Complex mixed linker structures

Abstract

A method for synthesizing complex mixed linker structures is provided. [Solution] Embodiments of the present disclosure describe materials comprising a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form a complex mixed linker structure having a merge net. Embodiments of the present disclosure further describe methods of synthesizing the complex mixed linker structure, including contacting a metal precursor, a first ligand precursor, and a second ligand precursor under reaction conditions sufficient to form the complex mixed linker structure having a merge net.

Description

background

[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 widespread interest in academia and industry alike due to their high porosity, unique functionalized architectures, and facile modular construction. The metrics and capabilities of MOFs' easily tunable pore systems position them as ideal porous material candidates to address persistent challenges related to energy and environmental sustainability, such as gas storage, gas separation, catalysis, and chemical sensing.

[0002] The creation of reticular chemistry has paved the way for the design, discovery, and development of novel functional crystalline solid-state materials, including MOFs. Primarily, the molecular building block (MBB) approach has emerged as a notable route toward the design and synthesis of novel functional MOFs. Desired geometric and connectivity features, functions, and properties can be intentionally included in preselected MBBs during the design phase, prior to the assembly process. Indeed, the prospects for effective design depend on the ability to access and deploy building blocks with geometric information and encoded connectivity to provide extension points that match the vertex shape of the target net. Indeed, edge-transitive nets (where all edges are equivalent by symmetry) are considered favorable design targets in reticular chemistry and crystal chemistry. The past two decades have seen a rapid growth in MOF chemistry, driven by the design and construction of countless MOF materials based on the reticulation of edge-transitive nets or their derived nets. Indeed, MOFs based on edge-transitive nets are a major class of materials in MOF chemistry, fueling exploration in a myriad of applications due to their relative ease of isoretiation and functionalization.

[0003] Logically, extending the rational design of MOFs to include multiple distinct linkers based on reticulation of multiedge nets is of paramount importance, as this offers the prospect of purposefully accessing complex materials with the diverse functionalities required for anticipated applications. Nevertheless, the majority of complex mixed-linker MOFs encompassing multiple ligands with distinct shapes and dimensions have been realized primarily through laborious trial-and-error approaches. Notably, implementing isoreticularization of complex MOF platforms based on multiedge nets remains a continuing challenge, as the connecting polytopic ligands must be mathematically correlated and their relative extensions must be interconnected and coordinated / synchronized; that is, selecting the appropriate combination of linkers with suitable dimensions to provide the required net extension and construct the desired isoreticular MOF is crucial. It should be noted that various relatively simple examples of mixed linker structures have been reported, such as by linking period 0 polyhedra, or by pillaring period 2 layers in an axis-to-axis fashion, or by inserting / placing a second linker into a particular MOF containing an "acceptor" site such as an open metal, or by exchanging terminal coordinating groups (e.g., hydroxide, acetate, or benzoate groups). Clearly, despite notable success in the design of MOFs based on edge-transition nets, the rational design of more complex mixed-linker MOFs in a deliberate one-pot synthesis using network chemistry has yet to be demonstrated or streamlined.

[0004] Methods for synthesizing complex mixed linker structures, complex mixed linker structures, and the like are described.

[0005] In one aspect, the present invention provides a method for producing a pharmaceutical composition comprising: (a) selecting a target merged-net in the synthesis of a complex mixed linker structure, and a first edge-transition net and a second edge-transition net that can be combined to provide the target merged-net, wherein the first and second edge-transition nets share a common signature net; (b) determining connectivity and a geometric configuration of each node of a merge net, the nodes of the merge net including merge nodes and non-merge nodes, the non-merge nodes including a first non-merge node and a second non-merge node; (c) selecting an MBB that has the same connectivity and geometric configuration as the merge node and has two sets of extension points, each set of extension points being capable of being connected to a separate MBB; (d) selecting a first MBB that has the same connectivity and geometric configuration as the first non-merge node; (e) inputting the length of the selected first MBB into a merge net equation to calculate an appropriate length of the complementary MBB; (f) selecting a second MBB having the same connectivity and geometric configuration as the second non-merge node and the same length as the complementary MBB; (g) reacting precursors of the MBB, the first MBB, and the second MBB to synthesize a complex mixed linker structure with a target merge network; The present invention relates to a method for synthesizing complex mixed linker structures, including:

[0006] In another aspect, the present invention relates to a composition comprising a complex mixed linker structure having a merge-net topology, wherein the metal-organic framework comprises a molecular building block (MBB) having a first extension point and a second extension point, the first extension point coordinates to the first MBB and the second extension point coordinates to the second MBB, and the first MBB and second MBB are different.

[0007] In a further aspect, the present invention relates to a method for synthesizing a complex mixed linker structure, comprising contacting a metal precursor, a first ligand precursor, and a second ligand precursor under reaction conditions sufficient to form a complex mixed linker structure having a merge net.

[0008] In an additional aspect, the present invention provides a method for synthesizing a complex mixed linker structure by reacting precursors of the first and second polytopic ligands with polynuclear cluster precursors, the method comprising: extracting a signature net from a plurality of edge-transitive parent nets having transitivity

[11] and / or transitivity

[21] by one or more of the following: edge transformation, binary transformation, and direct transformation; selecting a first edge-transitive net and a second edge-transitive net having a common signature net from the plurality of edge-transitive nets; selecting a first polytopic ligand suitable for the first edge-transitive net and a second polytopic ligand suitable for the second edge-transitive net; and synthesizing a complex mixed linker structure by reacting precursors of the first polytopic ligand and the second polytopic ligand with polynuclear cluster precursors. The present invention relates to a method comprising one or more of the following:

[0009] In another aspect, the present disclosure provides a method for generating a signature net from a plurality of parent nets by one or more of edge transformation, binary transformation, and direct transformation; merging parent nets having a common signature net to obtain a plurality of merged nets; determining a coordination number of nodes present in each of the plurality of merged nets; The present invention relates to a method for designing complex mixed linker structures, including:

[0010] The details of one or more examples are set forth in the description below. Other features, objects, and advantages will become apparent from the description and the claims. [Brief explanation of the drawings]

[0011] This written disclosure describes non-limiting and non-exhaustive example embodiments. In the drawings, which are not necessarily drawn to scale, like reference numerals substantially represent like components throughout the several views. Like reference numerals with different letter suffixes represent different instances of substantially similar components. The drawings illustrate generally, by way of example, and not limitation, various embodiments discussed in this document.

[0012] Referring to the exemplary embodiment shown in the figures, in which:

[0013] [Figure 1] FIG. 1 is a map showing the signature nets of all edge-transitive nets, according to one or more embodiments of the present disclosure; the three methods used to extract signature nets from parent nets are indicated by green, purple, and red arrows, respectively, and the two-period and one-period signature nets are indicated by orange blocks.

[0014] [Figure 2] 1 is a flowchart of a method for synthesizing complex mixed linker structures according to one or more embodiments of the present disclosure.

[0015] [Figure 3] 1 is a flowchart of a method for synthesizing complex mixed linker structures according to one or more embodiments of the present disclosure.

[0016] [Figure 4A] FIG. 1 is a graphical representation of the H NMR spectrum of (A) compound 4 and (B) H3BTBPB, and (C) the C NMR spectrum of H3BTBPB, according to one or more embodiments of the present disclosure. [Figure 4B] FIG. 1 is a graphical representation of the H NMR spectrum of (A) compound 4 and (B) H3BTBPB, and (C) the C NMR spectrum of H3BTBPB, according to one or more embodiments of the present disclosure. [Figure 4C] FIG. 1 is a graphical representation of the H NMR spectrum of (A) compound 4 and (B) H3BTBPB, and (C) the C NMR spectrum of H3BTBPB, according to one or more embodiments of the present disclosure.

[0017] [Figure 5](FIGS. 5A and 5B) Calculated PXRD pattern of as-synthesized Tb-spn-MOF-1 (left); and TGA plot of as-synthesized Tb-spn-MOF-1 (right), according to one or more embodiments of the present disclosure. As-synthesized Tb-spn-MOF-1 exhibited a weight loss (approximately 13%) between room temperature and 250°C, which is attributed to the removal of water, DMF, and other unreacted species in the pores, and a second weight loss (approximately 45%) between 300°C and 550°C, which is primarily attributed to the removal of organic ligands.

[0018] [Figure 6] (Figures 6A, 6B, 6C, 6D, 6E, 6F) Schematic diagrams illustrating the organization of sph-MOFs, by way of example, sph-a nets and sph-MOF-3, according to one or more embodiments of the present disclosure: (a) the 12-c cuboctahedral building unit can be divided into two groups, i.e., 6-c antitriangular prisms and 6-c hexagonal building units; (b) the corresponding RE hexanuclear cluster shown in atomic mode (left) and polyhedral mode (center and right); (c) the linking of the divided building units with triangular and hexagonal building units to form spn-a and hxg-a nets; (d) the corresponding spn and hxg subscaffolds assembled from BTTC and BHPB linkers; and (e) the spn-a and hxg-a nets merge to form the sph-a net. (f) The corresponding spn and hxg subskeleton merge to form the sph-MOF. RE, C, O, and S are represented in purple, gray, red, and dark yellow, respectively, with H atoms omitted for clarity; cages are shown as yellow and green balls.

[0019] [Figure 7] FIG. 1 is a schematic diagram showing the assembly of sph-MOF-2 and sph-MOF-3 by adjusting the "hxg" linker, according to one or more embodiments of the present disclosure.

[0020] [Figure 8]FIG. 10 is a topological analysis of Tb-spn-MOF-1, revealing the underlying (3,6)-connected spn network, according to one or more embodiments of the present disclosure.

[0021] [Figure 9] FIG. 10 is a topological analysis of the Tb-sph-MOF, revealing the underlying (3,6,12)-connected sph net, according to one or more embodiments of the present disclosure.

[0022] [Figure 10] (Figures 10A, 10B, 10C, 10D) Schematic diagrams of the design of sph-MOFs by utilizing the merge-net equation, according to one or more embodiments of the present disclosure: (a) if the edge ratio between an spn net and an hxg net exactly satisfies a constant, the two nets can be merged into an sph net; (b) the half size of a Tb hexanuclear cluster is 4.7 Å; (c) the merge-net equation shows the relationship between the spn linker and the hxg linker; (d) the sizes of both linkers in the sph-MOF can be designed from the merge-net equation.

[0023] [Figure 11] FIG. 10 is a schematic diagram illustrating the calculation of the ratio constant of the sph net according to the sine rule, in accordance with one or more embodiments of the present disclosure.

[0024] [Figure 12] (FIGS. 12A, 12B, 12C) Schematic diagrams of ligands used in the synthesis of sph-MOFs according to one or more embodiments of the present disclosure: (a) spn subscaffold ligands, where size indicates the distance from the center of the linker to the carboxylic acid carbon or triazole center; (b) hxg subscaffold ligands; (c) structures of sph-MOF-1 to 4.

[0025] [Figure 13] FIG. 1 is a schematic diagram showing the organization of sph-MOF-1 with a hexanuclear cluster, TIA, and a BTCB linker, according to one or more embodiments of the present disclosure.

[0026] [Figure 14] (FIG. 14A, FIG. 14B) Calculated PXRD patterns (left) of as-synthesized and solvent-exchanged Tb-sph-MOF-1 according to one or more embodiments of the present disclosure; TGA plots (right) of as-synthesized and solvent-exchanged Tb-sph-MOF-1, where the as-synthesized Tb-sph-MOF-1 exhibits a weight loss (approximately 28%) between room temperature and 250°C, which is attributed to the removal of water, DMF, and other unreacted species in the pores, and a second weight loss (approximately 19%) between 300°C and 500°C, which is primarily attributed to the removal of organic ligands; the DCM-exchanged sample exhibits two weight losses: the first loss between room temperature and 150°C, which is attributed to the removal of DCM (approximately 6%), and the second loss (approximately 51%) between 300°C and 450°C, which is primarily attributed to the removal of organic ligands.

[0027] [Figure 15] 1 shows the H NMR spectrum of sph-MOF-1 after digesting the sample in HCl, DMSO-d solution, according to one or more embodiments of the present disclosure.

[0028] [Figure 16] FIG. 1 is a schematic diagram showing cages and corresponding sizes in sph-MOFs, according to one or more embodiments of the present disclosure.

[0029] [Figure 17] 1 is an Ar adsorption isotherm for sph-MOFs at 87 K according to one or more embodiments of the present disclosure.

[0030] [Figure 18] (FIG. 18A, FIG. 18B) N adsorption data for compound Tb-sph-MOF-1, according to one or more embodiments of the present disclosure. Fully reversible N isotherm collected at 77 K (left) and a plot of the linear region of the N isotherm from the BET equation (right).

[0031] [Figure 19] (FIG. 19A, FIG. 19B) Shows Ar adsorption data for compound Tb-sph-MOF-1, according to one or more embodiments of the present disclosure. Fully reversible Ar isotherm collected at 87 K (left), and a plot of the linear region of the Ar isotherm from the BET equation (right).

[0032] [Figure 20] 1 shows the DFT pore size distribution of Tb-sph-MOF-1 determined from Ar adsorption at 87 K, according to one or more embodiments of the present disclosure.

[0033] [Figure 21] 1 shows the H NMR spectrum of sph-MOF-2 after digesting the sample in HCl, DMSO-d solution, according to one or more embodiments of the present disclosure.

[0034] [Figure 22] (FIG. 22A, FIG. 22B) Calculated PXRD patterns (left) of as-synthesized and solvent-exchanged Tb-sph-MOF-2 according to one or more embodiments of the present disclosure; TGA plots (right) of as-synthesized and solvent-exchanged Tb-sph-MOF-2, where the as-synthesized Tb-sph-MOF-2 exhibits a weight loss (approximately 32%) between room temperature and 250°C, which is attributed to the removal of water, DMF, and other unreacted species in the pores, and a second weight loss (approximately 21%) between 400°C and 550°C, which is primarily attributed to the removal of organic ligands; the acetone-exchanged sample exhibits two weight losses: the first loss between room temperature and 250°C, which is attributed to the removal of acetone (approximately 12%), and the second loss (approximately 26%) between 350°C and 550°C, which is primarily attributed to the removal of organic ligands.

[0035] [Figure 23](Figures 23A, 23B, 23C, 23D) Schematic diagrams showing a comparison between sph-MOF-2 and sph-MOF-3, according to one or more embodiments of the present disclosure. The differences in the chemical environment between the BTPB and BHPB linkers in sph-MOF-2 and sph-MOF-3 are shown in (a) top view and (b) horizontal view; correspondingly, the cage shapes and sizes, (c) small tetrahedral cages, and (d) large truncated tetrahedral cages, are also shown, which are slightly adjusted.

[0036] [Figure 24] (FIG. 24A, FIG. 24B) N adsorption data for compound Tb-sph-MOF-2, according to one or more embodiments of the present disclosure. Fully reversible N isotherm collected at 77 K (left) and a plot of the linear region of the N isotherm from the BET equation (right).

[0037] [Figure 25] (FIG. 25A, FIG. 25B) Ar adsorption data for compound Tb-sph-MOF-2, according to one or more embodiments of the present disclosure. Fully reversible Ar isotherm collected at 87 K (left) and a plot of the linear region of the Ar isotherm from the BET equation (right).

[0038] [Figure 26] 1 shows the DFT pore size distribution of Tb-sph-MOF-2 determined from Ar adsorption at 87 K, according to one or more embodiments of the present disclosure.

[0039] [Figure 27] 1 shows the H NMR spectrum of sph-MOF-3 after digesting the sample in HCl, DMSO-d solution, according to one or more embodiments of the present disclosure.

[0040] [Figure 28](FIG. 28A, FIG. 28B) Calculated PXRD patterns (left) of as-synthesized and solvent-exchanged Tb-sph-MOF-3 according to one or more embodiments of the present disclosure; TGA plots (right) of as-synthesized and solvent-exchanged Tb-sph-MOF-3, where the as-synthesized Tb-sph-MOF-3 exhibits a weight loss (approximately 31%) between room temperature and 200°C, which is attributed to the removal of water, DMF, and other unreacted species in the pores, and a second weight loss (approximately 41%) between 350°C and 550°C, which is primarily attributed to the removal of organic ligands; the acetone-exchanged sample exhibits two weight losses: the first loss (approximately 12%) between room temperature and 250°C, which is attributed to the removal of acetone, and the second loss (approximately 27%) between 300°C and 600°C, which is primarily attributed to the removal of organic ligands.

[0041] [Figure 29] (FIG. 29A, FIG. 29B) N adsorption data for compound Tb-sph-MOF-3, according to one or more embodiments of the present disclosure. Fully reversible N isotherm collected at 77 K (left) and a plot of the linear region of the N isotherm from the BET equation (right).

[0042] [Figure 30] (FIG. 30A, FIG. 30B) Shows Ar adsorption data for compound Tb-sph-MOF-3, according to one or more embodiments of the present disclosure. Fully reversible Ar isotherm collected at 87 K (left), and a plot of the linear region of the Ar isotherm from the BET equation (right).

[0043] [Figure 31] FIG. 1 shows the DFT pore size distribution of Tb-sph-MOF-3 determined from Ar adsorption at 87 K, according to one or more embodiments of the present disclosure.

[0044]

[0045] [Figure 32] 1 shows the H NMR spectrum of sph-MOF-4 after digesting the sample in HCl, DMSO-d solution, according to one or more embodiments of the present disclosure.

[0046] [Figure 33] (Figures 33A, 33B) Calculated PXRD patterns (left) of as-synthesized and solvent-exchanged Tb-sph-MOF-4 according to one or more embodiments of the present disclosure; TGA plots (right) of as-synthesized and solvent-exchanged Tb-sph-MOF-4, where the as-synthesized Tb-sph-MOF-4 exhibits a weight loss (approximately 40%) between room temperature and 200°C, which is attributed to the removal of water, DMF, and other unreacted species in the pores, and a second weight loss (approximately 40%) between 350°C and 450°C, which is primarily attributed to the removal of organic ligands; the acetone-exchanged sample exhibits two weight losses: the first loss (approximately 14%) between room temperature and 250°C, which is attributed to the removal of acetone, and the second loss (approximately 22%) between 350°C and 550°C, which is primarily attributed to the removal of organic ligands.

[0047] [Figure 34] FIG. 1 is a schematic diagram showing the assembly of sph-MOF-4 with a hexanuclear cluster, TATB, and BTBPB linkers, according to one or more embodiments of the present disclosure.

[0048] [Figure 35] (FIG. 35A, FIG. 35B) N adsorption data for compound Tb-sph-MOF-4, according to one or more embodiments of the present disclosure. Fully reversible N isotherm collected at 77 K (left) and a plot of the linear region of the N isotherm from the BET equation (right).

[0049] [Figure 36] (FIG. 36A, FIG. 36B) Ar adsorption data for compound Tb-sph-MOF-4, according to one or more embodiments of the present disclosure. Fully reversible Ar isotherm collected at 87 K (left) and a plot of the linear region of the Ar isotherm from the BET equation (right).

[0050] [Figure 37]FIG. 1 shows the DFT pore size distribution of Tb-sph-MOF-4 determined from Ar adsorption at 87 K, in accordance with one or more embodiments of the present disclosure.

[0051] [Figure 38] 1 shows the CO 2 sorption isotherm of Tb-sph-MOF-1 according to one or more embodiments of the present disclosure.

[0052] [Figure 39] FIG. 39 shows the Qst of CO2 adsorption of Tb-sph-MOF-1 calculated from the corresponding isotherm in FIG. 38, according to one or more embodiments of the present disclosure.

[0053] [Figure 40] 1 shows light hydrocarbon adsorption data for Tb-sph-MOF-1, according to one or more embodiments of the present disclosure.

[0054] [Figure 41] 1 shows high-pressure gas adsorption measurements of Tb-sph-MOF-1, according to one or more embodiments of the present disclosure.

[0055] [Figure 42] 1 shows high-pressure gas adsorption measurements of C3H8, CH4, and N2 on Tb-sph-MOF-1 up to 25 bar, according to one or more embodiments of the present disclosure.

[0056] [Figure 43] FIG. 1 is a schematic diagram illustrating three methods for extracting signature nets from parent nets according to one or more embodiments of the present disclosure: the three methods show the corresponding reo nodes in the pcu, nbo, and ftw nets; the symbols used to describe each type of net and method; and a map showing the vertex relationships of the edge-transitive nets. Detailed Description

[0057] The present disclosure relates to a new class of materials with complex structural complexity. In particular, the present disclosure relates to materials described and referred to herein as complex mixed linker structures. The complex mixed linker structures of the present disclosure have a novel underlying topology based on two separate edge-transition nets that merge through a shared node to provide a new minimal edge-transition net with two different types of linkers. The present disclosure refers to these new minimal edge-transition nets as merge-nets or merge-net topologies.

