Method for synthesizing novel nanostructure

Abstract

The present disclosure provides: a three-dimensional molecule having a specific three-dimensional shape; and a method for producing the same. In one aspect, the present disclosure provides a three-dimensional molecule having a polyhedral shape. The polyhedron may be a bipartite biregular polyhedron which satisfies (p, q) biregularity, or a vertex-deficient form thereof or a barrel-type vertex-deficient form derivative (where p and q are each independently selected from integers of 2 to 6). A three-dimensional molecule according to the present disclosure can have a closed three-dimensional structure, unlike a metal organic framework (MOF) in which the number of appearances of a repeating structure is not limited.

Description

Novel Nanostructure Synthesis Method

[0001] This disclosure relates to stereomolecules having a specific three-dimensional shape, methods for producing the same, and the use of the same.

[0002] Techniques for constructing structures with specific three-dimensional structures through self-assembly are known in this field, such as crystalline sponges (Patent Document 1, etc.). Various other organometallic frames (MOFs) have also been developed. Such structures are synthesized as polymer compounds with repeating structures. On the other hand, closed three-dimensional molecules have different utility than polymer compounds in terms of dispersibility in a medium, but examples of constructing such three-dimensional molecules are limited.

[0003] International Publication No. 2007 / 102594

[0004] The inventors have developed a method for designing and fabricating stereomolecules having specific three-dimensional shapes, and have discovered various synthesizable stereomolecules.

[0005] This disclosure provides, for example, the following items: (Item 1) A stereomolecule having a polyhedral shape, wherein the polyhedron is a bipartite bihedra satisfying (p,q) bihedra, or a vertex-deficient or barrel-shaped vertex-deficient derivative thereof, where p and q are independently selected from integers 2 to 6. (Item 2) Any stereomolecule of the above item, wherein the bihedra satisfy the bihedra of (3,4), (3,5), (2,5), or (2,3). (Item 3) Any stereomolecule of the above item, wherein the number of vertices of the bihedra is in the range of 8 to 50. (Item 4) Any stereomolecule of the above item, wherein the isolated radius of the bihedra is 4 or more. (Item 5) Any stereomolecule of the above item, wherein the bihedra is a rhombic dodecahedron or a rhombic triaconahedron. (Item 6) A stereomolecule of any of the above items, wherein the vertex-defective body is deficient in vertices at symmetrical positions in the biregular polyhedron. (Item 7) A stereomolecule of any of the above items, wherein the polyhedron is a vertex-defective body of a rhombic dodecahedron or a rhombic triaconahedron. (Item 8) A stereomolecule of any of the above items, wherein the polyhedron is one of the vertex-defective bodies listed in Tables 1 to 4. (Item 9) A stereomolecule of any of the above items, wherein the stereomorphic shape of the graph does not contain edges with discrete Ricci curvature values ​​less than -0.5, or the stereomorphic shape of a weighted graph does not contain edges with discrete Ricci curvature values ​​less than -0.5. (Item 10) The polyhedron is a stereomorphic body of any of the above items, wherein the Jaccard harmonic mean (J) is in the range of 50 to 100% for any of the stereomorphic shapes listed in Tables 1 to 4. ｈａｒｍ A stereomolecule having any of the above items. (Item 11) A stereomolecule having any of the above items, wherein the stereomolecule is constructed of two types of constructors. (Item 12) The two types of constructors include a first constructor and a second constructor, wherein the first constructor is given by the following formula: The compound has the following characteristics, where each A is an independent vertex skeleton having a vertex degree of m, and each R ２ This is independently the first bonding part, and each R １ A and R are independent of each other. ２ It is an arm that connects to each L１ is a vertex linker that independently connects different As and does not exist when p = 1. Each m is an integer independently selected from 2 to 6. p is an integer selected from 1 to 4. The second building element is a compound having the following formula: where each B is a vertex skeleton having a vertex degree of n, and each R ４ is independently a second bonding moiety, and each R ３ is independently an arm connecting B and R ４ and each L ２ is a vertex linker that independently connects different Bs and does not exist when q = 1. Each n is an integer independently selected from 2 to 6. q is an integer selected from 1 to 4. The three-dimensional molecule according to any one of the above items. (Item 13) A three-dimensional molecule according to any one of the above items having a diameter exceeding about 6 nm. (Item 14) A three-dimensional molecule according to any one of the above items having a diameter of about 8 nm to about 12 nm. (Item 15) For all pairs of AB distances in the three-dimensional molecule, a three-dimensional molecule according to any one of the above items in which the AB distances have a variation of less than 10% from each other. (Item 16) A three-dimensional molecule according to any one of the above items in which the first building elements and the second building elements do not form a bond with each other. (Item 17) A or B is selected from the group consisting of carborane or its condensed ring, 6-membered aromatic ring or its condensed ring, 5-membered aromatic ring or its condensed ring, corannulene, cyanostar, porphyrin, tetraarylethene, triiary of the above items. (Item 18) A combination in which R ２ and R ４ has a reaction energy of about 10 to 500 kJ / mol, a three-dimensional molecule according to any one of the above items. (Item 19) R ２ and R ４A stereomolecule of any of the above items, in which the combination is a lone pair of electrons of -COOH and a pair of metal atoms, or a pair of bonding moieties that are bonded by electrophilic or nucleophilic addition reactions. (Item 20) R １ or R ３ However, each arm is independently composed of 5 to 100 atoms, and is a stereomolecule of any of the above items. (Item 21) A method for producing a stereomolecule having a polyhedral shape, the method comprising: (A) a step of preparing a first constructing element, wherein the first constructing element is given by the following formula: The compound has the following characteristics, where each A is an independent vertex skeleton having a vertex degree of m, and each R ２ This is independently the first bonding part, and each R １ A and R are independent of each other. ２ It is an arm that connects to each L １ (B) A is an intervertex linker that connects independently different A's, and does not exist when p = 1, where each m is an integer independently selected from 2 to 6, and p is an integer selected from 1 to 4, (B) a step of preparing a second construction element, where the second construction element is given by the following equation: The compound has the following characteristics, where each B is an independent vertex skeleton having a vertex degree of n, and each R ４ This is an independent second bonding part, and each R ３ B and R are independent of each other. ４ It is an arm that connects to each L ２ (C) a method comprising the steps of (C) a vertex linker that connects independently different Bs, which does not exist when q=1, where each n is an integer independently selected from 2 to 6, and q is an integer selected from 1 to 4, and (D) a method comprising mixing the first and second construction elements to form a plurality of bonds between the first bonding portion and the second bonding portion, thereby forming a stereomolecule having the shape of the polyhedron with A and B positioned at its vertices.

[0006] The stereomolecules of this disclosure may exhibit various usefulness, such as their use as novel molecular carriers.

[0007] This shows the number of types of regular polyhedra with vertex degree 4. This can be expressed as the number of combinations of 4-regular planar graphs. The number of combinations (logarithmic) is shown on the vertical axis, and the number of vertices is shown on the horizontal axis. The isolation radii of several planar biregular graphs are shown (see Example 1). The three-dimensional shapes of exemplary (3,4) biregular graphs other than the 14-vertex (rhombic dodecahedron) are shown. The results of calculating the average chemical bond density per unit molecule, assuming a three-dimensional molecule constructed from two types of unit molecules corresponding to a simple biregular planar graph, are shown. An example of design guidelines for vertex-defective bodies based on a rhombic triacontahedron is shown. An example of design guidelines for vertex-defective bodies based on a rhombic dodecahedron is shown. Exemplary structures of three-dimensional molecules having the shape of a rhombic triacontahedron of various sizes (A: 6.0 nm, B: 7.5 nm, C: 9.0 nm, D: 10.5 nm, E: 12.0 nm) are shown. The three-dimensional molecular structures constructed from three-dimensional structural data obtained from single-crystal X-ray diffraction analysis of representative three-dimensional molecules constructed in the examples are shown. The results of gel permeation chromatography (GPC) analysis of representative stereomolecules and their constituent elements constructed in the examples are shown. The results of dynamic light scattering (DLS) measurements of representative stereomolecules constructed in the examples are also shown. In each graph, the horizontal axis represents particle size, and the vertical axis represents intensity-based, volume-based, and number-based measurements, respectively.

[0008] The present invention will be described below with reference to illustrative examples, as necessary, with reference to the accompanying drawings. Throughout this specification, singular expressions should be understood to include the concept of their plural forms unless otherwise specified. Furthermore, terms used herein should be understood to have the meaning commonly used in the art unless otherwise specified. Thus, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention pertains. In case of any conflict, this specification (including definitions) shall prevail.

[0009] (Definition) As used herein, "molecule" refers not only to a series of atomic groups linked by covalent bonds, but also to atomic groups that are united by any interaction, such as coordinate bonds, ionic bonds, and intermolecular forces. Therefore, the term "molecule" includes salts, complexes, protein complexes, and so on.

[0010] As used herein, the term "ring" includes not only rings as they are commonly understood in the field of chemistry (rings formed by covalent bonds connecting their constituent members), but also rings in which any number of covalent bonds are replaced by ionic bonds and / or coordinate bonds. Therefore, rings also include paddle-wheel complexes. Unless otherwise specified herein, if a molecule contains fused rings (rings sharing at least one edge (bond)) or rings containing rings (e.g., porphyrin rings containing pyrrole rings), the term "ring" refers to the entire group (e.g., anthracenes, porphyrins, carboranes, etc.) and counts them as a single ring. For example, coronenes, porphyrins, and cyanosters (with or without a centrally coordinated metal atom) shown below are single rings. Unless otherwise specified herein, two rings linked by a spiro bond are considered to be two separate rings.

[0011] As used herein, “stereomolecule” refers to a molecule containing two rings sharing three or more contiguous atoms (two or more contiguous bonds). Therefore, “stereomolecule” includes small molecules such as cyclobutane, carborane, and adamantane, which are methylene-bridged between positions 1 and 3, but the stereomolecules of this disclosure are larger molecules. The stereomolecules of this disclosure are formed by the assembly of building elements to take on a three-dimensional geometric shape. The stereomolecules of this disclosure contain only one polyhedral portion in the molecule and are distinguished from MOFs, which contain multiple repeating structures having a specific shape. It will be understood by those skilled in the art that compounds containing multiple polyhedral portions in the molecule can be easily prepared by chemically linking multiple stereomolecules of this disclosure.

