c peg merged-net.

[0228] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pch merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c pcu net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c pch merged-net.

[0229] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pek merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c pcu net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c pek merged-net.

[0230] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pem merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c pem merged-net.

[0231] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pcs merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c pcs merged-net.4053.277PCT1

[0232] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pfm merged-net. In some embodiments, the first edge- transitive net is a (4,8)-c flu net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,12)-c pfm merged-net.

[0233] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a psp merged-net. In some embodiments, the first edge- transitive net is a (4,4)-c pts net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,8)-c psp merged-net.

[0234] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pss merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pts net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c pss merged-net.

[0235] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pst merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pts net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c pst merged-net.

[0236] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ptg merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pth net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,10)-c ptg merged-net.

[0237] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ptk merged-net. In some embodiments, the first edge-transitive net is a (4,24)-c pth net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,10)-c ptk merged-net.4053.277PCT1

[0238] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ptl merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pth net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c ptl merged-net.

[0239] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ptx merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pth net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c ptx merged-net.

[0240] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pyh merged-net. In some embodiments, the first edge- transitive net is a (3,6)-c pyr net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,12)-c pyh merged-net.

[0241] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pyq merged-net. In some embodiments, the first edge-transitive net is a (3,6)-c pyr net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,10)-c pyq merged-net.

[0242] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pys merged-net. In some embodiments, the first edge-transitive net is a (3,6)-c pyr net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,3,10)-c pys merged-net.

[0243] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhh merged-net. In some embodiments, the first edge-transitive net is a (3,24)-c rht net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,30)-c rhh merged-net.4053.277PCT1

[0244] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhq merged-net. In some embodiments, the first edge-transitive net is a (3,24)-c rht net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,28)-c rhq merged-net.

[0245] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhs merged-net. In some embodiments, the first edge- transitive net is a (3,24)-c rht net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,28)-c rhs merged-net.

[0246] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an scm merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,8)-c scm merged-net.

[0247] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an scq merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,8)-c scq merged-net.

[0248] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an scs merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c scs merged-net.

[0249] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shd merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c she net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,8)-c shd merged-net.4053.277PCT1

[0250] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shg merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c shp net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,12)-c shg merged-net.

[0251] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shh merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c shp net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,18)-c shh merged-net.

[0252] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shk merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c shp net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,18)-c shk merged-net.

[0253] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shm merged-net. In some embodiments, the first edge-transitive net is a (4, 12)- c shp net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c shm merged-net.

[0254] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shq merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c she net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c shq merged-net.

[0255] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an shx merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c shp net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (6,6,12)-c shx merged-net.4053.277PCT1

[0256] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sqq merged-net. In some embodiments, the first edge- transitive net is a (4,8)-c sqc net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c sqq merged-net.

[0257] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ssg merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c ssa net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c ssg merged-net.

[0258] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ssh merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c ssa net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c ssh merged-net.

[0259] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ssq merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c ssb net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c ssq merged-net.

[0260] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sss merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c stp net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (6,6,6)-c sss merged-net.

[0261] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ssx merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c ssa net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,6)-c ssx merged-net.4053.277PCT1

[0262] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sti merged-net. In some embodiments, the first edge- transitive net is a (4,6)-c stp net and the second edge- transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,9)-c sti merged-net.

[0263] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an stm merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c stp net and the second edge-transitive net is a (3)-c hcb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c stm merged-net.

[0264] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an stn merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c stp net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,9)-c stn merged-net.

[0265] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sus merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c sen net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c sus merged-net.

[0266] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ted merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,10)-c ted merged-net.

[0267] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a thk merged-net. In some embodiments, the first edge-transitive net is a (3,8)-c the net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,12)-c thk merged-net.4053.277PCT1

[0268] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a thx merged-net. In some embodiments, the first edge-transitive net is a (3,8)-c the net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (3,6,10)-c thx merged-net.

[0269] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tob merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c toe net and the second edge-transitive net is a (3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,8)-c tob merged-net.

[0270] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tod merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c toe net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,10)-c tod merged-net.

[0271] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tol merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c toe net and the second edge- transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (6,6,6)-c tol merged-net.

[0272] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tom merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c toe net and the second edge-transitive net is a (3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c tom merged-net.

[0273] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tow merged-net. In some embodiments, the first edge- transitive net is a (4,6)-c toe net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c tow merged-net.4053.277PCT1

[0274] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tox merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c toe net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,12)-c tox merged-net.

[0275] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a toy merged-net. In some embodiments, the first edge- transitive net is a (4,6)-c toe net and the second edge-transitive net is a (4)-c kgm net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,8)-c toy merged-net.

[0276] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tsi merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,8)-c tsi merged-net.

[0277] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tsn merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c acs net and the second edge-transitive net is a (3,3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c tsn merged-net.

[0278] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ttj merged-net. In some embodiments, the first edge- transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (2,3,18)-c ttj merged-net.

[0279] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ttk merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (3,3)-c heb net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,3,15)-c ttk merged-net.4053.277PCT1

[0280] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ttm merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,16)-c ttm merged-net.

[0281] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ttn merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,16)-c ttn merged-net.

[0282] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a twk merged-net. In some embodiments, the first edge-transitive net is a (4,24)-c twf net and the second edge-transitive net is a (3,6)-c kgd net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,30)-c twk merged-net.

[0283] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a twl merged-net. In some embodiments, the first edge-transitive net is a (4,24)-c twf net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,28)-c twl merged-net.

[0284] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a twq merged-net. In some embodiments, the first edge-transitive net is a (4,24)-c twf net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,28)-c twq merged-net.

[0285] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a twx merged-net. In some embodiments, the first edge-transitive net is a (4,24)-c twf net and the second edge-transitive net is a (6)-c hxl net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,30)-c twx merged-net.4053.277PCT1

[0286] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an urj merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c pts net and the second edge-transitive net is a (4,4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,8)-c urj merged-net.

[0287] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xak merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,8)-c xak merged-net.

[0288] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xal merged-net. In some embodiments, the first edge-transitive net is a (8,8)-c bcu net and the second edge-transitive net is a (4)-c sql net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,12)-c xal merged-net.

[0289] Enumeration of 3p-lp merged nets. Among the 53 3-periodic edge-transitive nets, Eight nets were identified that can be merged with the lew net using the signature net map. The standard lew net is a 3-periodic packing of the 1 -periodic linear rod based on the Pm-3n symmetry. The pto, and ith can merge with lew while retaining full symmetry, generating the (pto, lew)- merged (3,6)-c ith-d net and the (ith, lcw)-merged (6,12)-c itw net. The sod net can merge with lew through a binary transformation, generating (sod, lcw)-merged (4,6)-c sww net. In the lew net, the nodes on lew can shift to preserve the 1 -periodic rod. When the coordination of node (0.25, 0.50, 0.00) is shifted to (0.00, 0.50, 0.00), the nodes in lew and in reo occupy the same position, allowing for the generation of a (reo, lcw)-merged 10-c rew net with reduced symmetry, Pm-3. Additionally, the net, bor net, tbo net, and ftw net can merge with lew net using lew net / reo net as the signature net, generating (the, lcw)-merged (3,10)-c thw net, (bor, lcw)-merged (3,6)-c brw net, (tbo, lcw)-merged (3,6)-c tbw net, and (ftw, lcw)-merged (6,12)-c flw net.

[0290] In some embodiments, the Ip parent net is embedded within a compatible three- dimensional setting prior to compatibility analysis, and any edge lengths used in merged-net equations are taken in this 3D embedding. In some embodiments, the resulting merged-net transitivity follows the general outcomes:

[0022] when a parent net is merged with its signature net4053.277PCT1(-s), and

[0032] for same-method or mixed-method parent net pairs; the examples listed herein are consistent with these outcomes. A 3p parent net and an embedded Ip parent net may be merged if they share a common signature net obtained by edge, binary, or direct transformation.

[0291] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a brw merged-net. In some embodiments, the first edge- transitive net is a (3,4)-c bor net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,6)-c brw merged-net.

[0292] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an flw merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c flw merged-net.

[0293] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ith-d merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c pto net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,6)-c ith-d merged-net.

[0294] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an itw merged-net. In some embodiments, the first edge- transitive net is a (4,12)-c ith net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c itw merged-net.

[0295] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a rew merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,2,10)-c rew merged-net.

[0296] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sww merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c4053.277PCT1sod net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,6)-c sww merged-net.

[0297] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tbw merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c tbo net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,6)-c tbw merged-net.

[0298] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a thw merged-net. In some embodiments, the first edge-transitive net is a (3,8)-c the net and the second edge-transitive net is a (2)-c lew net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,10)-c thw merged-net.

[0299] Enumeration of 3p-0p merged nets. The 0-periodic nets, also represented as polyhedra, often serve as the underlying nets of coordination cages and supermolecular building blocks. By applying a method similar to that used for determining 3 -periodic signature nets, the signature nets of 0-periodic polyhedra were also identified. Analysis began with the 13 0-periodic edge-transitive nets. Among these, the tet net is the signature net of hxt, cub-b, and ada nets. The oct net is the signature net of rdo, ada, onb, and tet nets. The cuo net is the signature net of oct, cub, and onb nets. Based on their symmetry, these 13 nets can be divided into two groups: eight nets with Td or Oh symmetry, and fire nets with Ih symmetry. Notably, the five nets with Ih symmetry do not feature as tilings or signature nets within the 53 3-periodic edge-transitive nets. Therefore, only the eight Td- or Oh- symmetry nets can serve as tilings for 3-periodic edgetransitive nets.

[0300] In some embodiments, a Op structure is embedded in a compatible 3D setting to yield a signature net, and edge lengths referenced in the merged-net equation are taken in that embedding. A 3p parent net and an embedded Op parent net may be merged if they share a common signature net obtained by edge, binary, or direct transformation.

[0301] Examination of the tiling information of all 53 edge-transitive nets and found 18 of them contain the 0-periodic edge-transitive nets as tilings. Among them, 4 nets contain two 0- periodic edge-transitive nets as tilings, tet / oct in feu, cub (cub-b) / rdo in rht, cub-b / ada in ttt, and cuo / oct in reo. All eight 0-periodic nets used here serve as tilings of 3-periodic edge-transitive4053.277PCT1nets with rdo net appearing as tilings in six nets, flu, ftw, soc, ocu, the, and rht. According the 0- periodic signature nets map, cub and oct are also 0-periodic signature nets of these six nets. Using the 0-periodic signature net map and tiling information, the 67 3p-0p merged nets were systematically enumerated.

[0302] In some embodiments, the resulting merged-net transitivity follows the general outcomes stated herein:

[0022] for a parent net merged with its signature net (-s), and

[0032] for samemethod or mixed-method pairs involving the embedded Op parent net and the 3p parent net.

[0303] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a hoc merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c boc merged-net.

[0304] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a era merged-net. In some embodiments, the first edge-transitive net is a (6)-c ers net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c era merged-net.

[0305] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a crc merged-net. In some embodiments, the first edge-transitive net is a (6)-c ers net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c crc merged-net.

[0306] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a ere merged-net. In some embodiments, the first edge-transitive net is a (6)-c ers net and the second edge- transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c ere merged-net.

[0307] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a erf merged-net. In some embodiments, the first edge-transitive net is a (6)-c ers4053.277PCT1net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c erf merged-net.

[0308] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a erv merged-net. In some embodiments, the first edge-transitive net is a (6)-c ers net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,6,6)-c erv merged-net.

[0309] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a did merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c dia net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,7)-c did merged-net.

[0310] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a dig merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c dia net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,7)-c dig merged-net.

[0311] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a dih merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,7)-c dih merged-net.

[0312] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a dii merged-net. In some embodiments, the first edge-transitive net is a (4)-c dia net and the second edge- transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,7)-c dii merged-net.

[0313] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ffe merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu4053.277PCT1net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (3,4,12)-c ffe merged-net.

[0314] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ffh merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,15)-c ffh merged-net.

[0315] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ffk merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c ffk merged-net.

[0316] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ffl merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c ffl merged-net.

[0317] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ffv merged-net. In some embodiments, the first edge-transitive net is a (12)-c feu net and the second edge- transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (3,4,12)-c ffv merged-net.

[0318] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a fid merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,7,8)-c fid merged-net.

[0319] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a fie merged-net. In some embodiments, the first edge-transitive net is a (4,8)-c flu4053.277PCT1net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,7,8)-c fle merged-net.

[0320] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwm merged-net. In some embodiments, the first edge-transitive net is a (4,12)- c ftw net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c fwm merged- net.

[0321] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fwn merged-net. In some embodiments, the first edge-transitive net is a (4,12)-c ftw net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,8,12)-c fwn merged-net.

[0322] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an fww merged-net. In some embodiments, the first edge-transitive net is a (4,12)- c ftw net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,8,12)-c fww merged-net.

[0323] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an hxa merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c hxg net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c hxa merged-net.

[0324] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an hxc merged-net. In some embodiments, the first edge-transitive net is a (6)-c hxg net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c hxc merged-net.

[0325] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an hxe merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c4053.277PCT1hxg net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,9)-c hxe merged-net.

[0326] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a kpl merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,6,8)-c kpl merged-net.

[0327] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mga merged-net. In some embodiments, the first edge-transitive net is a (6,12)- c mgc net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (3,9,12)-c mga merged-net.

[0328] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an mge merged-net. In some embodiments, the first edge-transitive net is a (6,12)- c mgc net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,9,12)-c mge merged-net.

[0329] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nam merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c nbo net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c nam merged-net.

[0330] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a nbb merged-net. In some embodiments, the first edge-transitive net is a (4)-c nbo net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (2,3,6)-c nbb merged-net.

[0331] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nbr merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c4053.277PCT1nbo net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,8)-c nbr merged-net.

[0332] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an nbu merged-net. In some embodiments, the first edge-transitive net is a (4)-c nbo net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,8)-c nbu merged-net.

[0333] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an neb merged-net. In some embodiments, the first edge- transitive net is a (6)-c pen net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge- transitive nets merge to form an intricate mixed-linker structure with a (2,2,9)-c neb merged-net.

[0334] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pea merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c pen net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,9)-c pea merged-net.

[0335] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a peb-e merged-net. In some embodiments, the first edge-transitive net is a (6)-c pen net and the second edge-transitive net is a (4)-c cuo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,6)-c peb-e merged-net.

[0336] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pee merged-net. In some embodiments, the first edge-transitive net is a (6,6)-c pen net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,9)-c pee merged-net.

[0337] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pef merged-net. In some embodiments, the first edge-transitive net is a (6)-c pen4053.277PCT1net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c pcf merged-net.

[0338] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pcj merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (4,4,6)-c pcj merged-net.