[0058] Surprisingly, applicants have discovered approximately 140 new merge nets using a novel merge net approach that allows for the deliberate design and construction of complex mixed linker structures using network chemistry. No previously available approach has been available for designing and constructing the complex mixed linker structures described herein. In general, complex mixed linker structures can be designed and / or constructed from any two parent nets that share a signature net. Parent nets are generally edge-transitive nets with transitivity

[11] or transitivity

[21] , while signature nets are nets that result from transformations of the parent nets. Examples of transformations include edge transformations, binary transformations, and direct transformations. Using this approach, Figure 1 was constructed to map the relationship between parent nets and their signature nets. This disclosure explains how the diagram shown in Figure 1 can be used to design and synthesize an unprecedented number of new materials.

[0059] definition The terms listed below are defined as set forth below. All other terms and phrases in this disclosure are to be interpreted according to their ordinary meanings as understood by those of ordinary skill in the art.

[0060] As used herein, "complex mixed linker structure" refers to any chemical composition that has a merge net as the underlying topology and two different types of linkers.

[0061] As used herein, the term "merge net" refers to the underlying topology of complex mixed linker structures.

[0062] As used herein, the term "node" refers to any component of a complex mixed linker structure having three or more attachment points (e.g., three or more coordination and / or functional sites). An attachment point can, but need not, be connected to an attachment point of another node. A node can include a metal component, a polytopic ligand, or both a metal component and a polytopic ligand. Additionally or alternatively, a node can include, among other things, a molecular building block (MBB) (which can include inorganic MBBs, organic MBBs, and / or inorganic-organic hybrid MBBs), a structural building unit, a supramolecular building layer.

[0063] As used herein, the term "edge" refers to a linker or a ligand. In some cases, linker and ligand are used interchangeably throughout this disclosure. In other instances, linker and ligand are used to refer to coordinating and non-coordinating ligands, respectively.

[0064] As used herein, the term "metal component" generally refers to a metal-containing component. Examples of metal components include, but are not limited to, metal ions or metal clusters, and a metal component can include one or more metal ions as well as precursor moieties.

[0065] As used herein, the term "polytopic ligand" generally refers to any chemical species that can coordinate to two or more nodes (e.g., metals). Polytopic ligands can include neutral or charged species, such as ions. The type of bond formed is not particularly limited and can include bonds ranging from covalent to ionic bonds. Polytopic ligands generally refer to bridging or linking ligands, but can also refer to capping ligands, as these terms are understood in the art.

[0066] As used herein, the term "minimal edge-transitive net" refers to a net that has only one or two types of edges or linkers, while the term "edge-transitive net" refers to a net that has only one type of edge or linker.

[0067] As used herein, the term "parent net" refers to a net that undergoes a transformation. In some cases, the term "parent net" is used in reference to a "signature net," which is the net that results from the transformation. Examples of transformations include edge transformations, binary transformations, and direct transformations.

[0068] As used herein, the terms "coordination number," and "nc," as in n-coordination and / or n-linkage, refer to the number of coordination sites of a component. The value of n is typically at least 1.

[0069] Merge Net Approach This disclosure describes, for the first time, a novel approach called the merge-net approach, which allows for the intentional design and construction of more complex materials. Such materials are referred to herein as complex mixed linker structures. The disclosed complex mixed linker structures are based on two separate edge-transition nets that merge through a shared node to provide a new minimal edge-transition net with two different types of linkers. Using the merge-net approach, complex mixed linker structures can be created with a variety of functions and properties suitable for a wide range of applications, from gas storage and gas separation to catalysis, chemical sensing, and more.

[0070] The merge-net approach is based on previously inaccessible relationships / correlations between edge-transition nets. The coded information embedded in building units can be extracted using the merge-net approach, thereby obtaining the connectivity and geometric information necessary for the design and construction of complex mixed linker structures. Once the coded information is extracted, it can be used to identify pairs of distinct edge-transition nets that can be merged through shared nodes, providing a new minimal edge-transition net with two different types of linkers. A series of isomesh-like complex mixed linker structures can be constructed using merge-net equations that embody the unique geometric features of the resulting merge-net. Generally, the merge-net equations are based on the correlations between the dimensions / lengths of the relevant edges of the two distinct edge-transition nets from which the merge-net was formed. A unique merge-net equation can be derived for each merge-net and used to determine the size of the complementary linkers appropriate for the target complex mixed linker structure.

[0071] According to the merge-net approach, any two parent nets that share a common signature net can be merged through a shared node (e.g., in one-pot synthesis) to form complex mixed linker structures. Parent nets are generally edge-transitive nets selected from nets with transitivity

[11] and / or transitivity

[21] . An edge-transitive net with transitivity

[11] represents a net with one type of node and one type of edge. An edge-transitive net with transitivity

[21] represents a net with two types of nodes and one type of edge. A parent net can be transformed to obtain the signature net of the parent net. Thus, a signature net is a net resulting from the transformation of the parent net. Examples of such transformations include, but are not limited to, edge transformation, binary transformation, and direct transformation. Figure 1 was constructed to map the relationship between parent nets and their signature nets.

[0072] Using the relationship map shown in Figure 1, edge-transition nets with a common signature net were merged. The coding information necessary for the design and construction of complex mixed linker structures was extracted from the resulting merged net, which is summarized in Table 2. In particular, Table 2 presents a non-exhaustive list of approximately 140 novel merged net topologies previously unavailable or unknown. Each merged net shown in Table 2 is associated with a first parent net (PN1) and a second parent net (PN2), as well as a signature net (SN) shared by the first and second parent nets. Additionally, because each merged net contains nodes with various connectivity, the coordination numbers or connectivity of the non-merge and merged nodes were extracted and summarized in Table 2.

[0073] 2 is a flowchart of a method for synthesizing complex mixed linker structures using a merge-net approach, according to one or more embodiments of the present disclosure. As shown in FIG. 2, the method includes steps (a) to (g), namely: (a) selecting 201 a target merge net in the synthesis of a complex mixed linker structure, and a first edge transition net and a second edge transition net that can be combined to provide the target merge net, wherein the first and second edge transition nets share a common signature net; (b) determining 202 connectivity and geometric configuration of each node of a merge net, the nodes of the merge net including merge nodes and non-merge nodes, the non-merge nodes including a first non-merge node and a second non-merge node; (c) selecting 203 an MBB having the same connectivity and geometric configuration as the merge node and having two sets of extension points, each set of extension points being capable of being connected to a separate MBB; (d) selecting 204 a first MBB that has the same connectivity and geometric configuration as the first non-merge node; (e) Step 205 of inputting the length of the selected first MBB into a merge net equation to calculate the appropriate length of the complementary MBB; (f) selecting 206 a second MBB having the same connectivity and geometric configuration as the second non-merge node and the same length as the complementary MBB; and (g) Step 207: reacting precursors of the MBB, the first MBB, and the second MBB to synthesize a complex mixed linker structure with the target merge network; It includes one or more of the following.

[0074] In a particular embodiment, the merge net is a minimum edge transitive net with transitivity

[22] or transitivity

[32] . In a particular embodiment, the merge net is aca-net, acb-net, ach-net, anl-net, ast-d-net, bob-net, bof-net, bsc-net, bsl-net, bsp-net, buo-net, bup-net, bus-net, crd-net, crh-net, crn-net, csa-net, cst-net, ctl-net, dif-net, epr-net, flf-net, flh-net, flp-net, flr-net, fls-net, fwb-net, fwc-net, fwf-net, fwo-net, fwp-net. tt, fwt net, gal net, gas net, hxd net, hxn net, hxp net, hxs net, ias net, ifc net, ifl net, ifr net, ifs net, itb net, itp net, its net, lvs net, lys net, mga net, mgh net, mgi net, mgr net, mgs net, nbf net, nbo-xd net, nic net, nku net, nso net, occ net, ocf net, och net, ocp net, ocs net, pco net, pcp net, pct net, phq net, pht net, psb net, pyi net, pyp net, pyu net, pyy net, qtq net, reb net, ren net, reo-d net, rep net, ret net, rhb net, rhc net, rhd net, rhf net, rht-x net, scc net, scp net, sdr net, ses net, sha net, shc net, shn net, sho net, shs net, sht net, spc net, spd net, sph net, s qd net, sqv net, ssl net, ssr net, sts net, sub net, suc net, sup net, tam net, tbc net, tbf net, tbn net, tdi net, tec net, tef net, ter net, thc net, tht net, toh net, ton net, top net, ttb net, tte net, tth net, tti net, ttl net, ttr net, tts net, twb net, twh net, twn net, two net, tws net, urk net,The net is selected from the group consisting of urr net, wzz net, xam net, xau net, xaz net, xbk net, xbn net, xbo net, xbp net, and combinations thereof.

[0075] In a particular embodiment, each of the first edge transition net and the second edge transition net is independently selected from edge transition nets having transitivity

[11] or transitivity

[21] . In a particular embodiment, the edge transition nets having transitivity

[11] are selected from hxg-net, lcw-net, hxl-net, kgm-net, hcb-net, dia-net, crs-net, nbo-net, sod-net, rhr-net, acs-net, sql-net, lvt-net, bcu-net, pcu-net, fcu-net, reo-net, qtz-net, srs-net, lcv-net, lcy-net, bcs-net, lcs-net, ana-net, thp-net, or combinations thereof. In a particular embodiment, the edge-transitive net having transitivity

[21] is selected from shp-net, alb-net, stp-net, mgc-net, spn-net, toc-net, nia-net, ssa-net, csq-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, ctn-net, or a combination thereof.

[0076] In certain embodiments, the common signature net is selected from a kgm net, an ana net, an fcu net, a reo net, a bcs net, a pcu net, a crs net, a nbo net, a thp net, an lcw net, an lcs net, a sod net, an hxg net, an lcv net, a srs net, a bcu net, an lcy net, a dia net, an acs net, a qtz net, an fcu net, an op net, a rhr net, an hxl net, an lvt net, or a thp net.

[0077] In certain embodiments, the first MBB and the second MBB are different. In certain embodiments, each of the MBB, the first MBB, and the second MBB is independently selected from an organic MBB or an inorganic MBB. In certain embodiments, each of the MBB, the first MBB, and the second MBB is independently selected from a first polytopic ligand, a second polytopic ligand, or a metal component. In certain embodiments, at least one of the MBB, the first MBB, and the second MBB is an inorganic MBB comprising a metal cluster or a metal ion.

[0078] In a particular embodiment, a first MBB associates with at least one of the two sets of extension points to provide a first edge-transition net, and in a particular embodiment, a second MBB associates with at least one of the two sets of extension points to provide a second edge-transition net.

[0079] In one particular embodiment, the margin net equation is Equation (1):

number

number

number

[0080] In certain embodiments, the method further comprises selecting additional pairs of first and second MBBs to form isoreticular complex mixed linker structures.

[0081] Embodiments of the present disclosure further describe compositions comprising a complex mixed linker structure having a merge-net topology, wherein the metal-organic framework comprises a molecular building block (MBB) having a first extension point and a second extension point, the first extension point coordinates to the first MBB and the second extension point coordinates to the second MBB, and the first MBB and second MBB are different.

[0082] In certain embodiments, the first MBB is a first polytopic ligand and the second MBB is a second polytopic ligand.

[0083] In one particular embodiment, the coordination of the first MBB with the first expansion point provides a first edge-transition net.

[0084] In one particular embodiment, the coordination of the second MBB with the second extension point provides a second edge-transition net.

[0085] While various features have been described, other aspects of the above features are described elsewhere throughout this disclosure. Accordingly, embodiments should be understood to include other such features, even if not explicitly described above, without departing from the scope of the present invention. Accordingly, such disclosures and descriptions are incorporated herein by reference in their entirety.

[0086] Having described one example of how to synthesize a complex mixed linker structure, various aspects of the complex mixed linker structure will now be described.

[0087] Complex mixed linker structures Embodiments of the present disclosure describe materials comprising a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form a complex mixed linker structure having a merge-net topology. The first polytopic ligand is typically different from the second polytopic ligand, or vice versa. A merge-net topology generally comprises a net comprising a first edge-transition net and a second edge-transition net, which are merged via a shared node to provide a merge-net. In addition to forming a new minimal edge-transition net—e.g., a merge-net—subskeletons of the parent nets—the first edge-transition net and the second edge-transition net—may, in some embodiments, be maintained in the merge-net.

[0088] The complex mixed linker structure can comprise any of a variety of materials. For example, in some embodiments, the complex mixed linker structure is one or more of metal-organic frameworks (MOFs), 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), hypercrosslinked polymers (HCPs), coordination polymers (CPs), porous coordination polymers (PCPs), porous coordination networks (PCNs), and metal-organic materials (MOMs), among others.

[0089] Merge Net Topology As described above, the underlying topology of complex mixed linker structures is a merge-net topology, or merge-net. Generally, a merge-net is a three-period minimal edge-transitive net with two types of edges or linkers. In some embodiments, a merge-net has two types of edges or linkers and either two or three types of vertices or nodes. For example, in some embodiments, a merge-net is a net with transitivity

[22] , which represents a net with two types of nodes and two types of edges. In some embodiments, a merge-net is a net with transitivity

[32] , which represents a net with three types of nodes and two types of edges.

[0090] Examples of merge nets are aca net, acb net, ach net, anl net, ast-d net, bob net, bof net, bsc net, bsl net, bsp net, buo net, bup net, bus net, crd net, crh net, crn net, csa net, cst net, ctl net, dif net, epr net, flf net, flh net, flp net, flr net, fls net, fwb net, fwc net, fwf net, fwo net, fwp net, fwt net, gal net, ga s net, hxd net, hxn net, hxp net, hxs net, ias net, ifc net, ifl net, ifr net, ifs net, itb net, itp net, its net, lvs net, lys net, mga net, mgh net, mgi net, mgr net, mgs net, nbf net, nbo-xd net, nic net, nku net, nso net, occ net, ocf net, och net, ocp net, ocs net, pco net, pcp net, pct net, phq net, pht net, psb net, pyi net, pyp net, pyu net, pyy net, qtq net, reb net, ren net, reo-d net, rep net, ret net, rhb net, rhc net, rhd net, rhf net, rht-x net, scc net, scp net, sdr net, ses net, sha net, shc net, shn net, sho net, shs net, sht net, spc net, spd net, sph net, sqd net, sqv net, ssl net, ssr net, sts net, sub net, suc Net, sup net, tam net, tbc net, tbf net, tbn net, tdi net, tec net, tef net, ter net, thc net, tht net, toh net, ton net, top net, ttb net, tte net, tth net, tti net, ttl net, ttr net, tts net, twb net, twh net, twn net, two net, tws net, urk net, urr net, wzz net, xam net, xau net, xaz net, xbk net, xbn net, xbo net,and xbp nets.

[0091] In some embodiments, each edge or linker of a merge net corresponds to or can be assigned to a three-cycle edge transition net (e.g., a first edge transition net and a second edge transition net). For example, in some embodiments, a merge net includes two edge transition nets, such as a first edge transition net and a second edge transition net. In some embodiments, a merge net includes a first edge transition net and a second edge transition net that share a node. In embodiments where the first edge transition net and the second edge transition net share a node (e.g., inorganic, organic, and / or organic-inorganic MBB), the first edge transition net and the second edge transition net are said to be merged. For example, in some embodiments, a merge net includes a first edge transition net and a second edge transition net that are merged via a shared node.

[0092] In some embodiments, the merge net is a novel minimal edge-transition net with two different types of linkers. In some embodiments, the merge net encompasses and / or preserves each of the merged edge-transition nets. For example, in some embodiments, the merge net encompasses and / or preserves structural properties of the first edge-transition net, the second edge-transition net, or both the first and second edge-transition nets.

[0093] In some embodiments, each of the first edge-transition net and the second edge-transition net is a net having only one type of edge or linker. For example, in some embodiments, the first edge-transition net and / or the second edge-transition net has one type of edge or linker and either one or two types of vertices or nodes. In some embodiments, the first edge-transition net and / or the second edge-transition net is a net with transitivity

[11] , which represents a net having one type of node and one type of edge. In some embodiments, the first edge-transition net and / or the second edge-transition net is a net with transitivity

[21] , which represents a net having two types of nodes and one type of edge. Thus, in some embodiments, the first and second edge-transition nets are nets with transitivity

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

[11] , and the second edge-transition net is a net with transitivity

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

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

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

[21] .

[0094] Examples of nets with transitivity

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

[11] , a second edge-transitive net with transitivity

[11] , or both) are selected from: hxg-net, lcw-net, hxl-net, kgm-net, hcb-net, dia-net, crs-net, nbo-net, sod-net, rhr-net, acs-net, sql-net, lvt-net, bcu-net, pcu-net, fcu-net, reo-net, qtz-net, srs-net, lcv-net, lcy-net, bcs-net, lcs-net, ana-net, and thp-net.

[0095] Examples of nets with transitivity

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

[21] , a second edge-transitive net with transitivity

[21] , or both) are selected from: shp-net, alb-net, stp-net, mgc-net, spn-net, toc-net, nia-net, ssa-net, csq-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.

[0096] In some embodiments, a merge net includes a first edge transition net and a second edge transition net, where the first and second edge transition nets share a common signature net. As used herein, the term "signature net" generally refers to any net that results from a transformation of an edge transition net. In such embodiments, the first and second edge transition nets may be described or referred to as "parent nets." As used herein, the term "parent net" generally refers to the edge transition net that undergoes the transformation. In some embodiments, edge transition nets that have a common signature net can be combined or merged to provide a complex mixed linker structure with a merge net. Thus, in some embodiments, identifying a common signature net between parent nets is an approach that can be used to design the complex mixed linker structures of the present disclosure.

[0097] Examples of signature nets include nets selected from kgm net, ana net, fcu net, reo net, bcs net, pcu net, crs net, nbo net, thp net, lcw net, lcs net, sod net, hxg net, lcv net, srs net, bcu net, lcy net, dia net, acs net, qtz net, fcu net, op net, rhr net, hxl net, lvt net, and thp net.

[0098] In some embodiments, to identify a signature net, the parent net, i.e., the edge-transitive net, is transformed into a net with transitivity

[21] . For example, in some embodiments, an edge-transitive net with transitivity

[11] (e.g., a parent net with transitivity

[11] ) is transformed into a net with transitivity

[21] by edge transformation, which involves adding a node (e.g., a 2-c node) at the midpoint of the edge of the parent net. In some embodiments, an edge-transitive net with transitivity

[11] (e.g., a parent net with transitivity

[21] ) is transformed into a net with transitivity

[21] by binary transformation, which includes separating the nodes of the parent net into two groups of nodes. In some embodiments, an edge-transitive net with transitivity

[21] (e.g., a parent net with transitivity

[21] ) is transformed into a net with transitivity

[21] by direct transformation, which includes connecting nodes of the same type.

[0099] In some embodiments, the merge net includes an edge transformation net and a signature net of the edge transformation net (e.g., an “es” merge net). In some embodiments, the configuration of the “es” merge net is (2,v e ,v s +2)-c, where v e is the configuration of the edge transformation parent net, and v s is the configuration of the signature net of the edge transformation net.

[0100] In some embodiments, the merge net includes a binary translation net and a signature net of the binary translation net (e.g., a "bs" merge net). In some embodiments, the configuration of the "bs" merge net is (2,v b ,v b +v s )-c, where v b is the configuration of the binary transformation parent net, and v s is the configuration of the signature net of the binary transformation net.

[0101] In some embodiments, the merge net includes a direct transformation net and a signature net of the direct transformation net (e.g., a "ds" merge net). In some embodiments, the configuration of the "ds" merge net is (2,v d ,v dm +v s )-c, where v d is the configuration of the direct transformation parent net (exclusive), where v dm is the configuration of the direct transformation parent net (shared), and v s is the configuration of the signature net of the direct transformation net.

[0102] In some embodiments, the merge net includes a first edge transformation net and a second edge transformation net (e.g., an "ee" merge net). In some embodiments, the configuration of the "ee" merge net is (v e1 ,v e2 ,4)-c, where v e1 is the configuration of the first edge transformation net, and v e2 is the configuration of the second edge transformation net.

[0103] In some embodiments, the merge net includes a first binary translation net and a second binary translation net (e.g., a "bb" merge net). In some embodiments, the configuration of the "bb" merge net is (v b1 ,v b2 ,v b1 +v b2 )-c, where v b1 is the configuration of the first binary transformation net, and v b2 is the configuration of the second binary transformation net.

[0104] In some embodiments, the merge net includes a first direct conversion net and a second direct conversion net (e.g., a "dd" merge net). In some embodiments, the configuration of the "dd" merge net is (v d1 ,v d2 ,v dm1 +v dm2 )-c, where vd1 is the configuration of the first direct transformation net (exclusive), and v d2 is the configuration of the second direct transformation net (exclusive), and v dm1 is the configuration of the first direct transformation net (shared), and v dm2 is the configuration of the second direct transformation net (shared).