[0012] As used herein, "polyhedron" refers to a three-dimensional solid enclosed by four or more planes. Polyhedra are defined by vertices and edges. Typically, the polyhedra described herein are convex polyhedra. For example, the rhombic dodecahedron consists of 14 vertices, 24 edges and 12 faces, and the rhombic triacontahedron consists of 32 vertices, 60 edges and 30 faces.

[0013] In this specification, a polyhedron that satisfies "biregularity" refers to a polyhedron whose vertices are divided into two groups, such that no edges exist between vertices belonging to the same group, and the number of edges extending from each vertex is the same for each vertex in both groups. In this specification, a polyhedron that satisfies "biregularity" is called a bipartite biregular polyhedron. In the description of (p,q) biregularity, p and q represent the number of edges extending from each vertex in the two vertex groups, respectively. For a mathematical definition of (p,q) biregularity, see Example 1. For a particular number of p and q, there may be multiple polyhedra that satisfy (p,q) biregularity, differing in the number of vertices (see also Figure 3). For example, the rhombic dodecahedron has the smallest number of vertices among the bipartite biregular polyhedra that satisfy (3,4) biregularity, and the rhombic triacontahedron has the smallest number of vertices among the bipartite biregular polyhedra that satisfy (3,5) biregularity.

[0014] As used herein, "vertex-deficient polyhedron" refers to a polyhedron formed by removing one or more vertices and edges extending from those vertices from a bipartite biregular polyhedron. A vertex-deficient polyhedron may be a concave polyhedron. A vertex-deficient polyhedron may also be a bipartite biregular polyhedron, in which case it may be treated as either a bipartite biregular polyhedron or a vertex-deficient polyhedron. For example, of the polyhedra shown below, the one on the left is a rhombic triacontahedron, and the one on the right is a vertex-deficient polyhedron of a rhombic triacontahedron, and at the same time has the third smallest number of vertices among bipartite biregular polyhedra that satisfy (3,4) biregularity.

[0015] In this specification, "barrel-type vertex-deficient derivative" refers to a polyhedron obtained by changing the number of repeating units in a barrel-type vertex-deficient polyhedron (a vertex-deficient polyhedron formed by removing at least two vertices that are mirror-symmetric or 180° rotationally symmetric). For example, the barrel-type vertex-deficient polyhedron on the left in the figure below consists of five repeating units, each consisting of two quintic vertices and two linker-linked composite quintic vertices, while the barrel-type vertex-deficient polyhedron on the right in the figure below consists of four repeating units, each consisting of two quartic vertices and two linker-linked composite quartic vertices. Those skilled in the art can easily understand the three-dimensional shapes obtained by varying the number of repeating units in such structures. Barrel-type vertex-deficient derivatives are also one of the structures that can be constructed according to the design guidelines for stereomolecules described herein.

[0016] As used herein, a stereomolecule "having the shape" of a particular polyhedron means that the stereomolecule has atomic center points (or geometric centroids of the vertex skeletal parts of the constructor) located within 10% or 5% of the length of the circumscribing sphere diameter of the polyhedron from the position of each vertex of the polyhedron where the edge lengths are uniform. In this specification, a stereomolecule having the shape of a polyhedron does not include stereomolecules assembled into a polyhedron shape by interatomic bonding (e.g., polyhedron molecules consisting of Si and O atoms) and their modified molecules (except when such molecules are used as constructors). In particular, stereomolecules having the shape of a vertex-deficient body may have physicochemical distortions compared to mathematically symmetric structures, so the angles between the edges of the polyhedron are not particularly limited here. If necessary, a standard bipartite bihedra with only one or two types of edge angles (less than 180°) may be assumed, and whether a polyhedron "has the shape" of a polyhedron may be determined using polyhedra where each edge angle is within ±10° or ±5° of any angle in the standard bipartite bihedra. Depending on the presence of substituents in the constructing element, some of the atoms constituting the three-dimensional molecule may be located outside the polyhedron that defines the three-dimensional molecule. For example, if a constructing element with substituents introduced into the lower half of the substituted carborane in the figure below is used, these substituents may protrude outside the polyhedron.

[0017] In this specification, the "diameter" of a stereomolecule refers to the diameter of the circumscribing sphere of the stereomolecule. However, since substituents that protrude outside the polyhedron can be introduced as described above, such substituent parts are not considered in the calculation of the diameter. That is, in one embodiment, the "diameter" of a stereomolecule refers to the diameter of the circumscribing sphere (or the circumscribing sphere approximated by the least squares method with respect to the distance to these point groups) of the point group consisting of the centers of the atoms constituting the vertex skeleton of the constructing elements in the stereomolecule. Furthermore, for example, when a stereomolecule is constructed using two constructing elements with long arms, the bonding points between bonding parts (the intersection of the thick lines in the right-hand box in the figure below) may protrude outside the circumscribing sphere of the vertex skeleton of the stereomolecule (even in this case, "having the shape of a polyhedron" can be determined as described above). Therefore, in one embodiment, the "diameter" of a stereomolecule refers to the diameter of the circumscribing sphere consisting of the point group consisting of the centers of the atoms constituting the bonding parts (those involved in bond formation) of the constructing elements in the stereomolecule. The larger of the diameter of the circumscribing sphere of the point group consisting of the centers of atoms constituting the vertex skeleton and the diameter of the circumscribing sphere of the point group consisting of the centers of atoms constituting the bonding region can be the "diameter" of the three-dimensional molecule.

[0018] As used herein, “constructor” refers to a molecule comprising at least one vertex skeleton and a bonding moiety. Typically, the “stereomolecules” of this disclosure are constructed of two types of “constructors.” The first and second constructors of the two types each comprise one of a pair of bonding moieties that bond to one another. The first constructor (and / or the second constructor) may be a group of molecules comprising multiple molecular species, which may differ from one another in vertex order (number of bonding moieties), arm structure, intervertex linker structure, and chemical modifications by substituents and / or isotopic atoms. In particular, modifications by substituents (such as those on the vertex skeleton, arms, and / or intervertex linkers) and isotopic atoms are considered to have little effect on the formation of the stereomolecules of this disclosure; therefore, stereomolecules can still be formed even when constructors comprising multiple molecular species that differ from one another in these chemical modifications are used.

[0019] In this specification, a stereomolecule constructed with a constructing element does not require a history of being constructed with that constructing element, and means that the structure of the constructing element can be understood from the structure of the stereomolecule based on the description herein. While the chemical structure may change due to reactions between bonding parts during the construction of a stereomolecule, those skilled in the art can understand the structure of the constructing element, including the bonding parts, based on the chemical structure of the stereomolecule. Furthermore, this disclosure is essentially intended to provide stereomolecules with characteristic structures, and the constructed stereomolecule can be subjected to any chemical modifications based on prior knowledge. Stereomolecules constructed with a constructing element include molecules in which the structure of the constructing element can be understood from the structure of the stereomolecule based on the description herein, and which can also be understood to have been prepared by further chemical modifications.

[0020] For example, typically, vertex defects can be used to form stereomolecules that appear to be constructed of three or more types of constructors, but such stereomolecules are considered a type of stereomolecule constructed of two types of constructors. For example, by using a 4th-order vertex constructor, which has one binding moiety removed from the 5th-order vertex constructor used to form the stereomolecule in the left figure below, the stereomolecule in the right figure below can be formed. In this case, instead of removing binding moiety A, binding moiety A can be replaced with a binding moiety B that has another reactivity, thereby forming a stereomolecule in the vertex defect portion of the stereomolecule in the right figure below in which three binding moieties B are clustered together. Those skilled in the art will understand that it is possible to attach a suitable molecule corresponding to a constructor of the present disclosure to the portion in which three binding moieties B are clustered together. Furthermore, a vertex-deficient body (B2 in Table 2) may exist in which four symmetrical vertices are missing from the eight cubic vertices of a rhombic dodecahedron. It is similarly possible to attach molecules corresponding to the constructing elements of this disclosure to the locations of the four missing vertices in such a vertex-deficient body. As described above, when a stereomolecule has a structure in which it is thought to be constructed from two types of constructing elements in two or more ways, the part formed by the assembly of the largest number of constructing element molecules can be considered as the basic skeleton, and the other parts can be considered as modifications. Based on this basic skeleton, the shape of the stereomolecule can be considered.

[0021] As used herein, “bonding moiety” refers to a moiety capable of reacting with a specific functional group to form a covalent bond, an ionic bond, and / or a coordinate bond. Typically, bonds are formed between two identical or different bonding moieties, and such pairs of bonding moieties are referred to herein as a “bonding moiety pair.” When the vertex skeleton is a metal atom, the bonding moiety can be a metal atom and can form a coordinate bond with a pair of bonding moieties that are lone pairs of electrons. In this specification, unless otherwise specified, “bonding moiety” refers to a bonding moiety such that the first bonding moiety of the first constructor and the second bonding moiety of the second constructor are a pair of bonding moieties, i.e., a bonding moiety that is actually involved in the formation of a stereomolecule (sometimes referred to herein as a “basic bonding moiety”). Constructors may also include bonding moieties other than basic bonding moieties (sometimes referred to herein as “potential bonding moieties”), which can be used, for example, as reaction sites when conjugating a protein into a constructed stereomolecule.

[0022] In this specification, "vertex skeleton" refers to a portion having at least two bonding chain substituents (typically a ring or metal atom). "Bonding chain" refers to a portion having at least one bonding portion (e.g., a basic bonding portion). The portion of a "bonding chain" other than the bonding portion is called an "arm" (i.e., substituents on the vertex skeleton when there is no bonding portion at the end are not arms). Arms do not include the vertex skeleton. Therefore, even if ring A is substituted with substituent X (which has a bonding portion and includes ring B), substituent X is not a bonding chain if ring B is the vertex skeleton. When there are multiple vertex skeletons in the building blocks of a single molecule, the portion connecting the vertex skeletons is called an "intervertex linker".