[0339] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pcq merged-net. In some embodiments, the first edge-transitive net is a (6)-c pcu net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,9)-c pcq merged-net.

[0340] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pha merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c bor net and the second edge- transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,6)-c pha merged-net.

[0341] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a pyc merged-net. In some embodiments, the first edge-transitive net is a (4)-c nbo net and the second edge- transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,8)-c pyc merged-net.

[0342] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rea merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,8)-c rea merged-net.

[0343] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rec merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo4053.277PCT1net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,10)-c rec merged-net.

[0344] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ree merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,4,10)-c ree merged-net.

[0345] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an ref merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,12)-c ref merged-net.

[0346] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an reg merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,3,10)-c reg merged-net.

[0347] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an reh merged-net. In some embodiments, the first edge-transitive net is a (8)-c reo net and the second edge-transitive net is a (4)-c cuo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,8)-c reh merged-net.

[0348] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rha merged-net. In some embodiments, the first edge-transitive net is a (3,24)-c rht net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,24)-c rha merged-net.

[0349] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhe merged-net. In some embodiments, the first edge- transitive net is a (3,24)-c4053.277PCT1rht net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,24)-c rhe merged-net.

[0350] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhg merged-net. In some embodiments, the first edge-transitive net is a (3,24)-c rht net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,24)-c rhg merged-net.

[0351] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an rhi merged-net. In some embodiments, the first edge-transitive net is a (3,24)-c rht net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,24)-c rhi merged-net.

[0352] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an scj merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c scj merged-net.

[0353] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an scr merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,8)-c scr merged-net.

[0354] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an sew merged-net. In some embodiments, the first edge-transitive net is a (4,6)-c soc net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c sew merged-net.

[0355] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an spa merged-net. In some embodiments, the first edge-transitive net is a (3,6)-c4053.277PCT1spn net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,6)-c spa merged-net.

[0356] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an spb merged-net. In some embodiments, the first edge-transitive net is a (3,6)-c spn net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,3,9)-c spb merged-net.

[0357] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an str merged-net. In some embodiments, the first edge-transitive net is a (3,6)-c spn net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,6)-c str merged-net.

[0358] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tbm merged-net. In some embodiments, the first edge- transitive net is a (3,4)-c tbo net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,4,6)-c tbm merged-net.

[0359] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tew merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c tew merged-net.

[0360] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tex merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (3,3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (3,6,12)-c tex merged-net.

[0361] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tew merged-net. In some embodiments, the first edge-transitive net is a (3,12)-c4053.277PCT1ttt net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c tew merged-net.

[0362] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tex merged-net. In some embodiments, the first edge- transitive net is a (3,12)-c ttt net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,6,12)-c tex merged-net.

[0363] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a thi merged-net. In some embodiments, the first edge-transitive net is a (3,8)-c the net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,6,8)-c thi merged-net.

[0364] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a thm merged-net. In some embodiments, the first edge-transitive net is a (3,8)-c the net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,6,8)-c thm merged-net.

[0365] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with a tvv merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c tbo net and the second edge-transitive net is a (3,4)-c rdo net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (4,4,6)-c tw merged-net.

[0366] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xay merged-net. In some embodiments, the first edge-transitive net is a (6)-c hxg net and the second edge- transitive net is a (3)-c tet net, wherein the first and second edge-transitive nets merge to form an intricate mixed-linker structure with a (2,2,9)-c xay merged-net.

[0367] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xbf merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c4053.277PCT1tbo net and the second edge-transitive net is a (3)-c cub net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,6)-c xbf merged-net.

[0368] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xbh merged-net. In some embodiments, the first edge-transitive net is a (3,4)-c tbo net and the second edge-transitive net is a (3)-c tet net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,6)-c xbh merged-net.

[0369] In certain embodiments, the composition comprises a metal component associated with a first polytopic ligand and a second polytopic ligand to form an intricate mixed-linker structure with an xbi merged-net. In some embodiments, the first edge-transitive net is a (4,4)-c nbo net and the second edge-transitive net is a (4)-c oct net, wherein the first and second edgetransitive nets merge to form an intricate mixed-linker structure with a (2,4,8)-c xbi merged-net.MERGED-NET EQUATION

[0370] The merged-net equation can be used to describe and / or form series of isoreticular intricate mixed-linker structures with the same underlying merged-net. In general, the merged-net equation describes the dimensions (lengths or sizes) of the edges (or ligands) of two parent nets placed in common signature-net geometry. For example, in some embodiments, the merged-net equation describes the length or size of a first polytopic ligand to the length or size of a second polytopic ligand. In some embodiments, the merged-net equation describes the length or size of the second polytopic ligand to the length or size of the first polytopic ligand. For parent nets made from embedded 3-dimensional representations of 2p, Ip, and Op nets, all edge lengths are taken after embedding in a compatible three-dimensional crystallographic setting.

[0371] In some embodiments, a dimension or size ratio of edges from the first edge-transitive net (or first parent net) and the second edge-transitive net (or second parent net) is defined by the law of sines as shown in equation (1):where x is a dimension or length of the edge (e.g., first polytopic ligand) of the first edge-transitive net and y is a dimension or length of the edge (e.g., second polytopic ligand) of the second edgetransitive net. In some embodiments, the first edge-transitive net and second edge-transitive net merge only where their edge ratio meets a ratio constant, CR, as defined in equation (2):4053.277PCT1x. 3CR = - = y 3

[0372] In some embodiments, the ratio constant of edges further requires consideration of the molecular building blocks (MBBs). For example, in some embodiments, the ratio constant of edges is based on the size of the ligands and a half size of the MBBs, as shown in equation (3):where L is the size of the edge (e.g., first polytopic ligand) of the first edge-transitive net, L2is the size of the edge (e.g., second polytopic ligand) of the second edge-transitive net, and CMis the constant size defined as the half size of the MBB. In some embodiments, the half size of the MBB is calculated from the center of the MBB or cluster to a carbon atom of a point of extension. In this way, equation (3) can be used to describe pairs of ligands suitable for the preparation of two or more isoreticular intricate mixed-linker structures.

[0373] Tables 2-4 provide edge ratio values for 3p-2p, 3p-lp, and 3p-0p merged nets. The original edge ratio refers to the ratio of the two parent edge-transitive nets. The Systre edge ratio is the ratio found in Systre- optimized models. Edge ratios in nets with more than two types of edge sizes due to symmetry reduction are labeled as ‘non’.Table 2. Edge ratio values for 3p-2p merged nets.4053.277PCT1Table 3. Edge ratio values for 3p-lp merged nets.Table 4. Edge ratio values for 3p-0p merged nets.4053.277PCT1POLYTOPIC LIGANDS

[0374] In some embodiments, the intricate mixed-linker structures comprise a first polytopic ligand and a second polytopic ligand. For minimal edge-transitive nets with two kinds of edges, the first polytopic ligand and second polytopic ligand are generally different. Otherwise, the first polytopic and second polytopic ligands are not particularly limited and can be selected from any polytopic ligands suitable for the intricate mixed-linker structures of the present disclosure.

[0375] In some embodiments, the first polytopic ligand and second polytopic ligand are each independently ^-connected nodes, where n ranges from 1 to 40. For example, in some embodiments, the first polytopic ligand and second polytopic ligand are each independently a 2-c node, 3-c node, 4-c node, 5-c node, 6-c node, 7-c node, 8-c node, 9-c node, 10-c node, 12-c node, 14-c node, 16-c node, 18-c node, 20-c node, 24-c node, 26-c node, 28-c node, 30-c node, 32-c node, 36-c node, or combinations thereof. In other embodiments, one of the first polytopic ligand and second polytopic ligand is an ^-connected node. In other embodiments, one or more of the first polytopic ligand and second polytopic ligand are ^-connected nodes.

[0376] In some embodiments, the first polytopic ligand and second polytopic ligand are each independently ^-connected molecular building blocks (MBBs), where n ranges from 1 to 40. For4053.277PCT1example, in some embodiments, the first polytopic ligand and second polytopic ligand are each independently a 2-c MBB, 3-c MBB, 4-c MBB, 5-c MBB, 6-c MBB, 7-c MBB, 8-c MBB, 9-c MBB, 10-c MBB, 12-c MBB, 14-c MBB, 16-c MBB, 18-c MBB, 20-c MBB, 24-c MBB, 26-c MBB, 28-c MBB, 30-c MBB, 32-c MBB, 36-c MBB, or combinations thereof. In other embodiments, one of the first polytopic ligand and second polytopic ligand is an 77-connected MBB. In other embodiments, one or more of the first polytopic ligand and second polytopic ligand are ^-connected MBBs.

[0377] In some embodiments, the first polytopic ligand or the second polytopic ligand, or both the first polytopic ligand and the second polytopic ligand each independently comprise two or more polytopic ligands with coordination numbers that are lower than the first polytopic ligand. For example, in one embodiment, the first polytopic ligand is a 6-c node, wherein the first polytopic ligand comprises two 3-c polytopic ligands (or three 2-c polytopic ligands). In this embodiment, the 6-c first polytopic ligand can comprise two 4,4’,4”-((benzene-l,3,5-tricarbonyl) tris(azanediyl)) tribenzote (BTCB) - a tricarboxylate linker - where the 1,3,5-position carbon atoms of the center benzene ring of double BTCB moieties act as points of extension of the 6-c node. Other ligands with different functionalities or coordination numbers can be used herein without departing from the scope of the present disclosure. This is provided only as an example, as the principles can be extended to any 77-connected node using any of the ligands of the present disclosure.

[0378] In some embodiments, the polytopic ligands include one or more coordinating N-, S- , and O-donor functional groups. In some embodiments, the first polytopic ligand and / or second polytopic ligand are polycarboxylic acid ligands. In some embodiments, the first polytopic ligand and / or second polytopic ligand include one or more of the following coordinating groups: amides (including sulfonamide and phosphoramides), sulfinic acids, sulfonic acids, phosphonic acids, phosphates, phosphodiesters, phosphines, boronic acids, boronic esters, borinic acids, borinic esters, nitrates, nitrites, nitriles, nitro, nitroso, thiocyanates, cyanates, azos, azides, imides, imines, amines, acetals, ketals, ethers, esters, aldehydes, ketones, alcohols, thiols, sulfides, disulfides, sulfoxides, sulfones, sulfinic acids, thiones, and thials. In some embodiments, the first polytopic ligand and / or second polytopic ligand include one or more moieties independently selected from: a polycarboxylic acid moiety, a polytetrazole moiety, a polytriazole moiety, a polypyrazole moiety, and a polypyridyl moiety. In some embodiments, the first polytopic ligand and / or second4053.277PCT1polytopic ligand include polytetrazoles ligands, polytriazoles ligands, polypyrazoles ligands, polyimidazoles ligands, and polypyridyls ligands.

[0379] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1In some embodiments, R and / or R’ is a point of extension. In some embodiments, R and / or R’ is selected from hydrocarbons, ethers, esters, amides, sulfur-containing groups, and combinations thereof. In some embodiments R and / or R’ is selected from -H, -OH, -OR, -COOH, -COOR, -4053.277PCT1CONH2, -NH2, -NHR1, -NR'R2, -SH, -SR, -SO2R1, -SO2H, -SOR1, R1, alkyl, alkenyl, akynyl, phenyl, biphenyl, azo, and halo, where each of R1and R2is independently selected from substituted and unsubstituted hydrocarbonyls. In some embodiments, the substituted and unsubstituted hydrocarbonyls are derived from: substituted or unsubstituted alkyl, substituted or unsubstituted cycloalkyl, substituted or unsubstituted alkenyl, substituted or unsubstituted cycloalkenyl, substituted or unsubstituted alkynyl, substituted or unsubstituted aryl, or substituted or unsubstituted aralkyl.

[0380] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where A = C, N, O, S, P, Se, Si, Te, B, As; B = C, N, O, S, P, Se, Si, Te, B, As; C = C, N, O, S, P, Se, Si, Te, B, As; D = C, N, O, S, P, Se, Si, Te, B, As; E = C, N, O, S, P, Se, Si, Te, B, As; F = C, N, O, S, P, Se, Si, Te, B, As; G = C, N, O, S, P, Se, Si, Te, B, As; I = C, N, O, S, P, Se, Si, Te, B, As; J = C, N, O, S, P, Se, Si, Te, B, As; K = C, N, O, S, P, Se, Si, Te, B, As.

[0381] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where A = C, N, O, S, P, Se, Si, Te, B, As; B = C, N, O, S, P, Se, Si, Te, B, As; C = C, N, O, S, P, Se, Si, Te, B, As; D = C, N, O, S, P, Se, Si, Te, B, As; E = C, N, O, S, P, Se, Si, Te, B, As; F = C, N, O, S, P, Se, Si, Te, B, As; G = C, N, O, S, P, Se, Si, Te, B, As; I = C, N, O, S, P, Se, Si, Te, B, As; J = C, N, O, S, P, Se, Si, Te, B, As; K = C, N, O, S, P, Se, Si, Te, B, As; L = C, N, O, S, P, Se, Si, Te, B, As; M = C, N, O, S, P, Se, Si, Te, B, As; R'"""" = alkyl, alkenyl, akynyl, phenyl, biphenyl, azo, etc.;

[0382] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where A = C, N, O, S, P, Se, Si, Te, B, As; B = C, N, O, S, P, Se, Si, Te, B, As; C = C, N, O, S, P, Se, Si, Te, B, As; D = C, N, O, S, P, Se, Si, Te, B, As; E = C, N, O, S, P, Se, Si, Te, B, As; F = C,4053.277PCT1N, O, S, P, Se, Si, Te, B, As; G = C, N, O, S, P, Se, Si, Te, B, As; I = C, N, O, S, P, Se, Si, Te, B, As; J = C, N, O, S, P, Se, Si, Te, B, As; K = C, N, O, S, P, Se, Si, Te, B, As; L = C, N, O, S, P, Se, Si, Te, B, As; M = C, N, O, S, P, Se, Si, Te, B, As; R'"""" = alkyl, alkenyl, akynyl, phenyl, biphenyl, azo, etc.

[0383] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where R = any length linker, as described herein.

[0384] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where M = a metal with an oxidative state of1+(e.g., Li, Na, K, Ag, etc.),2+(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.),3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)),4+(e.g., Zr, Ti, V, etc.), or other higher oxidative state metals such as +5, +6, +7, and +8; and where R = any length linker, as described herein.4053.277PCT1

[0385] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where R = any flexible, quadrangular core. Examples include:4053.277PCT1where all porphyrins and related compounds (e.g., phthalocyanines) can optionally be metallated.