[0105] In some embodiments, merge nets include edge transformation nets and binary transformation nets (e.g., "eb" merge nets). In some embodiments, the configuration of an "eb" merge net is (v e ,v b ,v b +2)-c, where v e is the configuration of the edge transformation net, and v b is the configuration of the binary transformation net.

[0106] In some embodiments, a merge net includes an edge transformation net and a direct transformation net (e.g., an "ed" merge net). In some embodiments, the configuration of an "ed" merge net is (v e ,v d ,v dm +2)-c, where v e is the configuration of the edge transformation net, and v d is the configuration of the direct transformation net (exclusive), and v dm is the configuration of the direct transformation net (shared).

[0107] In some embodiments, merge nets include binary transformation nets and direct transformation nets (e.g., "bd" merge nets). In some embodiments, the configuration of a "bd" merge net is (v b ,v d ,v b +v dm )-c, where v b is the configuration of the binary transformation net, and v d is the configuration of the direct transformation net (exclusive), and v dm is the configuration of the direct transformation net (shared).

[0108] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an aca merge net. In some embodiments, the first edge transition net is a (4,4)-c ssa net and the second edge transition net is a 6-c acs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,4,6)-c aca merge net.

[0109] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ac-b merge net. In some embodiments, the first edge transition net is a (4,4)-c ssa net and the second edge transition net is a 6-c acs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,4,6)-c ac-b merge net.

[0110] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ach merge net. In some embodiments, the first edge transition net is a 6-c acs net and the second edge transition net is a (4,12)-c shp net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,6,12)-c ach merge net.

[0111] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an anl merge net. In some embodiments, the first edge transition net is a 4-c an-a net and the second edge transition net is a 4-c lcs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,6)-c anl merge net.

[0112] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ast-d merge net. In some embodiments, the first edge transition net is a 12-c fcu net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,18)-c ast-d merge net.

[0113] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a bob merge net. In some embodiments, the first edge transition net is a (3,4)-c bor net and the second edge transition net is a 4-c nbo net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,8)-c bob merge net.

[0114] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a bof merge net. In some embodiments, the first edge transition net is a (3,4)-c bor net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,12)-c bof merge net.

[0115] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a bsc merge net. In some embodiments, the first edge transition net is a 6-c bcs net and the second edge transition net is a (3,4)-c ctn net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,9)-c bsc merge net.

[0116] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a BSL merge net. In some embodiments, the first edge transition net is a 4-c lcs net and the second edge transition net is a 6-c bcs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,4,6)-c bsl merge net.

[0117] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a bsp merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a 6-c bcs net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,6,12)-c bsp merge net.

[0118] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a buo merge net. In some embodiments, the first edge transition net is a (4,6)-c soc net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,8,8)-c buo merge net.

[0119] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a bup merge net. In some embodiments, the first edge transition net is a (3,4)-c pto net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,5,8)-c bup merge net.

[0120] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a bus merge net. In some embodiments, the first edge transition net is a (4,6)-c she net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,8,8)-c bus merge net.

[0121] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a crd merge net. In some embodiments, the first edge transition net is a 6-c crs net and the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,8)-c crd merge net.

[0122] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a crh merge net. In some embodiments, the first edge transition net is a 6-c crs net and the second edge transition net is a 6-c hxg net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,12)-c crh merge net.

[0123] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a crn merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a 6-c crs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,6)-c crn merge net.

[0124] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a csa merge net. In some embodiments, the first edge transition net is a (4,8)-c csq net and the second edge transition net is a 6-c acs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,10)-c csa merge net.

[0125] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a cst merge net. In some embodiments, the first edge transition net is a (4,8)-c csq net and the second edge transition net is a (4,6)-c stp net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,6,12)-c cst merge net.

[0126] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a ctl merge net. In some embodiments, the first edge transition net is a (3,4)-c ctn net and the second edge transition net is a 4-c lcs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,8)-c ctl merge net.

[0127] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a dif merge net. In some embodiments, the first edge transition net is a 12-c fcu net and the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,16)-c dif merge net.

[0128] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an EPR merge net. In some embodiments, the first edge transition net is a (3,4)-c PTO net and the second edge transition net is a 4-c SOD net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,8)-c EPR merge net.

[0129] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an flf merge net. In some embodiments, the first edge transition net is a 12-c fcu net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,20)-c flf merge net.

[0130] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an flh merge net. In some embodiments, the first edge transition net is a (4,6)-c she net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,8,10)-c flh merge net.

[0131] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a flp merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,8,10)-c flp merge net.

[0132] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an flr merge net. In some embodiments, the first edge transition net is a (3,6)-c pyr net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,14)-c flr merge net.

[0133] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a fls merge net. In some embodiments, the first edge transition net is a (4,6)-c soc net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,10)-c fls merge net.

[0134] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a fwb merge net. In some embodiments, the first edge transition net is a (3,4)-c bor net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,8,12)-c fwb merge net.

[0135] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an fwc merge net. In some embodiments, the first edge transition net is a (4,12)-c ftw net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,14)-c fwc merge net.

[0136] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a fwf merge net. In some embodiments, the first edge transition net is a (4,12)-c ftw net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,16)-c fwf merge net.

[0137] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a fwo merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,8,12)-c fwo merge net.

[0138] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an fwp merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,18)-c fwp merge net.

[0139] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an fwt merge net. In some embodiments, the first edge transition net is a (3,8)-c the net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,12,12)-c fwt merge net.

[0140] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a gal merge net. In some embodiments, the first edge transition net is a 4-c lcs net, the second edge transition net is a (4,6)-c gar net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,6,8)-c gal merge net.

[0141] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a gas merge net. In some embodiments, the first edge transition net is a 6-c bcs net and the second edge transition net is a (4,6)-c gar net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,4,12)-c gas merge net.

[0142] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an hxd merge net. In some embodiments, the first edge transition net is a 4-c dia net and the second edge transition net is a 6-c hxg net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,8)-c hxd merge net.

[0143] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an hxn merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a 6-c hxg net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,4,6)-c hxn merge net.

[0144] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an hxp merge net. In some embodiments, the first edge transition net is a 6-c hxg net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,12)-c hxp merge net.

[0145] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an HXS merge net. In some embodiments, the first edge transition net is a 4-c sod net and the second edge transition net is a 6-c hxg net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,6)-c hxs merge net.

[0146] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ias merge net. In some embodiments, the first edge transition net is a 6-c bcs net, the second edge transition net is a (4,6)-c iac net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,12)-c ias merge net.

[0147] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ifc merge net. In some embodiments, the first edge transition net is a (4,4)-c ssc net and the second edge transition net is a (4,6)-c ifi net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,8)-c ifc merge net.

[0148] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ifl merge net. In some embodiments, the first edge transition net is a 4-c lcv net and the second edge transition net is a (4,6)-c ifi net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,8)-c ifl merge net.

[0149] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ifr merge net. In some embodiments, the first edge transition net is a 3-c srs net and the second edge transition net is a (4,6)-c ifi net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,6)-c ifr merge net.

[0150] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ifs merge net. In some embodiments, the first edge transition net is a 3-c srs net and the second edge transition net is a (4,6)-c ifi net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,9)-c ifs merge net.

[0151] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an itb merge net. In some embodiments, the first edge transition net is an 8-c bcu net, the second edge transition net is a (4,12)-c ith net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,20)-c itb merge net.

[0152] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an itp merge net. In some embodiments, the first edge transition net is a (3,4)-c pto net and the second edge transition net is a (4,12)-c ith net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,8,12)-c itp merge net.

[0153] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an its merge net. In some embodiments, the first edge transition net is a 4-c sod net and the second edge transition net is a (4,12)-c ith net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,12)-c its merge net.

[0154] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an lvs merge net. In some embodiments, the first edge transition net is a 4-c lcv net and the second edge transition net is a 3-c srs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,6)-c lvs merge net.

[0155] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a lys merge net. In some embodiments, the first edge transition net is a 6-c lcy net and the second edge transition net is a 3-c srs net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,3,9)-c lys merge net.

[0156] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an mga merge net. In some embodiments, the first edge transition net is a 4-c dia net and the second edge transition net is a (6,12)-c mgc net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,8,12)-c mga merge net.

[0157] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an mgh merge net. In some embodiments, the first edge transition net is a 6-c hxg net and the second edge transition net is a (6,12)-c mgc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,12,12)-c mgh merge net.

[0158] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an mgi merge net. In some embodiments, the first edge transition net is a 4-c dia net, the second edge transition net is a (6,12)-c mgc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,16)-c mgi merge net.

[0159] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an mgr merge net. In some embodiments, the first edge transition net is a 6-c crs net, the second edge transition net is a (6,12)-c mgc net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,12,12)-c mgr merge net.

[0160] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an MGS merge net. In some embodiments, the first edge transition net is a (3,6)-c spn net and the second edge transition net is a (6,12)-c mgc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,12,12)-c mgs merge net.

[0161] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an nbf merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,6,12)-c nbf merge net.

[0162] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an nbo-xd merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,8,8)-c nbo-xd merge net.

[0163] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a nic merge net. In some embodiments, the first edge transition net is a 6-c acs net, the second edge transition net is a (6,6)-c nia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,12)-c nic merge net.

[0164] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an nku merge net. In some embodiments, the first edge transition net is a 4-c ana net and the second edge transition net is a 6-c bcs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,6)-c nku merge net.

[0165] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an nso merge net. In some embodiments, the first edge transition net is a 4-c sod net and the second edge transition net is a 4-c nbo net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,6)-c nso merge net.

[0166] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an occ merge net. In some embodiments, the first edge transition net is a (4,8)-c scu net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,14)-c occ merge net.

[0167] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ocf merge net. In some embodiments, the first edge transition net is a (4,12)-c ftw net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,18)-c ocf merge net.

[0168] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an och merge net. In some embodiments, the first edge transition net is a (4,6)-c she net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,12)-c och merge net.

[0169] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ocp merge net. In some embodiments, the first edge transition net is a (3,4)-c pto net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,9)-c ocp merge net.

[0170] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an ocs merge net. In some embodiments, the first edge transition net is a (4,6)-c soc net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,12)-c ocs merge net.

[0171] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a pco merge net. In some embodiments, the first edge transition net is a (3,4)-c bor net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,6,6)-c pco merge net.

[0172] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pcp merge net. In some embodiments, the first edge transition net is a 6-c pcu net, the second edge transition net is a (3,4)-c pto net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,9)-c pcp merge net.

[0173] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pct merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,6)-c pct merge net.

[0174] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a phq merge net. In some embodiments, the first edge transition net is a 4-c ptz net, the second edge transition net is a (4,4)-c pth net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,8)-c phq merge net.

[0175] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pht merge net. In some embodiments, the first edge transition net is a (4,4)-c pth net, the second edge transition net is a 4-c qtz net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,4,8)-c pht merge net.

[0176] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a psb merge net. In some embodiments, the first edge transition net is an 8-c bcu net, the second edge transition net is a (4,4)-c pts net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,4,12)-c psb merge net.

[0177] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pyi merge net. In some embodiments, the first edge transition net is a (3,6)-c pyr net and the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,10)-c pyi merge net.

[0178] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pyp merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (3,6)-c pyr net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,9)-c pyp merge net.

[0179] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a pyu merge net. In some embodiments, the first edge transition net is a 12-c fcu net and the second edge transition net is a (3,6)-c pyr net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,3,18)-c pyu merge net.

[0180] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a pyy merge net. In some embodiments, the first edge transition net is a (3,6)-c pyr net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,12)-c pyy merge net.

[0181] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a qtq merge net. In some embodiments, the first edge transition net is a 4-c qtz net, the second edge transition net is a 4-c qtz net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,18)-c qtq merge net.

[0182] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a reb merge net. In some embodiments, the first edge transition net is an 8-c reo net, the second edge transition net is a (3,4)-c bor net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,12)-c reb merge net.

[0183] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a Ren merge net. In some embodiments, the first edge transition net is an 8-c Reo net and the second edge transition net is a 4-c NbO net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,12)-c Ren merge net.

[0184] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a reo-d merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,8,14)-c reo-d merge net.

[0185] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a rep merge net. In some embodiments, the first edge transition net is an 8-c reo net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,6,10)-c rep merge net.

[0186] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a ret merge net. In some embodiments, the first edge transition net is an 8-c reo net, the second edge transition net is a (3,4)-c tbo net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,12)-c ret merge net.

[0187] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an rhb merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net, the second edge transition net is a (3,24)-c rht net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,24)-c rhb merge net.

[0188] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an rhc merge net. In some embodiments, the first edge transition net is a (3,24)-c rht net, the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,30)-c rhc merge net.

[0189] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an rhd merge net. In some embodiments, the first edge transition net is a (3,24)-c rht net, the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,28)-c rhd merge net.

[0190] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an rhf merge net. In some embodiments, the first edge transition net is a (3,24)-c rht net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,32)-c rhf merge net.

[0191] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an rht-x merge net. In some embodiments, the first edge transition net is a 12-c fcu net, the second edge transition net is a (3,24)-c rht net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,36)-c rht-x merge net.

[0192] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an scc merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (4,6)-c soc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,12)-c scc merge net.

[0193] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an scp merge net. In some embodiments, the first edge transition net is a (4,6)-c soc net, the second edge transition net is a (3,4)-c pto net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,4,9)-c scp merge net.

[0194] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an sdr merge net. In some embodiments, the first edge transition net is a 4-c rhr net, the second edge transition net is a 4-c sod net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,6)-c sdr merge net.

[0195] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a ses merge net. In some embodiments, the first edge transition net is a 4-c sod net, the second edge transition net is a (4,6)-c she net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,6,8)-c ses merge net.

[0196] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sha merge net. In some embodiments, the first edge transition net is a (4,12)-c shp net and the second edge transition net is a 6-c acs net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,18)-c sha merge net.

[0197] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an shc merge net. In some embodiments, the first edge transition net is a (4,8)-c csq net and the second edge transition net is a (4,12)-c shp net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,12,12)-c sh merge net.

[0198] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a shn merge net. In some embodiments, the first edge transition net is a (4,12)-c shp net and the second edge transition net is a (6,6)-c nia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,8)-c shn merge net.

[0199] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sho merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a (4,6)-c she net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,6)-c sho merge net.

[0200] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an shs merge net. In some embodiments, the first edge transition net is a (4,4)-c ssa net and the second edge transition net is a (4,12)-c shp net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,12)-c shs merge net.

[0201] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an sht merge net. In some embodiments, the first edge transition net is a (4,6)-c stp net and the second edge transition net is a (4,12)-c shp net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,8,12)-c sht merge net.

[0202] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an spc merge net. In some embodiments, the first edge transition net is a 6-c crs net and the second edge transition net is a (3,6)-c spn net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,12)-c spc merge net.

[0203] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an spd merge net. In some embodiments, the first edge transition net is a (3,6)-c spn net and the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,8)-c spd merge net.

[0204] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an sph merge net. In some embodiments, the first edge transition net is a (3,6)-c spn net and the second edge transition net is a 6-c hxg net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,12)-c sph merge net.

[0205] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sqd merge net. In some embodiments, the first edge transition net is a 4-c dia net, the second edge transition net is a (4,8)-c sqc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,12)-c sqd merge net.

[0206] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sqv merge net. In some embodiments, the first edge transition net is a 4-c lvt net and the second edge transition net is a (4,8)-c sqc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,8,8)-c sqv merge net.

[0207] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an SSL merge net. In some embodiments, the first edge transition net is a 4-c lcv net, the second edge transition net is a (4,4)-c ssc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,8)-c SSL merge net.

[0208] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with an ssr merge net. In some embodiments, the first edge transition net is a 3-c srs net and the second edge transition net is a (4,4)-c ssc net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,4,6)-c ssr merge net.

[0209] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an sts merge net. In some embodiments, the first edge transition net is a (4,4)-c ssa net and the second edge transition net is a (4,6)-c stp net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,8)-c sts merge net.

[0210] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sub-merged net. In some embodiments, the first edge transition net is a (4,8)-c scu net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,16)-c sub-merged net.

[0211] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a suc merge net. In some embodiments, the first edge transition net is a (4,8)-c scu net and the second edge transition net is an 8-c bcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,8,10)-c suc merge net.

[0212] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a sup merge net. In some embodiments, the first edge transition net is a 6-c pcu net, the second edge transition net is a (4,8)-c scu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,14)-c sup merge net.

[0213] In certain embodiments, the composition is associated with a first polytopic ligand and a second polytopic ligand, tam i The present invention includes a method for fabricating a complex mixed linker structure with a metal component that forms a complex mixed linker structure with a merge net. In some embodiments, the first edge transition net is a 6-c pcu net, the second edge transition net is a (4,6)-c she net, and the first and second edge transition nets merge to form a (2,4,12)-c tam i Form complex mixed linker structures with merge nets.

[0214] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a tbc merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,6,12)-c tbc merge net.

[0215] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a tbf merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net and the second edge transition net is a (12)-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,6,12)-c tbf merge net.

[0216] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a tbn merge net. In some embodiments, the first edge transition net is a (3,4)-c tbo net and the second edge transition net is a 4-c nbo net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,4,8)-c tbn merge net.

[0217] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a tdi merge net. In some embodiments, the first edge transition net is a 4-c dia net and the second edge transition net is a (3,12)-c ttt net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,5,12)-c tdi merge net.

[0218] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tec merge net. In some embodiments, the first edge transition net is a (3,8)-c the net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,10)-c tec merge net.

[0219] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tef merge net. In some embodiments, the first edge transition net is a (3,8)-c the net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,10,12)-c tef merge net.

[0220] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a ter merge net. In some embodiments, the first edge transition net is an 8-c reo net, the second edge transition net is a (3,8)-c the net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,3,16)-c ter merge net.

[0221] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a THC merge net. In some embodiments, the first edge transition net is an 8-c THP net, the second edge transition net is a 4-c LCS net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,4,12)-c THC merge net.

[0222] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tht merge net. In some embodiments, the first edge transition net is an 8-c thp net, the second edge transition net is a (3,4)-c ctn net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,12)-c tht merge net.

[0223] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a toh merge net. In some embodiments, the first edge transition net is a 6-c hxg net and the second edge transition net is a (4,6)-c toc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,12)-c toh merge net.

[0224] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a ton merge net. In some embodiments, the first edge transition net is a 4-c nbo net, the second edge transition net is a (4,6)-c toc net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,8)-c ton merge net.

[0225] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a top merge net. In some embodiments, the first edge transition net is a (4,6)-c toc net, the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (4,6,12)-c top merge net.

[0226] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a ttb merge net. In some embodiments, the first edge transition net is a 12-c fcu net, the second edge transition net is a (3,12)-c ttt net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,3,24)-c ttb merge net.

[0227] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tte merge net. In some embodiments, the first edge transition net is a (3,12)-c ttt net, the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,6,18)-c tte merge net.

[0228] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tth merge net. In some embodiments, the first edge transition net is a 6-c hxg net and the second edge transition net is a (3,12)-c ttt net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,9,12)-c tth merge net.

[0229] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tti merge net. In some embodiments, the first edge transition net is a (3,12)-c ttt net, the second edge transition net is a 4-c dia net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,16)-c tto merge net.

[0230] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a ttl merge net. In some embodiments, the first edge transition net is a (3,12)-c ttt net and the second edge transition net is a (4,8)-c flu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (3,4,20)-c ttl merge net.

[0231] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a ttr merge net. In some embodiments, the first edge transition net is a 6-c crs net, the second edge transition net is a (3,12)-c ttt net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,9,12)-c ttr merge net.

[0232] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tts merge net. In some embodiments, the first edge transition net is a (3,6)-c spn net and the second edge transition net is a (3,12)-c ttt net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,9,12)-c tts merge net.

[0233] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a twb merge net. In some embodiments, the first edge transition net is an 8-c bcu net, the second edge transition net is a (4,24)-c twf net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,4,32)-c twb merge net.

[0234] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a twh merge net. In some embodiments, the first edge transition net is a 6-c hxg net and the second edge transition net is a (4,24)-c twf net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,6,24)-c twh merge net.

[0235] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a twn merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a (4,24)-c twf net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,24)-c twn merge net.

[0236] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a two merge net. In some embodiments, the first edge transition net is a 4-c sod net and the second edge transition net is a (4,24)-c twf net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,8,24)-c two merge net.

[0237] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a tws merge net. In some embodiments, the first edge transition net is a (4,6)-c she net and the second edge transition net is a (4,24)-c twf net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,8,24)-c tws merge net.

[0238] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a urk merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,6)-c urk merge net.

[0239] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an urr merge net. In some embodiments, the first edge transition net is a (3,8)-c the net and the second edge transition net is a 4-c nbo net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (3,4,12)-c urr merge net.