[0023] The "vertex degree" of a vertex skeleton refers to the number of bond chains attached to that vertex skeleton. The degree of a constructor element refers to the number of bond chains that the constructor element molecule possesses.

[0024] When forming a stereomolecule, the bonding parts of the constituent elements may undergo chemical reactions, and therefore the chemical structure of the bonding parts may be lost in the stereomolecule. However, those skilled in the art can understand the pair of bonding parts of the constituent elements from the chemical structure of the stereomolecule. For example, two constituent elements may have a bonding part pair consisting of an aldehyde group (-CHO) and a hydrazo group (-C=NNH). ２ If it has ), a -C=NNH-C- group is formed in the stereomolecule.

[0025] Unless otherwise specified, as used herein, “alkyl group,” either alone or as part of another group, refers to a linear or branched saturated hydrocarbyl group having carbon atoms. A alkyl group may typically have 1 to 8 carbon atoms, and in some embodiments, it may have 1 to 6 carbon atoms. In some embodiments, it may have 1 to 4 carbon atoms. In some embodiments, it may have 1 to 3 carbon atoms. １～３ Examples of alkyl groups include methyl, ethyl, propyl, and isopropyl groups. １～４ An example of an alkyl group is C, as mentioned earlier. １～３ Examples include alkyl groups, as well as butyl groups, isobutyl groups, sec-butyl groups, and tert-butyl groups. １～６ An example of an alkyl group is C, as mentioned earlier. １～４ Examples include alkyl groups, as well as pentyl groups, isopentyl groups, neopentyl groups, hexyl groups, etc. Additional examples of alkyl groups include heptyl groups, octyl groups, etc.

[0026] As used herein, "alkylene group" is a divalent group obtained by removing one more hydrogen atom from an "alkyl group". Specific examples of alkylene groups include -CH ２ -ien-CH ２ CH ２ -, - (CH ２ ) ３ -ien-CH ２ CH (CH ３ )-,-(CH ２ ) ４ -ien-CH２ CH ２ CH (CH ３ ) -, -CH ２ CH (CH ３ )CH ２ -, - (CH ２ ) ５ -ien-CH ２ CH ２ CH ２ CH (CH ３ ) -, -CH ２ CH ２ CH (CH ３ )CH ２ -, - (CH ２ ) ６ -, - (CH ２ ) ７ -, - (CH ２ ) ８ -, - (CH ２ ) ９ -, and - (CH ２ ) １０ These are some examples, but the list is not limited to these.

[0027] Unless otherwise specified, as used herein, “alkenyl group,” either alone or as part of another group, refers to a linear or branched hydrocarbyl group having a carbon atom and one or more carbon-carbon double bonds. An alkenyl group may typically have 2 to 8 carbon atoms, and in some embodiments, an alkenyl group may have 2 to 6 carbon atoms. In some embodiments, an alkenyl group may have 2 to 4 carbon atoms. The one or more carbon-carbon double bonds may be internal (e.g., the double bond in 2-butenyl) or terminal (e.g., the double bond in 1-butenyl). ２～４ Examples of alkenyl groups include ethenyl group (vinyl group), 1-propenyl group, 2-propenyl group, 1-butenyl group, 2-butenyl group, and butadienyl group. ２～６ An example of an alkenyl group is the aforementioned C ２～４ Examples of alkenyl groups include pentenyl groups, pentadienyl groups, and hexenyl groups. Additional examples of alkenyl groups include heptenyl groups, octenyl groups, and octatrienyl groups.

[0028] As used herein, an "alkenylene group" is a divalent group formed by further removing one hydrogen from an "alkenyl group". Specific examples of the alkenylene group include -CH=CH-, -CH=CH-CH ２ -, -CH=CH-(CH ２ ) ２ -, -CH ２ -CH=CH-CH ２ -, -CH=C(CH ３ )-CH ２ -, -CH=CH-CH=CH-, -CH=CH-(CH ２ ) ３ -, -CH=CH-CH=CH-CH ２ -, -CH=CH-(CH ２ ) ４ -, -CH=CH-(CH ２ ) ５ -, -CH=CH-(CH ２ ) ６ -, -CH=CH-(CH ２ ) ７ -, and -CH=CH-(CH ２ ) ８ - etc., but are not limited thereto.

[0029] Unless otherwise specified, as used herein, the "alkynyl group", either alone or as part of another group, refers to a straight-chain or branched-chain hydrocarbyl group having carbon atoms and one or more carbon-carbon triple bonds. The alkynyl group may typically have 2 to 8 carbon atoms, and in some embodiments, the alkynyl group may have 2 to 6 carbon atoms. In some embodiments, the alkynyl group may have 2 to 4 carbon atoms. The one or more carbon-carbon triple bonds may be internal (e.g., the triple bond in 2-butynyl) or terminal (e.g., the triple bond in 1-butynyl). C ２～４ Examples of the alkynyl group include ethynyl group, propyn-1-yl group, propyn-3-yl group, 1-butyn-1-yl group, 1-butyn-4-yl group, 2-butyn-1-yl group, etc. C ２～６ Examples of the alkenyl group include the aforementioned C ２～４Examples include an alkynyl group, a pentynyl group, a hexynyl group, etc. Additional examples of alkynyl include a heptynyl group, an octynyl group, etc.

[0030] As used herein, an "alkynylene group" is a divalent group formed by further removing one hydrogen from an "alkynyl group". Specific examples of the alkynylene group include -C≡C-, -C≡C-CH ２ -, -C≡C-(CH ２ ) ２ -, -CH ２ -C≡C-CH ２ -, -C≡C-C≡C-, -C≡C-(CH ２ ) ３ -, -CH ２ -C≡C-(CH ２ ) ２ -, -C≡C-C≡C-CH ２ -, -C≡C-(CH ２ ) ４ -, -(CH ２ ) ２ -C≡C-(CH ２ ) ２ -, -CH ２ -C≡C-C≡C-CH ２ -, -C≡C-C≡C-C≡C-, -C≡C-(CH ２ ) ５ -, -(CH ２ ) ２ -C≡C-(CH ２ ) ３ -, -(CH ２ ) ２ -C≡C-C≡C-(CH ２ ) ３ -, -C≡C-(CH ２ ) ６ -, -C≡C-(CH ２ ) ７ -, and -C≡C-(CH ２ ) ８ - etc., but are not limited thereto.

[0031] As used herein, an "aliphatic group" refers to an alkyl group, an alkenyl group, and an alkynyl group, and does not include a cyclic hydrocarbon group.

[0032] As used herein, "heteroliphatic group" refers to a group in which some of the aliphatic group is replaced by heteroatoms (e.g., nitrogen, oxygen, sulfur, etc.).

[0033] As used herein, the term “aryl group” refers to a monoaromatic ring or fused polycyclic system in which at least one of the rings is aromatic and all ring atoms are carbon. For example, an aryl group may have 6 to 26 carbon atoms (6 to 26 members), 6 to 20 carbon atoms (6 to 20 members), 6 to 14 carbon atoms (6 to 14 members), or 6 to 12 carbon atoms (6 to 12 members). The aryl group includes the phenyl group. The aryl group also includes a fused polycyclic system having 8 to 20 carbon atoms (e.g., a ring system containing 2, 3, or 4 rings) in which at least one ring is aromatic and the other rings may or may not be aromatic. Such a fused polycyclic system may optionally have one or more (e.g., 1, 2, or 3) oxo groups substituted in any carbon ring portion of the fused polycyclic system. The rings of a fused polycyclic system may be linked to each other via condensation and bridging bonds, where the valency requirements allow. It should be understood that the bond sites in the previously defined condensed polycyclic systems can be located at any position in the cyclic system, including the aromatic ring or the carbocyclic portion of the ring. Typical aryl groups include, but are not limited to, the phenyl, indenyl, naphthyl, 1,2,3,4-tetrahydronaphthyl, anthryl, and pyrenyl groups.

[0034] As used herein, the term “heteroaryl group” means a monoaromatic ring or fused polycyclic system having at least one heteroatom in the ring, the heteroatom being selected from the group consisting of oxygen, nitrogen, and sulfur. A heteroaryl group can typically have 5 to 26 members, and in some embodiments, 5 to 20 members. In some embodiments, a heteroaryl group can have 5 to 14 members. In some embodiments, a heteroaryl group can have 5 to 12 members. In some embodiments, a heteroaryl group can have 5 to 10 members. A heteroaryl group comprises a monoaromatic ring having about 1 to 6 carbon atoms and about 1 to 4 heteroatoms selected from the group consisting of oxygen, nitrogen, and sulfur. Examples of such rings include, but are not limited to, pyridyl, pyrimidinyl, pyrazinyl, oxazolyl, and furyl groups. A heteroaryl group may also contain a metal atom. Sulfur and nitrogen atoms can also be present in oxidized forms if the ring is aromatic. The heteroaryl group also includes fused polycyclic systems (e.g., systems containing two, three, or four rings) in which the previously defined heteroaryl group can condense with one or more rings selected from heteroaryl (e.g., naphthilidinyl, e.g., 1,8-naphthilidinyl), heterocyclic (e.g., 1,2,3,4-tetrahydronaphthilidinyl, e.g., 1,2,3,4-tetrahydro-1,8-naphthilidinyl), carbocyclic (e.g., 5,6,7,8-tetrahydroquinolyl), and aryl (e.g., indazolyl) to form a fused polycyclic system. In some embodiments, the heteroaryl group (single aromatic ring or fused polycyclic system) has about 1 to 20 carbon atoms and about 1 to 6 heteroatoms in the heteroaryl ring. Such fused polycyclic systems may have one or more (e.g., one, two, three, or four) oxo groups substituted in the carbocyclic or heterocyclic portion of the fused ring. The rings in a fused polycyclic system can be linked to each other via condensation and bridging, provided the valency requirements permit. It should be understood that the individual rings in a fused polycyclic system can be linked to each other in any order.It should also be understood that the bonding sites of the above-mentioned condensed polycyclic systems can be located at any position in the condensed polycyclic system, including the heteroaryl, heterocyclic, aryl, or carbocyclic portions of the condensed polycyclic system, as well as at any suitable atom in the condensed polycyclic system, including carbon atoms and heteroatoms (e.g., nitrogen). Exemplary heteroaryl groups include pyridyl, pyrrolyl, pyrazinyl, pyrimidinyl, pyridadinyl, pyrazolyl, thienyl, indolyl, imidazolyl, oxazolyl, isoxazolyl, thiazolyl, furyl, oxadiazolyl, thiadiazolyl, quinolyl, isoquinolyl, benzothiazolyl, benzoxazolyl, indazolyl, quinoxalyl, quinazolyl, 5,6 ,7,8-tetrahydroisoquinolinylbenzofuranyl group, benzimidazolyl group, thianaphthenyl group, pyrrolo[2,3-b]pyridinyl group, quinazolinyl-4(3H)-one group, triazolyl group, 4,5,6,7-tetrahydro-1H-indazole group and 3b,4,4a,5-tetrahydro-1H-cyclopropa[3,4]cyclopenta[1,2-c]pyrazole group, as well as porfin group, porphyrin group. These are some examples, but are not limited to these.