[0386] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where M1+(e.g., Li, Na, K, Ag, etc.); M2(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other higher oxidative state metals such as +5, +6, +7, and +8; R = any length linker, as described herein. Examples include:4053.277PCT1

[0387] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where R = any flexible, tetrahedral core. Examples include:4053.277PCT1

[0388] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where M1+(e.g., Li, Na, K, Ag, etc.); M2+(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other higher oxidative state metals such as +5, +6, +7, and +8; R = any length linker, as described herein. Examples include:4053.277PCT1

[0389] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:any N-donor trigonal ligand or pillar, where M1+(e.g., Li, Na, K, Ag, etc.); M2(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other higher oxidative state metals such as +5, +6, +7, and +8; R = any length linker, as described herein. Examples include:where M = Y.

[0390] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where R = any octahedral core. Examples include:4053.277PCT1

[0391] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where R = any trigonal prismatic core. Examples include:4053.277PCT1where X = OR, SR, NHR; R = any length linker, as described herein. Examples include:where X = OR, SR, NHR; R = any length linker, as described herein.

[0392] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where M1+(e.g., Li, Na, K, Ag, etc.); M2(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other higher oxidative state metals such as +5, +6, +7, and +8; X = C, N, NH, etc.; Y = C,N, etc.; O = O, OH, H2O, N, halogen (Cl, Br, I, F, etc.); M-M single bond or multiple can exist in some examples (e.g., W, Mo, etc.); R = any length linker, as described herein. Examples include:4053.277PCT1

[0393] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where M1+(e.g., Li, Na, K, Ag, etc.); M2(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other higher oxidative state metals such as +5, +6, +7, and +8; X = C, N, NH, etc.; Y=C,N, etc.; 0 = 0, OH, H2O, N, halogen (Cl, Br, I, F, etc.); M-M single bond or multiple can exist in some examples (e.g., W, Mo, etc.); R = any length linker, as described herein. Examples include:

[0394] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:where M1+(e.g., Li, Na, K, Ag, etc.); M2+(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M3+(e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M4+(e.g., Zr, Ti, V, etc.) or other4053.277PCT1higher oxidative state metals such as +5, +6, +7, and +8; X = C, N, NH, etc.; Y = C,N, etc.; O = O, OH, H2O, N, halogen (Cl, Br, I, F, etc.); M-M single bond or multiple can exist in some examples (e.g., W, Mo, etc.); R = any length linker, as described herein. Examples include:

[0395] In some embodiments, each of the first polytopic ligand and / or second polytopic ligand are independently selected from:4053.277PCT1where X is hydrogen, -NHR, -N(R)2, halides, Ci-io alkyl, Ce-18 aryl, Ce-18 aralky, -NH2, alkenyl, alkynyl, -Oalkyl, -NH(aryl), cyclalkyl, cycloalkenyl, cycloalkynyl, -(CO)R, -(SO2)R, -(CO2)R, -SH, -S(alkyl), -SO3H, -SO3M+, -COOH, -COO M+, -PO3H2, -PO3H M+, -PO32M2+, -NO2, - CO2H, silyl derivatives, borane derivatives, ferrocenes, and other metallocenes, where M is a metal atom and R is C1-10 alkyl. Examples of polytopic ligands include: 1 ,4-benzenedi carboxylate (BDC), 4,4'-biphenyldicarboxylate (BPDC), tetrahydropyrene-2,7-dicarboxylate (HPDC), and 4,4"-terphenyldicarboxylate (TPDC), l,3,5-tris(4-carboxyphenyl)benzene (BTB).4053.277PCT1METAL COMPONENTS

[0396] In some embodiments, the metal component comprises one or more of metals and metal ions. In some embodiments, the metal component further optionally comprises one or more precursor moieties, such as clustering precursor moieties. In some embodiments, the metal component comprises a metal or a metal ion. In some embodiments, the metal component comprises a plurality of metals or metal ions. In some embodiments, the metal component comprises mono- or polynuclear metal clusters. In some embodiments, the metal component comprises inorganic molecular building blocks (MBBs).

[0397] The metals and / or metal ions of the metal component are not particularly limited and thus can be selected from any metal of the periodic table. For example, in some embodiments, the metal component comprises metals and / or metal ions selected from the following periodic groups: IA, IIA, IIIB, IVB, VB, VIB, VIIB, VIIIB, VIIIIB, IB, IIB, IIIA, IVA, VA, VIA, any cations thereof, and any combinations thereof. In some embodiments, the metal component comprises metals selected from rare earth metals, alkali metals, alkaline earth metals, transition metals, lanthanoids, actinoids, post-transition metals, any cations thereof, and any combinations thereof. In some embodiments, the metals and / or metal ions of the metal component have an oxidation state selected from 0, +1, +2, +3, +4, +5, +6, +7, +8, and combinations thereof.

[0398] In some embodiments, the metal is selected from Mg, Ca, Sr, Ba, Sc, Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W, Mn, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd, Pt, Cu, Ag, Au, Zn, Cd, Hg, Al, Ga, In, Ti, Si, Ge, Sn, Pb, As, Sb, and Bi. In some embodiments, the metal is selected from Ce, Dy, Er, Eu, Gd, Ho, La, Lu, Nd, Pr, Pm, Sm, Sc, Tb, Tm, Yb, Y, any cations thereof, and any combinations thereof. In some embodiments, the metal is selected from Na, K, Li, Ag, Cu, Zn, Co, Ni, Mn, Mo, Cr, Fe, Ca, Ga, Ba, Cs, Pb, Pt, Pd, Ru, Rh, Cd, Mg, Al, In, Sc, Nb, Y, Ln, Yb, Tb, Zr, Ti, V, any cations thereof, and any combinations thereof. In some embodiments, the metal is selected from Cu2+, Zn2+, Co2+, Ni2+, Mn2+, Zr2+, Fe2+, Ca2+, Ba2+, Pb2+, Pt2+, Pd2+, Ru2+, Rh2+, Cd2+, Mg+2, Al+3, Fe+2, Fe+3, Cr2+, Cr3+, Ru2+, Ru3+, Co3, Ti3+, V3+, V5+, Sc3+, In3+, Nb5+, Y3+, and any combinations thereof. In some embodiments, the metal is selected from Al+3, Ga3+, Fe+2, Fe+3, Cr2+, Cr3+, Ti3+, V3+, V5+, Sc3+, In3+, Nb5+, Y3+, and any combinations thereof.

[0399] In some embodiments, the metal component comprises ^-connected inorganic MBB, where n ranges from 1 to 40. For example, in some embodiments, the metal component comprises 2-c inorganic MBBs, 3-c inorganic MBBs, 4-c inorganic MBBs, 5-c inorganic MBBs, 6-c4053.277PCT1inorganic MBBs, 7-c inorganic MBBs, 8-c inorganic MBBs, 9-c inorganic MBBs, 10-c inorganic MBBs, 12-c inorganic MBBs, 14-c inorganic MBBs, 16-c inorganic MBBs, 18-c inorganic MBBs, 20-c inorganic MBBs, 24-c inorganic MBBs, 26-c inorganic MBBs, 28-c inorganic MBBs, 30-c inorganic MBBs, 32-c inorganic MBBs, 36-c inorganic MBBs, or combinations thereof.

[0400] In some embodiments, the metal component comprises ^-connected polynuclear clusters, where n ranges from 1 to 40. For example, in some embodiments, the metal component comprises 2-c polynuclear metal clusters, 3-c polynuclear metal clusters, 4-c polynuclear metal clusters, 5-c polynuclear metal clusters, 6-c polynuclear metal clusters, 7-c polynuclear metal clusters, 8-c polynuclear metal clusters, 9-c polynuclear metal clusters, 10-c polynuclear metal clusters, 12-c polynuclear metal clusters, 14-c polynuclear metal clusters, 16-c polynuclear metal clusters, 18-c polynuclear metal clusters, 20-c polynuclear metal clusters, 24-c polynuclear metal clusters, 26-c polynuclear metal clusters, 28-c polynuclear metal clusters, 30-c polynuclear metal clusters, 32-c polynuclear metal clusters, 36-c polynuclear metal clusters, or combinations thereof.

[0401] In some embodiments, the metal component comprises ^-connected mono- or polynuclear metal clusters comprising a metal of the formula: Mx, where x is 1 to 20. For example, in some embodiments, the metal component comprises dinuclear clusters (e.g., where x is 2). In some embodiments, the metal component comprises trinuclear clusters (e.g., where x is 3). In some embodiments, the metal component comprises tetranuclear clusters (e.g., where x is 4). In some embodiments, the metal component comprises pentanuclear clusters (e.g., where x is 5). In some embodiments, the metal component comprises hexanuclear clusters (e.g., where x is 6). In some embodiments, the metal component comprises heptanuclear clusters (e.g., where x is 7). In some embodiments, the metal component comprises octanuclear clusters (e.g., where x is 8). In some embodiments, the metal component comprises nonanuclear clusters (e.g., where x is 9). In some embodiments, the metal component comprises decanuclear clusters (e.g., where x is 10). In some embodiments, the metal component comprises dodecanuclear clusters (e.g., where x is 11).METHODS OF PREPARING INTRICATE MIXED-LINKER STRUCTURES

[0402] Embodiments of the present disclosure also describe a method of synthesizing an intricate mixed-linker structure, according to one or more embodiments of the present disclosure. The method comprises one or more of the following steps:(a) selecting 201 a merged- net to target in a synthesis of the intricate mixed-linker structure, a first 3-periodic (3p) edge-transitive net, and second 3p edge-transitive net,4053.277PCT1wherein the first and second edge-transitive nets share a common signature net and are capable of combining to afford the targeted merged-net and wherein one of the first and second edge-transitive nets is an embedded 3 -dimensional representation of a lower- periodicity net selected from 2-periodic (2p), 1 -periodic (Ip), and 0-periodic (Op);(b) determining 202 a connectivity and geometrical configuration of each node of the merged-net, wherein the nodes of the merged-net comprise a merged node and unmerged nodes, wherein the unmerged nodes include a first unmerged node and second unmerged node;(c) selecting 203 a first molecular building block (MBB) with identical connectivity and geometrical configuration to the merged node and having two sets of points of extension, wherein each set of points of extension is capable of linking to distinct MBBs;(d) selecting 204 a second MBB with the same connectivity and geometrical configuration as the first unmerged node;(e) inputting 205 a length of the selected second MBB into a merged-net equation to calculate a length of a complementary MBB;(f) selecting 206 a third MBB with the same connectivity and geometrical configuration as the second unmerged node, and the same length as the complementary MBB; and(g) reacting 207 precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net.

[0403] Reacting 207 comprises reacting precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net. In some embodiments, the precursor of the first MBB is a metal precursor, the precursor of the second MBB is a first ligand precursor, and the precursor of the third MBB is a second ligand precursor. In some embodiments, these materials are sufficient to form any of the intricate mixed-linker structures with merged-net topologies of the present disclosure.

[0404] The reacting 207 can proceed by bringing the metal precursor, first ligand precursor, and second ligand precursor into physical contact, or immediate or close proximity. In some embodiments, the contacting proceeds in solution. In some embodiments, the contacting proceeds with solid phase reactants and thus proceeds solvent-free. In some embodiments, the contacting proceeds at or to temperatures of about 25 °C or greater. For example, in some embodiments, the contacting proceeds under solvothermal reaction conditions. In other embodiments, the contacting4053.277PCT1proceeds at or to temperatures of less than about 25 °C. The metal precursor is not particularly limited and can be selected from any compound containing the metals or metal components of the present disclosure. In some embodiments, the metal precursor is a metal salt or metal chelate. The first and second ligand precursors are similarly not particularly limited and can include any of the ligands of the present disclosure. In some embodiments, the first ligand precursor is the first polytopic ligand with a neutral charge (e.g., it is protonated or has H atoms). In some embodiments, the second ligand precursor is the second polytopic ligand with a neutral charge (e.g., it is protonated or has H atoms).

[0405] The following Examples are intended to illustrate the above invention and should not be construed as to narrow its scope. One skilled in the art will readily recognize that the Examiners suggest many other ways in which the invention could be practiced. It should be understood that numerous variations and modifications may be made while remaining within the scope of the invention.EXAMPLES

[0406] Example 1. Materials and General Procedures. The organic ligands used in this study were prepared according to the procedures outlined in the following pages. All other reagents were obtained from commercial sources and were used without further purification unless otherwise noted.

[0407] The original merged net models and cif files were built by BIOVIA Materials Studio and CrystalMaker 10. The topological analysis of merged nets and the generation of cgd files were conducted using the Systre program. All proposed structures were simulated using BIOVIA Materials Studio, and the geometry optimization was performed using the Universal force field (UFF) on the For cite model of BIO VIA Materials Studio. The topological analysis of synthesized MOF structures were conducted using the TOPOS and Systre program.

[0408] NMR and13C NMR spectra were recorded on Bruker Avance III 400, 500, and 600 MHz instruments. Chemical shifts for 'H NMR spectra are reported in ppm (8, relative to TMS) using DMSO residual peak (8 = 2.50 ppm) in DMSO-t / e as an internal standard and for13C NMR spectra solvent peaks at 39.52 ppm, and solutions in CDCh solvent peaks at 7.26 and 77.16 ppm, respectively.4053.277PCT1

[0409] Powder X-ray diffraction (PXRD) measurements were carried out at room temperature on a PANalyticalX’Pert PRO diffractometer 45kV, 40mA for CuKa (X = 1.5418 A), with a scan speed of 1.0° min'1and a step size of 0.02° in 20.

[0410] Single Crystal X-ray Diffraction (SCXRD) data were collected using Bruker X8 PROSPECTOR APEX2 CCD diffractometer using CuKa (X = 1.54178 A). Indexing was performed using APEX3 v2018.7-2 with the Difference Vectors method. Data integration and reduction were performed using SaintPlus 8.38 A. Absorption correction was performed by a multiscan method implemented in SADABS-2016 / 2. The space group was determined using XPREP implemented in APEX3. The structure was solved using Direct Methods (SHELXS-2008) and refined using SHELXL-2018 / 3 (full-matrix least-squares on / 2with anisotropic displacement parameters for the non-H atoms) contained OLEX2 program package.

[0411] Low-pressure gas adsorption studies of all materials were conducted on a fully automated micropore gas analyzer 3Flex Analyzer (Micromeritics Instruments) at relative pressures up to 1 atm. The cryogenic temperature was controlled using liquid argon baths at 87 K. The Brunauer-Emmett-Teller (BET) surface areas were determined from argon adsorption isotherms collected at 87 K by applying the Surface Identification (BETSI) method.

[0412] Example 2. Ligand synthesis.

[0413] Synthesis of H6BTPHB, H3BTTC, and H3TMBTB. The ligands l,3,5-tns(3,5- bis(4-carboxyphenyl)phenyl)benzene (HeBTPHB), benzo-tris-thiophene carboxylic acid (H3BTTC), and 4,4',4"-(2,4,6-trimethylbenzene-l,3,5-triyl)tribenzoic acid (H3TMBTB) were synthesized using known synthetic methods described in the chemical literature.