[0240] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a wzz merge net. In some embodiments, the first edge transition net is a (4,8)-c flu net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,14)-c wzz merge net.

[0241] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure with a xam merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure with a (2,6,12)-c xam merge net.

[0242] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a xau merge net. In some embodiments, the first edge transition net is an 8-c reo net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,10,12)-c xau merge net.

[0243] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having a xaz merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (6,8)-c ocu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (2,8,12)-c xaz merge net.

[0244] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an xbk merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a 12-c fcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,12)-c xbk merge net.

[0245] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an xbn merge net. In some embodiments, the first edge transition net is a 4-c nbo net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,8,12)-c xbn merge net.

[0246] In certain embodiments, the composition includes a metal component associated with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an xbo merge net. In some embodiments, the first edge transition net is a 6-c pcu net and the second edge transition net is a (4,12)-c ftw net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (6,6,12)-c xbo merge net.

[0247] In certain embodiments, the composition includes a metal component that associates with a first polytopic ligand and a second polytopic ligand to form a complex mixed linker structure having an xbp merge net. In some embodiments, the first edge transition net is a 4-c dia net and the second edge transition net is a 6-c pcu net, and the first and second edge transition nets merge to form a complex mixed linker structure having a (4,6,10)-c xbp merge net.

[0248] Merge Net Equations The merge net equation can be used to describe and / or form a series of iso-mesh complex mixed linker structures that have the same underlying merge net. Generally, the merge net equation describes the length or size of one ligand (e.g., an edge of a parent net) versus the length or size of another ligand (e.g., an edge of another parent net). For example, in some embodiments, the merge net equation describes the length or size of a first polytopic ligand versus the length or size of a second polytopic ligand. In some embodiments, the merge net equation describes the length or size of a second polytopic ligand versus the length or size of the first polytopic ligand.

[0249] In some embodiments, the edge dimension or size ratio of a first edge transition net (or first parent net) to a second edge transition net (or second parent net) is calculated using equation (1):

number

number

[0250] In some embodiments, the edge ratio constant further requires consideration of molecular building blocks (MBBs). For example, in some embodiments, the edge ratio constant is calculated using equation (3):

number

[0251] Polytopic Ligands The complex mixed linker structure includes a first polytopic ligand and a second polytopic ligand. The first polytopic ligand and the second polytopic ligand are generally different from each other as a minimum edge-transitive net having two types of edges. Otherwise, the first polytopic ligand and the second polytopic ligand are not particularly limited and can be selected from any polytopic ligand suitable for the complex mixed linker structure of the present disclosure.

[0252] In some embodiments, the first polytopic ligand and the second polytopic ligand are each independently an n-connected node, where n ranges from 1 to 40. For example, in some embodiments, the first polytopic ligand and the second polytopic ligand are each independently a 2-c node, a 3-c node, a 4-c node, a 5-c node, a 6-c node, a 7-c node, an 8-c node, a 9-c node, a 10-c node, a 12-c node, a 14-c node, a 16-c node, an 18-c node, a 20-c node, a 24-c node, a 26-c node, a 28-c node, a 30-c node, a 32-c node, a 36-c node, or a combination thereof. In other embodiments, one of the first polytopic ligand and the second polytopic ligand is an n-connected node. In other embodiments, one or more of the first polytopic ligand and the second polytopic ligand are n-connected nodes.

[0253] In some embodiments, the first polytopic ligand and the second polytopic ligand are each independently an n-linked molecular building block (MBB), where n ranges from 1 to 40. For example, in some embodiments, the first polytopic ligand and the second polytopic ligand are each independently a 2-c MBB, a 3-c MBB, a 4-c MBB, a 5-c MBB, a 6-c MBB, a 7-c MBB, an 8-c MBB, a 9-c MBB, a 10-c MBB, a 12-c MBB, a 14-c MBB, a 16-c MBB, an 18-c MBB, a 20-c MBB, a 24-c MBB, a 26-c MBB, a 28-c MBB, a 30-c MBB, a 32-c MBB, a 36-c MBB, or a combination thereof. In other embodiments, one of the first polytopic ligand and the second polytopic ligand is an n-linked MBB. In other embodiments, one or more of the first polytopic ligand and the second polytopic ligand is an n-linked MBB.

[0254] 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 having a smaller coordination number than the first polytopic ligand. For example, in one embodiment, the first polytopic ligand is a 6-c node, and 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-1,3,5-tricarbonyl)tris(azanediyl))tribenzoate (BTCB)-tricarboxylate linkers, with the 1,3,5 carbon atoms of the central benzene ring of the double BTCB moiety serving as extension points for the 6-c node. Other ligands with different functionality or coordination numbers can be used herein without departing from the scope of the present disclosure. This is provided as an example only, as the principle can be extended to any n-connected node using any of the ligands of the present disclosure.

[0255] In some embodiments, the polytopic ligand comprises one or more coordinating N-, S-, and O-donor functional groups. In some embodiments, the first polytopic ligand and / or the second polytopic ligand is a polycarboxylic acid ligand. In some embodiments, the first polytopic ligand and / or the second polytopic ligand comprises one or more of the following coordinating groups: amide (including sulfonamide and phosphoramide), sulfinic acid, sulfonic acid, phosphonic acid, phosphate, phosphodiester, phosphine, boronic acid, boronic acid ester, borinic acid, borinic acid ester, nitrate, nitrito, nitrile, nitro, nitroso, thiocyanate, cyanate, azo, azide, imide, imine, amine, acetal, ketal, ether, ester, aldehyde, ketone, alcohol, thiol, sulfide, disulfide, sulfoxide, sulfone, sulfinic acid, thione, and thiar. In some embodiments, the first polytopic ligand and / or the second polytopic ligand comprises one or more moieties independently selected from polycarboxylic acid moieties, polytetrazole moieties, polytriazole moieties, polypyrazole moieties, and polypyridyl moieties, hi some embodiments, the first polytopic ligand and / or the second polytopic ligand comprises polytetrazole ligands, polytriazole ligands, polypyrazole ligands, polyimidazole ligands, and polypyridyl ligands.

[0256] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] [ka] In some embodiments, R and / or R' are independently selected from: In some embodiments, R and / or R' are extension points. In some embodiments, R and / or R' are selected from hydrocarbons, ethers, esters, amides, sulfur-containing groups, and combinations thereof. In some embodiments, R and / or R' are independently selected from: -H, -OH, -OR, -COOH, -COOR, -CONH, -NH, -NHR 1 , -NR 1 R 2 , -SH, -SR, -SO2R 1 , -SO2H, -SOR 1 , R 1 , alkyl, alkenyl, alkynyl, phenyl, biphenyl, azo, and halo, wherein each of R and R is independently selected from substituted and unsubstituted hydrocarbonyl. In some embodiments, the substituted and unsubstituted hydrocarbonyl is 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.

[0257] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (Wherein 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) are independently selected from

[0258] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] [ka] (Wherein 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, alkynyl, phenyl, biphenyl, azo, etc.), are independently selected from

[0259] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (Wherein 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, alkynyl, phenyl, biphenyl, azo, etc.), are independently selected from

[0260] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] [ka] where R=a linker of any length described herein. are independently selected from

[0261] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; R = a linker of any length described herein) are independently selected from

[0262] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] where R=any flexible rectangular core. Examples include: [ka] [ka] [ka] [ka] [ka] wherein all porphyrins and related compounds (e.g., phthalocyanines) can be optionally metallated. Examples include:

[0263] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; R=a linker of any length described herein). Examples include: [ka] [ka] Examples include:

[0264] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] where R=any flexible tetrahedral core. Examples include: [ka] [ka] [ka] Examples include:

[0265] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; R=a linker of any length described herein). Examples include: [ka] Examples include:

[0266] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] Any N-donor triangular ligand or pillar (wherein M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; R = a linker of any length described herein. Examples include [ka] (wherein M=Y) Examples include:

[0267] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] where R=any octahedral core. Examples include: [ka] [ka] [ka] [ka] Examples include:

[0268] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] where R=any triangular prismatic core. Examples include: [ka] where X=OR, SR, NHR; and R=a linker of any length described herein. Examples include: [ka] (wherein X=OR, SR, NHR; R=a linker of any length described herein).

[0269] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; X=C, N, NH, etc.; Y=C, N, etc.; O=O, OH, HO, N, halogens (Cl, Br, I, F, etc.); in some instances, M-M single or multiple bonds may be present (e.g., W, Mo, etc.); R=a linker of any length described herein). Examples include: [ka] [ka] Examples include:

[0270] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+(e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; X=C, N, NH, etc.; Y=C, N, etc.; O=O, OH, HO, N, halogens (Cl, Br, I, F, etc.); in some instances, M-M single or multiple bonds may be present (e.g., W, Mo, etc.); R=a linker of any length described herein). Examples include: [ka] Examples include:

[0271] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] (In the formula, M 1+ (e.g., Li, Na, K, Ag, etc.); M 2+ (e.g., Mg, Ca, Ba, Cs, Pb, Cu, Zn, Co, Mn, Mo, Cr, Fe, Pt, Pd, Ru, Rh, Cd, etc.); M 3+ (e.g., In, Fe, Y, Ln (Yb, Tb, etc.)); M 4+ (e.g., Zr, Ti, V, etc.), or other higher oxidation state metals such as +5, +6, +7, and +8; X=C, N, NH, etc.; Y=C, N, etc.; O=O, OH, HO, N, halogens (Cl, Br, I, F, etc.); in some instances, M-M single or multiple bonds may be present (e.g., W, Mo, etc.); R=a linker of any length described herein). Examples include: [ka] Examples include:

[0272] In some embodiments, each of the first polytopic ligand and / or the second polytopic ligand is [ka] [ka] [ka] [ka] (Wherein, X is hydrogen, —NHR, —N(R)2, halide, C 1~10 Alkyl, C 6~18 Aryl, C 6~18 Aralkyl, -NH2, alkenyl, alkynyl, -Oalkyl, -NH(aryl), cycloalkyl, cycloalkenyl, cycloalkynyl, -(CO)R, -(SO2)R, -(CO2)R, -SH, -S(alkyl), -SO3H, -SO 3- M + , -COOH, -COO - M + , -PO3H2, -PO3H - M + , -PO3 2- M 2+ , -NO2, -CO2H, silyl derivatives, borane derivatives, ferrocene, and other metallocenes, where M is a metal atom and R is C 1~10 Examples of polytopic ligands include 1,4-benzenedicarboxylate (BDC), 4,4'-biphenyldicarboxylate (BPDC), tetrahydropyrene-2,7-dicarboxylate (HPDC), 4,4''-terphenyldicarboxylate (TPDC), and 1,3,5-tris(4-carboxyphenyl)benzene (BTB).

[0273] Metallic components In some embodiments, the metal component comprises one or more metals and metal ions. In some embodiments, the metal component optionally further comprises one or more precursor moieties, such as clustered precursor moieties. In some embodiments, the metal component comprises a metal or a metal ion. In some embodiments, the metal component comprises multiple metals or metal ions. In some embodiments, the metal component comprises a mononuclear or polynuclear metal cluster. In some embodiments, the metal component comprises an inorganic molecular building block (MBB).

[0274] The metal and / or metal ion of the metal component is not particularly limited and can therefore be selected from any metal in the periodic table. For example, in some embodiments, the metal component comprises a metal and / or metal ion selected from the following periodic group: IA, IIA, IIIB, IVB, VB, VIB, VIIB, VIIIB, VIIIIB, IB, IIB, IIIA, IVA, VA, VIA, any cation thereof, and any combination thereof. In some embodiments, the metal component comprises a metal selected from rare earth metals, alkali metals, alkaline earth metals, transition metals, lanthanides, actinides, post-transition metals, any cation thereof, and any combination thereof. In some embodiments, the metal and / or metal ion of the metal component has an oxidation state selected from 0, +1, +2, +3, +4, +5, +6, +7, +8, and combinations thereof.

[0275] 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 cation thereof, and any combination 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 cation thereof, and any combination thereof. 2+ , Zn 2+ , Co 2+ , Ni 2+ , Mn 2+ , Zr 2+ , Fe 2+ , Ca 2+ , Ba 2+ , Pb 2+ , Pt 2+ , Pd 2+ , Ru 2+ , Rh 2+ , Cd 2+ , Mg +2 , Al +3 , Fe +2 , Fe +3 , Cr 2+ , Cr 3+ , Ru 2+ , Ru 3+ , Co 3 , Ti 3+ , V 3+ , V 5+ ,Sc. 3+ , In 3+ , Nb 5+ , Y 3+ In some embodiments, the metal is selected from Al +3 , Ga 3+ , Fe +2 , Fe+3 , Cr 2+ , Cr 3+ , Ti 3+ , V 3+ , V 5+ ,Sc. 3+ , In 3+ , Nb 5+ , Y 3+ , and any combination thereof.

[0276] In some embodiments, the metal component comprises an n-linked inorganic MBB, where n is in the range of 1 to 40. For example, in some embodiments, the metal component comprises a 2-c inorganic MBB, a 3-c inorganic MBB, a 4-c inorganic MBB, a 5-c inorganic MBB, a 6-c inorganic MBB, a 7-c inorganic MBB, an 8-c inorganic MBB, a 9-c inorganic MBB, a 10-c inorganic MBB, a 12-c inorganic MBB, a 14-c inorganic MBB, a 16-c inorganic MBB, an 18-c inorganic MBB, a 20-c inorganic MBB, a 24-c inorganic MBB, a 26-c inorganic MBB, a 28-c inorganic MBB, a 30-c inorganic MBB, a 32-c inorganic MBB, a 36-c inorganic MBB, or a combination thereof.

[0277] In some embodiments, the metal component comprises an n-linked polynuclear cluster, where n is in the range of 1 to 40. For example, in some embodiments, the metal component comprises a 2-c polynuclear metal cluster, a 3-c polynuclear metal cluster, a 4-c polynuclear metal cluster, a 5-c polynuclear metal cluster, a 6-c polynuclear metal cluster, a 7-c polynuclear metal cluster, an 8-c polynuclear metal cluster, a 9-c polynuclear metal cluster, a 10-c polynuclear metal cluster, a 12-c polynuclear metal cluster, a 14-c polynuclear metal cluster, a 16-c polynuclear metal cluster, an 18-c polynuclear metal cluster, a 20-c polynuclear metal cluster, a 24-c polynuclear metal cluster, a 26-c polynuclear metal cluster, a 28-c polynuclear metal cluster, a 30-c polynuclear metal cluster, a 32-c polynuclear metal cluster, a 36-c polynuclear metal cluster, or a combination thereof.

[0278] In some embodiments, the metal component has the formula: M x(x is 1-20). For example, in some embodiments, the metal component comprises a dinuclear cluster (e.g., where x is 2). In some embodiments, the metal component comprises a trinuclear cluster (e.g., where x is 3). In some embodiments, the metal component comprises a tetranuclear cluster (e.g., where x is 4). In some embodiments, the metal component comprises a pentanuclear cluster (e.g., where x is 5). In some embodiments, the metal component comprises a hexanuclear cluster (e.g., where x is 6). In some embodiments, the metal component comprises a heptanuclear cluster (e.g., where x is 7). In some embodiments, the metal component comprises an octanuclear cluster (e.g., where x is 8). In some embodiments, the metal component comprises a nonanuclear cluster (e.g., where x is 9). In some embodiments, the metal component comprises a decanuclear cluster (e.g., where x is 10). In some embodiments, the metal component comprises a dodecanuclear cluster (eg, where x is 11).

[0279] Methods for the preparation of complex mixed linker structures Embodiments of the present disclosure also describe methods for synthesizing complex mixed linker structures according to one or more embodiments of the present disclosure, the methods including one or more of the following steps: 201 contacting a metal precursor, a first ligand precursor, and a second ligand precursor sufficient to form any of the complex mixed linker structures having merge-net topologies of the present disclosure.

[0280] The contacting step 201 can proceed by bringing the metal precursor, first ligand precursor, and second ligand precursor into physical contact or close or very close proximity. In some embodiments, the contacting step proceeds in solution. In some embodiments, the contacting step proceeds with solid-phase reactants and thus without solvent. In some embodiments, the contacting step proceeds at or to a temperature of about 25° C. or greater. For example, in some embodiments, the contacting step proceeds under solvothermal reaction conditions. In other embodiments, the contacting step proceeds at or to a temperature of less than about 25° C. The metal precursor is not particularly limited and can be selected from any compound containing a metal or metal component of the present disclosure. In some embodiments, the metal precursor is a metal salt or a 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 a first polytopic ligand having a neutral charge (e.g., it is protonated or has H atoms). In some embodiments, the second ligand precursor is a second polytopic ligand having a neutral charge (e.g., it is protonated or has H atoms).

[0281] Various embodiments of the present disclosure are described herein:

[0282] In one aspect, the present invention provides a method for producing a pharmaceutical composition comprising: (a) selecting a target merge net in the synthesis of a complex mixed linker structure, and a first edge transition net and a second edge transition net that can be combined to provide the target merge net, wherein the first and second edge transition nets share a common signature net; (b) determining connectivity and a geometric configuration of each node of a merge net, the nodes of the merge net including merge nodes and non-merge nodes, the non-merge nodes including a first non-merge node and a second non-merge node; (c) selecting an MBB that has the same connectivity and geometric configuration as the merge node and has two sets of extension points, each set of extension points being capable of being connected to a separate MBB; (d) selecting a first MBB that has the same connectivity and geometric configuration as the first non-merge node; (e) inputting the length of the selected first MBB into a merge net equation to calculate an appropriate length of the complementary MBB; (f) selecting a second MBB having the same connectivity and geometric configuration as the second non-merge node and the same length as the complementary MBB; (g) reacting precursors of the MBB, the first MBB, and the second MBB to synthesize a complex mixed linker structure with the target merge network; The present invention relates to a method for synthesizing complex mixed linker structures, including:

[0283] In a particular embodiment, the merge net is a minimum edge transitive net with transitivity

[22] or transitivity

[32] .

[0284] In certain embodiments, the merge nets include aca net, acb net, ach net, anl net, ast-d net, bob net, bof net, bsc net, bsl net, bsp net, buo net, bup net, bus net, crd net, crh net, crn net, csa net, cst net, ctl net, dif net, epr net, flf net, flh net, flp net, flr net, fls net, fwb net, fwc net, fwf net, fwo net, fwp net, fwt net, ga l net, gas net, hxd net, hxn net, hxp net, hxs net, ias net, ifc net, ifl net, ifr net, ifs net, itb net, itp net, its net, lvs net, lys net, mga net, mgh net, mgi net, mgr net, mgs net, nbf net, nbo-xd net, nic net, nku net, nso net, occ net, ocf net, och net, ocp net, ocs net, pco net, pcp net, pct net, phq net, pht net, psb net, pyi net, pyp net, pyu net, pyy net, qtq net, reb net, ren net, reo-d net, rep net, ret net, rhb net, rhc net, rhd net, rhf net, rht-x net, scc net, scp net, sdr net, ses net, sha net, shc net, shn net, sho net, shs net, sht net, spc net, spd net, sph net, sqd net, sqv net, ssl net, ssr net, sts net, sub Net, suc net, sup net, tam net, tbc net, tbf net, tbn net, tdi net, tec net, tef net, ter net, thc net, tht net, toh net, ton net, top net, ttb net, tte net, tth net, tti net, ttl net, ttr net, tts net, twb net, twh net, twn net, two net, tws net, urk net, urr net, wzz net, xam net, xau net, xaz net, xbk net, xbn net,xbo net, xbp net, or a combination thereof.

[0285] In one particular embodiment, each of the first edge-transition net and the second edge-transition net is independently selected from edge-transition nets having transitivity

[11] or transitivity

[21] .

[0286] In a particular embodiment, the edge-transitive net having transitivity

[11] is selected from: hxg-net, lcw-net, hxl-net, kgm-net, hcb-net, dia-net, crs-net, nbo-net, sod-net, rhr-net, acs-net, sql-net, lvt-net, bcu-net, pcu-net, fcu-net, reo-net, qtz-net, srs-net, lcv-net, lcy-net, bcs-net, lcs-net, ana-net, thp-net, or a combination thereof.

[0287] In a particular embodiment, the edge-transitive net having transitivity

[21] is selected from shp-net, alb-net, stp-net, mgc-net, spn-net, toc-net, nia-net, ssa-net, csq-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, ctn-net, or a combination thereof.

[0288] In certain embodiments, the common signature net is selected from a kgm net, an ana net, an fcu net, a reo net, a bcs net, a pcu net, a crs net, a nbo net, a thp net, an lcw net, an lcs net, a sod net, an hxg net, an lcv net, a srs net, a bcu net, an lcy net, a dia net, an acs net, a qtz net, an fcu net, an op net, a rhr net, an hxl net, an lvt net, or a thp net.