[0035] As used herein, "arylene group" refers to a divalent aromatic monocyclic or fused polycyclic 6-26 member aryl or 5-26 member heteroaryl group, or a divalent group in which multiple 6-26 member aryl and / or 5-26 member heteroaryl groups are directly bonded to each other by ring atoms. Arylene groups can typically have 6-16 members, and in some embodiments, 6-14 members. In some embodiments, arylene groups can have 6-12 members. Examples of such arylene groups include phenylene, naphthylene, anthrene, biphenylene, -(phenylene)-(naphthylene), and binaphthylene.

[0036] Unless otherwise specified, as used herein, “halo” or “halogen,” either alone or as part of another group, refers to fluorine (fluoro), chlorine (chloro), bromine (bromo), or iodine (iod).

[0037] Unless otherwise specified, as used herein, “haloalkyl group,” either alone or as part of another group, refers to an alkyl group in which one or more hydrogen atoms are independently substituted with a halo. In some embodiments (“perhaloalkyl groups”), all hydrogen atoms are substituted with fluoro or chloro. In some embodiments (“perfluoroalkyl groups”), all hydrogen atoms are substituted with fluoro. An example of a perfluoroalkyl group is -CF ３ , -CF ２ CF ３ , -CF ２ CF ２ CF ３ Examples include the perhaloalkyl groups mentioned above, as well as -CCl ３ , -CFCl ２ , -CF ２ Cl, -CCl ２ CCl ３ Examples include the perhaloalkyl groups mentioned above, as well as -CH ２ F, -CHF ２ ien-CH ２ Cl, -CH ２ Br, -CH(Cl)CH ２ Br, -CH ２ CH(F)CH ２ Examples include Cl. "Haloalkenyl group," "perhaloalkenyl group," "haloalkynyl group," "perhaloalkynyl group," "haloaliphatic group," and "perhaloaliphatic group" are defined in the same way as the aforementioned "haloalkyl group" and "perhaloalkyl group."

[0038] As used herein, “carbocyclic” or “carbocyclic group,” either alone or as part of another group, refers to a monocyclic, dicyclic, tricyclic, tetracyclic, or more polycyclic hydrocarbon group that is fully saturated or contains one or more unsaturated units but is not aromatic. In one embodiment, the carbocyclic group is a monocyclic C ３～９ It can be a hydrocarbon group. In one embodiment, the carbocyclic group is a bicyclic C ８～１２It can be a hydrocarbon group. In one embodiment, the carbocyclic group is a tricyclic C １０～１６ It can be a hydrocarbon group. In one embodiment, the carbocyclic group is a tetracyclic C １２～２１ It may be a hydrocarbon group. Any individual ring in the above carbocyclic group may have 3 to 7 ring atoms. Examples of carbocyclic groups include cycloalkyl groups such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, cyclooctyl, and cyclononyl groups; cycloalkenyl groups such as cyclopropenyl, cyclobutenyl, cyclopentenyl, cyclohexenyl, cycloheptenyl, cyclooctenyl, and cyclononenyl groups; and cycloalkynyl groups such as cyclopropynyl, cyclobutynyl, cyclopentinyl, cyclohexynyl, cycloheptinyl, cyclooctinyl, and cyclononinyl groups; as well as adamantyl groups. These are some examples, but are not limited to them. In carbocyclic groups, any ring atom may be bonded to the rest of the molecule, if possible.

[0039] As used herein, “heterocycle,” “heterocyclic group,” or “heterocyclic group,” either alone or as part of another group, refers to a monocyclic, bicyclic, tricyclic, tetracyclic, or more polycyclic ring system in which at least one ring in the ring system contains one or more identical or different heteroatoms and is fully saturated or contains one or more unsaturated units but is not aromatic. In some embodiments, the “heterocycle” or “heterocyclic group” has 3 to 14 ring atoms, where one or more ring atoms are heteroatoms independently selected from oxygen, sulfur, nitrogen, or phosphorus, and each ring in the ring system contains 3 to 8 ring atoms.

[0040] Examples of heterocyclic groups include 2-tetrahydrofuranyl group, 3-tetrahydrofuranyl group, 2-tetrahydrothiophenyl group, 3-tetrahydrothiophenyl group, 2-morpholino group, 3-morpholino group, 4-morpholino group, 2-thiomorpholino group, 3-thiomorpholino group, 4-thiomorpholino group, 1-pyrrolidinyl group, 2-pyrrolidinyl group, 3-pyrrolidinyl group, 1-tetrahydropiperazinyl group, 2-tetrahydropiperazinyl group, 3-tetrahydropiperazinyl group, 1-piperidinyl group, 2-piperidinyl group, 3-piperidinyl group, 1-pyrazolinyl group, 3-pyrazolinyl group, 4-pyrazolinyl group, and 5-pyrazolinyl group. Examples of monocyclic groups include, but are not limited to, monocyclic groups such as 1-piperidinyl, 2-piperidinyl, 3-piperidinyl, 4-piperidinyl, 2-thiazolidinyl, 3-thiazolidinyl, 4-thiazolidinyl, 1-imidazolidinyl, 2-imidazolidinyl, 4-imidazolidinyl, and 5-imidazolidinyl groups, as well as bicyclic groups such as 3-1H-benzimidazole-2-one, 3-(1-alkyl)-benzimidazole-2-one, indolinyl, tetrahydroquinolinyl, tetrahydroisoquinolinyl, benzothiolane, benzodithiane, and 1,3-dihydroimidazole-2-one. In heterocyclic groups, any ring atom may be bonded to the rest of the molecule if possible.

[0041] As used herein, a monovalent organic group refers to a monovalent group comprising at least one of carbon, oxygen, nitrogen, and sulfur. This includes, for example, 5-26 membered, 5-20 membered, 5-14 membered, or 5-12 membered nitrogen-containing heteroaryl groups, di(5-26 membered, 5-20 membered, 5-14 membered, or 5-12 membered nitrogen-containing heteroaryl groups), phenyl groups, nitrile groups, optionally substituted amino groups, and carboxylic acid groups (-COOH or -COO). － These may include, for example, 5-12 membered monocyclic or condensed bicyclic nitrogen-containing heteroaryl groups, and di(5-12 membered monocyclic or condensed bicyclic nitrogen-containing heteroaryl group)phenyl groups.

[0042] As used herein, a divalent organic group refers to a divalent group comprising at least one of carbon, oxygen, nitrogen, and sulfur. This is, for example, (a) to (r) below: (a)-NR ａ -, (b) -O-, (c) -S-, (d) -C(=O)O-, (e) -C(=O)-, (f) -C(=O)NR ａ -, (g)-C(=N-CN)-, (h)-NR ａ C(=O)O-, (i)-S(=O) ２ NR ａ -, (j)-NR ａ C(=O)NR ａ -, (k)-NR ａ S (=O) ２ NR ａ -, (l)-S(=O)-, (m)-S(=O) ２ -, (n) C may be substituted. １～６ Alkylene group, (o) C which may be substituted ２～６ Alkenylene group, (p) substituted C ２～６ R is a divalent group in which one or more (e.g., two, three, four, or five or more) groups are linked, selected from the group consisting of an alkynylene group, an (q) optionally substituted arylene group, and an (r) optionally substituted adamantyl group, ａ Each of these is independently a hydrogen atom or a substituted C atom. １～６ It is an aliphatic group.

[0043] As used herein, the term “unsaturated” means that a part has one or more unsaturated units.

[0044] In this specification, the divalent group may have either of its two bonding sites attached to the parent molecule (either the inner or central part of the molecule). For example, the group -O-CH ２ - may be in any of the following forms: [Parent molecule]-O-CH ２ - [Another group] [Parent molecule] - CH ２ -O- [another base]

[0045] In chemical structural formulas, When a wavy line intersects a bond (line) as shown, it indicates a bond point with the rest of the molecule or with other groups or ligands.

[0046] If a "heteroaliphatic group," "heterocyclic group," "heterocyclic group," "heteroaryl group," or "arylene group" is substituted, it may have substituents on the heteroatom if it is substituted.

[0047] When a group is described as "substituted," it means that at least one hydrogen atom of that group is replaced by a non-hydrogen group (substituent), and the number of substituents is not particularly limited as long as they are substituteable, and can be one or more. Also, unless otherwise specified, the description of each group applies even if that group is a part of or a substituent of another group. For example, C １～６ When an alkyl group is substituted, the number of carbon atoms in the substituent is not included in the number of carbon atoms in the alkyl group. The same applies to other groups.