[0414] Synthesis of 4,4'-(ethyne-l,2-diyl)dibenzoic acid (H2ABPDC). An oven-dried round-bottom flask was charged with ethyl 4-iodobenzoate (2.76 g, 1 Eq, 10.0 mmol), 1,8- Diazabicyclo[5.4.0]undec-7-ene (DBU) (9.13 g, 9 mL, 6.0 Eq, 60.0 mmol), and argonated. To this mixture, anhydrous toluene (50 mL) was added and the flask was covered with aluminum foil. Copper(I) iodide (190 mg, 10 mol%, 1.00 mmol) and Pd(PPh3)2C12 (421 mg, 6 mol%, 600 pmol) were added under argon, followed by ethynyltrimethylsilane (491 mg, 0.69 mL, 0.5 Eq, 5.00 mmol) and deionized (DI) H2O (72.1 mg, 72.1 pL, 0.4 Eq, 4.00 mmol). The mixture was stirred in darkness at 20 °C for 22 hours. The mixture was partitioned between Et2O (100 mL) and DI H2O (100 mL), and the organic phase was washed with 1 N HC1 (3 x 75 mL), brine (1 x 75 mL), and dried over MgSO-i. The solvent was evaporated and the residue was purified on silica (100%4053.277PCT1too hexanes to 40% CH2CI2 in hexanes) to give diethyl 4,4'-(ethyne-l,2-diyl)dibenzoate (1.09 g, 68 %) as a light brown solid.XH NMR (400 MHz, CDCh): 8, 8.05-8.03 (d, J= 8.0, 4H), 7.61-7.59 (d, J = 8.0, 4H), 4.42-4.36 (q, J = 7.2, 4H), 1.42-1.39 (t, J = 7.2, 6H) ppm.13C NMR (100 MHz, CDCh): 8, 166.1, 131.7, 130.4, 129.7, 127.4, 91.5, 61.4, 14.5 ppm.

[0415] Diethyl 4,4'-(ethyne-l,2-diyl)dibenzoate (0.4 g, 1 Eq, 1.24 mmol) was dissolved in 40 mL THF / EtOH (1 / 1), and 2 N NaOH (1 g, 12 mL, 20 Eq, 24.8 mmol) was added. The reaction was kept at 90 °C for 18 hours. The mixture was concentrated, diluted with DI H2O (75 mL), and washed with EtOAc (2 x 40 mL, discarded). The aqueous phase was acidified with 2 N HC1, a light precipitate was collected by filtration, washed thoroughly with DI H2O, and dried on suction overnight to give 4,4'-(ethyne-l,2-diyl)dibenzoic acid (0.3 g, 90 %) as a cream solid. 'H NMR (400 MHz, DMSO- e) 8 13.19 (S, 2H), 8.02 - 7.96 (m, 4H), 7.74 - 7.69 (m, 4H) ppm.13C NMR (101 MHz, DMSO-t / e) 8 166.7, 131.74, 131.0, 129.6, 126.1, 91.1 ppm.Scheme 1. Synthesis of 4,4'-(ethyne-l,2-diyl)dibenzoic acid (H2ABPDC).COOEt

[0416] Synthesis of 4,4',4"-nitrilotribenzoic acidoven-dried 250 mL Schlenk flask tris(4-bromophenyl)amine (1.0 g, 1 Eq, 2.07 mmol) was dissolved in anhydrous THF (60 mL) under argon, and the solution was kept at -78 °C for 30 min. 1.6 N solution of n-BuLi in hexane (1.59 g, 16 mL, 12 Eq, 24.90 mmol) was added dropwise. The mixture was stirred at -78 °C for 30-45 min. under argon, and then excess CO2 gas was bubbled into the solution through a needle for 1 hour. The resulting mixture was stirred at -78 °C for another 30 min. and then allowed to slowly warm to room temperature overnight. DI H2O (50 mL) was added and the mixture was concentrated. The residual aqueous phase was acidified with 1 N HC1 to give a suspension. The solid was separated by filtration, washed with DI H2O, Hexane, EtOAc, and Et2O, and finally dried in a vacuum oven to afford 4,4',4"-nitrilotribenzoic acid (0.74 g, 94 %). 'H NMR (500 MHz, DMSO- e) 8 12.76 (s, 3H), 7.92 - 7.89 (m, 6H), 7.16 - 7.12 (m, 6H) ppm.13C NMR (126 MHz, DMSO- e) 8 166.7, 149.8, 131.2, 125.9, 123.7 ppm.4053.277PCT1Scheme 2. Synthesis of 4,4',4"-nitrilotribenzoic acid (H3NTB).

[0417] Synthesis of anthracene-2,6-dicarboxylic acid (H2A11DC). A 100-mL, Schlenk round bottom flask equipped with a reflux condenser and a gas outlet tube was charged with anhydrous copper (II) bromide (6.75 g, 2.4 Eq, 30.2 mmol), tert-butyl nitrite (3.9 g, 4.5 mL, 3 Eq, 37.8 mmol) and anhydrous acetonitrile (50 mL). The mixture was heated to 65 °C, and 2,6- diaminoanthracene-9, 10-dione (3.0 g, 1 Eq, 12.6 mmol) was slowly added over a period of 5 min. After complete gas evolution (4 hours), the reaction mixture was cooled to room temperature and poured into 6 N HC1 (50 mL). The precipitate was filtered and washed with DI H2O and EtOH. Purification by sublimation (0.1 torr, 200 °C) gave 2,6-dibromoanthracene-9, 10-dione (3.27 g, 71 %) as a yellow solid. 'H NMR (500 MHz, CDCI3) 8 8.44 (d, J= 2.0 Hz, 2H), 8.17 (d, J= 8.2 Hz, 2H), 7.94 (dd, J= 8.3, 2.0 Hz, 2H) ppm.13C NMR(126 MHz, CDCI3) 8 181.5, 137.6, 134.5, 132.7, 131.9, 130.5, 129.3 ppm.

[0418] A mixture of 2,6-dibromoanthracene-9, 10-dione (3.0 g, 1 Eq, 8.2 mmol), H3PO2 (24 g, 20 mL, 22 Eq, 180.3 mmol), hydriodic acid (HI) (28 g, 16 mL, 15 Eq, 122.9 mmol) and acetic acid (150 mL) was refluxed for 5 days. The mixture was cooled down to room temperature and poured into ice water. The precipitate was filtered and washed with DI H2O and EtOH. Recrystallization from Toluene gave the desired product 2,6-dibromoanthracene (2.48 g, 90 %) as pale-yellow crystals. 'H NMR (500 MHz, CDCI3) 8 8.32 (s, 2H), 8.19 (d, J = 2.0 Hz, 2H), 7.89 (d, J= 9.0 Hz, 2H), 7.56 (dd, J= 9.0, 2.0 Hz, 2H) ppm.13C NMR (126 MHz, CDCI3) 8 132.6, 130.4,130.1, 129.9, 129.8, 125.8, 120.1 ppm.

[0419] In an oven-dried 250 mL Schlenk flask, 2,6-dibromoanthracene (1.0 g, 1 Eq, 2.98 mmol) was dissolved in anhydrous THF (100 mL) under argon, and the solution was kept at -78 °C for 30 min. 1.6 N solution of n-BuLi in hexane (1.52 g, 15 mL, 8 Eq, 23.81 mmol) was added drop wise. The mixture was stirred at -78 °C for 30-45 min. under argon, and then excess CO2 gas was bubbled into the solution by a needle for 1 hour. The resulting mixture was stirred at -78 °C for another Ih and then allowed to warm slowly to room temperature overnight. DI H2O (50 mL) was added, the mixture was concentrated by partial evaporation under reduced pressure, and the residual aqueous phase was acidified with 1 N HC1 to give a suspension. The solid was separated4053.277PCT1by filtration, then washed with DI H2O, Hexane, AcOEt, and Et2O, and finally dried in a vacuum oven to afford anthracene-2,6-dicarboxylic acid (0.60 g, 76 %). 'H NMR (500 MHz, DMSO- e) 8 13.15 (s, 1H), 8.89 (s, 1H), 8.83 (s, 1H), 8.21 (d, J = 8.9 Hz, 1H), 7.98 (d, J= 8.8 Hz, 1H) ppm.13C NMR (126 MHz, DMSO-t / 6) 8 167.3, 132.4, 131.6, 131.4, 128.8, 128.6, 124.6 ppm.Scheme 3. Synthesis of anthracene-2,6-dicarboxylic acid (H2AnDC).

[0420] Synthesis of 5'-(lH-tetrazol-5-yl)-[l,l':3',l"-terphenyl]-4,4"-dicarboxylic acid (H3TTDA). 3,5 -dibromobenzonitrile (6.0 g, 1.0 Eq, 23.0 mmol), 4-boronobenzoic acid (8.0 g, 2.1 Eq, 48.3 mmol), and Na2CCh (19.5 g, 8.0 Eq, 184.0 mmol) were placed in 1 L Schlenk round bottom flask, EtOH absolute (400 mL) was added and the mixture was degassed by purging argon for 30 min. 5% palladium on carbon (2.94 g, 6 mol%, 1.380 mmol) was added. The flask was sealed and placed in a preheated oil bath at 80 °C for 5 hours. The reaction mixture was cooled to room temperature and 200 mL DI H2O was added; the solution was filtrated on a funnel. The water phase was acidified with 2 N HC1 to pH ~ 2. Obtained particles were collected by filtration, washed with DI H2O and EtOH, and dried in a vacuum oven overnight to afford 5'-cyano-[l,l':3',l"- terphenyl]-4,4"-dicarboxylic acid (7.0 g, 89 %) as off white solid. 'H NMR (500 MHz, DMSO-<7r>) 8 13.11 (s, 2H), 8.34 (t, J= 1.7 Hz, 1H), 8.24 (d, J= 1.8 Hz, 2H), 8.08 - 8.03 (m, 4H), 8.01 - 7.97 (m, 4H) ppm.13C NMR (126 MHz, DMSO- r,) 8 167.1, 142.0, 141.0, 130.7, 130.3, 130.1, 128.2, 127.6, 118.6, 113.2 ppm. 5'-cyano-[l,r:3',l"-terphenyl]-4,4"-dicarboxylic acid (7.0 g, 1 Eq, 20.4 mmol), NH4CI (2.34 g, 2.15 Eq, 43.8 mmol) and NaNs (2.78 g, 2.1 Eq, 42.8 mmol) were placed in 0.5 L round bottom flask and dissolved in DMF (140 mL). The reaction flask was placed in a preheated oil bath at 100 °C for 24 hours. The reaction mixture was cooled to room temperature and 50 mL of DI H2O was added. Solution acidified with 2 N HC1 to pH ~l-2. Obtained particles were collected by filtration, washed with DI H2O, and dried in a vacuum oven overnight to afford 5'-(lH-tetrazol-5-yl)-[l,l':3',l"-terphenyl]-4,4"-dicarboxylic acid (7.19 g, 91%) as beige solid. 'H NMR (500 MHz, DMSO- r,) 8 13.12 (s, 2H), 8.47 (d, J = 2.2 Hz, 2H), 8.28 (s, 1H), 8.10 (d, J = 8.2 Hz, 4H), 8.05 (d, J= 8.2 Hz, 4H) ppm.13C NMR (126 MHz, DMSO- e) 8 167.1, 143.0, 141.1, 130.4, 130.1, 128.2, 127.4, 125.3 ppm.4053.277PCT1Scheme 4. Synthesis of 5'-(lH-tetrazol-5-yl)-[l,l':3',l"-terphenyl]-4,4"-dicarboxylic acid (H3TTDA).

[0421] Synthesis of hexakis(4-(4-carboxyphenyl)phenyl)benzene (HeBHPB). The mixture of hexakis(4-bromophenyl)benzene (1.0 g, 1 Eq, 992.0 pmol), (4- (ethoxycarbonyl)phenyl)boronic acid (1.54 g, 8 Eq, 7.936 mmol) in THF (60 mL) and 2 N K2CO3 (3.43 g, 12.4 mL, 25 Eq, 24.80 mmol) was degassed with argon for 50 min. Then, Pd(PPh3)4 (114.6 mg, 10 mol%, 99.20 pmol) was added, and the reaction was sealed and placed in a preheated oil bath at 90 °C for 5 days. The product precipitated from the reaction mixture and was isolated by filtration. The solid was washed with THF (40 mL) and H2O (40 mL) to afford pure hexakis(ethyl- 4-(4-carboxyphenyl)phenyl)benzene (0.912 g, 65 %) as a grey solid. 'H NMR (500 MHz, CDCI3) 8 8.00 - 7.96 (m, 12H), 7.50 - 7.45 (m, 12H), 7.24 - 7.19 (m, 12H), 7.02 - 6.98 (m, 12H), 4.35 (q, J= 7.1 Hz, 12H), 1.37 (t, J= 7.1 Hz, 18H) ppm.13C NMR (126 MHz, CDCI3) 8 166.6, 145.0, 140.5, 140.4, 136.9, 132.1, 130.0, 129.1, 126.7, 125.8, 61.1, 14.5 ppm.

[0422] Hexakis(ethyl-4-(4-carboxyphenyl)phenyl)benzene (1.0 g, 1 Eq, 702.4 pmol) was dissolved in 80 mL THF / MeOH (1 / 1), and 2 N KOH (0.67 g, 8.4 mL, 24 Eq, 16.86 mmol) was added. The reaction was kept at 90 °C for 18 hours. The mixture was concentrated to remove the organic solvents and then diluted with DI H2O (75 mL) and washed with EtOAc (2 x 40 mL, discarded). The aqueous phase was acidified with 2 N HC1, a light precipitate was separated by filtration, washed thoroughly with DI H2O, and dried in air overnight to hexakis(4-(4- carboxyphenyl)phenyl)benzene (0.648 g, 73 %). 'H NMR (500 MHz, DMSO-t / e) 8 12.86 (s, 5H), 7.83 (d, J= 8.2 Hz, 12H), 7.56 (d, J= 8.3 Hz, 12H), 7.35 (d, J= 8.0 Hz, 12H), 7.14 (d, J= 8.0 Hz, 12H) ppm.13C NMR (126 MHz, DMSO- r,) 8 167.0, 143.1, 140.1, 139.9, 135.5, 131.8, 129.8, 129.4, 126.1, 125.1 ppm.4053.277PCT1Scheme 5. Synthesis of hexakis(4-(4-carboxyphenyl)phenyl)benzene (HeBHPB).