[0289] In certain embodiments, the first MBB and the second MBB are different. In certain embodiments, each of the MBB, the first MBB, and the second MBB is independently selected from an organic MBB or an inorganic MBB. In certain embodiments, each of the MBB, the first MBB, and the second MBB is independently selected from a first polytopic ligand, a second polytopic ligand, or a metal component. In certain embodiments, at least one of the MBB, the first MBB, and the second MBB is an inorganic MBB comprising a metal cluster or a metal ion.

[0290] In a particular embodiment, a first MBB associates with at least one of the two sets of extension points to provide a first edge-transition net, and in a particular embodiment, a second MBB associates with at least one of the two sets of extension points to provide a second edge-transition net.

[0291] In one particular embodiment, the margin net equation is Equation (1):

number

number

number

[0292] In certain embodiments, the method further comprises selecting additional pairs of first and second MBBs to form isoreticular complex mixed linker structures.

[0293] In another aspect, the present invention relates to a composition comprising a complex mixed linker structure having a merge-net topology, wherein the metal-organic framework comprises a molecular building block (MBB) having a first extension point and a second extension point, the first extension point coordinates to the first MBB and the second extension point coordinates to the second MBB, and the first MBB and second MBB are different.

[0294] In certain embodiments, the first MBB is a first polytopic ligand and the second MBB is a second polytopic ligand.

[0295] In one particular embodiment, the coordination of the first MBB with the first expansion point provides a first edge-transition net.

[0296] In one particular embodiment, the coordination of the second MBB with the second extension point provides a second edge-transition net.

[0297] In a further aspect, the present invention relates to a material comprising a metal component, a first polytopic ligand, and a second polytopic ligand that associate to form a complex mixed linker structure having a merge net.

[0298] In certain embodiments, the first polytopic ligand and the second polytopic ligand are different. In certain embodiments, each of the first polytopic ligand and the second polytopic ligand is independently selected from ligands having O-, N-, and S-donor functional groups. In certain embodiments, each of the first polytopic ligand and the second polytopic ligand is independently selected from polycarboxylate acid ligands, polytetrazole ligands, polytriazole ligands, polypyrazole ligands, polyimidazole ligands, and polypyridyl ligands. In certain embodiments, the metal component is an inorganic molecular building block (MBB) comprising a metal cluster or metal ion.

[0299] In certain embodiments, the metal of the metal component is selected from rare earth metals, alkali metals, alkaline earth metals, and transition metals.

[0300] In certain embodiments, the merge nets include aca net, acb net, ach net, anl net, ast-d net, bob net, bof net, bsc net, bsl net, bsp net, buo net, bup net, bus net, crd net, crh net, crn net, csa net, cst net, ctl net, dif net, epr net, flf net, flh net, flp net, flr net, fls net, fwb net, fwc net, fwf net, fwo net, fwp net, fwt net, ga l net, gas net, hxd net, hxn net, hxp net, hxs net, ias net, ifc net, ifl net, ifr net, ifs net, itb net, itp net, its net, lvs net, lys net, mga net, mgh net, mgi net, mgr net, mgs net, nbf net, nbo-xd net, nic net, nku net, nso net, occ net, ocf net, och net, ocp net, ocs net, pco net, pcp net, pct net, phq net, pht net, psb net, pyi net, pyp net, pyu net, pyy net, qtq net, reb net, ren net, reo-d net, rep net, ret net, rhb net, rhc net, rhd net, rhf net, rht-x net, scc net, scp net, sdr net, ses net, sha net, shc net, shn net, sho net, shs net, sht net, spc net, spd net, sph net, sqd net, sqv net, ssl net, ssr net, sts net, sub Net, suc net, sup net, tam net, tbc net, tbf net, tbn net, tdi net, tec net, tef net, ter net, thc net, tht net, toh net, ton net, top net, ttb net, tte net, tth net, tti net, ttl net, ttr net, tts net, twb net, twh net, twn net, two net, tws net, urk net, urr net, wzz net, xam net, xau net, xaz net, xbk net, xbn net,xbo net and xbp net are selected.

[0301] In one particular embodiment, the merge net includes a first edge transition net and a second edge transition net merged via a shared node.

[0302] In one particular embodiment, the merge net preserves the structural skeleton of the first edge-transition net and the second edge-transition net.

[0303] In one particular embodiment, the first edge-transition net and the second edge-transition net each have a transitivity selected from transitivity

[11] and transitivity

[21] .

[0304] In one particular embodiment, the edge-transitive nets having transitivity

[11] are selected from hxg-net, lcw-net, hxl-net, kgm-net, hcb-net, dia-net, crs-net, nbo-net, sod-net, rhr-net, acs-net, sql-net, lvt-net, bcu-net, pcu-net, fcu-net, reo-net, qtz-net, srs-net, lcv-net, lcy-net, bcs-net, lcs-net, ana-net, and thp-net.

[0305] In a particular embodiment, the edge-transitive nets having transitivity

[21] are selected from shp-net, alb-net, stp-net, mgc-net, spn-net, toc-net, nia-net, ssa-net, csq-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.

[0306] In one particular embodiment, the first edge transition net and the second edge transition net have a common signature net.

[0307] In certain embodiments, the common signature net is selected from kgm-net, ana-net, fcu-net, reo-net, bcs-net, pcu-net, crs-net, nbo-net, thp-net, lcw-net, lcs-net, sod-net, hxg-net, lcv-net, srs-net, bcu-net, lcy-net, dia-net, acs-net, qtz-net, fcu-net, op-net, rhr-net, hxl-net, lvt-net, and thp-net.

[0308] In one particular embodiment, the merge net is selected from an edge transformation net merged with a signature net, a binary transformation net merged with a signature net, and a direct transitive [2,1] net merged with a signature net.

[0309] In one particular embodiment, the merge net is selected from an edge transformation net merged with another edge transformation net, a binary transformation net merged with another binary transformation net, and a direct transitive [2,1] net merged with another direct transitive [2,1] net.

[0310] In one particular embodiment, the merge net is selected from an edge transformation net merged with a binary transformation net, an edge transformation net merged with a direct transitive [2,1] net, and a binary transformation net merged with a direct transitive [2,1] net.

[0311] In one particular embodiment, the merge net has a transitivity selected from transitivity

[22] and transitivity

[32] .

[0312] In an additional aspect, the present invention relates to a method for synthesizing a complex mixed linker structure, comprising contacting a metal precursor, a first ligand precursor, and a second ligand precursor under reaction conditions sufficient to form a complex mixed linker structure having a merge net.

[0313] In another aspect, the present invention relates to a method comprising one or more of the following steps: extracting a signature net from a plurality of edge-transitive parent nets with transitivity

[11] and / or transitivity

[21] by one or more of edge transformation, binary transformation, and direct transformation; selecting a first edge-transitive net and a second edge-transitive net having a common signature net from the plurality of edge-transitive nets; selecting a first polytopic ligand suitable for the first edge-transitive net and a second polytopic ligand suitable for the second edge-transitive net; and synthesizing a complex mixed linker structure by reacting precursors of the first polytopic ligand and the second polytopic ligand with a polynuclear cluster precursor.

[0314] In another aspect, the present disclosure relates to a method for designing a complex mixed linker structure, including: extracting a signature net from a plurality of parent nets by one or more of edge transformation, binary transformation, and direct transformation; merging parent nets having 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.

[0315] In one particular embodiment, the parent nets are edge-transitive nets with transitivity

[11] and transitivity

[21] .

[0316] In one particular embodiment, edge transformations are used on parent nets with transitivity

[11] .

[0317] In one particular embodiment, binary transformations are used for parent nets with transitivity

[11] .

[0318] In one particular embodiment, direct transformations are used for parent nets with transitivity

[21] .

[0319] In one particular embodiment, each of the multiple merge nets has two types of linkers.

[0320] In a particular embodiment, the merge nets are minimum edge transitive nets with transitivity

[22] or transitivity

[32] .

[0321] In one particular embodiment, the plurality of merge nets includes an edge transformation net merged with a signature net.

[0322] In one particular embodiment, the plurality of merge nets includes a binary transformation net merged with a signature net.

[0323] In one particular embodiment, the plurality of merge nets includes a direct conversion net merged with a signature net.

[0324] In one particular embodiment, the plurality of merge nets includes a first edge transformation net merged with a second edge transformation net.

[0325] In one particular embodiment, the plurality of merge nets includes a first binary translation net merged with a second binary translation net.

[0326] In one particular embodiment, the plurality of merge nets includes a first direct conversion net merged with a second direct conversion net.

[0327] In one particular embodiment, the plurality of merge nets includes edge transformation nets merged with binary transformation nets.

[0328] In a particular embodiment, the plurality of merge nets includes an edge transformation net merged with a direct transformation net. In a particular embodiment, the plurality of merge nets includes a binary transformation net merged with a direct transformation net. In a particular embodiment, at least one of the nodes of the merge net is a merge node.

[0329] The following examples are illustrative of the above invention and should not be construed to narrow its scope. Those skilled in the art will readily recognize that the tester will suggest many other ways in which the invention can be practiced. It should be understood that numerous variations and modifications can be made while remaining within the scope of the invention. [Example]

[0330] Example 1 A merge-net approach for the rational design of complex mixed-linker MOF platforms The rational design and construction of metal-organic frameworks (MOFs) with complex structural complexity is of paramount importance in network chemistry. This example demonstrates a recent addition to the network chemistry design toolbox. Specifically, the concept of merged nets, based on merging two edge-transitive nets into a minimal edge-transitive net, is demonstrated for the rational design and construction of complex mixed-linker MOFs. In particular, by merging two edge-transitive nets, i.e., a (3,6)-coordinated spn and a 6-coordinated hxg, we rationally generated a valuable net for design encompassing two edges (not related by symmetry). The resulting merged net, i.e., a (3,6,12)-coordinated sph net with net transitivity

[32] encompassing three nodes and two distinct edges, offers the potential for the deliberate design and construction of complex mixed-linker MOFs. In this example, we report the implementation of the merge-net approach for the design and synthesis of a series of highly symmetric isoreticular RE mixed-linker MOFs, i.e., sph-MOF-1–4, based on the organization of a 12-c hexanuclear carboxylate-based MBB, demonstrating cuboctahedral building units, 3-c tritopic ligands, and 6-c hexatopic ligands. The resulting sph-MOFs represented the first examples of MOFs in which the underlying net was merged from two three-period edge-transitive nets, i.e., a (3,6)-c spn net and a 6-c hxg net. sph-MOF-3 represented the first example of a mixed-linker MOF encompassing both triangular and hexagonal linkers. The merge-net approach described herein enables the logical implementation of isoreticular chemistry, allowing the expansion of 3-c and 6-c polytopic ligands in a concerted manner, taking into account the mathematically correlated dimensionality of the two ligands, to provide the purposeful construction of a mixed-linker mesoporous MOF, i.e., sph-MOF-4. The fundamental equation for net-merge, i.e., the merge-net equation, and two key parameters, the ratio constant and the molecular building block (MBB) constant, are disclosed. A systematic design principle, referred to herein as the merge-net strategy, for targeting the design of mixed-linker MOFs is illustrated by tightly controlling the edge-to-edge size ratio.

[0331] The ongoing quest to develop practical strategies for the logical design of MOFs has prompted a thorough analysis of edge-transitive nets, aiming to uncover plausible correlations / interrelationships between paired nets. Recently, the prominence of developing highly connected building units in combination with minimal edge-transitive derived nets (transitive

[32] ) based on partitioning one type of vertex in an edge-transitive net into groups of lower-coordinated link vertices (e.g., from one 12-c to one 6-c and one type of 3-c) has been considered a powerful strategy for designing and constructing MOFs employing branched ligands, for purposeful access to necessary and complex highly coordinated net cBUs. Rationally, it has been realized that merging two edge-transitive nets (transitive

[21] or

[11] ), provided they provide shared nodes, can yield a new, more complex minimal edge-transitive net (transitive

[32] ) that encompasses structural properties from both parent nets, offering great promise for materials designers. In practice, it was envisioned that two frameworks would merge via a shared inorganic MBB, successfully implementing network chemistry for the design of complex mixed-linker MOFs. Therefore, for the reasonable design of mixed-linker MOFs, several important requirements were devised and pursued: (i) the two designated merged MOFs were based on a minimal edge-transitive net; (ii) the embedded subframeworks connecting the inorganic building units and each organic linker were based on an edge-transitive net; and (iii) the two subframeworks needed to merge and connect with each other via a shared inorganic MBB.

[0332] In this example, we introduce a systematic design principle, termed the merge-net strategy, aimed at the design of highly complex mixed-linker MOFs. In particular, the validity of this concept is asserted using a mathematical relationship, termed the merge-net equation, which takes into account the inherent geometric features of the nets that make up the resulting merge-net. Remarkably, we reveal that to construct isoreticular mixed-linker MOFs, the linker pairs used need to be scaled linearly, but not proportionally, addressing the long-standing issue of reliable design of isoreticular mixed-linker MOFs.

[0333] The selection of building units with the requisite connectivity and geometric information to encode a target net is central to the practice of reticulation chemistry and the design of MOFs. For example, the expansion of a (3,6)-coordinated spn net allows the identification of the spn net's vertex shapes as a 3-c antitriangular prism and a 6-c antitriangular prism, which then provides the coding information embedded in the building units for the reticulation of the spn-a net. Similarly, a single-node 6-coordinated hxg net requires hexagonal building units for its expected reticulation. However, the plausible relationship / connection between the aforementioned two edge-transitive nets is not clear, and the possibility of joining related building units has unfortunately been dismissed and not considered for the past 20 years. As described herein, the juxtaposition of an antitriangular prism (the building unit of an spn net) and a hexagon (the building unit of an hxg net) resulted in a cuboctahedron building unit; that is, the cuboctahedron building unit provided two expected building units by intentionally dividing its extension points into two sets to give antitriangular prisms (the building unit of an spn net) and hexagons (the building unit of an hxg net). As proposed, each set of extension points could be connected to additional building units (triangles in spn nets and hexagons in hxg nets) to form a three-periodic net, and the cuboctahedron building unit was utilized to assert the possibility of simultaneously introducing spn and hxg nets in the same resulting three-periodic structure.

[0334] In practice, by precisely controlling the ratio between the relevant edges of the spn and hxg nets, we merged all antitriangular prism building units in the spn net and half of the hexagonal building units in the hxg net to form a cuboctahedron building unit. Consequently, we completely merged two edge-transitive nets, the (3,6)-c spn net (transitive

[21] ) and the 6-c hxg net (transitive

[11] ), to form a new minimal edge-transitive (3,6,12)-c net (transitive

[32] ), named the sph net (from "spn" to "sp" and "hxg" to "h"). The concept of merging two three-period edge-transitive nets to provide a new minimal edge-transitive sph net offers great potential for the intentional design of the sph-MOF platform.

[0335] Reasonably, the applicant recently introduced a 12-connected rare earth (RE) hexanuclear [RE6(μ3-OH)8(μ3-O)2(O2C-) 12 The 12-c cuboctahedral building unit based on carboxylate-based clusters has inspired the design of mixed-linker MOF platforms based on the reticulation of sph-nets. To implement the merge-net approach for the design of mixed-linker sph-MOF platforms, in addition to the deployment of rare-earth hexanuclear clusters as the essential 12-c cuboctahedral MBB, we derived several key prerequisites: (i) a 3-c triangular MBB provided by tricarboxylate ligands, (ii) a 6-c hexagonal MBB provided by predesigned hexacarboxylate ligands or two π-π interacting 3-c tricarboxylate ligands, and (iii) a mathematical equation defining the relationship between the dimensions of the essential 3-c and 6-c organic MBBs.

[0336] Indeed, a series of highly symmetric isoreticular mixed-linker MOFs, i.e., sph-MOF-1–4, exhibiting cuboctahedral building units, 3-c tritopic ligands, and 6-c hexatopic ligands or paired π-π interacting 3-c tritopic ligands, were rationally designed and synthesized based on the organization of 12-c hexanuclear carboxylate-based MBBs. Notably, the sph-MOF platform represents the first example of an underlying net that is a minimal edge-transitive net merged from two three-period edge-transitive nets. Furthermore, sph-MOF-3 represents the first example of a mixed-linker MOF that encompasses both 3-c triangular linkers and 6-c hexagonal linkers. This novel merge-net approach enabled the logical implementation of isoreticular chemistry, allowing the extension of 3-c and 6-c polytopic ligands in a concerted manner, taking into account the mathematically correlated dimensions of the two ligands, and provided the purposeful construction of a mixed-linker mesoporous MOF, namely, sph-MOF-4, with a cage dimension of 22 Å, confirmed by argon sorption studies.

[0337] experiment Materials and Basic Procedure The organic ligands used in this example, 5-(4H-1,2,4-triazol-4-yl)-isophthalic acid (H2TIA), 4,4',4"-((benzene-1,3,5-tricarbonyl)tris(azanediyl))tribenzoic acid (H3BTCB), benzo-tris-thiophenecarboxylic acid (H3BTTC), 4,4',4"-(benzene-1,3,5-triyl-tris(benzene-4,1-diyl))tribenzoic acid (H3BTPB), hexakis(4-(4-carboxyphenyl)phenyl)benzene (H6BHPB), and 4,4',4"-(benzene-1,3,5-triyl-tris(biphenyl-4,4'-diyl))tribenzoic acid (H3BTBPB), were prepared as follows. Unless otherwise noted, all other reagents were obtained from commercial sources and used without further purification.

[0338] 1 H NMR spectrum and 13C NMR spectra were recorded on Bruker Avance III 400, 500, and 600 MHz instruments. 1 The chemical shifts in the H NMR spectrum are 6 are reported in ppm (δ relative to TMS) using the DMSO residual peak at (δ = 2.50 ppm) as an internal standard. 13 For the C NMR spectrum the solvent peak was at 39.52 ppm, and for the solution in CDCl3 solvent the peaks were at 7.26 and 77.16 ppm, respectively.

[0339] Powder X-ray diffraction (PXRD) measurements were performed on a PANalytical X'Pert PRO diffractometer using Cu Kα (λ = 1.5418 Å) at 45 kV, 40 mA, and a scan rate of 1.0° min 2θ. -1 and a step size of 0.02°, and was performed at about room temperature.

[0340] High-resolution dynamic thermogravimetric analysis (TGA) was performed under continuous N2 flow and recorded on a TA Instruments high-resolution TGA Q500 thermogravimetric analyzer at a heating rate of 1 °C per minute.

[0341] Fourier transform infrared (FT-IR) spectrum (4000-600 cm -1 ) were recorded on a Thermo Scientific Nicolet 6700 instrument. Peak intensities were described as very strong (vs), strong (s), medium (m), weak (w), and broad (br) in each spectrum.

[0342] Low-pressure gas adsorption measurements were performed on a 3Flex surface characterization analyzer (Micromeritics) at relative pressures up to 1 atmosphere. Cryogenic temperatures were controlled using a liquid argon bath at 87 K, respectively. Bath temperature for CO adsorption measurements was controlled using an ethylene glycol / HO recirculating bath.

[0343] Single-crystal X-ray diffraction data were collected using a Bruker X8 PROSPECTOR APEX2 CCD diffractometer with CuKα (λ = 1.54178 Å). Indexing was performed using APEX2 (difference vector method). Data integration and reduction were performed using SaintPlus 6.01.2. Adsorption correction was performed by a multiscan method implemented in SADABS3. Space groups were determined using XPREP implemented in APEX2. The structure was solved using direct methods (SHELXS-97) and analyzed using SHELXS-97 (F) included in the WinGX v1.70.01 and OLEX2 program packages. 2 The full matrix least squares method was used for refinement.

[0344] Topological analysis was performed using TOPOS. Potential solvent accessible volumes were calculated using PLATON.

[0345] Ligand synthesis 1. Synthesis of 5-(4H-1,2,4-triazol-4-yl)-isophthalic acid (H2TIA). This compound was synthesized according to a modified version of a reported procedure. N,N-Dimethylformamide azine dihydrochloride (approximately 4.0 g, approximately 18.6 mmol) and 5-aminoisophthalic acid (approximately 3.38 g, approximately 18.6 mmol) were added to a 100 mL flask along with 1,2-dimethylbenzene (approximately 50 mL) and refluxed for approximately 16 hours. A white precipitate formed, which was filtered off and subsequently washed with ethanol and diethyl ether to give a sufficiently pure product (approximately 1.62 g, approximately 37.3%).