[0048] In this specification, examples of any substituents that can be introduced into the constructs and stereomolecules described herein without limiting the context of use include: • Halogen•=O •-OR' (where R' is hydrogen, or R, -OR, -SR or -NR) ２ R) -SR' (where R' is hydrogen, or R, -OR, -SR or -NR) may be optionally substituted by 0 to 10 substituents independently selected from R. ２ R) -NR'2 (where R' is independently hydrogen, or R, -OR, -SR or -NR) may be optionally substituted by 0 to 10 substituents selected independently of R) ２ R) may be optionally substituted by 0 to 10 substituents independently selected from the group consisting of nitro groups, cyano groups, sulfonic acid groups, phosphate groups, polyethylene glycol (PEG) groups, and 0 to 10 heteroatoms selected from the group consisting of N, O, and S. Linear or branched saturated or unsaturated C １～５０ Aliphatic group, which is R, -OR, -SR, or -NR ２A 1-20 member saturated or unsaturated carbon ring comprising substitutions by 0-5 heteroatoms selected from the group consisting of aliphatic groups, N, O, and S, which may be optionally substituted by 0-10 substituents independently selected from the aliphatic group, and which are R, -OR, -SR, or -NR ２ A 1-20 membered aryl comprising substitutions by 0-5 heteroatoms selected from the group consisting of a carbocyclic ring, N, O, and S, which may be optionally substituted by 0-10 substituents independently selected from, and which are R, -OR, -SR, or -NR ２ An aryl compound which may be optionally substituted by 0 to 10 substituents independently selected from, where R is a linear or branched saturated or unsaturated C compound including substitution by 0 to 10 heteroatoms selected from the group consisting of N, O, and S. １～５０ A substituent selected from the group consisting of an aliphatic group, a saturated or unsaturated carbon ring with 1 to 20 members including substitutions by 0 to 5 heteroatoms selected from the group consisting of N, O, and S, and a 1 to 20-membered aryl halogen, =O, nitro group, cyano group, sulfonic acid group, and phosphate group. (A substituent substituted with one R substituent having one R substituent is considered to have two R substituents. A substituent that can be recognized in multiple ways, such as a tert-butyl group being recognized in multiple ways as either a branched aliphatic group or an aliphatic group substituted with one or two methyl groups, is included in the range if it can be recognized in any of these ways.)

[0049] In this specification, the term "approximately" refers to plus or minus 10% of the indicated value unless otherwise specified. When "approximately" is used for temperature, it refers to plus or minus 5°C of the indicated temperature; when "approximately" is used for pH, it refers to plus or minus 0.5 of the indicated pH.

[0050] In this specification, any compound (in particular, its constituent elements and stereomolecules) also refers to those existing in the form of a salt, unless otherwise specified. That is, descriptions of compounds may be made similarly regardless of the presence or absence of the acid and / or base used in the formation of the salt. Similarly, in this specification, any compound (in particular, its constituent elements and stereomolecules) is described as existing in both its ionized and non-ionized forms.

[0051] (Preferred Embodiments) Preferred embodiments of the Disclosure are described below. The embodiments provided below are provided for a better understanding of the Disclosure, and it will be understood that the scope of the Disclosure is not limited to the descriptions below. Accordingly, it will be obvious that those skilled in the art can make appropriate modifications within the scope of the Disclosure by taking into consideration the descriptions herein. It will also be understood that the embodiments of the Disclosure below can be used individually or in combination.

[0052] This specification primarily describes stereomolecules, but various embodiments are also intended as inventions, including methods for fabricating stereomolecules and their use, elements (constructing elements) or combinations (compositions, kits, etc.) for use in fabricating stereomolecules, systems for carrying out methods, and programs for carrying out methods. Descriptions of one embodiment, such as a method, apply similarly to other embodiments. For example, a description of stereomolecules is understood to simultaneously include descriptions of elements used in methods for fabricating stereomolecules, descriptions of the operation of systems for carrying out methods for fabricating stereomolecules, or descriptions of instructions coded in programs for carrying out methods.

[0053] (Stereomolecules) In one aspect, the present disclosure provides stereomolecules having a polyhedral shape. The polyhedron may be a bipartite biregular polyhedron satisfying (p,q) biregularity, or a vertex-deficient or barrel-shaped vertex-deficient derivative thereof (where p and q are each independently selected from integers 2 to 6).

[0054] In one embodiment, the polyhedron is a bipartite biregular polyhedron satisfying the biregularity of (3,3), (3,4), (3,5), (2,5), or (2,3), or a vertex-defected or barrel-shaped vertex-defected derivative thereof. In one embodiment, the number of vertices of the polyhedron is in the range of 8 to 100 (e.g., 8 to 50). In one embodiment, the isolated radius of the polyhedron (as described in the examples; see also Figure 2) is 4 or greater, 7 or greater, or 10 or greater. In one embodiment, the polyhedron is a bipartite biregular polyhedron having the minimum number of vertices, or a vertex-defected or barrel-shaped vertex-defected derivative thereof. In one embodiment, the polyhedron is a rhombic dodecahedron or a rhombic triaconahedron, or a vertex-defected or barrel-shaped vertex-defected derivative thereof.

[0055] In one embodiment, the vertex-deficient body is missing several vertices at symmetrical positions in a biregular polyhedron (e.g., mirror-symmetric positions, or 1 / 2, 1 / 3, 1 / 4, or 1 / 5 rotational symmetric positions).

[0056] The following table shows representative shapes of the stereomolecules of this disclosure (also showing the intervertex linkers used for constructing the stereomolecules). Note that pairs of shapes, such as A14 and A16, have the same polyhedron shape but different intervertex linker configurations. Notations such as (4,5) indicate the number of bonding parts per constructing element molecule. In notations such as (3,(4,5)), (4,5) represents a mixture of quartic and quintic constructing elements. Table 1. Exemplary (3,5) bipartite biregular polyhedra and their vertex-deficient forms. Table 2. Exemplary (3,4) bipartite biregular polyhedra and their vertex-missing bodies Table 3. Exemplary (2,5) bipartite biregular polyhedra and their vertex-deficient fields (here, quadratic vertices are shown as a single edge along with the two edges extending from them). Table 4. Exemplary (2,3) bipartite biregular polyhedra and their vertex-deficient fields (here, quadratic vertices and the two edges extending from them are shown together as a single edge).

[0057] (3,5) Among bipartite biregular polyhedra and their vertex-missing bodies, A1 to A7 can be easily constructed in particular. (3,4) Among bipartite biregular polyhedra and their vertex-missing bodies, B1 to B11 can be easily constructed in particular.

[0058] In one embodiment, the three-dimensional shape of the stereomolecule is a barrel-shaped vertex-defect derivative. In one embodiment, the barrel-shaped vertex-defect derivative is a derivative composed of three, four, six, seven, or eight repeating units of a barrel-shaped vertex-defect derivative based on a rhombic triacontahedron. In one embodiment, the barrel-shaped vertex-defect derivative is a derivative composed of three, five, six, seven, or eight repeating units of a barrel-shaped vertex-defect derivative based on a rhombic dodecahedron. Stereomolecules having the shape of such barrel-shaped vertex-defect derivatives can be constructed by adjusting the lengths of the intervertex linkers and / or arms of the constructing elements used to construct the barrel-shaped vertex-defect derivative.

[0059] In one embodiment, the stereomolecule has a diameter of about 5 nm to about 20 nm (for example, a range of about 5 nm, about 6 nm, about 7 nm, about 8 nm, about 9 nm, about 10 nm, about 11 nm, about 12 nm, about 13 nm, about 14 nm, about 15 nm, about 16 nm, about 17 nm, about 18 nm, about 19 nm, about 20 nm, or any two of these values). In one embodiment, the stereomolecule has a diameter of about 6 nm or more. In one embodiment, the stereomolecule has a diameter of about 6 nm to about 15 nm. In one embodiment, the stereomolecule has a diameter of about 6 nm to about 12 nm.

[0060] In one embodiment, the stereomolecule of the present disclosure has the lowest discrete Ricci curvature (κ) in the graph. min Characterized by (for example, as defined in the examples). κ of the stereomolecule minThe larger the value, the easier and more stable the stereomolecule is expected to be in terms of synthesis. In one embodiment, the stereomolecule of the present disclosure has a graph shape that does not contain edges with discrete Ricci curvature values ​​less than -0.5, less than -0.3, less than -0.1, or less than 0. In one embodiment, the stereomolecule has a weighted graph shape that does not contain edges with discrete Ricci curvature values ​​less than -0.5, less than -0.3, less than -0.1, or less than 0. A "weighted graph that does not contain edges with discrete Ricci curvature values ​​of a certain value" means a graph that, if unweighted, contains edges with discrete Ricci curvature values ​​of that value, but is modified by weighting specific edges (e.g., a set of edges located in line-symmetric and / or point-symmetric positions) so that no edges with discrete Ricci curvature values ​​of that value exist. The weighting range may be, for example, graph distance = 1 to 100. For example, graph distance = 100 can be used to reflect sufficiently stable bonds, such as irreversible bonds. When considering the substitution of a reversible bond (bond A between bonding parts A and A') with a more stable reversible bond (bond B between bonding parts B and B'), the graph distance may be used = (formation rate of bond B) / (formation rate of bond A) (where the formation rate of bond X is (concentration of bond X) / (concentration of bonding part X + concentration of bonding part X') when bonding parts X and X' of the same specific concentration coexist under specific conditions (such as the conditions for forming the desired stereomolecule)), or a fixed value such as 1.1, 1.2, 1.3, 1.5, or 2 may be used.

[0061] The three-dimensional shapes of the three-dimensional molecules described herein can also be represented based on their similarity in topology (graph) when compared to other three-dimensional shapes. Jaccard's harmonic mean (J) can be used as a measure to quantify topological similarity. ｈａｒｍ ) can be used (J ｈａｒｍ See Example 9 for the definition of ( ). In one embodiment, the stereomolecule of the present disclosure has a J of about 60 to 100% (e.g., about 60% or more, about 70% or more, about 80% or more, or about 90% or more) relative to any of the stereomorphologies listed in Tables 1 to 4. ｈａｒｍThe three-dimensional shape of the graph has the following characteristics. In one embodiment, the three-dimensional molecule of the present disclosure is a (3,5) bipartite binormal polyhedron, a (3,4) bipartite binormal polyhedron, a (2,5) bipartite binormal polyhedron and a (2,3) bipartite binormal polyhedron For a three-dimensional shape selected from the group consisting of the above, J is in the range of approximately 60-100% (for example, approximately 60% or more, approximately 70% or more, approximately 80% or more, or approximately 90% or more). ｈａｒｍ It has a three-dimensional shape of a graph.