[0423] Synthesis of [l,l,l’h4',l":4",l"'-quaterphenyl]-4,4"'-dicarboxylic acid (H2TBDC). A mixture of ethyl 4'-iodo-[l,l'-biphenyl]-4-carboxylate (3.0 g, 1 Eq, 8.52 mmol), bis(pinacolato)diboron (1.3 g, 0.6 Eq, 5.11 mmol) and K^CCE (3.53 g, 3 Eq, 25.6 mmol) in DMSO (35 mL) was purged with nitrogen for 10 min. Then Pd(PPh3)4 (0.98 g, 0.1 Eq, 0.85 mmol) was added and heated at 85 °C for 12 hours. After completion of the reaction, the mixture was cooled to room temperature and quenched with water. Then, the precipitate formed was filtered and washed with water and methanol to remove all the soluble impurities. The crude material was then purified by silica gel column chromatography using chloroform to obtain pure diethyl [l,r:4',l":4",r"-quaterphenyl]-4,4"'-dicarboxylate as a white solid (1.71 g, 94%).JH NMR (500 MHz, CDCI3) 8 8.14 (d, J= 10 Hz, 4H), 7.78 - 7.69 (m, 12H), 4.41 (q, J= 6.6 Hz, 4H), 1.43 (t, J = 7.5 Hz, 6H) ppm.

[0424] A mixture of diethyl [l,r:4',l":4",r"-quaterphenyl]-4,4"'-dicarboxylate (1.5 g, 1 Eq, 3.33 mmol) and KOH (18.7 g, 100 Eq, 333 mmol) in tetrahydrofuran (50 mL), n-propanol (100 mL) and DI H2O (100 mL) was refluxed at 120 °C for 24 hours. After completion of the reaction, organic solvents were removed by a rotary evaporator, and the precipitate was filtered, washed with THF (20 mL), and dried. Then, the dry precipitate was suspended in 50 mL of 2 N HC1 and heated at 70 °C for 4 hours. After completion, the reaction mixture was cooled to room temperature, and the precipitate was filtered and dried to afford [l,l':4',l":4",l"'-quaterphenyl]-4,4"'- dicarboxylic acid as a white solid (1.28 g, 97%). 'H NMR (400 MHz, DMSO-<7r>) 8 8.05 (d, J= 8 Hz, 4H), 7.93 - 7.85 (m, 12H) ppm.Scheme 6. Synthesis of [l,l':4',l":4",l"'-quaterphenyl]-4,4"'-dicarboxylic acid (H2TBDC).4053.277PCT1

[0425] Example 3. Synthesis of MOFs.

[0426] Synthesis of Tb-sph-MOF-6. Tb(NO3)35H2O (10.0 mg, 0.0221 mmol), H3BTTC (2.1 mg, 0.0056 mmol), H3BTPB (5.0 mg, 0.0075 mmol), 2-FBA (287.0 mg, 2.05 mmol), DMF (1.5 mL) and H2O (1.5 mL) were combined in a 20 mL scintillation vial. The vial was sealed, sonicated for 30 min, then placed in a preheated oven at 115 °C for 48 hours, and cooled to room temperature. The mother liquor was removed, and the colorless polyhedral crystals Tb-sph-MOF- 3 were washed three times with DMF and exchanged with anhydrous CH2C12for 3 days. Under the argon atmosphere, approximately 20 mg of the crystals and anhydrous CH2C12(5 mL) were added to a 20 mL scintillation vial. A solution of FeCl3(144 mg, 0.888 mmol) in CH3NO2(1 mL) was then added to the vial. The vial was sealed and kept undisturbed for 2 hours. The mother liquor was removed, and the brown polyhedral crystals were washed with anhydrous CH2C12, followed by methanol. The yield is 78%, based on Tb(NO3)35H2O and the activated MOF sample.

[0427] Synthesis of Y-BTPHB-pcu-MOF. Y(NO3)3 4H2O (40 mg, 0.115 mmol), H6BTPHB (5 mg, 0.0049 mmol), 2-FBA (420 mg, 3.0 mmol), and DMF (3 mL) were combined in a 20 mL scintillation vial. The vial was sealed, sonicated for 30 min, then placed in a preheated oven at 105 °C for 7 days, and cooled to room temperature. The colorless cubic crystals were collected and washed with DMF.

[0428] Synthesis of Y-pch-MOF-1. Y(NO3)3 4H2O (40 mg, 0.115 mmol), H6BTPHB (5 mg, 0.0049 mmol), 2-FBA (420 mg, 3.0 mmol), and DMF (3 mL) were combined in a 20 mL scintillation vial. The vial was sealed, sonicated for 30 min, then kept in a preheated oven at 105 °C for 7 days, and cooled to room temperature. The mother liquor was removed and the crystals were washed with DMF three times. Then, H2BPDC (5 mg, 0.021 mmol) and DMF (5 mL) were combined, sonicated, and added to the vial. The vial was sealed, kept in a preheated oven at 1154053.277PCT1°C for 24 hours, and cooled to room temperature. The yellow crystals were collected and washed with DMF. The yield is 51%, based on the BTPHB linker and the activated MOF sample.

[0429] Synthesis of Y-pch-MOF-2. Y(NO3)3 4H2O (40 mg, 0.115 mmol), H6BTPHB (5 mg, 0.0049 mmol), 2-FBA (420 mg, 3.0 mmol), and DMF (3 mL) were combined in a 20 mL scintillation vial. The vial was sealed, sonicated for 30 min, then kept in a preheated oven at 105 °C for 7 days, and cooled to room temperature. The mother liquor was removed and the crystals were washed with DMF three times. Then, H2AnDC (5 mg, 0.019 mmol) and DMF (5 mL) were combined, sonicated, and added to the vial. The vial was sealed, kept in a preheated oven at 115 °C for 24 hours, and cooled to room temperature. The yellow crystals were collected and washed with DMF. The yield is 51%, based on the BTPHB linker and the activated MOF sample.

[0430] Synthesis of Zr-thw-MOF-1. ZrC14 (12 mg, 0.051 mmol), H3TMBTB (10 mg, 0.021 mmol), benzoic acid (350 mg, 2.87 mmol), and DMF (2 mL) were combined in a 7 mL Pyrex Tube with PTFE liner screw cap. The tube was sealed, sonicated for 30 min, then placed in a preheated oven at 120 °C for 48 hours, and cooled to room temperature. The mother liquor was removed, and the crystals Zr-the-MOF were washed with DMF three times in the tube. Then H2TBDC (5 mg, 0.013 mmol) and DMF (5 mL) were combined, sonicated, and added to the tube. The tube was sealed again, placed in a preheated oven at 120 °C for 24 hours, and cooled to room temperature. The colorless crystals were collected and washed with DMF. The yield is 80%, based on the TMTB linker and the activated MOF sample.

[0431] Synthesis of Fe-nam-MOF-1. FeC13 6H2O (18.0 mg, 0.067 mmol), H4BBPTC (6.1 mg, 0.015 mmol), H3BTTC (4.0 mg, 0.011 mmol), DMF (2 mL), and trifluoroacetic acid (0.2 mL) were combined in a 20*150 mm Pyrex Tube with PTFE liner screw cap. The tube was sealed, sonicated for 30 min, then placed in a preheated oven at 150 °C for 24 hours, and cooled to room temperature. The orange polyhedral crystals were collected and washed with DMF. The yield is 23%, based on the BBPTC linker and the activated MOF sample.

[0432] Synthesis of Y-pck-MOF-1. Y(NO3)3 4H2O (40 mg, 0.115 mmol), H6BTPHB (5 mg, 0.0049 mmol), 2-FBA (420 mg, 3.0 mmol), and DMF (3 mL) were combined in a 20 mL scintillation vial. The vial was sealed, sonicated for 30 min, then kept in a preheated oven at 105 °C for 7 days, and cooled to room temperature. The mother liquor was removed and the crystals were washed with DMF three times. Then, H3NTB (5 mg, 0.013 mmol) and DMF (5 mL) were combined, sonicated, and added to the vial. The vial was sealed, placed in a preheated oven at 1154053.277PCT1°C for 24 hours, and cooled to room temperature. The yellow crystals were collected and washed with DMF. The yield is 50%, based on the BTPHB linker and the activated MOF sample.

[0433] Synthesis of Tb-nih-MOF-1. Tb(NO3)3 5H2O (15 mg, 0.034 mmol), H3TTDA (8 mg, 0.021 mmol), DMF (3 mL), chlorobenzene (0.2 mL), and H2O (0.5 mb) were combined in a 20 mL scintillation vial. Then, 0.155 mL of 4 M 2-FBA in DMF was added to the mixture. The vial was sealed, sonicated for 30 min, then placed in a preheated oven at 115 °C for 72 hours, and cooled to room temperature. The mother liquor was removed and the crystals Tb-urx-MOF-1 were washed with DMF three times in the vial. Then, H2ABPDC (8 mg, 0.030 mmol) and DMF (5 mL) were combined, sonicated, and added to the vial. The vial was sealed, placed in a preheated oven at 115 °C for 24 hours, and cooled to room temperature. The colorless hexagonal prism-shaped crystals were collected and washed with DMF. The yield is 66%, based on Tb(NO3)3 5H2O and the activated MOF sample.

[0434] Example 4. Generation of signature net map. The node relationships among the Example 4. Generation of signature net map. The node relationships among the merged net sph (transitivity

[0032] ) and the edge-transitive nets hxg (transitivity

[0011] ) and spn (transitivity

[0021] ) were analyzed to reveal the underlying principle of merged nets. The hxg net isolated from the merged sph net is the binary -transformed net (hxg-b, transitivity

[0021] ) rather than the prismatic hxg (see FIG. 8). In this case, the transitivity of both parent nets is

[0021] , which indicates that the three node types in the merged sph net are fewer than the sum of node types in the parent nets (two from spn and two from hxg-b). This decrease in the number of node types results from the merging process, during which one group of nodes from each parent network is positioned at the same spatial location to enable merging by sharing that position.

[0435] The edges in the parent nets spn and hxg-b were removed to separate the two node types, yielding two groups of nodes in each net (see FIG. 8). Each group can then be identified by relinking its nodes to form a new net. Using this method, the two groups in the spn net can be relinked to form a 0-periodic ordered tetrahedron and a 3 -periodic edge-transitive crs net, respectively. Similarly, the two node groups in the hxg-b net can be relinked to form two crs nets. The relinked nets are referred to as the signature nets of the parent nets and are used to recognize and describe the positions of nodes in the parent nets (see FIG. 8). Indeed, the crs net is the signature net of both the spn and hxg-b nets, which underlies the ability of these parent nets to merge into the more intricate merged net sph.4053.277PCT1

[0436] By considering the mutual nodes, the nodes in sph nets can be distinguished into three groups, nodes belonging only to spn net, the nodes belonging only to hxg-b net, and nodes shared by spn and hxg-b nets. These three groups of nodes contain all the nodes' information of parent nets. Combining all the nodes and relinking all the edges in spn and hxg nets produces the sph net (see FIG. 8). If two nets contain the same signature net, they can potentially merge into one net with higher complexity. In the merged net, the number of node types will be one less than the total types of nodes from parent nets and the number of edge types will equal the total edge types in parent nets. As a result, the coordination of merged nodes is always equal to the sum of the coordination of shared nodes, while the coordination of other nodes remains unchanged as the unshared nodes in parent nets. The symmetry of the merged net is determined by both parent nets, which will be a co-subgroup symmetry of the parent nets. For example, the space group of the standard spn net and hxg nets are Fd-3m and Pn-3m correspondingly. As Fd-3m is a maximal subgroup of Pn-3m, the space group of merged sph net is Fd-3m.

[0437] By definition, signature nets are uninodal nets. Among the 53 3 -periodic edgetransitive nets, there are 20 uninodal nets and 33 binodal nets. Including four 2-periodic uninodal edge-transitive nets and one 1 -periodic uninodal edge- transitive net, there are a total of 25 (20+4+1) uninodal edge-transitive nets that can be potential signature nets. The search for signature nets requires splitting nodes, and the methods differ for uninodal and binodal nets. For binodal nets, they can be directly split into two groups of nodes. The systematic searching of the signature nets of binodal edge-transitive nets was established by relinking all the same types of nodes in the 33 edge-transitive nets of transitivity

[0021] , On the signature net map, the signature net of binodal nets is represented by red arrows, starting from signature nets and pointing to parent nets. Typically, a parent net can have two signature nets.

[0438] However, for uninodal nets, they must first be transformed into their binodal versions. This transformation can be achieved in two ways: binary transformation and edge transformation.

[0439] The binary transformation creates binodal versions by evenly splitting the nodes into two groups, resulting in

[0021] nets with two types of nodes of the same vertex figure and coordination. For example, the binary versions of both the 4-c dia net and the 6-c pcu net have the signature net feu (see FIG. 9). One pair of 4-c nodes from dia and 6-c nodes from pcu can merge into a 10-c merged node, resulting in a (4,6,10)-c merged net xbp. Systematically searching for4053.277PCT1signature nets through binary transformation involves examining all possible binary versions of edge-transitive nets. It is worth noting that not all nets have a binary version; the criterion for a net to have a binary version is that the vertex number of all rings remains even. Among the 20 uninodal edge-transitive nets, 14 meet this criterion. On the signature net map, binary transformations are represented by purple arrows, starting from the signature nets and pointing to their parent nets.

[0440] The edge transformation creates a pseudo-binodal net with transitivity

[0021] by adding nodes at the midpoint of edges to all the uninodal edge-transitive nets, treating the edge as a 2- coordinated (2-c) node. Normally, for topologies, the 2-c part is considered an edge rather than a node. However, during the merging process, the pseudo 2-c node in uninodal edge-transitive nets can merge with other nodes, creating a merged node with connectivity higher than 2-c. For example, by edge transformation, both 4-c nbo and 6-c hxg net has signature net sod (see FIG. 10). In the merging process, the pseudo 2-c node in parent nets can merge into a 4-c node, resulting in a (4,4,6)-c merged net hxn. The signature nets of edge-transformed nets were systematically searched, mapping the resulting signature nets and linking them to their parent nets with green arrows. Additionally, a signature net can also act as a parent net, and linking its midpoint can generate another signature net until no 3 -periodic net can be obtained. The longest chain of signature nets starts from the dia net; by linking midpoints, Linking midpoints sequentially yields the crs, nbo, sod, and rhr nets. This chain ends with the rhr net, as it does not have an edgetransitive signature net.