[0346] 2. Synthesis of 4,4',4''-((benzene-1,3,5-tricarbonyl)tris(azanediyl))tribenzoic acid (H3BTCB). This compound was synthesized according to a reported procedure. Under an Ar atmosphere, 4-aminobenzoic acid (approximately 4.94 g, approximately 36 mmol) was dissolved in approximately 100 mL of anhydrous acetone. Dry K2CO3 (approximately 4.54 g, approximately 33 mmol) was added to the solution. To the reaction mixture, a solution of 1,3,5-benzenetricarbonyl trichloride (approximately 2.5 g, approximately 9 mmol) in approximately 5 mL of anhydrous acetone was added dropwise. The suspension was refluxed for approximately 16 hours, resulting in the formation of a yellow solid. After filtration, the solid was washed with a large amount of acetone and 1 M aqueous HCl to give approximately 5.0 g of pure product (approximately 9.0 mmol, approximately 92%). 1 H NMR (500MHz, DMSO-d6): δ(ppm)=7.96-8.04(m,12H),8.79(s,3H),11.0(s,3H).

[0347] 3. Synthesis of benzo-tris-thiophenecarboxylic acid (H3BTTC) [ka] Preparation of 1: In a 100 mL flask, 2,4,6-tribromobenzene-1,3,5-tricarbaldehyde (g, mmol) was added to approximately 30 mL of trimethylamine. This was cooled to approximately 0°C under an Ar atmosphere. Ethyl mercaptoacetate (approximately 1.9 g, approximately 16 mmol) was added dropwise to the mixture, which was then refluxed for approximately 5 hours. After the reaction was cooled to approximately room temperature, methanol (approximately 10 mL) was added and cooled to approximately 0°C. The precipitate was filtered off and washed with cold methanol to give 1 (approximately 1.5 g, approximately 71%). 1 H NMR(δ, CDCl3):8.31(s,3H),4.46(q,6H,J=7Hz),1.46(t,9H,J=7Hz).

[0348] Preparation of H3BTTC: 1 (approximately 0.6 g, approximately 1.2 mmol) and sodium hydroxide (approximately 3.0 g, approximately 75 mmol) were added to a mixed solvent of ethanol / water (approximately 25 / 25 mL), which was refluxed for approximately 24 hours. The resulting solution was acidified to approximately pH 3, and the precipitate was filtered off and washed with water to give a pale yellow product (approximately 0.50 g, approximately 96%). 1H NMR(δ,DMSO-d6):8.43(s).

[0349] 4. Synthesis of 4,4',4''-(benzene-1,3,5-triyl-tris(benzene-4,1-diyl))tribenzoic acid (H3BTPB) This compound was synthesized according to reported procedures. [ka]

[0350] Preparation of 2: Under an Ar atmosphere, 4-methoxycarbonylphenylboronic acid (approximately 1.32 g, approximately 7.36 mmol), 4,4″-dibromo-5′-(4-bromophenyl)-1,1′:3′,1″-terphenyl (approximately 1.0 g, approximately 1.84 mmol), K2CO3 (approximately 2.3 g, approximately 16.56 mmol), and Pd(dppf)Cl2 (approximately 0.135 g, approximately 0.184 mmol) were added to a 150 mL round-bottom flask, followed by approximately 60 mL of dioxane and approximately 15 mL of water. The solution was heated at approximately 90 °C under inert gas for approximately 48 hours. Approximately 50 mL of HO was added, and the compound was extracted with CHCl2. The organic phase was dried, filtered through Celite, evaporated under reduced pressure, and the solid was washed with ether to give the sufficiently pure compound (1.05 g, 81%). 1 H NMR (400MHz, CDCl3): d=8.15(d,6H,J=8.0Hz),7.90(s,3H),7.74-7.85(m,18H),3.96(s,9H)

[0351] Preparation of HBTPB: To a suspension of 2 (about 1.05 g, about 1.49 mmol) in about 60 mL of THF / MeOH / HO (30 / 15 / 15 mL) was added NaOH (about 1.1 g, about 27.5 mmol), and the mixture was stirred at about 60° C. for about 48 h. The pH value was adjusted to about 3 using concentrated HCl. The compound was collected by filtration, washed with water, and dried under reduced pressure to give a white solid (0.94 g, 95%). 1 H NMR(400MHz,DMSO-d6):d=8.04-8.06(m,15H),7.89(d,12H,J=8Hz)

[0352] 5. Synthesis of hexakis(4-(4-carboxyphenyl)phenyl)benzene (H6BHPB) [ka] Preparation of 3: Under an Ar atmosphere, 4-methoxycarbonylphenylboronic acid (approximately 0.66 g, approximately 3.68 mmol), 4,4″-dibromo-3′,4′,5′,6′-tetrakis(4-bromophenyl)-1,1′:2′,1″-terphenyl (approximately 0.47 g, approximately 0.46 mmol), KCO (approximately 1.15 g, approximately 8.28 mmol), and Pd(dppf)Cl (approximately 0.068 g, approximately 0.092 mmol) were added to a 150 mL round-bottom flask, followed by approximately 60 mL of dioxane and approximately 15 mL of water. The solution was heated at approximately 90° C. under inert gas for approximately 48 hours. Approximately 50 mL of HO was added, and the compound was extracted with CHCl. The organic phase was dried, filtered through celite, evaporated under reduced pressure and the solid was washed with ether to give the sufficiently pure compound (approximately 524 mg, approximately 85%). 1 H NMR (500MHz, CDCl3):7.99(d,J=8Hz,12H),7.49(d,J=8Hz,12H),7.24(d,J=8Hz,12H),7.00(d,J=8Hz,12H),3.91(s,18H).

[0353] Preparation of H6BHPB: To a suspension of 3 (about 524 mg, about 0.391 mmol) in about 60 mL of THF / MeOH / HO (about 30 / 15 / 15 mL) was added NaOH (about 0.6 g, about 15 mmol), and the mixture was stirred at about 60° C. for about 48 h. The pH value was adjusted to about 3 using concentrated HCl. The compound was collected by filtration, washed with water, and dried under reduced pressure to give a white solid (about 493 mg, about 96%). 1 H NMR(500MHz,DMSO-d6):12.87(br.s,6H),7.13(d,J=8Hz,12H),7.32(d,J=8Hz,12H),7.53(d,J=8Hz,12H),7.81(d,J=8Hz,12H).

[0354] 6. Synthesis of 4,4',4''-(benzene-1,3,5-triyl-tris(biphenyl-4,4'-diyl))tribenzoic acid (H3BTBPB) [ka] Preparation of 4: Under an Ar atmosphere, (4-(ethoxycarbonyl)phenyl)boronic acid (approximately 1.32 g, approximately 7.36 mmol), 4,4'''-dibromo-5''-(4'-bromo-[1,1'-biphenyl]-4-yl)-1,1':4',1'':3'',1':4''',1''''-quinquphenyl (approximately 1.42 g, approximately 1.84 mmol), KCO (approximately 2.3 g, approximately 16.56 mmol), and Pd(dppf)Cl (approximately 0.135 g, approximately 0.184 mmol) were added to a 150 mL round-bottom flask, followed by approximately 60 mL of dioxane and approximately 15 mL of water. The solution was heated at approximately 90 °C under inert gas for approximately 48 hours. Approximately 50 mL of HO was added, and the compound was extracted with CHCl. The organic phase was dried, filtered through celite, evaporated under reduced pressure and the solid was washed with ether to give the sufficiently pure compound (ca. 1.59 g, ca. 88%). 1 H NMR (400MHz, CDCl3): d=8.13(d,6H,J=8.0Hz),7.92(s,3H),7.72-7.89(m,30H),4.42(d,6H,J=8.0Hz),1.43(s,9H)

[0355] Preparation of H3BTBPB: To a suspension of 4 (about 1.59 g, about 1.62 mmol) in about 60 mL of THF / MeOH / HO (about 30 / 15 / 15 mL) was added NaOH (about 0.6 g, about 15 mmol), and the mixture was stirred at about 60° C. for about 48 h. The pH value was adjusted to about 3 using concentrated HCl. The compound was collected by filtration, washed with water, and dried under reduced pressure to give a white solid (about 1.39 g, about 96%). 1 H NMR (400MHz,DMF-d7)δ13.36(s,3H),8.16(s,18H),7.97(s,21H). 13C NMR (400 MHz, DMF-d): δ 167.50, 144.44, 141.85, 140.14, 139.42, 38.84, 130.43, 130.33, 129.28, 128.18, 127.93, 127.62, 127.54, 127.03, 124.80. See Figures 4A-4C.

[0356] Synthesis of MOFs Synthesis of Tb-spn-MOF-1 (1). Tb(NO3)3·5HO (approximately 50 mg, approximately 0.115 mmol), H2TIA (approximately 13 mg, approximately 0.058 mmol), 2-FBA (approximately 300 mg, approximately 2.14 mmol), DMF (approximately 1.5 mL), and HO (approximately 0.25 mL) were combined in a 20 mL scintillation vial, sealed, and heated to approximately 115 °C for approximately 48 hours and cooled to approximately room temperature. Colorless polyhedral crystals were collected and washed with DMF. The as-synthesized material was found to be insoluble in HO and common organic solvents. FT-IR (4000-650 cm) analysis revealed that the as-synthesized material was insoluble in HO and common organic solvents. -1 ):3383(br),1650(s),1610(s),1484(m),1451(s),1384(vs),1299(w),1252(m),1217( m),1161(w),1095(s),1058(w),1010(w),858(w),796(w),760(s),734(m),710(m).Tb6C 65 N7H 55 O 29 Elemental analysis of F6: Measured (calculated): C%: 31.1 (31.6), H%: 1.99 (2.25), N%: 4.06 (3.98).

[0357] Synthesis of Tb-sph-MOF-1 (2). Tb(NO3)3·5HO (approximately 50 mg, approximately 0.115 mmol), H2TIA (approximately 13 mg, approximately 0.058 mmol), H3BTCB (approximately 33 mg, approximately 0.058 mmol), 2-FBA (approximately 300 mg, approximately 2.14 mmol), DMF (approximately 1.5 mL), and HO (approximately 0.25 mL) were combined in a 20 mL scintillation vial, sealed, and heated to approximately 115 °C for approximately 48 hours and cooled to approximately room temperature. Colorless polyhedral crystals were collected and washed with DMF. The as-synthesized material was found to be insoluble in HO and common organic solvents. FT-IR (4000-650 cm) indicated that the as-synthesized material was insoluble in HO and common organic solvents. -1 ):3485(br),2930(w),1651(vs),1495(m),1437(m),1386(s),1315(w),1253( m),1177(w),1093(s),1060(w),864(w),786(m),777(m),732(m),709(m).Tb6C 80 N 12 H 84 O 43 Elemental analysis measured values ​​(calculated values): C%: 31.8 (33.6), H%: 2.82 (2.97), N%: 5.96 (5.89).

[0358] Synthesis of Tb-sph-MOF-2 (3). Tb(NO3)3·5HO (approximately 8.3 mg, approximately 0.0191 mmol), H3BTTC (approximately 2.5 mg, approximately 0.0066 mmol), H3BTPB (approximately 5.0 mg, approximately 0.0075 mmol), 2-FBA (approximately 75.0 mg, approximately 0.535 mmol), DMF (approximately 1.5 mL), and HO (approximately 1.0 mL) were combined in a 20 mL scintillation vial, sealed, and heated to approximately 115 °C for approximately 48 hours and cooled to approximately room temperature. Pale yellow polyhedral crystals were collected and washed with DMF. The as-synthesized material was found to be insoluble in HO and common organic solvents. FT-IR (4000-650 cm) analysis revealed that the as-synthesized material was insoluble in HO and common organic solvents. -1 ):3399(br),2929(w),1652(s),1604(s),1517(m),1385(vs),1253(m),1094(m),1004(w),833(w),786(s),735(m),702(m).Tb6C 124N2H 106 O 43 Elemental analysis of S6: C%: 41.1 (43.1), H%: 3.24 (3.09), N%: 0.98 (0.81).

[0359] Synthesis of Tb-sph-MOF-3 (4). Tb(NO3)3·5HO (approximately 8.3 mg, approximately 0.0191 mmol), H3BTTC (approximately 2.5 mg, approximately 0.0066 mmol), H6BHPB (approximately 5.0 mg, approximately 0.0039 mmol), 2-FBA (approximately 75.0 mg, approximately 0.535 mmol), DMF (approximately 1.5 mL), HO (approximately 1.5 mL), and 3.5 M HNO3 (approximately 0.2 mL) were combined in a 20 mL scintillation vial, sealed, heated to approximately 115 °C for approximately 48 hours, and cooled to approximately room temperature. Pale yellow polyhedral crystals were collected and washed with DMF. The as-synthesized material was found to be insoluble in HO and common organic solvents. FT-IR (4000-650 cm) analysis revealed that the as-synthesized material was insoluble in HO and common organic solvents. -1 ):3209(br),1651(m),1603(m),1557(m),1392(vs),1178(w),1099(m),1005(w),838(w),776(s),736(m),703(m).Tb6C 118 N2H 98 O 42 Elemental analysis of S6: C%: 39.8 (42.1), H%: 2.91 (2.94), N%: 0.74 (0.83).

[0360] Synthesis of Tb-sph-MOF-4 (5). Tb(NO3)3·5HO (approximately 7.5 mg, approximately 0.0173 mmol), H3TATB (approximately 2.5 mg, approximately 0.0057 mmol), H3BTBPB (approximately 5.0 mg, approximately 0.0075 mmol), 2-FBA (approximately 75.0 mg, approximately 0.535 mmol), and DMF (approximately 1.5 mL) were combined in a 20 mL scintillation vial, sealed, and heated to approximately 115 °C for approximately 48 hours and cooled to approximately room temperature. Pale yellow polyhedral crystals were collected and washed with DMF. The as-synthesized material was found to be insoluble in HO and common organic solvents. FT-IR (4000-650 cm) analysis revealed that the as-synthesized material was insoluble in HO and common organic solvents. -1):3027(br),1651(w),1600(m),1507(s),1398(vs),1355(vs),1101(w),1017(w),1003(w),816(s),775(vs),700(s).Tb6C 178 N8H 218 O 54 Elemental analysis measured values ​​(calculated values): C%: 46.7 (49.8), H%: 4.97 (5.13), N%: 2.69 (2.61).

[0361] Low-pressure gas adsorption measurements Low-pressure gas adsorption tests of sph-MOFs were carried out at relative pressures up to 1 atmosphere on a fully automated micropore gas analyzer, the 3Flex analyzer (Micromeritics Instruments). The bath temperature for CO adsorption measurements was controlled using a recirculating bath containing an ethylene glycol / HO mixture. Cryogenic temperatures were controlled using liquid nitrogen and argon baths at 77 K and 87 K, respectively. The apparent surface areas were determined from nitrogen adsorption isotherms collected at 77 K and argon adsorption isotherms collected at 87 K by applying the Brunauer-Emmett-Teller (BET) and Langmuir models.

[0362] Unless otherwise stated, CO2 isotherms measured at 253, 273, 288, and 298 K were used to estimate the determination of the isosteric heat of adsorption (Qst) of CO2 by applying the Clausius-Clapeyron equation.

[0363] Homogeneous microcrystalline samples of sph-MOFs were activated by washing the as-synthesized crystals with 3 × 20 mL of DMF, followed by solvent exchange for 3 days into DCM for Tb-sph-MOF-1 and into acetone for Tb-sph-MOF-2, 3, and 4. During this period, the solution was exchanged several times daily. In a typical experiment, approximately 50 mg of each activated sample was transferred to a 12 mm glass sample cell, first evacuated to approximately room temperature using a turbomolecular vacuum pump, and then gradually heated (at a rate of approximately 1 °C / min) to approximately 160 °C for Tb-sph-MOF-1, approximately 120 °C for Tb-sph-MOF-2 and Tb-sph-MOF-3, and approximately 105 °C for Tb-sph-MOF-4, and held there for approximately 16 h before being cooled to approximately room temperature.

[0364] High-pressure gas adsorption measurements Adsorption equilibrium measurements of high-purity gases were carried out using a Rubotherm gravimetric density analyzer (Bochum, Germany) (Scheme S1a-d), which primarily consists of a magnetic suspension balance (MSB) and a network of valves, mass flow meters, and temperature and pressure sensors. The MSB overcomes the drawbacks of other commercially available gravimetric analyzers by isolating a highly sensitive microbalance from the sample and measurement atmosphere, allowing adsorption measurements to be performed over a wide pressure range (i.e., from about 0 to about 20 MPa). The adsorption temperature may also be controlled within a range of about 77 K to about 423 K. In a typical adsorption experiment, the adsorbent was accurately weighed and placed in a basket suspended by a permanent magnet via an electromagnet. The cell containing the basket was then closed and vacuum or high pressure was applied. Gravimetric measurements allowed direct measurement of the gas adsorption loss (Ω). To determine the excess and absolute adsorption amounts using Equations 1 and 2, correction for buoyancy effects was required, where V adsorbent and V ss and V adorbed phase are the amount of adsorbent, the volume of the flotation system, and the amount of adsorbed phase, respectively. Equation 1:

number

number

[0365] Buoyancy effects arising from the adsorbed phase can be taken into account through correlation with the pore volume or theoretical density of the sample.

[0366] Results and Discussion Synthesis of Tb-spn-MOF-1. Various polycarboxylate ligands were investigated with the aim of constructing a prototype MOF suitable for the rational design of mixed-linker MOFs. During screening of various ligands, an spn-MOF based on terbium and 5-(4H-1,2,4-triazol-4-yl)-isophthalate (TIA) was obtained, which provided an opportunity for the design of mixed-linker MOFs based on spn-nets.

[0367] Colorless polyhedral single crystals of Tb-spn-MOF-1 were obtained by the solvothermal reaction of Tb(NO3)3·5H2O and H2TIA in N,N-dimethylformamide (DMF) / water solution in the presence of 2-fluorobenzoic acid (2-FBA) at approximately 115 °C for approximately 48 h. Single-crystal X-ray diffraction studies revealed that Tb-spn-MOF-1 has the formula [Tb6(μ3-OH)8(TIA)2(2-FBA)6(H2O)6]·(solvent) in the space group Fd-3m. x The formula was also confirmed by thermogravimetric analysis (TGA) and elemental analysis. The phase purity of the crystalline material was confirmed by the similarity between the calculated powder X-ray diffraction (PXRD) pattern derived from the associated SCXRD data and the experimental PXRD pattern of the as-synthesized material (Figures 5A-5B).

[0368] Tb-spn-MOF-1 was the first spn-MOF constructed with a less symmetric TIA linker containing two carboxylate groups and one triazole group. In the structure of Tb-spn-MOF-1, each inorganic MBB was connected to six TIA linkers, each of which coordinated three inorganic MBBs. Furthermore, each inorganic MBB was also coordinated to six 2-fluorobenzoic acid terminal ligands for charge balancing.

[0369] Structural and topological analyses revealed that a hexanuclear terbium cluster, i.e., 6-c MBB, was linked to the ligand, TIA, i.e., 3-c MBB, to form a three-period MOF with a basic (3,6)-c spn network. The carbon atoms at positions 1, 3, and 5 of the benzene ring of TIA served as extension points for the 3-c node. The carbon atom of the coordinated carboxylate moiety and the nitrogen atom at position 1 of the coordinated triazole moiety served as extension points for the 6-c node.

[0370] The overall framework of Tb-spn-MOF-1 contained two types of cages. The larger cage had a diameter of approximately 19.5 Å, while the smaller cage had an internal pore diameter of approximately 5.4 Å and was separated by four TIA linkers. Using PLATON software, the corresponding solvent-accessible volume of Tb-spn-MOF-1 was estimated to be approximately 78% by summing voxels located more than 1.2 Å away from the framework.

[0371] Design of a mixed-linker sph-MOF platform based on merge nets. Analysis of the crystal structure of Tb-spn-MOF-1 revealed that Tb-spn-MOF-1 possesses the appropriate structural features to accept a second linker using conventional installation methodologies. More importantly, careful analysis of the resulting MOFs showed that the partial framework based on only one second linker could also be described as a three-periodic framework with an underlying edge-transitive HxG net. In other words, the underlying net of the resulting mixed-linker MOF could be decomposed into two distinct nets, namely, an spn net and an HxG net, by considering that the cuboctahedral building unit can be decomposed into antitriangular prism and hexagonal building units. Specifically, the underlying net of the target framework was merged from both parent nets (Figures 6A-6F, Figure 7). Therefore, mixed-linker MOFs of variable size can be directly designed based on the underlying merge net by utilizing knowledge of reticulate structure chemistry.