[0062] Once constructed, the stereomolecules of this disclosure may be stable and can be stored at room temperature without degradation or aggregation. Furthermore, the stereomolecules of this disclosure may be dryable and reconstituted after solvent removal without forming modified aggregates.

[0063] (Construction Elements) Typically, the stereomolecules of this disclosure are constructed from two types of constructive elements (a first constructive element and a second constructive element). As described above, stereomolecules constructed from two types of constructive elements also include those that have been further modified after being constructed from the two types of constructive elements. For example, as in Example 2, the stereomolecules that are constructed can be predicted based on the structure of the constructive elements.

[0064] In one embodiment, the first structural element is given by the following formula: The compound has the following characteristics, where each A is an independent vertex skeleton having a vertex degree of m, and each R ２ This is independently the first bonding part (one R １ Regarding one or more R ２ (Possible existence), each R １ A and R are independent of each other. ２ It is an arm that connects to each L １ This is an intervertex linker that connects independently different A's, and does not exist when p=1, each m is an integer independently selected from 2 to 6, p is an integer selected from 1 to 4, and the second construction element is given by the following formula: The compound has the following characteristics, where each B is an independent vertex skeleton having a vertex degree of n, and each R ４ This is independently the second bonding part (one R３ Regarding one or more R ４ (Possible existence), each R ３ B and R are independent of each other. ４ It is an arm that connects to each L ２ This is an intervertex linker that connects independently different B vertices, and does not exist when q = 1. Each n is an integer independently selected from 2 to 6, and q is an integer selected from 1 to 4.

[0065] As described above, the first and second structural elements may each contain multiple molecular species. In one embodiment, the first structural elements and / or the second structural elements do not form bonds with each other.

[0066] (Bonding moieties) Bonding moieties are the parts responsible for bonding or affinity between the constituent element molecules when the stereomolecules described herein are assembled by the constituent elements. The presence of at least two bonding moieties in the constituent element molecule allows for the construction of stereomolecules without the reaction ending with a single bond formation.

[0067] Typically, the first bonding moiety in the first construct is a different chemical group from the second bonding moiety in the second construct, and forms a specific bond with the second bonding moiety in the second construct. Other moieties that react under specific reaction conditions may be present in the first and / or second constructs, but during the construction of the stereomolecule, the reaction is promoted under conditions that preferentially form a bond between the first and second bonding moieties.

[0068] In one embodiment, multiple bonding parts within the same structural element molecule are all bonding parts of the same classification (the classification of bonding parts will be described later). In one embodiment, multiple bonding parts within the same structural element molecule all have the same structure. In one embodiment, bonding parts present in the same group of structural element molecular species are all bonding parts of the same classification (the classification of bonding parts will be described later). In one embodiment, bonding parts present in the same group of structural element molecular species all have the same structure.

[0069] In one embodiment, a pair of bonding parts (R ２ and R ４ ) is a combination having a reaction energy (heat of reaction) of about 10 to 500 kJ / mol (for example, about 10 kJ / mol, about 15 kJ / mol, about 20 kJ / mol, about 30 kJ / mol, about 40 kJ / mol, about 50 kJ / mol, about 70 kJ / mol, about 100 kJ / mol, about 150 kJ / mol, about 200 kJ / mol, about 300 kJ / mol, about 400 kJ / mol, about 500 kJ / mol, or a range between any two of these values). The reaction energy between bonding parts is the reaction energy of 1 mol of (CH ３ - A value calculated or measured based on a molecule having the structure of a bonding portion (however, if the bonding portion is a metal atom, a pure metal atom), and the starting material is (CH ３ It is the value obtained by subtracting the total potential energy of the products from the total potential energy of the bonding portion (however, if the bonding portion is a metal atom, it is the total potential energy of the pure metal atom). The potential energy of a compound can be, for example, the energy released when the compound is completely oxidized (combusted).

[0070] Pair of bonding parts (R ２ and R ４ ) can also be expressed based on the state after they have formed a bond. The table below shows examples of bond energy (kJ / mol), bond distance (interatomic distance) (Å), and bond energy density (bond energy / bond distance) for the formed bond.

[0071] In one embodiment, a pair of bonding parts (R ２ and R ４ ) form bonds having bond energies of approximately 10 to 500 kJ / mol (for example, approximately 10 kJ / mol, approximately 15 kJ / mol, approximately 20 kJ / mol, approximately 30 kJ / mol, approximately 40 kJ / mol, approximately 50 kJ / mol, approximately 70 kJ / mol, approximately 100 kJ / mol, approximately 150 kJ / mol, approximately 200 kJ / mol, approximately 300 kJ / mol, approximately 400 kJ / mol, approximately 500 kJ / mol, or a range between any two of these values).

[0072] In one embodiment, a pair of bonding parts (R ２ and R ４ ) form a bond having a bond distance of approximately 1.2 to 2.5 Å (for example, approximately 1.2 Å, approximately 1.25 Å, approximately 1.3 Å, approximately 1.4 Å, approximately 1.5 Å, approximately 1.6 Å, approximately 1.7 Å, approximately 1.8 Å, approximately 1.9 Å, approximately 2.0 Å, approximately 2.1 Å, approximately 2.2 Å, approximately 2.3 Å, approximately 2.4 Å, approximately 2.5 Å, or a range between any two of these values).

[0073] In one embodiment, a pair of bonding parts (R ２ and R ４ ) forms a bond having a bond energy density of about 30 to 200 kJ / mol (for example, about 30, about 40, about 50, about 60, about 70, about 80, about 90, about 100, about 110, about 120, about 130, about 140, about 150, about 160, about 170, about 180, about 190, about 200, or a range between any two of these values).

[0074] The binding moieties can be classified according to their reaction mechanism. Binding moieties of the same classification can be bound to the same functional group by the same reaction mechanism. Those skilled in the art will easily understand binding moieties with the same reaction mechanism, but non-restrictive examples are given below. Table 5. Examples of Classification of Binding Moieties (Reaction Mechanisms) - Activated hydroxyl groups (such as -ONa) may be used as substitutes for hydroxyl groups, and activated carboxyl groups (such as -COCl) may be used as substitutes for carboxyl groups. - Additional elements necessary for the reaction, such as catalysts and light, can be used as appropriate by those skilled in the art.

[0075] In one embodiment, a pair of bonding parts (R ２ and R ４ ) consists of the lone pair of electrons in -COOH and the metal atom, -CHO and -C=NNH ２ (or -C(=O)NRNH ２ ), and -CHO and -NH ２ Selected from the group consisting of .

[0076] A bonding portion other than the specific examples above may refer to a group of atoms where the number of covalent bonds (single, double, or triple) changes when a new bond is formed between atoms belonging to bonding portion A and atoms belonging to bonding portion B. For example, if a long conjugated system exists near the bonding portion, the number of covalent bonds may change throughout the entire conjugated system during bond formation, so the bonding portion may include the entire conjugated system. As another example, if an aromatic ring exists near the bonding portion, the number of covalent bonds may change beyond the aromatic ring from the bonding point during bond formation; in this case, the aromatic ring is considered to be included in the bonding portion.

[0077] (Vertex Skeleton) The vertex skeleton is typically a part of the structural elements located near the vertices of the polyhedra of the stereomolecules described herein.

[0078] In one embodiment, the vertex framework is a ring or a metal atom (such as aluminum (Al), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), zinc (Zn), germanium (Ge), zirconium (Zr), molybdenum (Mo), technetium (Tc), ruthenium (Ru), rhodium (Rh), palladium (Pd), silver (Ag), cadmium (Cd), indium (In), tin (Sn), osmium (Os), iridium (Ir), platinum (Pt), lead (Pb), etc.) or a phosphorus atom.

[0079] Examples of vertex skeletons are given below. These exemplary vertex skeletons are considered as a single vertex skeleton.

[0080] Examples of structures that can be used as vertex skeletons (located at the 5th vertex positions in a bipartite biregular polyhedron) in constructing stereomolecules having the shape of a (5,q) bipartite biregular polyhedron or its vertex-deficient derivative or barrel-shaped vertex-deficient derivative include, for example, carborane, five-membered aromatic rings (such as pyrrole, thiophene, furan, imidazole, triazole, tetrazole, oxazole, isoxazole, thiazole, isothiazole, oxadiazole, thiadiazole, etc.), corannulene, cyanoster, succinimide, and their fused rings.

[0081] (4,q) Examples of structures that can be used as vertex skeletons (located at the quaternary vertex positions in a bipartite biregular polyhedron) in constructing a stereomolecule having the shape of a bipartite biregular polyhedron or its vertex-deficient derivative or barrel-shaped vertex-deficient derivative include metal atoms, porphyrins, tetraarylethenes, and azosines. Here, the metal atoms may be Pd and Pt, which have a tendency to form four-plane coordination on their own, but Cu, Rh, Ru, Mo, Cr, etc. can form the vertices of the stereomolecule by forming a paddlewheel structure, as shown in the following example structure (example of Cu). When forming such a paddlewheel structure in a stereomolecule, it may not be possible to form the paddlewheel structure if a metal atom exists alone as a building element; however, in this specification, this case is included as an example where a metal atom is used as a building element. In this case, the vertex skeleton is considered to be the part of the two metal atoms corresponding to Cu in the figure above. Stereomolecules containing a paddlewheel structure can be constructed in particular with pairs of bonding parts of carboxyl groups and metal atoms, forming one group of bonding part classifications.

[0082] (3,q) Structures that can be used as vertex skeletons (placed at the cubic vertices in a bipartite polyhedron) in a constructor element for building a stereomolecule having the shape of a bipartite polyhedron or its vertex-deficient derivative or barrel-shaped vertex-deficient derivative include, for example, metal atoms (Fe, Pd, Ni, etc.), six-membered aromatic rings (benzene, pyridine, pyridazine, pyrimidine, pyrazine, triazine, pyran, pyrilium, dioxin, thiopyran, oxazine, thiaidine, etc.), and triarylamines (Ar ３ N), triarylphosphine (Ar ３ P; may be phosphonium), triarylmethane (Ar ３ C), Triarylsilyl (Ar ３ Examples include Si, cyclopropane, and their fused rings.