[0441] Example 5. Analysis of edge ratio and proposed structures simulation. The edgeratios of the enumerated merged nets were analyzed. One of the lowest ratios observed was — (-0.378), as seen in the (srs, ifi)-merged ifr net. Another low ratio includes -y (-0.447), found in the (twf, nbo)-merged twn net. In some cases, the ratio can be exactly 0.5. For instance, in the (rht, tbo)-merged rhb net, the edge size of tbo net is exactly half of that of rht net. As a comparison, the ratio in the (mgc, spn)-merged mgs net is very close to 0.5, but the exact ratio isSome most commonly observed ratios include: s• — (-0.577), exemplified by (spn, hxg)-merged sph net.• — (-0.612), exemplified by (dia, hxg)-merged hxd net.44053.277PCT1• exemplified by (nbo, sod)-merged nso net.• exemplified by (pcu, bor)-merged pco net.• exemplified by (nbo, ocu)-merged xam net.•, exemplified by (nbo, flu)-merged rhf net.• 1 , exemplified by (crs, hxg)-merged crh net.Less commonly observed ratios include:• , exemplified by (mgc, dia)-merged kfo net.• , exemplified by (twf, she)-merged tws net.• , exemplified by (gar, bcs)-merged gas net.• , exemplified by (thp, lcs)-merged the net.• , exemplified by (ifi, srs)-merged ifs net.• ), exemplified by (mgc, hxg)-merged mgh net.•, exemplified by (mgc, dia)-merged mgi net.

[0442] Although most merged nets have fixed edge ratios in 3p-3p merged nets, some exhibit greater freedom of flexibility in tuning the edge ratio, especially those with non-cubic symmetry. This flexibility is more commonly observed in 3p-2p and 3p-0p merged nets (see FIG. 20). For example, the 3 -periodic binary pcu net in trigonal symmetry and 2-periodic hxl net can be merged into the (6,12)-c pch net (see FIG. 20). Adjustment of the c-axis yields either compressed models s(edge in pcu net shorter than in hxl net), resulting in an edge ratio between and 1, or stretched models (edge in pcu net longer than in hxl net), resulting in an edge ratio between 0 and 1 (see FIG. 20). Correspondingly, for the 6-c unmerged pcu nodes, in the standard pch net, the angles in its vertex figure are 60° and 120°, with a ratio of 1. In one of the compressed models, the angles are 90° and 90°, with an edge ratio of approximately 0.70. In one of the stretched models, the angles are 30° and 150°, with an edge ratio of approximately 0.52 (see FIG. 20). This example demonstrates that in lower-symmetry merged nets, there is greater flexibility in linker sizes for structure design, as long as the geometry changes of the building blocks remain within a tolerable range that matches the vertex figures of nodes in the merged nets. This increased flexibility can reduce the size limitation for the material design of these merged nets.

[0443] The most commonly used inorganic cluster-based building blocks were selected for simulation of proposed merged-net structures. Representative figures are presented in FIGS. 21-4053.277PCT128. For each MOF platform, a single structure was proposed that can be expanded into a list of isoreticular structures. Only one specific metal was used for the clusters in the simulations. For example, although paddlewheel building blocks can be made with various metals such as Cu, Mo, Zn, or Cr, the Cu-paddlewheel was exclusively used in these simulations. In proposed structures, the Cu-paddlewheels serve as 4-c square building blocks linking carboxylate linkers such as structures based on (acs, hcb)-merged acn net, (acs, hxl)-merged aco net, and (nbo, hxg)-merged hxn net, as well as 6-c octahedral building blocks linking both carboxylate and pyridine linkers such as structures based on (ssb, bcu)-merged ssu net and (nbo, pcu)-merged urk net (see FIG. 21). Although merged net structures typically involve mixed-linker systems, Structures based on a mixed-cluster system with a single type of linker were also proposed. In this case, the merging occurs at the center of the organic linker. An example is the proposed (rht, tbo)-merged rhb structure, where one nonatopic carboxylate linker with two types of arms forms both the rht and tbo frameworks, with the center core of the linker representing the 6-c merged nodes.

[0444] Structures with trinuclear clusters were proposed, functioning as 6-c trigonal-prism building blocks linking to carboxylate linkers or 9-c tricapped-trigonal building blocks linking to both carboxylate and pyridine linkers (see FIG. 22). Some proposed structures with 6-c clusters are based on nets such as the (nbo, ada)-merged nam net and (tbo, tet)-merged xbh net. Some proposed structures with 9-c cluster are based on nets such as the (acs, hcb)-merged aci net and the (the, rdo)-merged thm net. Structures with tetranuclear clusters (see FIG. 23) were further proposed, functioning as 6-c octahedral building blocks linking to carboxylate linkers, 8-c cube building blocks linking to tetrazole linkers, and 8-c cube building blocks linking to carboxylate linkers. Structures with hexanuclear clusters were proposed, working as saturated 12-c cuboctahedral building blocks (see FIG. 24) or as unsaturated (connectivity < 12) building blocks (see FIG. 25). Structures with octanuclear clusters were proposed as 12-c cuboctahedral building blocks linking to pyrazole linkers (see FIG. 26). Structures based on supermolecular building blocks were further proposed, assembled by the hexa-paddlewheel (see FIG. 27) and dodecapaddlewheel (see FIG. 28).

[0445] Example 6. Structure description and characterization of synthesized MOFs. Due to poor diffraction and disorder, a set of restraints and constraints was applied to make both geometries and the atomic thermal parameters reasonable. There are more details in the *.res file embedded in each CIF. C-0 Bonds in the carboxylates were restrained to 1.26 A The geometry of4053.277PCT1the whole aromatic rings in the asymmetric units of each structure were constrained by AFIX 66 command. 1,2- and 1,3 -C-C distances in aromatic rings which are only partially included in the asymmetric unit were restrained by DFIX 1.39 and DFIX 2.41, respectively. Single C-C bonds between the benzene rings and carboxylates or benzene rings themselves were restrained to 1.50 A. Double C=C bonds in BTTC were restrained by DFIX 1.34, single C-C by DFIX 1.41, and single C-S bonds were restrained by DFIX 1.74. FLAT was used to keep the planarity of the flat fragments. A set of DFIXes was also used to keep the geometry of the disordered DMF molecule. Anisotropic Displacement Parameters (ADPs) of the non-hydrogen atoms were often restrained by SIMU. EADP was applied for close-located atoms of different parts of the disorder. Hydrogen atoms were placed at the calculated positions and refined using a riding model with UIS0(H) = 1.2Deq(Csp2) or 1.5t / eq(CSp3, O). The structures contain significant solvent-accessible voids. No substantial electron density peaks were found in the solvent accessible voids and the residual electron density peaks are not arranged in an interpretable pattern (except a DMF molecule in Y- BTPHB-pcu-MOF and water in Y-pch-MOF-2). The structure factors were instead augmented via reverse Fourier transform methods using the SQUEEZE routine implemented in the program PLATON. The resultant FAB file containing the structure factor contribution from the electron content of the void space was used together with the original *.hkl file in further refinement.

[0446] Tb-sph-MOF-6: The SCXRD studies revealed that brown octahedral crystals of Tb- sph-MOF-6 crystallize in the cubic space group Fd-3m with the unit cell parameter a = 46.103(1) A. It was not possible to localize H-atoms of water molecules and whole dimethylammonium (DMA) cations but they are included in the final formula. Strongly delocalized residual electron density was found in the voids and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals 59850 A3and contains 14835 electrons). The crystallographically estimated formula of the MOF is |DMA|2[(Tbe(p3- OH)8(BTTC)2(HBCHB)(H2O)2] x(solv). In the structure of Tb-sph-MOF-6, each 12-c hexanuclear terbium cluster links to six 3-c BTTC linkers occupy the trigonal antiprism position of the cuboctahedron, and six 6-c HBCHB linkers occupy the planar hexagonal position, forming a structure based on the underlying (3,6,12)-c sph merged net.

[0447] PXRD patterns of Tb-sph-MOF-6were calculated from SCXRD data and measured using as-synthesized Tb-sph-MOF-6. FIG. 31A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Tb-sph-MOF-6.4053.277PCT1

[0448] Low-pressure argon physisorption analysis was performed on an activated sample of Tb-sph-MOF-6 (see FIGS. 31B-D). The material was activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with acetone several times daily for 3 days, and then degassed under vacuum at 120 °C. Argon physisorption isotherms at 87 K showed fully reversible Type-I isotherms. The apparent BET surface area for Tb-sph-MOF-6 was estimated to be 1822 m2g'1. The pore volume at P / Po = 0.95 was estimated to be 0.72 cm3g'1, with the theoretical pore volume being 0.75 cm3g'1. The pore size distribution of the sample was calculated using the NLDFT method of the carbon slit pores model. The sample exhibited two types of pores approximately 6.5 A and 13 A. The smaller pore corresponds to the tetrahedral cage delimited by four clusters and four BTTC linkers, and the larger pore corresponds to the truncated tetrahedral cage delimited by twelve clusters, four BTTC linkers, and four HBCHB linkers.

[0449] Y-BTPHB-pcu-MOF: The SCXRD studies revealed that colorless rhombohedral crystals of Y-BTPHB-pcu-MOF crystallize in the trigonal space group R-3 with the unit cell parameters a = 18.2187(9) A and c = 112.607(5) A. There is a significant disorder of o- fluorobenzoate (FBA, ligand B) in the structure. FBA reveals site-occupancy disorder with a pair of H2O / OH- with an equal occupancy of 0.5. F-C bonds in FBA were restrained to 1.35 A and 1,3- distances F—C were restrained to be the same to keep the directionality of the F-C bond. It was not possible to localize DMA cations in the structure as well as H-atoms of the disordered water molecules / hydroxyls, but the reported formula includes them. Strongly delocalized residual electron density was found in six solvent-accessible voids of 2918 A3each and omitted from the refinement using the PLATON's SQUEEZE procedure (total 3990 electrons). The crystallographically estimated formula of the MOF is MA|2[Ye(p3- OH)8(BTPHB)(FBA)3(OH)3(H2O)4.5] DMF x(solv). In the structure of Y-BTPHB-pcu-MOF, each hexanuclear yttrium cluster is connected to six BTPHB linkers, and each of the linkers is coordinated to six clusters. The topological analysis of the resulting crystal structure reveals a 3- periodic MOF based on the underlying pcu net. The PXRD of as-synthesized Y-BTPHB-pcu- MOF was also experimentally obtained and it matches with calculated PXRD from SCXRD data. The single linker Y-BTPHB-pcu-MOF shows nonporous after degassing, which may indicate structure collapse upon removal of guest molecule incorporated during synthesis. FIG. 304053.277PCT1illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-BTPHB-pcu-MOF.

[0450] Y-pch-MOF-1 and -2: The SCXRD studies revealed that colorless rhombohedral crystals of Y-pch-MOF-1 crystallize in the trigonal space group R-3c with the unit cell parameters a = 19.4890(4) A and c = 105.843(3) A. Biphenyl-4,4'-dicarboxylate (BPDC, ligand B) is disordered over two positions with an equal occupancy of 0.5. One carboxylate of the ligand is coordinated by two Y3+in (^-coordination mode, whereas the second one is coordinated by only one Y3+cation in a ^-coordination mode. The second Y3+is coordinates then a water molecule with a half occupancy. It was not possible to localize DMA cations in the structure as well as Id- atoms of the disordered water molecules, but the reported formula includes them. Strongly delocalized residual electron density was found in the void and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals 21660 A3and contains 7514 electrons). The crystallographically estimated formula of the MOF is |DMA|2[(Y6(p3-OH)8(BTPHB)(BPDC)3(H2O)3] x(solv). In the structure of Y-pch-MOF-1, each 12-c hexanuclear yttrium cluster links to six 6-c BTPHB linkers occupy the trigonal antiprism position of the cuboctahedron, and six 2-c BPDC linkers occupy the planar hexagonal position, forming a MOF based on the underlying (6,12)-c pch merged net.

[0451] The SCXRD studies revealed that yellow rhombohedral crystals of Y-pch-MOF-2 crystallize in the trigonal space group R-3c with the unit cell parameters a = 19.4627(8) A and c = 105.683(5) A. There is a significant positional disorder of anthracene-2,6-dicarboxylate in the structure (AnDC, ligand B) and water. It was not possible to localize DMA cations in the structure as well as H-atoms of the disordered water molecules, but the reported formula includes them. Strongly delocalized residual electron density was found in the voids and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals 19946 A3and contains 6484 electrons). The crystallographically estimated formula of the MOF is |DMA|2[Y6(p3-OH)8(BTPHB)(AnDC)3(H2O)2.32] L I6H2O x(solv). In the structure of Y-pch- MOF-2, each 12-c hexanuclear yttrium cluster links to six 6-c BTPHB linkers occupy the trigonal antiprism position of the cuboctahedron, and six 2-c AnDC linkers occupy the planar hexagonal position, forming a MOF based on the underlying (6,12)-c pch merged net.

[0452] PXRD patterns of Y-pch-MOF-1 and Y-pch-MOF-2 were calculated from SCXRD data and measured using as-synthesized Y-pch-MOF-1 and Y-pch-MOF-2. FIG. 32A and 33A4053.277PCT1illustrate graphs showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-pch-MOF-1 and Y-pch-MOF-2, respectively.

[0453] Low-pressure argon physisorption analysis was performed on an activated sample of Y-pch-MOF-1 (see FIGS. 32B-D) and Y-pch-MOF-2 (see FIGS. 33B-D). The materials were activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with acetone several times daily for 3 days, then degassed under vacuum at room temperature. Argon physisorption isotherms at 87 K for both acetone-exchanged samples showed fully reversible Type-I isotherms. The apparent BET surface area for Y-pch- MOF-1 was estimated to be 2442 m2g'1and the pore volume at P / Po = 0.95 was estimated to be 0.87 cm3g'1, with the theoretical pore volume being 0.87 cm3g'1. The pore size distribution of the sample was calculated from the Ar physisorption isotherm using the DFT method with a carbon slit pores model. The material shows a uniform pore of about 12 A, which corresponds to the tetrahedral cage delimited by three BTPHB linkers and three BPDC linkers. The apparent BET surface area for Y-pch-MOF-2 was estimated to be 2077 m2g'1and the pore volume at P / Po = 0.95 was estimated to be 0.77 cm3g'1, with the theoretical pore volume being 0.77 cm3g'1. The pore size distribution of the sample was calculated from argon adsorption isotherm using the NLDFT method with carbon slit pores model. The material shows a uniform pore of about 11 A, which corresponds to the tetrahedral cage delimited by three BTPHB linkers and three AnDC linkers.

[0454] Zr-thw-MOF-1: The SCXRD studies revealed that colorless cubic crystals of Zr- thw-MOF-1 crystallize in the cubic space group Pm-3m with the unit cell parameter a = 28.038(1) A. Due to poor diffraction, a set of restraints and constraints was applied to make both geometries the ADPs of organic ligands reasonable. There is an occupational disorder of TBDC ligand and water / hydroxylic groups. It was not possible to localize H-atoms of water molecule and hydroxyl group but they are included in the final formula. Strongly delocalized residual electron density was found in the voids and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals 15317 A3and contains 3433 electrons). The crystallographically estimated formula of the MOF is [Zre(p3-O)4(p3- OH)4(TMBTB)8 / 3(TBDC)O.56(OH)2.88(H20)2.88] x(solv). In the structure of Zr-thw-MOF-1, each hexanuclear zirconium cluster links to ten linkers, eight TMBTB linkers, and two TBDC linkers, forming a structure based on the underlying (3,10)-c thw merged net. In the single-crystal data,4053.277PCT1the TBDC linker is disordered in two positions, forming a pseudo 4-c linker, and the whole pseudostructure can be regarded as a structure based on underlying (3,4,10)-c urr merged net.