[0372] Topological analysis revealed that the perceived mixed-linker MOF adopted a new underlying net, herein referred to as sph (Figures 8-9). The rationalization of this merging process was mathematically demonstrated using geometric system relationships that take into account the inherent geometric features of the sph net. Indeed, analysis / decomposition of the resulting sph net showed a clear correlation between the relevant edge dimensions / lengths of the spn and hxg nets, set as x and y, respectively (Figure 10A). Precisely, the relationship between x and y is shown in Figure 11:

number

[0373] From equation (1), the ratio of the side dimensions between the spn net and the hxg net was constant, which is an inherent property of the sph net. That is, the spn net and the hxg net have a constant side ratio, i.e., the specified ratio constant C Rcan be merged into the sph net only if

number

[0374] Alternatively, the ratio constant C R The approximate value of can also be calculated from the coordinates of the nodes of the sph net deposited in the Reticular Chemistry Structural Resource (RCSR) database. The coordinates of the 3-c node are (a1, b1, c1), the coordinates of the 6-c node are (a2, b2, c2), and the coordinates of the 12-c node are (a s ,b s ,c s ), and then

number

[0375] ratio constant C R was clearly an important factor for determining the dimensions of the linkers in the mixed-linker sph-MOF. However, it was worth considering that the size ratio between the sides of the two parent nets was equal to the size ratio of the sum of the ligands and half of the MBB, rather than the size ratio of the ligands alone (Figure 10B). The merge net equation for the sph net is illustrated by the following equation (4):

number

number

number

number

[0376] Using equation (5), material designers can determine the appropriate size of the complementary linkers required for the design of their desired mixed-linker sph-MOF. Furthermore, equation (5) also determines the conditions for applying isoreticular chemistry within the mixed-linker system, as exemplified here by the design of four new compounds, namely, sph-MOF-1, 2, 3, and 4 (Figure 10D). By identifying the sizes of available 3-c or 6-c linkers, four ligand pairs based on three pairs of different sizes were predicted to fit precisely into the sph-MOF, thereby enabling the purposeful synthesis of the corresponding mixed-linker sph-MOFs (Figures 12A-12C).

[0377] Design and synthesis of sph-MOF-1. Based on previous results, TIA was selected as the first linker of the spn moiety for the synthesis of sph-MOF-1. Because the linker is asymmetric, the size of the TIA linker could be calculated as 3.5 Å based on a weighted average value. The corresponding size of the hxg linker could be calculated as 9.5 Å by the merge net equation, which was compatible with the acylamide-functionalized group-based linker (Figure 12B).

[0378] However, attempts to obtain the corresponding hexacarboxylate linker were unsuccessful due to synthetic difficulties encountered in inserting six acylamide functional moieties into a single benzene ring. Instead, the tricarboxylate linker 4,4',4''-((benzene-1,3,5-tricarbonyl)tris(azanediyl))tribenzoate (BTCB) was synthesized and used, as it could potentially function as a 6-c building block by filling two BTCB linkers (Figure 13).

[0379] As expected, colorless polyhedral single crystals of Tb-sph-MOF-1 were obtained by the solvothermal reaction of Tb(NO3)3·5H2O, H2TIA, and H3BTCB in DMF / water solution in the presence of 2-FBA at approximately 115 °C for approximately 48 h. Single-crystal X-ray diffraction studies revealed that sph-MOF-1 is a compound in the space group Fd-3m with the formula [Tb6(μ3-OH)8(TIA)2(BTCB)2(H2O)6]·(solvent). x The phase purity of the bulk crystalline material of sph-MOF-1 was confirmed based on the similarity between the calculated PXRD pattern and the as-synthesized PXRD pattern (Figures 14A-14B). The presence of the linkers TIA and BTCB was confirmed in the HCl-digested sample. 1 This was also confirmed by 1 H NMR, which showed that the molar ratio between the linkers was approximately 1:1 (Figure 15).

[0380] In the structure of sph-MOF-1, each Tb6 cluster was linked to 12 linkers in two groups. Six TIA linkers occupied antitriangular prisms in the cuboctahedron, and six BTCB linkers occupied hexagonal positions in the planar structure (Figure 13). Structural and topological analysis revealed that two tricarboxylate-linked BTCB moieties packed together to function as a 6-c MBB. The hexanuclear terbium cluster, i.e., a 12-c MBB, a TIA ligand, i.e., a 3-c MBB, and a pair of BTCB moieties, i.e., a 6-c MBB, were linked to form a three-period (3,6,12)-c MOF with an unprecedented sph-based topology. The carbon atoms at the 1, 3, and 5 positions of the benzene ring of the TIA served as the extension points of the 3-c node. The carbon atoms at the 1, 3, and 5 positions of the central benzene ring of the double BTCB moiety served as the extension points of the 6-c node. The carbon atom of the coordinated carboxylate moiety and the nitrogen atom at position 1 of the coordinated triazole moiety served as the extension points of the 12-c node. Further topological analysis of sph-MOF-1 revealed that the underlying (3,6,12)-c sph net was an assembly of two edge-transitive nets, the (3,6)-c spn net and the 6-c hxg net.

[0381] The overall framework of sph-MOF-1 contained two types of open cages. The larger truncated tetrahedral cages, approximately 6.5 Å in diameter, were separated by four pairs of BTCB and four TIA linkers, whereas the smaller tetrahedral cages, approximately 2.5 Å in diameter, were inaccessible to nitrogen or argon and separated by four TIA linkers (Figure 16). Using PLATON software, the corresponding solvent-accessible volume of sph-MOF-1 was estimated to be approximately 52% by summing voxels located more than 1.2 Å away from the framework.

[0382] The persistent porosity of sph-MOF-1 was investigated by argon adsorption experiments performed at approximately 87 K, which showed a fully reversible type I isotherm characteristic of microporous materials (Figure 17; Figures 18-20). The Brunauer-Emmett-Teller (BET) apparent surface area and Langmuir surface area were approximately 1020 m, respectively.2 ·g -1 and approximately 1,120 m 2 ·g -1 The experimental total pore volume was estimated to be about 0.42 cm 3 ·g -1 This corresponds to a theoretical pore volume of approximately 0.44 cm based on the relevant crystal structure. 3 ·g -1 It matched.

[0383] Design and Synthesis of sph-MOF-2. The successful design of sph-MOF-1 demonstrated the validity of the merge-net equation, which defines the mathematical correlation between two linkers, and encouraged the exploration of isoreticular sph-MOFs by extending the linkers to provide relatively larger cages. According to the merge-net equation for sph-MOFs, if the size of both linkers increases linearly by a factor of 1.73, the resulting linker pair is still suitable for the synthesis of sph-MOFs. Specifically, if the corresponding hxg linker increases by 1.73 Å, the linker participating in the spn network can be expanded by 1.0 Å. Indeed, the size of the linker benzo-tris-thiophenecarboxylate (BTTC) (5.1 Å) was found to be compatible with the size of the linker 4,4',4''-(benzene-1,3,5-triyl-tris(benzene-4,1-diyl))tribenzoate (BTPB) (12.3 Å) (Figures 12A-12C).

[0384] Indeed, pale yellow polyhedral single crystals of sph-MOF-2 were obtained by the solvothermal reaction of Tb(NO3)3·5H2O, H3BTTC, and H3BTPB in DMF / water solution in the presence of 2-FBA at approximately 115 °C for approximately 48 h. Single-crystal X-ray diffraction studies revealed that sph-MOF-2 is a crystalline solid in the space group Fd-3m with the formula [(CH3)2NH2]2[Tb6(μ3-OH)8(BTTC)2(BTPB)2(H2O)6]·(solvent). x The presence of the linkers BTTC and BTPB was evident in the HCl digested sample. 1This was confirmed by H NMR (Figure 21), which showed that the molar ratio between the linkers was approximately 1:1. The experimental PXRD was consistent with the calculated PXRD pattern based on the crystal structure, confirming the phase purity of sph-MOF-2 (Figures 22A-22B).

[0385] In the structure of sph-MOF-2, each 12-c Tb6 cluster was connected to two groups of 12 linkers. Six 3-c BTTC linkers occupied antitrigonal positions in the cuboctahedron, and six 3-c BTPB linkers occupied planar hexagonal positions (Figures 6A, 23A–23D). The paired BTPB moieties acted as 6-c MBBs, forming a three-periodic MOF with a basic (3,6,12)-c sph net, which was isorectic to sph-MOF-1. The carbon atoms adjacent to the sulfur atom of BTTC served as extension points for the 3-c node. The carbon atoms at the 1, 3, and 5 positions of the central benzene ring of the double BTPB moiety served as extension points for the 6-c node. In the case of the 12-c node, unlike the node of sph-MOF-1, which had extension points from both the carboxylate and triazole moieties, only the carbon atom of the coordinated carboxylate served as the extension point in sph-MOF-2.

[0386] As a result of the linker extension, both open cages of sph-MOF-2 were enlarged. The larger truncated tetrahedral cage, with a diameter of approximately 12.5 Å, was separated by four pairs of BTPB and four BTTC linkers. The smaller tetrahedral cage, with a diameter of approximately 6.5 Å, was surrounded by four BTTC linkers (Figure 16). Using PLATON software, the corresponding solvent-accessible volume of sph-MOF-2 was estimated to be approximately 61% by summing voxels farther away from the backbone than 1.2 Å.

[0387] The persistent porosity of sph-MOF-2 was investigated by argon adsorption experiments at 87 K, which showed a fully reversible type I isotherm characteristic of microporous materials (Figure 34; Figures 24-26). The apparent BET and Langmuir surface areas were approximately 1820 m, respectively. 2 ·g-1 and approximately 2000 m 2 ·g -1 The experimental total pore volume was estimated to be about 0.72 cm 3 ·g -1 This gives a theoretical pore volume of approximately 0.75 cm based on the relevant crystal structure. 3 ·g -1 It matched.

[0388] Design and synthesis of sph-MOF-3. The calculated size of the hxg linker (12.3 Å) provided an opportunity to synthesize an sph-MOF with a 6-c ligand. Instead of H3BTPB in sph-MOF-2, the hexacarboxylate ligand hexakis(4-(4-carboxy-phenyl)phenyl)benzoic acid (H6BHPB) was designed and synthesized. The BHPB linker remained the same size as BTCB and was compatible with BTTC (5.1 Å) in the merge net equation.

[0389] Pale yellow polyhedral single crystals of sph-MOF-3 were obtained by the solvothermal reaction of Tb(NO3)3·5H2O with H3BTTC and H6BHPB in a DMF / water solution in the presence of 2-FBA at approximately 115 °C for approximately 48 h. Single crystal X-ray diffraction studies revealed that sph-MOF-3 has the formula [(CH3)2NH2]2[Tb6(μ3-OH)8(BTTC)2(BHPB)(H2O)6]·(solvent) in the space group Fd-3m. x The presence of the linkers BTTC and BHPB was evident in the HCl digested sample. 1 This was confirmed by H NMR (Figure 27), which showed that the molar ratio between the linkers was approximately 2: 1. The phase purity of the bulk crystalline material of sph-MOF-3 was also confirmed based on the similarity between the calculated and as-synthesized PXRD patterns (Figures 28A-28B).

[0390] Topological analysis of sph-MOF-3 revealed that a hexanuclear terbium cluster, i.e., 12-cMBB, is linked to the ligand BTTC, i.e., 3-cMBB, and the ligand BHPB, i.e., 6-cMBB, to form a three-period MOF with a basic (3,6,12)-c sph net, which is isorectic to sph-MOF-1 and sph-MOF-2. The carbon atoms adjacent to the sulfur atom of BTTC could be considered as extension points of the 3-c triangular node. The carbon atoms at positions 1, 2, 3, 4, 5, and 6 of the central benzene ring of the double BTPB moiety could be considered as extension points of the 6-c hexagonal node. The carbon atoms from the coordinated carboxylate could be considered as extension points of the 12-c cuboctahedral node in sph-MOF-3. Compared with sph-MOF-2, the 6-c BHPB linker exhibits smaller cluster rotations and a more ordered structure in sph-MOF-3, which can be clearly seen from the horizontal views of the linker (Figures 23A–23D).

[0391] The overall framework of sph-MOF-3 also contained two types of open cages. A large truncated tetrahedral cage was separated by four BHPB linkers and four BTTC linkers. The larger cage had a diameter of approximately 13 Å, slightly larger than sph-MOF-2 because the BHPB linker occupies less space than the two BTCB linkers (Figures 23B and 23D). The smaller tetrahedral cage, with a diameter of approximately 6.5 Å, was surrounded by four BTTC linkers (Figure 16). Using PLATON software, the corresponding solvent-accessible volume of sph-MOF-3 was estimated to be approximately 63% by summing voxels farther away from the framework than 1.2 Å.

[0392] The persistent porosity of sph-MOF-3 was investigated by argon adsorption experiments at approximately 87 K, which showed a fully reversible type I isotherm characteristic of microporous materials (Figure 17; Figures 29-31). The apparent BET and Langmuir surface areas were approximately 1930 m, respectively. 2 g -1 and approximately 2250m 2 ·g -1The experimental total pore volume was estimated to be about 0.78 cm 3 g -1 This gives a theoretical pore volume of approximately 0.80 cm based on the relevant crystal structure. 3 g -1 It matched.

[0393] Design and synthesis of mesoporous sph-MOF-4. To test the validity of the merge-net equation in designing mesoporous MOFs, the size of both linkers was further expanded. The linkers 4,4',4''-s-triazine-2,4,6-triyl-tribenzoate (TATB), with a size of approximately 7.4 Å, and 4,4',4''-(benzene-1,3,5-triyl-tris(biphenyl-4,4'-diyl))tribenzoate (BTBPB), with a size of approximately 16.3 Å, were found to fit the equation. It is worth mentioning that a search of the Cambridge Structural Database (CSD) revealed that no structures using the BTBPB linker had been previously reported, highlighting the difficulty of obtaining MOFs using such elongated tricarboxylate linkers.

[0394] Pale yellow polyhedral single crystals of sph-MOF-4 were obtained by the solvothermal reaction of Tb(NO3)3·5H2O, H3TATB, and H3BTBPB in DMF / water solution in the presence of 2-FBA at approximately 115 °C for approximately 48 h. Single crystal X-ray diffraction studies revealed that sph-MOF-4 has the formula [(CH3)2NH2]2[Tb6(μ3-OH)8(TATB)2(BTBPB)2(H2O)6]·(solv) in the space group Fd-3m. x The presence of the linkers TATB and BTBPB was evident in the HCl digested sample. 1 This was confirmed by H NMR (Figure 32), which showed that the molar ratio between the linkers was approximately 1:1. The phase purity of the bulk crystalline material of sph-MOF-4 was confirmed by the similarity between the calculated and as-synthesized PXRD patterns (Figures 33A-33B).

[0395] Topological analysis of sph-MOF-4 revealed that a 12-c hexanuclear terbium cluster is linked to a 3-c TATB ligand and a pair of 6-c BTBPB moieties to form a three-periodic MOF with a basic (3,6,12)-c sph-net (Figures 6A-6F, 34). The central triazine carbon atom in TATB can be considered as the extension point of the 3-c node. The carbon atoms at the 1, 3, and 5 positions of the central benzene ring of the double BTBPB moiety can be considered as the extension point of the 6-c node. The coordinated carboxylate carbon atom can be represented as the extension point of the 12-c node. The successful synthesis of the isoreticular structure sph-MOF-4 demonstrated the validity of mathematical calculations even when the linker size is significantly enlarged.

[0396] Linker expansion provided both microporous and mesoporous cages in the structure of sph-MOF-4. The larger truncated tetrahedral cage, approximately 22 Å in diameter, was separated by four pairs of BTBPB linkers and four TATB linkers, while the smaller tetrahedral cage, approximately 9.5 Å in diameter, was surrounded by four TATB linkers (Figure 16). Using PLATON software, the corresponding solvent-accessible volume of sph-MOF-4 was estimated to be approximately 75% by summing voxels farther away from the framework than 1.2 Å.

[0397] The persistent porosity of sph-MOF-4 was investigated by argon adsorption experiments at approximately 87 K (Figure 34; Figures 35-37). The increase in the argon adsorption isotherm at p / p = 0.25 corresponded to approximately 2.2 nm mesoporous cages in sph-MOF-4.

[0398] The apparent BET surface area is approximately 2170 m 2 ·g -1 The experimental total pore volume was estimated to be about 1.20 cm 3 ·g -1 This gives a theoretical pore volume of approximately 1.28 cm based on the relevant crystal structure. 3 ·g -1 It matched.

[0399] Gas Sorption Study of sph-MOF-1. In light of the large library of known / existing adsorption data for MOFs and their relevance to important applications such as CO2 separation and natural gas upgrading, the single gas adsorption performance of Tb-sph-MOF-1 in this mixed linker system was evaluated, as well as the relationship of its adsorption properties to MOF benchmarks. The isosteric heat of adsorption (Qst) calculated using CO2 adsorption isotherms at approximately 258, 273, 288, and 298 K (Figures 38-39) showed a decreasing trend. The Qst value at low loadings was approximately 29.4 kJ / mol. -1 and further plateaued at values ​​typical of pore filling, indicating that the acylamide functional groups in Tb-sph-MOF-1 produce the same energetic effects on pore filling as reported in other acylamide-based MOFs. Furthermore, the adsorption of light hydrocarbons (C) compared to CO2, CH4, and N2 over a wide range of pressures was significantly enhanced. n H 2n+2 ;i.e., C2H6, C3H8, n-C4H 10 , and iso-C4H 10 ) (Figures 40-42) showed that the mixed-ligand sph MOF platform with the most closed pore system exhibited the typical behavior of enhanced affinity as a function, or increased polarizability, of the probe molecule. This, similar to the rare-earth fcu MOFs and unlike the typical 13X zeolite, indicates that the C n H 2n+2 This is exemplified by CO2, which has a lower adsorption affinity to the Tb-sph-MOF-1 framework than CO2. The adsorption results reported above demonstrate that further tuning and exploring the mixed-ligand sph platform may lead to powerful separation, preservation, and detection agents.

[0400] In summary, we describe a new systematic design principle in network chemistry, termed the merge-net approach, which asserts the suitability of minimal edge-transitive nets merged from edge-transitive nets as an ideal blueprint for the design of complex mixed-linker MOFs. The fundamental equation, the merge-net equation, reveals the laws of net merging and solves the long-standing problem of reliably designing equi-netted mixed-linker MOFs.

[0401] In this example, we report the design and synthesis of a series of highly symmetric isoreticular RE mixed-linker MOFs, i.e., sph-MOF-1–4, based on the assembly of 12-c hexanuclear carboxylate-based MBBs, exhibiting cuboctahedral building units, 3-c tritopic and 6-c hexatopic ligands, or paired π-π interacting 3-c tritopic ligands. The sph-MOFs represent the first examples of MOFs in which the underlying net is merged from two three-period edge-transition nets, i.e., a (3,6)-c spn net and a 6-c hxg net.

[0402] sph-MOF-3 represented the first example of a mixed-linker MOF based on the assembly of triangular and hexagonal linkers. By concertedly expanding both linkers, we constructed a mesoporous mixed-linker MOF, namely, sph-MOF-4, encompassing a cage with a diameter of approximately 22 Å.

[0403] The remarkable and unique control available to complex mixed-linker MOFs using mergenets paves the way for the development of highly tailored MOFs with distinct encoded functions. [Table 1] [Table 2]

[0404] Example 2 Enumeration of 140 merge nets Searching for shared signature nets of parent nets can be an important factor for the enumeration of merge nets. However, because there are two types of edge-transitive nets: transitive

[11] nets and transitive

[21] nets, this process had to be differentiated into different cases. Some transitive

[11] nets were converted to

[21] nets by edge transformation, denoted as "e" (Method 1 in Figure 43), or binary transformation, denoted as "b" (Method 2 in Figure 43). Transitive

[21] nets contain two types of nodes, and signature nets were recognized by directly connecting each group of nodes, denoted as "d" (Method 3 in Figure 43).

[0405] For edge transformation of edge-transitive nets

[11] , a group of 2-coordinate nodes was added to the midpoints of the edges. If the added midpoints of the parent net could be connected to form another edge-transitive net, the resulting net was the signature net of that parent net. For example, a 6-c PCu net was transformed into a (2,6)-c PCu net by adding 2-c nodes to the midpoints of the edges. By deleting all edges in the PCu net and reconnecting the newly added nodes, the resulting net was an 8-c REO net.

[0406] In the binary transformation of edge-transitive nets

[11] , the nodes of the parent net were evenly separated into two groups of nodes, and the edge-transitive net

[11] was converted into a binary version

[21] . The two groups of nodes were reconnected into two identical nets, and the resulting net was also the signature net of its parent net. For example, a 4-c nbo net was converted into a binary (4,4)-c nbo-b net. By deleting all edges in the nbo-b net and reconnecting nodes of the same type with the shortest distance, each resulting net was an 8-c reo net.

[0407] For transitive

[21] nets, the signature nets directly contained two types of nodes. The signature nets were obtained by connecting nodes of the same type in the parent nets. For example, the (4,12)-c FTW net contained two types of nodes. By deleting edges in the FTW net and reconnecting nodes of the same type, the resulting two nets were the REO and PCU nets, respectively.