[0083] (2,q) Structures that can be used as vertex skeletons (those positioned at the quadratic vertices in a bipartite polyhedron) in a constructor element for building a stereomolecule having the shape of a bipartite biregular polyhedron or its vertex-deficient derivative or barrel-shaped vertex-deficient derivative include, for example, metal atoms, six-membered aromatic rings, -C=C-, -C≡C-, and fused rings thereof.

[0084] In one embodiment, when a first structural element is used that includes a vertex skeleton with cone-shaped arms, such as carborane, colannulene, triarylphosphine, triarylmethane, or triarylsilyl, the second structural element includes a vertex skeleton with planar arms.

[0085] In one embodiment, the distances between multiple vertex skeletons of the stereomolecule described herein are similar, and the stereomolecular shape exhibits high symmetry. In one embodiment, for all A-B distances in the stereomolecule, the A-B distances vary from each other by less than 20%, less than 10%, or less than 5%. "A-B distance" is the minimum distance between the vertex skeletons of a first and second constructor that are bonded in the stereomolecule. The distance between vertex skeleton A of the first constructor and vertex skeleton B of the second constructor is the distance between the geometric centroid of vertex skeleton A and the geometric centroid of vertex skeleton B in the stereomolecule.

[0086] In one embodiment, in a constructor molecule having multiple vertex skeletons, the structures of the vertex skeletons may be identical. In one embodiment, in a constructor molecule having multiple vertex skeletons, the vertex order may differ between the vertex skeletons, and such a configuration may be particularly preferred when constructing stereomolecules having the shape of a vertex defect or a barrel-shaped vertex defect derivative. In one embodiment, all vertex skeletons in a group of molecular species of the same constructor may be identical. In one embodiment, the vertex order of vertex skeletons in a group of molecular species of the same constructor may differ.

[0087] (Arms) Arms are parts that can affect the diameter of a stereomolecule. Longer arms can provide stereomolecules with larger diameters. The part of the arm that connects the vertex skeleton and the bonding part with the minimum number of interatomic bonds is called the "main chain" of the arm. There can be multiple main chains of an arm, such as when the arm contains a ring, but unless otherwise specified, the description of the main chain of an arm in this specification means that there is at least one main chain of an arm that satisfies the conditions. In a typical embodiment, the main chain of an arm is a "rigid" part with a linear shape, and motion other than axial rotation is restricted in free building element molecules. Therefore, in one embodiment, the main chain of the arm satisfies one or more of the following conditions: - It does not contain any consecutive single bonds (covalent bonds), or it contains only one consecutive single bond (covalent bond) (where neither of the two consecutive single bonds (covalent bonds) is part of a ring); - One or both of the consecutive single bonds (covalent bonds) contained in the main chain of the arm are part of a ring (such as a spiro ring); - It is a repeating ring (especially aromatic ring)-single bond structure.

[0088] In one embodiment, the number of atoms constituting the main chain of an arm may be 0 to 100. In one embodiment, the number of atoms constituting the main chain of the arms of the first and second structural elements (the longest one if multiple types of arms exist) may independently be 2 to 100 (for example, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, or a range between any two of these values). In one embodiment, the total number of atoms constituting the main chain of the arms of the first and second structural elements (the longest one if multiple types of arms exist) may be 2 to 100 (for example, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, or a range between any two of these values). In particular, if the vertex skeleton is metallic atoms, there may be no arms.

[0089] In a typical embodiment, the length of the main chain is approximately the same across multiple arms in a single structural element molecule. For the construction of the stereomolecules described herein, the length of the main chain of an arm may be more important than the configuration of the arm itself. In one embodiment, the difference in main chain length between each arm in a single structural element molecule is 5 atoms or less, 4 atoms or less, 3 atoms or less, 2 atoms or less, or 1 atom. In one embodiment, the atomic arrangement of the main chains between each arm in a single structural element molecule is the same. In one embodiment, each arm in a single structural element molecule is identical.

[0090] While structural elements with main chains of arms of the same length may be easy to synthesize, it is also possible to design structural elements in which the arms are positioned so that the bonding portion is located at a specific location. In one embodiment, the arms of a structural element are configured such that the bonding portion (or the geometric centroid of the atomic group constituting it) is located on the circumference of the same circle or within 10% (or 5%) of the circle's diameter from the circumference, and at an angle of approximately 360° / m (where m is an integer between 3 and 6) from the center of this circle. For example, the following is a structural element structure: In such cases, the vertex skeleton is often not located at the vertices of the polyhedron of the stereomolecule; instead, the geometric centroids of the atomic groups constituting the bonding parts may be located at the vertices of the stereomolecule's polyhedron. The example on the right above may correspond to a compound in which two secondary vertex skeletons are linked by intervertex linkers, but can be used in the same way as a constructor element having one quaternary vertex skeleton. Therefore, a constructor element containing multiple bonding parts located on a specific circumference as described above (it is not necessary for all bonding parts of the constructor element molecule to be located on the same circumference) may define features such as arms or intervertex linkers described herein by considering the structure enclosed by this circle (for example, a structure in which multiple rings are bonded) as the vertex skeleton.

[0091] In one embodiment, the angle between the main chains of arms bonded to the same vertex skeleton (based on the straight line connecting the atoms at both ends of the main chain) is approximately 360° / m (where m is an integer between 2 and 6).

[0092] The arms may be modified with any substituents, as long as they do not interfere with the construction of the stereomolecule.

[0093] In a typical embodiment, there is one bonding moiety in a single bonding chain that is involved in the formation of the stereomolecule, but there may be multiple (e.g., two) bonding moieties in a single bonding chain. For example, an exemplary structure of a stereomolecule formed by a component comprising a vertex skeleton of a carborane having five bonding chains, each having two bonding moieties, and a component comprising a vertex skeleton of a triphenylene having six bonding chains, each having one bonding moiety, is shown below. This structure is a (3,5) bipartite biholomorphic polyhedron with each edge doubled. It can be treated as a stereomolecule having a three-dimensional shape.

[0094] (Intervertex Linkers) Intervertex linkers are parts that connect vertex skeletons. Typically, intervertex linkers connect vertex skeletons by irreversible covalent bonds that do not react under the reaction conditions that form stereomolecules from their constituent elements. In one embodiment, intervertex linkers are located at the points corresponding to the edges to which weighting was introduced when a weighting operation was performed from a graph containing edges with a certain value of discrete Ricci curvature to a weighted graph that does not contain edges with that value of discrete Ricci curvature. In one embodiment, intervertex linkers may have a chemical structure similar to that of an arm (for example, the number of atoms constituting the main chain of an intervertex linker may be 0 to 100). Intervertex linkers are typically introduced to construct stereomolecules with the shape of a vertex-defective polyhedron, but they may also be introduced into constructors to construct stereomolecules with the shape of a bipartite bihedra. When changing from a bipartite bihedra to a vertex-defective polyhedron, some vertices that were not removed from the bipartite bihedra may have a decrease in bond order, while others may have a constant bond order. To reflect this, if a mixture of two types of constructors—one with a vertex skeleton having only a p-order bond and another with a vertex skeleton having only a p-1-order bond—is used instead of a constructor having only a vertex skeleton having a p-order bond, the system becomes more complex, a large number of stereomolecules with unintended shapes may be generated, and the yield of stereomolecules with the desired shape may be significantly reduced. In addition, the stability of the constructed stereomolecules may decrease due to the reduction in bond order. By using intervertex linkers, it may be possible to avoid increasing the number of types of constructors to react and reducing the number of bonding moieties in the constructor molecules.

[0095] A (p,q) bipartite bihedra can be defined as a p-vertex polyhedron or a q-vertex polyhedron by selecting only the p-vertex or q-vertex vertices. Intervertex linkers should be designed to be positioned along the edges of the p-vertex or q-vertex polyhedron. However, for the construction of the three-dimensional molecule, it is preferable to design the vertex degree and intervertex linkers of each vertex skeleton of the constructing element in such a configuration that, even when the three-dimensional molecule is assembled, no intervertex linkers are positioned along any edge surrounding a certain face (face A) of the p-vertex or q-vertex polyhedron. In this case, vertices outside face A from the center of the polyhedron can be removed. Intervertex linkers can be designed to connect vertex skeletons corresponding to the same type of vertices in two types of vertex groups that constitute the bipartite bihedra, and to match the distance and angle between these vertex skeletons in a three-dimensional molecule having the shape of the bipartite bihedra.

[0096] In one embodiment, the intervertex linker may have a length that mimics the shortest distance between identical vertices of two different vertex groups constituting a bipartite biregular polyhedron. In one embodiment, the intervertex linker has a length based on the ratio of [edge length] / [extension between identical vertices] (length ratio) of the bipartite biregular polyhedron of the stereomolecule being constructed (or, if the stereomolecule being constructed has the shape of a vertex-deficient or barrel-shaped vertex-deficient derivative, the original bipartite biregular polyhedron) which has the highest symmetry (the structure with the maximum number of edges of equal length and angles of equal angle in the polyhedron). Specifically, the intervertex linker has a length such that the ratio of [intervertex skeleton distance (A-B distance)] / [intervertex linker length (distance between the geometric centroids of the first and second vertex skeletons in the same structural element molecule)] is within the length ratio plus or minus 10% or 5%, or the minimum number of interatomic bonds such that the ratio of [number of interatomic bonds when linking the vertex skeletons of the first and second structural elements in a stereomolecule with the minimum number of interatomic bonds] / [number of interatomic bonds when linking the first and second vertex skeletons in the same structural element molecule with the minimum number of interatomic bonds] is within the length ratio plus or minus 10% or 5%.