[0455] PXRD patterns of Zr-thw-MOF-1 were calculated from SCXRD data and measured using as-synthesized Zr-thw-MOF-1. FIG. 34 A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Zr-thw-MOF-1.

[0456] Low-pressure argon physisorption analysis was performed on an activated sample of Zr-thw-MOF-1 (see FIGS. 34B-C). The material was activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with ethanol several times daily for 3 days, then degassed under vacuum at 105 °C. Argon physisorption isotherms at 87 K show a permanent mesoporosity of Zr-thw-MOF-1. The experimental total pore volume was estimated to be 0.98 cm3g'1at P / Po = 0.95, with the theoretical pore volume being 1.31 cm3g'1. The pore size distribution of the sample was calculated from argon physisorption isotherm using the NLDFT method with carbon slit pores model. The sample exhibited two types of pores approximately 13 A and 18 A. The smaller pore corresponds to the octahedral cage delimited by six clusters and eight TMBTB linkers, and the larger pore corresponds to the truncated cube cage delimited by twelve clusters, eight TMBTB linkers and six TBDC linkers.

[0457] Fe-nam-MOF-1: The SCXRD studies revealed that red octahedral crystals of Fe- nam-MOF-1 crystallize in the cubic space group Fm-3m with the unit cell parameter a = 35.186(3) A. Due to poor diffraction, a set of restraints was applied to make both the geometry and ADPs of the ligands reasonable. The XPS study suggests there is only Fe3+. 15% of the counterion CF is coordinated to Fe, 85% is free. The free chloride is disordered in the MOF cavities and it was not possible to localize it. The coordinated CF was refined to have the same ADPs and coordinates as Olw, since these oxygen atoms revealed lower ADPs, with an occupancy of 0.15. It was not possible to localize H-atoms of the disordered water molecules but the reported formula includes them. Strongly delocalized residual electron density was found in the void and omitted from the refinement using the PLATON's SQUEEZE procedure. The total void volume per unit cell equals 21429 A3(one tetrahedral cage of 19143 A3and four octahedral cages of 570 A3) and contains 5461 electrons (4889 and 143 for the tetrahedral and the octahedral cages, respectively). The crystallographically estimated formula of the MOF is [Fe3(g3- 0)(BBPTC)(BTTC)2 / 3(H20)2.85C1O.I5]C1O.85 x(solv). In the structure of Fe-nam-MOF-1, each trinuclear iron cluster links to six linkers, four 4-c BBPTC linkers, and two 3-c BTTC linkers,4053.277PCT1forming a structure based on the underlying (3,4,6)-c nam merged net. In the single-crystal data, the TBDC linker is disordered in two positions, and the apparent structure can be regarded as a pseudo-structure based on the underlying (3,4,8)-c nbr merged net.

[0458] PXRD patterns of Fe-nam-MOF-1 were calculated from SCXRD data and measured using as-synthesized Fe-nam-MOF-1. FIG. 35A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Fe-nam-MOF-1.

[0459] Low-pressure argon physisorption analysis was performed on an activated sample of Fe-nam-MOF-1 (see FIGS. 35B-D). The material was activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with hexane several times daily for 3 days, then degassed under vacuum at room temperature. Argon physisorption isotherms at 87 K showed fully reversible Type-I isotherms. The apparent BET surface area for Fe-nam-MOF-1 was estimated to be 912 m2g'1and the pore volume at P / Po = 0.95 was estimated to be 0.35 cm3g’1, with the theoretical pore volume being 0.61 cm3g'1. The lower pore volume might be because the coordinated molecules on the open-metal site cannot be fully removed since this material can only be activated at room temperature. The pore size distribution of the sample was calculated from argon physisorption isotherm using the NLDFT method with a hybrid slit- cylindrical model. The sample exhibited two types of pores approximately 5 A and 9 A. The small pore corresponds to the octahedral cage delimited by six clusters and twelve BBPTC linkers. The large pore corresponds to the truncated cube cage delimited by twelve clusters, four BTTC linkers, and six BBPTC likers.

[0460] Y-pck-MOF-1 : The SCXRD studies revealed that yellow rhombohedral crystals of Y-pck-MOF-1 crystallize in the trigonal space group R-3c with the unit cell parameters a = 17.9255(6) A and c = 113.795(5) A. The structure was refined as a 2-component inversion twin with BASF 0.50(2). Due to poor diffraction, a set of restraints and constraints was applied to make ADPs of the ligands reasonable. It was not possible to localize DMA cations in the structure, but the reported formula includes them. Strongly delocalized residual electron density was found in the void and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals 19183 A3and contains 6801 electrons). The crystallographically estimated formula of the MOF is |DMA|2[Y6(p3-OH)8(BTPHB)(NTB)2 (DMF)o.75] x(solv). In the structure of Y-pck-MOF-1, each 12-c hexanuclear yttrium cluster links to six 6-c BTPHB linkers4053.277PCT1occupy the trigonal antiprism position of the cuboctahedron, and six 3-c BPDC linkers occupy the planar hexagonal position, forming a MOF based on the underlying (3,6,12)-c pck merged net.

[0461] PXRD patterns of Y-pck-MOF-lwere calculated from SCXRD data and measured using as-synthesized Y-pck-MOF-1. FIG. 36A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Y-pck-MOF-1.

[0462] Low-pressure argon physisorption analysis was performed on an activated sample of Y-pck-MOF-1 (see FIGS. 36B-D). The material was activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with acetone several times daily for 3 days, and then degassed under vacuum at 55 °C. Argon physisorption isotherms at 87 K showed fully reversible Type-I isotherms. The apparent BET surface area for Y-pck-MOF-1 was estimated to be 2446 m2g'1and the pore volume at P / Po = 0.95 was estimated to be 0.93 cm3g’1, with the theoretical pore volume being 0.87 cm3g'1. The pore size distribution of the sample was calculated from argon physisorption isotherm using the NLDFT method with carbon slit pores model. The material shows two types of pores approximately 6 A and 10 A. The small pore corresponds to the small tetrahedral cage delimited by one BTPHB linker and one NTB linker. The large pore corresponds to the large tetrahedral cage delimited by three BTPHB linkers and one NTB linker.

[0463] Tb-nih-MOF-1: The SCXRD studies revealed that colorless hexagonal plates of Tb- nih-MOF-1 crystallize in the hexagonal space group P6-Jmmc with the unit cell parameters a = 22.190(2) A and c = 53.052(5) A. There is an occupational disorder at two apical positions of Tb nonanuclear cluster, where 33% occupancy of hydrated Tb3+cation is observed as [Tb(H2O)3]3+; therefore, results in 67% of c-coordinated one OH and two H2O, and 33% of p2-bridging one OH and two H2O when the hydrated Tb3+is present. Strongly delocalized residual electron density was found in the voids in MOF and omitted from the refinement using the PLATON's SQUEEZE procedure (the total void volume per unit cell equals to 14696 A3and contains 3642 electrons). The crystallographically estimated formula of the MOF is |DMA|(3-3y) [(Tb9(p3-O)2(g3- OH)i2(OH)2(H2O)4(Tb(H2O)3)2y) (Tb6(p3-OH)8(H2O)6)(TTDA)6(ABPDC)3] x(solv) (y = 0.33 - occupancy of the hydrated Tb3+). In the structure of Tb-nih-MOF-1, there are two types of clusters, the 12-c hexanuclear clusters and 12-c nonanuclear clusters. The nonanuclear cluster further connects to two Tb3+through pi-OH bridge. Each hexanuclear cluster links to six TTDA linkers,4053.277PCT1and six ABPDC linkers. Each nonanuclear cluster links to twelve TTDA linkers. The whole structure is based on the underlying (3,12,12)-c net, which is the (6,12)-c nih related net.

[0464] PXRD patterns of Tb-nih-MOF-1 were calculated from SCXRD data and measured using as-synthesized Tb-nih-MOF-1. FIG. 37A illustrates a graph showing a comparison between the calculated and experimentally obtained PXRD patterns of Tb-nih-MOF-1.

[0465] Low-pressure argon physisorption analysis was performed on an activated sample of Tb-nih-MOF-1 (see FIGS. 37B-D). The material was activated by the following procedure. The as-synthesized crystals were washed with DMF, followed by solvent exchange with acetone several times daily for 3 days, and then degassed under vacuum at 55 °C. Argon physisorption isotherms at 87 K showed fully reversible Type-I isotherms. The apparent BET surface area for Tb-nih-MOF-1 was estimated to be 1584 m2g'1and the pore volume at P / Po = 0.95 was estimated to be 0.58 cm3g’1, with the theoretical pore volume being 0.69 cm3g'1. The pore size distribution of the sample was calculated from argon physisorption isotherm using the NLDFT method with carbon slit pores model. The material shows a uniform pore of about 12 A, which is matching with the tetrahedral space delimited by three TTDA linkers and three ADB linkers.

[0466] While the invention has been described with reference to an exemplary embodiment(s), it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment(s) disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.

[0467] Various examples have been described herein. These and other examples are within the scope of the following claims.DISCUSSION OF POSSIBLE EMBODIMENTS

[0468] The following are non-exclusive descriptions of possible embodiments of the present invention.

[0469] According to one aspect, intricate mixed-linker structure, comprising:(a) selecting a merged-net to target in a synthesis of the intricate mixed-linker structure, a first 3-periodic (3p) edge-transitive net, and second 3p edge-transitive net, wherein the first and second 3p edge-transitive nets share a common signature net and are capable of4053.277PCT1combining to afford the targeted merged-net and wherein one of the first and second 3p edge-transitive nets is an embedded 3 -dimensional representation of a lower-periodicity net selected from 2-periodic (2p), 1-periodic (Ip), and 0-periodic (Op);(b) determining a connectivity and geometrical configuration of each node of the merged-net, wherein the nodes of the merged-net comprise a merged node and unmerged nodes, wherein the unmerged nodes include a first unmerged node and second unmerged node;(c) selecting a first molecular building block (MBB) with identical connectivity and geometrical configuration to the merged node and having two sets of points of extension, wherein each set of points of extension is capable of linking to distinct MBBs;(d) selecting a second MBB with the same connectivity and geometrical configuration as the first unmerged node;(e) inputting a length of the selected second MBB into a merged-net equation to calculate a length of a complementary MBB;(f) selecting a third MBB with the same connectivity and geometrical configuration as the second unmerged node, and the same length as the complementary MBB; and(g) reacting precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net.

[0470] The method of the preceding paragraph can optionally include, additionally and / or alternatively any, one or more of the following features / steps, configurations and / or additional components,

[0471] For example, the method may further include at least one of the first and second 3p edge-transitive nets being an embedded 3 -dimensional representation of a 2-periodic net.

[0472] For example, the method may further include at least one of the first and second 3p edge-transitive nets being selected from: sql net, kgm net, hcb net, hxl net, and kgd net.

[0473] For example, the method may further include the merged net being selected from: acc net, nia-d net, ack net, aci net, tsn net, acl net, acg net, hep net, acn net, aco net, lon-e net, ali net, alh net, alk net, alj net, bsa net, xal net, bsd net, boh net, bok net, bos net, boq net, csb net, esm net, esg net, die net, ted net, dik net, tsi net, dib net, diq net, epx net, fka net, fuq net, fha net, fhx net, fkm net, flc net, fix net, fll net, flk net, flq net, xak net, pfm net, fib net, fwh net, fwg net, fwk net, fws net, fwl net, fwq net, itx net, itk net, Icq net, mgb net, mgt net, mgx net,4053.277PCT1mgq net, mgl net, nbh net, nbc net, epa net, nbm net, ats net, nid net, nix net, nih net, nik net, ocb net, ocx net, ock net, ocq net, ocv net, ocm net, ocl net, pcc net, peg net, pcs net, pch net, pek net, pem net, ahq net, ptx net, ptl net, ptk net, ptg net, pss net, pst net, urj net, psp net, pyh net, pys net, pyq net, rhh net, rhs net, rhq net, sus net, kty net, shq net, shd net, shm net, shh net, shx net, shk net, shg net, scs net, seq net, sem net, sqq net, ssh net, ssx net, ssg net, ssq net, sti net, stm net, sss net, stn net, eye net, thx net, thk net, tom net, tob net, tox net, tol net, toy net, tow net, tod net, ttk net, ttj net, ttm net, ttn net, twx net, twk net, twq net, and twl net.

[0474] For example, the method may further include at least one of the first and second 3p edge-transitive nets being an embedded 3-dimensional representation of a 1 -periodic net.

[0475] For example, the method may further include at least one of the first and second 3p edge-transitive nets being lew net.

[0476] For example, the method may further include the merged net being selected from: ith-d net, thw net, itw net, sww net, rew net, brw net, tbw net, and flw net.

[0477] For example, the method may further include at least one of the first and second 3p edge-transitive nets being an embedded 3-dimensional representation of a 0-periodic net.

[0478] For example, the method may further include at least one of the first and second 3p edge-transitive nets being selected from: cub net, cuo net, oct net, rdo net, and tet net.

[0479] For example, the method may further include the merged net being selected from: boc net, era net, crc net, ere net, erf net, erv net, did net, dig net, dih net, dii net, ffv net, ffe net, ffh net, ffk net, ffl net, fid net, fle net, fwm net, fwn net, fww net, hxa net, hxe net, hxc net, kpl net, mga net, mge net, nam net, nbb net, nbr net, nbu net, neb net, pea net, peb-e net, pee net, pef net, pej net, pcq net, pha net, pyc net, rea net, rec net, ree net, ref net, reg net, reh net, rha net, rhe net, rhg net, rhi net, sej net, scr net, sew net, spa net, spb net, str net, tbm net, tw net, tew net, tex net, tew net, tex net, thi net, thm net, xay net, xbf net, xbh net, and xbi net.

[0480] For example, the method may further include at least one of the first and second 3p edge-transitive nets being a 3-periodic net selected from: acs net, alb net, ana net, bes net, bcu net, bor net, ers net, esq net, ctn net, dia net, feu net, flu net, ftw net, hxg net, ith net, les net, lev net, ley net, Ivt net, mge net, nbo net, nia net, ocu net, peu net, pth net, pto net, pts net, pyr net, qtz net, reo net, rhr net, rht net, scu net, she net, shp net, soc net, sod net, spn net, sqc net, srs net, ssa net, ssb net, ssc net, stp net, tbo net, the net, thp net, toe net, ttt net, and twf net.4053.277PCT1

[0481] For example, the method may further include the second MBB and third MBB being different.