[0408] The nodes of the parent nets pcu, nbo, and ftw contained the entire group of reo nodes. Specifically, the reo node was a shared node among these parent nets, and the reo net was the signature net of all these parent nets. In fact, two of these parent nets merged to form new merged nets: urk as a (pcu, nbo)-merge net, xbo as a (pcu, ftw)-merge net, and xbn as a (nbo, ftw)-merge net (Figure 43).

[0409] Node relationship map of edge-transitive nets The selected nets were restricted by two constraints. First, nets were constrained to have a perfect symmetric embedding, where the distance between unconnected vertices was equal to or greater than the length of an edge. Without that constraint, the number of 3-periodic edge-transitive nets would be infinite. Second, nets containing multiple edges with the same end node were excluded. Currently, there are only two nets in the RCSR database with transitivity

[21] that contain multiple edges: cys and nts. Taking these two constraints into account, a total of 53 edge-transitive nets (20 nets with transitivity

[11] and 33 nets with transitivity

[21] ) were used as parent nets for the enumerated merge nets.

[0410] We systematically searched for signature nets of edge-transition nets by adding midpoints to all edge-transition nets with transitivity

[11] . In the node relationship map, these two nets are connected by a green arrow starting from the signature net and pointing to the parent net. A signature net itself can also serve as a parent net, and connecting midpoints will obtain another signature net until no three-period nets are obtained by connecting midpoints. The longest chain was the chain starting from the dia net. By connecting midpoints, we sequentially obtained the crs, nbo, sod, and rhr nets. All the resulting green arrows can be seen in Figure 1.

[0411] The systematic search for signature nets by binary transformation using Method 2 was established by checking all possible binary versions of edge-transitive nets. It is worth mentioning that not all nets have binary versions. The principle that a net can have a binary version is that the vertex numbers of all rings must be even. Of these 20 nets with transitivity

[11] , 14 nets meet the criterion. The list of binary nets and their corresponding signature nets is listed in Table S. In the node relationship map, signature nets are connected by purple arrows pointing to their parent nets.

[0412] The systematic search for signature nets in Method 3 was established by reconnecting all nodes of the same type in 33 transitive

[21] nets. In the node relationship map, signature nets are connected by red arrows pointing to their parent nets. Typically, a parent net can have two signature nets in Method 3. Some signature nets were not three-cycle and were omitted from the map.

[0413] Systematic Enumeration of Merge Nets The first three types of merge nets are merges between an edge-transitive net (transitive

[21] or

[11] ) and its signature net (transitive

[11] ), including those between an edge-transitive net and a signature net (es), between a binary-transitive net and a signature net (bs), and between a direct parent net

[21] and a signature net (ds). The nodes of the signature net were a subset of the total nodes of the parent net. For this reason, the merge process did not increase the number of nodes, and the resulting merge net contained two types of nodes instead of three. The number of edges was increased by one from the signature net. Therefore, in this case, the transitivity of the merge net becomes

[22] .

[0414] In the ES type merge process, both parent nets have transitivity

[11] . The configuration of the parent nets is defined as v e and the signature net configuration is set as v s In the merge net, the nodes from the parent net are not changed. e The nodes from the signature net were merged with the 2-c node added at the midpoint of the parent net, resulting in a configuration of v s +2. Therefore, the configuration of the merge net is (v e ,v s +2). A total of 11 es-type merge nets were found in this study.

[0415] Also, in the bs-type merge process, both parent nets have transitivity

[11] . The configuration is v for the parent net. b In the case of signature net, v s The parent net is transformed into a binary net with transitivity

[21] , and the configuration of both nodes is v b One group of nodes merges with a node from the signature net, and the node is placed in the configuration "v b +v s ". Therefore, the configuration of the merge net is (v b ,v b +v s) A total of 10 bs-type merge nets were found.

[0416] In a ds-type merge process, parent nets have transitivity

[21] . Their signature nets have transitivity

[11] . The configuration of parent nets is defined as v d and v dm and the signature net configuration is set as v s If you set it as , then in the merge net, v d The node is unchanged, and v dm The node is v s The merge node is merged with the node. The configuration of the merge node is (v dm +v s ) The configuration of the merge net is (v d ,v dm +v s ) A total of 39 ds-type merge nets were found.

[0417] The second three types of merged nets were merges between two parent nets achieved by the same analysis method, including the merge of two edge transformation nets (ee), two binary nets (bb), and two transitivity

[21] nets (dd) (Table 1). In this approach, the merge process produced three types of nodes: nodes from only the first parent net, nodes from only the second parent net, and shared nodes. Edges from both parent nets were preserved. Thus, the transitivity of the final merged net was

[32] .

[0418] In an ee-type merge process, both parent nets have transitivity

[11] . The configuration of the parent nets is v e1 and v e2 The edge transformation added 2-c nodes at the midpoints of the edges. These added nodes acted as shared nodes. Thus, nodes from both parent nets were connected to v e1 and v e2 Interestingly, since both added nodes were 2-c, the merge node configuration became a 4-c constant. Finally, the merge net configuration became (vg1 ,v g2 ,4). Furthermore, because both 2-c nodes are linearly connected at a 180° angle, the 4-c node is indeed square, but not tetrahedral. This unique property qualifies the ee-type as a merge node, being the only suitable target for the design of mixed-linker MOFs with the 4c ​​paddlewheel building block, which is one of the most common MBBs but is challenging for mixed-linker design. Only three ee-type merge nets were found.

[0419] In a bb-type merge process, both parent nets also have transitivity

[11] . The configuration of the parent nets is v b1 and v b2 The purple arrows transform the parent net into a binary net with transitivity

[21] . The configuration of the transformed net is (v b1 ,v b1 ) and (v b2 ,v b2 ) in the merge net. p1 Node and one group v p2 The nodes merge and the configuration (v b1 +v b2 ), while the other nodes remain unchanged and have the configuration v b1 and v b2 The final merge net configuration was (v b1 ,v b2 ,v b1 +v b2 ) The only merge net of type bb was found, the (4,6,10)-c(dia,pcu)-merge xbp net.

[0420] In a dd-type merge process, both parent nets have transitivity

[21] . The configuration of the parent nets is (v d1 ,v dm1 ) and (v d2 ,v dm2 ) was set. In the merge net, v d1 node and v d2 The node is unchanged, and v dm1 The node is vdm2 The merge node is merged with the node. dm1 +v dm2 Therefore, the configuration of the merge net is (v d1 ,v d2 ,v dm1 +v dm2 ) A total of 27 dd-type merge nets were found.

[0421] The final three types of merge nets were merges between two parent nets containing the same signature net, achieved by different analysis methods, including merging an edge transformation net with a binary transformation net (eb), merging an edge transformation net with a transitivity

[21] net (ed), and merging a binary transformation net with a transitivity

[21] net (bd). In this approach, the merge process also produced three types of nodes: nodes from only the first parent net, nodes from only the second parent net, and shared nodes. The final merge net was transitivity

[32] .

[0422] In the eb-type merge process, both parent nets have transitivity

[11] . The coordination number is v e and v b The final coordination number of the edge-transformed parent net is set to (2,v) by transitivity

[21] by adding a node to the midpoint of the edge. e ) The final coordination number of the binary transformation parent net is (v b ,v b ) The merge node configuration was "v b +2". Therefore, the configuration of the merge net is (v e ,v b ,v b +2). Only three eb-type merge nets were found.

[0423] In the ed-type merge process, the parent net is parent net 1 (configuration v e ) has transitivity

[11] , and parent net 2 (coordination is set to v d and vdm The final coordination number of the edge-transformed parent net is (2,v) by adding a node at the midpoint of the edge, with transitivity

[21] . e ) The merge node configuration was "v dm +2". The configuration of the merge net is (v e ,v d ,v dm +2). A total of 25 ed-type merge nets were found.

[0424] In the bd type merge process, the parent net is parent net 1 (coordination is v b ) has transitivity

[11] , and parent net 2 (coordination is set to v d and v dm The final coordination number of the binary transformation parent net is transitively set to (v b ,v b ) The configuration of the merge node is (v b +v dm ) Therefore, the configuration of the merge net is (v b ,v d ,v b +v dm ) A total of 25 bd-type merge nets were found.

[0425] Based on the node relationship map of edge-transitive nets and these nine types of merge processes, a total of 140 merge nets were found (Table 2).

[0426] Here, we present the naming rules for new merge nets. (a) If a net exists in the RCSR, the original name was retained and not listed in this table (e.g., "urr" for the merge net (the,nbo)-merge). (b) The first two letters were chosen from the net with higher coordination (e.g., the merge of 4-c ana and 6-c bcs was named bsa). (c) If two edge-transitives have the same highest coordination, the net with transitivity

[21] was used for the first two letters of the merge net (e.g., the merge net of (3,4)-c ctn

[21] and 4-c lcs

[11] was named ctl). (d) The third letter of the merge net was chosen from the net with lower coordination (the first letter). The second or third letter was used when a conflict occurred (e.g., (nbo,bor)-m was named bob. The third letter "b" in the merge net came from the second letter of "nbo"). (e) "fc" and "fu" are not used as the first two letters of a merge net because they were exhausted in RCSR. The first two letters of an fcu merge net are always chosen from another net (e.g., the (fcu,dia)-merge net was named dif).

[0427] Other embodiments of the present disclosure are possible. While the above description contains many specificities, these should not be construed as limiting the scope of the disclosure, but merely as providing some illustrations of presently preferred embodiments of the disclosure. It is also contemplated that various combinations or subcombinations of specific features and aspects of the embodiments can be made and still fall within the scope of the disclosure. It should be understood that various features and aspects of the disclosed embodiments can be combined with or substituted for one another to form various embodiments. Thus, it is intended that at least some scope of the present disclosure should not be limited by the specific disclosed embodiments described above.

[0428] The scope of the present disclosure should therefore be determined by the appended claims and their legal equivalents. Accordingly, the scope of the present disclosure fully encompasses other embodiments that may become apparent to those skilled in the art, and therefore, it is understood that the scope of the present disclosure is not limited by anything other than the appended claims. References to elements in the singular are not intended to mean "only one," but rather "one or more," unless expressly stated otherwise. All structural, chemical, and functional equivalents of the elements of the above-described preferred embodiments known to those skilled in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Furthermore, it is not necessary for a device or method to address any problem sought to be solved by the present disclosure to be encompassed by the claims. Furthermore, no element, component, or method step in the present disclosure is intended to disclose the invention, regardless of whether the element, component, or method step is explicitly recited in the claims.

[0429] The foregoing description of various preferred embodiments of the present disclosure has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise embodiments, and it is apparent that many modifications and variations are possible in light of the above teachings. Such exemplary embodiments are chosen and described in order to best explain the principles of the present disclosure and its practical application, and to thereby enable others skilled in the art to utilize the present disclosure to the fullest extent in various embodiments and with various modifications suited to the particular uses contemplated. It is intended that the scope of the present disclosure be defined by the claims appended hereto.

[0430] Various embodiments have been described. These and other embodiments are within the scope of the following claims. [Table 3] [Table 4] [Table 5] [Table 6]

[0431] [1] 1. A method for synthesizing complex mixed linker structures, comprising: (a) selecting a merge net to be targeted in the synthesis of the complex mixed linker structure, and a first edge transition net and a second edge transition net that can be combined to provide the merge net, wherein the first and second edge transition nets share a common signature net; (b) determining connectivity and a geometric configuration of each node of the merge net, the nodes of the merge net including merge nodes and non-merge nodes, the non-merge nodes including a first non-merge node and a second non-merge node; (c) selecting an MBB that has the same connectivity and geometric configuration as the merge node and has two sets of extension points, each set of extension points being capable of connecting to a separate MBB; (d) selecting a first MBB having the same connectivity and geometric configuration as the first non-merge node; (e) inputting the length of the selected first MBB into a merge net equation to calculate an appropriate length of a complementary MBB; (f) selecting a second MBB having the same connectivity and geometric configuration as the second non-merge node and the same length as the complementary MBB; (g) reacting the precursors of the MBB, the first MBB, and the second MBB to synthesize a complex mixed linker structure having the merge net; A method comprising: [2] The method according to [1], wherein the merge net is a minimum edge transitive net with transitivity

[22] or transitivity

[32] . [3] The merge nets are aca net, acb net, ach net, anl net, ast-d net, bob net, bof net, bsc net, bsl net, bsp net, buo net, bup net, bus net, crd net, crh net, crn net, csa net, cst net, ctl net, dif net, epr net, flf net, flh net, flp net, flr net, fls net, fwb net, fwc net, fwf net, fwo net, fwp net, fwt net, gal net, gas net , hxd net, hxn net, hxp net, hxs net, ias net, ifc net, ifl net, ifr net, ifs net, itb net, itp net, its net, lvs net, lys net, mga net, mgh net, mgi net, mgr net, mgs net, nbf net, nbo-xd net, nic net, nku net, nso net, occ net, ocf net, och net, ocp net, ocs net, pco net, pcp net, pct net, phq net, pht net, psb net, p yi net, pyp net, pyu net, pyy net, qtq net, reb net, ren net, reo-d net, rep net, ret net, rhb net, rhc net, rhd net, rhf net, rht-x net, scc net, scp net, sdr net, ses net, sha net, shc net, shn net, sho net, shs net, sht net, spc net, spd net, sph net, sqd net, sqv net, ssl net, ssr net, sts net, sub net, suc net, su p net, tam net, tbc net, tbf net, tbn net, tdi net, tec net, tef net, ter net, thc net, tht net, toh net, ton net, top net, ttb net, tte net, tth net, tti net, ttl net, ttr net, tts net, twb net, twh net, twn net, two net, tws net, urk net, urr net, wzz net, xam net, xau net, xaz net, xbk net, xbn net, xbo net, xbp net,The method according to any one of [1] to [2], selected from the following: [4] The method according to any one of [1] to [3], wherein each of the first edge-transition net and the second edge-transition net is independently selected from edge-transition nets having transitivity

[11] or transitivity

[21] . [5] The method according to [4], wherein the edge-transitive net having transitivity

[11] is selected from hxg-net, lcw-net, hxl-net, kgm-net, hcb-net, dia-net, crs-net, nbo-net, sod-net, rhr-net, acs-net, sql-net, lvt-net, bcu-net, pcu-net, fcu-net, reo-net, qtz-net, srs-net, lcv-net, lcy-net, bcs-net, lcs-net, ana-net, thp-net, or a combination thereof. [6] The method of claim 4, wherein the edge-transitive net having transitivity

[21] is selected from shp-net, alb-net, stp-net, mgc-net, spn-net, toc-net, nia-net, ssa-net, csq-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, ctn-net, or a combination thereof. [7] The method according to any one of [1] to [6], wherein the common signature net is selected from kgm net, ana net, fcu net, reo net, bcs net, pcu net, crs net, nbo net, thp net, lcw net, lcs net, sod net, hxg net, lcv net, srs net, bcu net, lcy net, dia net, acs net, qtz net, fcu net, op net, rhr net, hxl net, lvt net, or thp net. [8] The method according to any one of [1] to [7], wherein the first MBB and the second MBB are different. [9] The method according to any one of [1] to [8], wherein the MBB, the first MBB, and the second MBB are each independently selected from organic MBBs or inorganic MBBs.

[10] The method according to any one of [1] to [9], wherein the MBB, the first MBB, and the second MBB are each independently selected from a first polytopic ligand, a second polytopic ligand, or a metal component.

[11] The method according to any one of [1] to

[10] , wherein at least one of the MBB, the first MBB, and the second MBB is an inorganic MBB containing a metal cluster or a metal ion.

[12] A method according to any of [1] to

[11] , wherein the first MBB meets with at least one of two sets of extension points to provide the first edge-transitive net.

[13] The method according to any of [1] to

[12] , wherein the second MBB meets with at least one of two sets of extension points to provide the second edge-transitive net.

[14] The merge net equation is given by Equation (1):

number

[13] , wherein

[15] The merge net equation is expressed by equation (2) or (3):

number

number

[14] , wherein

[16] The method according to any one of [1] to

[15] , further comprising selecting additional pairs of the first and second MBBs to form an isoreticular complex mixed linker structure.

[17] A complex mixed linker structure comprising a metal-organic framework having a merge-net topology, the metal-organic framework comprising molecular building blocks (MBBs) having a first extension point and a second extension point, the first extension point coordinates to the first MBB and the second extension point coordinates to the second MBB, and the first MBB and the second MBB are different.

[18] The method of

[17] , wherein the first MBB is a first polytopic ligand and the second MBB is a second polytopic ligand.

[19] The method according to any one of

[17] to

[18] , wherein a first edge-transitive net is provided by coordinating the first MBB and the first extension point.

[20] The method according to any one of

[17] to

[19] , wherein a second edge-transitive net is provided by coordinating the second MBB with the second extension point.

Claims

1. A method for synthesizing complex mixed linker structures of metal-organic frameworks (MOFs), The process includes the step of bringing a metal precursor, a first ligand precursor, and a second ligand precursor into contact so that a complex mixed linker structure having a marginal topology is formed. The aforementioned metal precursor includes a multinuclear cluster, The first ligand precursor comprises a first polytopic ligand, The second ligand precursor comprises a second polytopic ligand, A method wherein the first polytopic ligand is different from the second polytopic ligand.

2. The method according to claim 1, wherein the first polytopic ligand is a tritopic ligand or a tetratopic ligand.

3. The method according to claim 1, wherein the second polytopic ligand is a tetratopic ligand, a hexatopic ligand, or an octatopic ligand.

4. The method according to claim 1, wherein the multinuclear cluster is a two-nuclear cluster, a three-nuclear cluster, a six-nuclear cluster, or an eight-nuclear cluster.

5. The method according to claim 1, wherein the multinuclear cluster includes a hexanuclear cluster.

6. The method according to claim 1, wherein the first polytopic ligand is a tritopic ligand and the second polytopic ligand is a hexatopic ligand.

7. The method according to claim 1, wherein the complex mixed linker structure of the metal-organic structure is sph-MOF.

8. A method for designing and synthesizing complex mixed linker structures, (a) A step of selecting a target margin net in the synthesis of a complex mixed linker structure, and a first edge transition net and a second edge transition net that can be combined to provide the margin net, wherein the first edge transition net and the second edge transition net share a common signature net, and the common signature net is a crs net; (b) A step of determining the connectivity and geometric configuration of each node of the merge net, wherein the nodes of the merge net include merge nodes and non-merge nodes, and the non-merge nodes include a first non-merge node and a second non-merge node; (c) A step of selecting a molecular building block (MBB) having the same connectivity and geometric configuration as the merge node and having two sets of extension points, wherein each set of extension points can be connected to a separate MBB; (d) the step of selecting a first MBB having the same connectivity and geometric configuration as the first non-merged node; (e) The step of inputting the length of the selected first MBB into the margin net equation to calculate the appropriate length of the complementary MBB; (f) Selecting a second MBB having the same connectivity and geometric configuration as the second non-merged node and the same length as the complementary MBB; (g) A step of reacting the MBB, the first MBB, and the precursor of the second MBB to synthesize a complex mixed linker structure having the marginnet, wherein the complex mixed linker structure is a metal-organic structure (MOF), Methods that include...

9. The method according to claim 8, wherein the merge net is selected from crd net, crh net, hxd net, mga net, mgh net, mgr net, mgs net, spc net, spd net, sph net, tdi net, tth net, ttr net, tts net, or a combination thereof.

10. The method according to claim 8, wherein the merge net is selected from the SPC net, the SPD net, and the SPH net.

11. The method according to claim 8, wherein the first edge transition network is selected from crs network, dia network, hxg network, and spn network.

12. The method according to claim 8, wherein the second edge transition network is selected from dia network, hxg network, mgc network, spn network, and ttt network.

13. The method according to claim 8, wherein the first MBB and the second MBB are different.

14. The method according to claim 8, wherein each of the MBB, the first MBB, and the second MBB is independently selected from organic MBBs or inorganic MBBs.

15. The method according to claim 8, wherein each of the MBB, the first MBB, and the second MBB is independently selected from a first polytopic ligand, a second polytopic ligand, or a metallic component.

16. The method according to claim 8, wherein at least one of the MBB, the first MBB, and the second MBB is an inorganic MBB containing a metal cluster or metal ions.

17. The aforementioned margin net equation is given by equation (1): [Math 1] (In the formula, C Ｒ is the ratio constant of the margin net, and S ＢＢ１ S is the size of all building blocks in the first edge transition network. ＢＢ２ (where is the size of all building blocks in the second edge transition network mentioned above) The method according to claim 8, as represented by [the specified method].

18. The aforementioned margin net equation is equation (2) or (3): [Math 2] [Math 3] (In the formula, S Ｏ１ and S Ｏ２ C is the total size of all organic building blocks in the first edge transition network and the second edge transition network, respectively; Ｒ is the ratio constant of the margin net; S Ｉ１ and S Ｉ２ (where is the total size of all inorganic building blocks in the first edge transition network and the second edge transition network, respectively.) The method according to claim 8, as represented by [the specified method].

Images