[0482] For example, the method may further include each of first MBB, second MBB, and third MBB being independently selected from an organic MBB or inorganic MBB.

[0483] For example, the method may further include each of first MBB, second MBB, and third MBB being independently selected from a first polytopic ligand, second polytopic ligand, or metal component.

[0484] For example, the method may further include at least one of first MBB, second MBB, and third MBB being an inorganic MBB comprising a cluster of metals or metal ions.

[0485] For example, the method may further include the second MBB associates with at least one of the two sets of points of extension to afford the first 3p edge-transitive net.

[0486] For example, the method may further include the third MBB associates with at least one of the two sets of points of extension to afford the second 3p edge-transitive net.

[0487] For example, the method may further include the merged-net equation being represented by formula (1):wherein CR is a ratio constant for a merged-net, SBBI is the size of all building blocks for the first 3p edge-transitive net, and SBB2 is the size of all building blocks for the second 3p edge-transitive net.

[0488] For example, the method may further include the merged-net equation being represented by formula (2) or (3):wherein Soi and S02 are the total sizes of all organic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively; CR is a ratio constant for a merged-net; and Sn and Sn are the total sizes of all inorganic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively.4053.277PCT1

[0489] For example, the method may further include the method further comprises selecting additional pairs of first and third MBBs to form an isoreticular intricate mixed-linker structure.

[0490] In a further aspect, the present invention being directed to materials comprising a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form an intricate mixed-linker structure with a merged-net.

[0491] For example, the method may further include the first polytopic ligand and second polytopic ligand being different.

[0492] For example, the method may further include each of the first polytopic ligand and second polytopic ligand being independently selected from ligands having O-, N-, and S-donor functional groups.

[0493] For example, the method may further include each of the first polytopic ligand and second polytopic ligand being independently selected from polycarboxylate acid ligands, polytetrazole ligands, polytriazole ligands, polypyrazole ligands, polyimidazole ligands, and polypyridyl ligands.

[0494] For example, the method may further include the metal component being an inorganic molecular building block (MBB) comprising a cluster of metals or metal ions.

[0495] For example, the method may further include the metal of the metal component being selected from rare earth metals, alkali metals, alkaline earth metals, and transition metals.

[0496] For example, the method may further include the merged-net comprises a first 3p edge- transitive net and a second 3p edge-transitive net merged through shared nodes.

[0497] For example, the method may further include the merged-net retains the structural framework of the first 3p edge-transitive net and second 3p edge-transitive net.

[0498] For example, the method may further include the first 3p edge-transitive net and the second 3p edge-transitive net each have a transitivity selected from transitivity

[0011] and transitivity

[0021] ,

[0499] For example, the method may further include edge-transitive nets having transitivity

[0011] being selected from a hxg net, lew net, hxl net, kgm net, heb net, dia net, ers net, nbo net, sod net, rhr net, acs net, sql net, Ivt net, bcu net, peu net, feu net, reo net, qtz net, srs net, lev net, ley net, bes net, les net, ana net, and thp net.

[0500] For example, the method may further include edge-transitive nets having transitivity

[0021] being selected from a shp net, alb net, stp net, mge net, spn net, toe net, nia net, ssa net, esq4053.277PCT1net, ith net, twf net, ocu net, she net, pto net, pth net, ssb net, pts net, soc net, ttt net, rht net, bor net, the net, scu net, sqc net, flu net, pyr net, ftw net, tbo net, ifi net, ssc net, iac net, gar net, and ctn net.

[0501] For example, the method may further include the first 3p edge-transitive net and a second 3p edge-transitive net have a common signature net.

[0502] For example, the method may further include the common signature net being selected from a kgm net, ana net, feu net, reo net, bes net, pen net, ers net, nbo net, thp net, lew net, les net, sod net, hxg net, lev net, srs net, bcu net, ley net, dia net, acs net, qtz net, feu net, o- p net, rhr net, hxl net, Ivt net, and thp net.

[0503] For example, the method may further include the merged-net being selected from an edge-transformed net merged with a signature net, a binary-transformed net merged with a signature net, a direct transitivity [2,1] net merged with a signature net.

[0504] For example, the method may further include the merged-net being selected from an edge- transformed net merged with another edge-transformed net, a binary -transformed net merged with another binary -transformed net, a direct transitivity

[0021] net merged with another direct transitivity

[0021] net.

[0505] For example, the method may further include the merged-net being selected from an edge- transformed net merged with a binary -transformed net, an edge- transformed net merged with a direct transitivity [2,1] net, and a binary-transformed net merged with a direct transitivity

[0021] net.

[0506] For example, the method may further include the merged-net has a transitivity selected from transitivity

[0022] and transitivity

[0032] ,

[0507] In an additional aspect, the present invention being directed to methods of synthesizing intricate mixed-linker structure comprising contacting a metal precursor, first ligand precursor, and second ligand precursor under reaction conditions sufficient to form an intricate mixed-linker structure with a merged net.

[0508] In other aspects, the present invention being directed to methods comprising one or more of the following steps: extracting signature nets from a plurality of edge-transitive parent nets having a transitivity

[0011] and / or transitivity

[0021] by one or more of edge transformation, binary transformation, and direct transformation; selecting a first 3p edge-transitive net and a second 3p edge-transitive net having a common signature net from the plurality of edge- transitive4053.277PCT1nets; selecting a first polytopic ligand suitable for the first 3p edge-transitive net and a second polytopic ligand suitable for the second 3p edge-transitive net; and synthesizing an intricate mixed- linker structure by reacting precursors for the first polytopic ligand and the second polytopic ligand with a polynuclear-cluster precursor.

[0509] In other aspects, the present disclosure being directed to methods of designing intricate mixed-linker structures, comprising extracting signature nets from a plurality of parent nets by one or more of edge transformation, binary transformation, and direct transformation; merging parent nets which have a common signature net to obtain a plurality of merged-nets; and determining the coordination number of nodes present in each of the plurality of merged-nets.

[0510] For example, the method may further include the plurality of parent nets being edgetransitive nets with

[0011] transitivity and

[0021] transitivity.

[0511] For example, the method may further include edge transformation being used for parent nets with

[0011] transitivity.

[0512] For example, the method may further include binary transformation being used for parent nets with

[0011] transitivity.

[0513] For example, the method may further include direct transformation being used for parent nets with

[0021] transitivity.

[0514] For example, the method may further include each of the plurality of merged-nets have two kinds of linkers.

[0515] For example, the method may further include the plurality of merged-nets being minimal edge-transitive nets with

[0022] transitivity or

[0032] transitivity.

[0516] For example, the method may further include the plurality of merged-nets include edge transformed nets merged with signature nets.

[0517] For example, the method may further include the plurality of merged-nets include binary transformed nets merged with signature nets.

[0518] For example, the method may further include the plurality of merged-nets include direct transformed nets merged with signature nets.

[0519] For example, the method may further include the plurality of merged-nets include first edge transformed nets merged with second edge transformed nets.

[0520] For example, the method may further include the plurality of merged-nets include first binary transformed nets merged with second binary transformed nets.4053.277PCT1

[0521] For example, the method may further include the plurality of merged-nets include first direct transformed nets merged with second direct transformed nets.

[0522] For example, the method may further include the plurality of merged-nets include edge transformed nets merged with binary transformed nets.

[0523] For example, the method may further include the plurality of merged-nets include edge transformed nets merged with direct transformed nets.

[0524] For example, the method may further include the plurality of merged-nets include binary transformed nets merged with direct transformed nets.

[0525] For example, the method may further include at least one of the nodes of a merged- net being a merged-node.4053.277PCT1

Claims

WHAT IS CLAIMED IS:

1. A method of synthesizing an intricate mixed-linker structure, comprising:(a) selecting a merged-net to target in a synthesis of the intricate mixed-linker structure, a first 3-periodic (3p) edge-transitive net, and second 3p edge-transitive net, wherein the first and second 3p edge-transitive nets share a common signature net and are capable of combining to afford the targeted merged-net and wherein one of the first and second 3p edge-transitive nets is an embedded 3-dimensional representation of a lower-periodicity net selected from 2-periodic (2p), 1 -periodic (Ip), and 0-periodic (Op);(b) determining a connectivity and geometrical configuration of each node of the merged-net, wherein the nodes of the merged-net comprise a merged node and unmerged nodes, wherein the unmerged nodes include a first unmerged node and second unmerged node;(c) selecting a first molecular building block (MBB) with identical connectivity and geometrical configuration to the merged node and having two sets of points of extension, wherein each set of points of extension is capable of linking to distinct MBBs;(d) selecting a second MBB with the same connectivity and geometrical configuration as the first unmerged node;(e) inputting a length of the selected second MBB into a merged-net equation to calculate a length of a complementary MBB;(f) selecting a third MBB with the same connectivity and geometrical configuration as the second unmerged node, and the same length as the complementary MBB; and(g) reacting precursors of the first MBB, the second MBB, and the third MBB to synthesize an intricate mixed-linker structure with the targeted merged-net.

2. The method according to claim 1, wherein at least one of the first and second 3p edgetransitive nets is an embedded 3 -dimensional representation of a 2-periodic net.

3. The method according to any one of claims 1-2, wherein at least one of the first and second 3p edge-transitive nets is selected from: sql net, kgm net, hcb net, hxl net, and kgd net.4053.277PCT14. The method according to any one of claims 1-3, wherein the merged net is selected from: acc net, nia-d net, ack net, aci net, tsn net, acl net, acg net, hep net, acn net, aco net, lon-e net, ali net, alh net, alk net, alj net, bsa net, xal net, bsd net, boh net, bok net, bos net, boq net, csb net, esm net, esg net, die net, ted net, dik net, tsi net, dib net, diq net, epx net, fka net, fuq net, fha net, fhx net, fkm net, flc net, fix net, fll net, flk net, flq net, xak net, pfm net, fib net, fwh net, fwg net, fwk net, fws net, fwl net, fwq net, itx net, itk net, Icq net, mgb net, mgt net, mgx net, mgq net, mgl net, nbh net, nbc net, epa net, nbm net, ats net, nid net, nix net, nih net, nik net, ocb net, ocx net, ock net, ocq net, oev net, ocm net, ocl net, pcc net, peg net, pcs net, pch net, pek net, pem net, ahq net, ptx net, ptl net, ptk net, ptg net, pss net, pst net, urj net, psp net, pyh net, pys net, pyq net, rhh net, rhs net, rhq net, sus net, kty net, shq net, shd net, shm net, shh net, shx net, shk net, shg net, scs net, seq net, sem net, sqq net, ssh net, ssx net, ssg net, ssq net, sti net, stm net, sss net, stn net, eye net, thx net, thk net, tom net, tob net, tox net, tol net, toy net, tow net, tod net, ttk net, ttj net, ttm net, ttn net, twx net, twk net, twq net, and twl net.

5. The method of claim 1, wherein at least one of the first and second 3p edge-transitive nets is an embedded 3 -dimensional representation of a 1 -periodic net.

6. The method according to any one of claims 1 and 5, wherein at least one of the first and second 3p edge-transitive nets is lew net.

7. The method according to any one of claims 1 and 5-6, wherein the merged net is selected from: ith-d net, thw net, itw net, sww net, rew net, brw net, tbw net, and flw net.

8. The method according to any one of claims 1, wherein at least one of the first and second 3p edge-transitive nets is an embedded 3-dimensional representation of a 0-periodic net.

9. The method according to any one of claims 1 and 8, wherein at least one of the first and second 3p edge-transitive nets is selected from: cub net, cuo net, oct net, rdo net, and tet net.

10. The method according to any one of claims 1 and 8-9, wherein the merged net is selected from: boc net, era net, crc net, ere net, erf net, erv net, did net, dig net, dih net, dii net, ffv net,4053.277PCT1ffe net, ffh net, ffk net, ffl net, fid net, fle net, fwm net, fwn net, fww net, hxa net, hxe net, hxc net, kpl net, mga net, mge net, nam net, nbb net, nbr net, nbu net, neb net, pea net, peb-e net, pee net, pef net, pej net, pcq net, pha net, pyc net, rea net, rec net, ree net, ref net, reg net, reh net, rha net, rhe net, rhg net, rhi net, sej net, scr net, sew net, spa net, spb net, str net, tbm net, tw net, tew net, tex net, tew net, tex net, thi net, thm net, xay net, xbf net, xbh net, and xbi net.

11. The method according to any one of claims 1-10, wherein at least one of the first and second 3p edge-transitive nets is a 3-periodic net selected from: acs net, alb net, ana net, bes net, bcu net, bor net, ers net, esq net, ctn net, dia net, feu net, flu net, ftw net, hxg net, ith net, les net, lev net, Icy net, Ivt net, mge net, nbo net, nia net, ocu net, peu net, pth net, pto net, pts net, pyr net, qtz net, reo net, rhr net, rht net, scu net, she net, shp net, soc net, sod net, spn net, sqc net, srs net, ssa net, ssb net, ssc net, stp net, tbo net, the net, thp net, toe net, ttt net, and twf net.

12. The method according to any one of claims 1-11, wherein the second MBB and third MBB are different.

13. The method according to any one of claims 1-12, wherein each of first MBB, second MBB, and third MBB is independently selected from an organic MBB or inorganic MBB.

14. The method according to any one of claims 1-13, wherein each of first MBB, second MBB, and third MBB is independently selected from a first polytopic ligand, second polytopic ligand, or metal component.

15. The method according to any one of claims 1-14, wherein at least one of first MBB, second MBB, and third MBB is an inorganic MBB comprising a cluster of metals or metal ions.

16. The method according to any one of claims 1-15, wherein the second MBB associates with at least one of the two sets of points of extension to afford the first 3p edge-transitive net.

17. The method according to any one of claims 1-16, wherein the third MBB associates with at least one of the two sets of points of extension to afford the second 3p edge-transitive net.4053.277PCT118. The method according to any one of claims 1-17, wherein the merged-net equation is represented by formula (1):wherein CR is a ratio constant for a merged-net, SBBI is the size of all building blocks for the first 3p edge-transitive net, and SBB2 is the size of all building blocks for the second 3p edge-transitive net.

19. The method according to any one of claims 1-18, wherein the merged-net equation is represented by formula (2) or (3):wherein Soi and S02 are the total sizes of all organic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively; CR is a ratio constant for a merged-net; and Sn and S12 are the total sizes of all inorganic building blocks for the first 3p edge-transitive net and second 3p edge-transitive net, respectively.

20. The method according to any one of claims 1-19, further comprising selecting additional pairs of first and third MBBs to form an isoreticular intricate mixed-linker structure.4053.277PCT1

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