[0097] (Molecular species of the constructing element) The first constructing element (and / or the second constructing element) may be a group of molecules comprising multiple molecular species, which may differ from one another in vertex order (number of bonding moieties), arm structure, intervertex linker structure, and chemical modifications by substituents and / or isotopic atoms. If there are molecular species with different numbers of bonding moieties among these multiple molecular species, it is preferable that there is only one type of different bonding moiety, and that the difference in the number of bonding moieties is 1. When these multiple molecular species include molecular species with different numbers of bonding moieties, the basic structure is a stereomolecule having the shape of a vertex-deficient based on the molecular species with the smallest number of bonding moieties. For example, in the construction of a stereomolecule having the shape of a rhombic icosahedron using a fifth-order vertex carborane, if an equimolar mixture of a fifth-order vertex carborane and a fourth-order vertex carborane is used instead of a fifth-order vertex carborane to construct the stereomolecule, a stereomolecule may be obtained in which unreacted binding sites derived from the fifth-order vertex carborane protrude into the vertex-deficient portions of the vertex-deficient body that would be constructed if only a fourth-order vertex carborane were used (see the example in "Synthesis of a Defective Rhombic Icosahedron from Constructing Elements car-5c-A', car-4c-A, and ben-3c-C").

[0098] In particular, modifications with substituents (such as those on the vertex skeleton, arms, and / or intervertex linkers) and isotopic atoms are considered to have little effect on the formation of the stereomolecules of this disclosure. Therefore, even if constructs containing multiple different molecular species are used in these chemical modifications, stereomolecules can still be formed. Modifications introducing any of the substituent examples described herein are possible.

[0099] (Modification) Stereomolecules can be modified as desired. Modification of a steric molecule may be applied after the construction of the steric molecule, or it may be carried out by constructing the steric molecule using the modified constructor. Examples of modifications to steric molecules (and / or constructors) include: - Modifications for bond formation unrelated to the construction of the steric molecule (including chemical groups that can be used in the bonding moieties described herein) - Modifications to improve the solvent solubility of constructors (e.g., PEG modification to improve solubility in aqueous solvents) - Modifications to adjust the angles between arms (e.g., introducing bulky groups at obtuse angles between arms to reduce the angle between them) - Modifications to adjust the angles of arms with respect to the plane of the bonding moiety (a plane approximated by least squares to the bonding moiety) (e.g., introducing bulky groups on the side of the arm furthest from that plane to reduce the angle) - Modifications to reduce aggregation between steric molecules (e.g., assigning the same positive or negative charge, combinations of lipophilic and hydrophilic groups) - Conjugates of drugs (including polypeptides and polynucleotides). Those skilled in the art will readily understand the specific chemical groups that can be used for each modification. Modifications are possible by introducing any of the substituent examples described herein.

[0100] (Method for fabricating stereomolecules) In one aspect, this disclosure provides a method for fabricating stereomolecules as described herein. The method is: (A) preparing a first constructor, wherein the first constructor is given by the following formula: The compound has the following characteristics, where each A is an independent vertex skeleton having a vertex degree of m, and each R ２ This is independently the first bonding part (one R １ Regarding one or more R ２ (Possible existence), each R １ A and R are independent of each other. ２ It is an arm that connects to each L １(B) A vertex linker that connects independently different A's, which does not exist when p = 1, where each m is an integer independently selected from 2 to 6, and p is an integer selected from 1 to 4, (B) A step of preparing a second construction element, where the second construction element is given by the following equation: The compound has the following characteristics, where each B is an independent vertex skeleton having a vertex degree of n, and each R ４ This is independently the second bonding part (one R ３ Regarding one or more R ４ (Possible existence), each R ３ B and R are independent of each other. ４ It is an arm that connects to each L ２ (C) a vertex linker that connects independently different Bs, which does not exist when q=1, where each n is an integer independently selected from 2 to 6, and q is an integer selected from 1 to 4, and the step of (C) mixing the first and second construction elements to form a stereomolecular having the shape of the polyhedron with A and B positioned at its vertices by forming a plurality of bonds between the first bonding portion and the second bonding portion.

[0101] In a preferred embodiment, the step of forming multiple bonds between the first and second bonding moieties may be carried out under conditions in which the bond formation reaction between the first and second bonding moieties proceeds reversibly. Since the stereomolecules of this disclosure can be entropically (statistically) promoted in one aspect, reversible reaction conditions may be advantageous. For example, conditions for this include 1 mol of (CH4). ３ - First bonding portion) and 1 mol of (CH ３ When the second bonding portion is mixed and sufficient time has passed for the system to reach equilibrium, approximately 1-99% (for example, approximately 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 95%, 99%, etc.) of unreacted (CH₂) remains. ３ - First bonding portion) and / or (CH ３The conditions for the presence of a second bonding moiety may include the type of solvent (which may be a mixed solvent), the concentration of the building blocks, temperature, pH, pressure, light, and additives (such as oxidizing agents). The specific conditions depend on the specific pair of bonding moieties, but those skilled in the field of chemistry can usually understand the conditions necessary to promote the bond formation reaction between pairs of bonding moieties. The constructed stereomolecule may be purified.

[0102] (Applications) The stereomolecules described herein can be used in any suitable application. Based on the description of the applications of the stereomolecules, it will be understood by those skilled in the art that the methods of using the stereomolecules are equivalent to those described herein. The stereomolecules described herein can capture specific molecules, such as MOFs. The stereomolecules described herein may have the effect of stabilizing the molecules (such as proteins) that are captured inside, and this effect may be beneficial in various applications. The stereomolecules described herein can prevent the formation of aggregates (such as molecules randomly bound to each other) by sequestering the captured molecules (such as proteins), while the stereomolecules described herein may be able to disperse in a solvent in a free state without binding to each other. Therefore, the stereomolecules described herein can also be used as dispersants for captured molecules. The stereomolecules described herein can be easily chemically modified on their surface, and the applications according to the function of the introduced functional groups will be understood by those skilled in the art. For example, any chemical modification applied to carriers such as liposomes or proteins can be applied to the stereomolecules described herein.

[0103] (Kit) In one aspect, this disclosure provides a kit for constructing the stereomolecules described herein. The kit comprises a first constructor and a second constructor. In one embodiment, the kit includes instructions for carrying out the method described herein.

[0104] (Other Embodiments) The present invention has been described above with reference to preferred embodiments for ease of understanding. The present invention will now be described based on examples, but the above description and the following examples are provided for illustrative purposes only and are not intended to limit the present invention. Accordingly, the scope of the present invention is not limited to the embodiments or examples specifically described herein, but is limited only by the claims.

[0105] Examples are described below. The reagents used were specifically those listed in the examples, but equivalent products from other manufacturers (Sigma-Aldrich, Fujifilm, Wako Pure Chemical Industries, Nakai, R&D Systems, USCN Life Science INC, Kanto Chemical, Funakoshi, Tokyo Chemical Industries, Merck, etc.) can be used as substitutes.

[0106] (Example 1: Theorization of the shape of a three-dimensional molecule suitable for construction by self-assembly) When attempting to construct a specific three-dimensional molecule from parts, it is possible to target a three-dimensional molecule that has the shape of a regular polyhedron, in which the parts are connected by regular bonding relationships. On the other hand, the condition of being a regular polyhedron alone is insufficient, as there can be countless regular polyhedra that can be constructed from a single type of part (see Figure 1), making it practically difficult to obtain a specific three-dimensional molecule. Therefore, the inventors investigated the three-dimensional shape that should be targeted in order to construct a specific three-dimensional molecule from parts.

[0107] 1.1 Foundations of Graph Theory - Theorem 1 (Euler's Polyhedron Theorem) When V, E, and F are the number of vertices, edges, and faces of a polyhedron (convex polyhedron) whose faces do not intersect, the following equation holds: V - E + F = 2 (1)

[0108] Theorem 2 (The Handshake Lemma) Let dv be the degree of the vertex of graph G = (V, E). Then the following equation holds:

[0109] 1.2 In an equitable partition graph, one method for dividing vertex sets into groups with similar properties is the equitable partition (C. Godsil, and G. Royle. Graduate Texts in Mathematics Springer, (2001).).

[0110] Definition 1 (Fair Partition) For a graph X = (V(X), E(X)), the partition of V(X) is π = (C １ , . . , C ｒ ) is considered equitable if cell C ｉ Among the vertices adjacent to vertex u, cell C ｊ The number contained in u is a constant b that does not depend on u. ｉｊ The equivalent definition is that the subgraph of X induced by each cell is regular, and the edges connecting any two different cells form a semiregular bipartite graph.

[0111] ・Definition 2 (quotient graph) Fair division π = (C １ , . . , C ｒ ) has r cells as vertices, and from the i-th cell to the j-th cell of π, b ｉｊ A directed graph with n edges is called a quotient graph of X by π, and is denoted as X / π. Therefore, the adjacency matrix of this quotient graph is given by: A(X / π) ｉｊ = b ｉｊ (3)

[0112] for example, In the example graph, the partition π = {{1, 2, 3}, {4, 5, 6}, {7}} is fair. Also, the adjacency matrix of its quotient graph is It is given by.

[0113] 2. Generalized Regular Graphs 2.1 Definition / Definition 3 (Generalized Regular Graph) A generalized regular graph is a graph G = (V, E) where the vertices V are set to a set V.１ , V ２ , . . . , V ｎ When divided into sets V, each set ｉ In V, each vertex has the same degree, and is further connected to a vertex belonging to Vi by an edge. １ , V ２ , . . . , V ｎ The number of vertices is {a} ｉｊ} = a ｉ，１ , a ｉ，２ , . . . , a ｉ，ｎ When expressed as such, all V ｉ {a} of the vertices belonging to ｉｊ This is a graph such that {a} are equal. Matrix A = {a ｉｊ Using}, we will call this graph an A-generalized regular graph.

[0114] Using the term "fair partitioning" mentioned earlier, an A-generalized regular graph is a graph that has a fair partitioning such that its quotient graph is A.

[0115] 3. Biholomorphic Graphs In particular, consider the case where the dimension of A in an A-generalized holomorphic graph is 2 and the diagonal terms are 0.

[0116] 3.1 Properties and Definitions of Biregular Graphs 4 (Biregular Graphs) A biregular graph is a bipartite graph G = (U, V, E) where V is an independent set. １ and V ２ A graph such that when partitioned into independent sets, each vertex in each set has the same degree. １ Let p be the degree of the vertex, V ２ If the degree of a vertex is q, then this graph is called (p,q) bimorphic.

[0117] (p, q) - Biholomorphic graphs are, This is equivalent to A-generalized holomorphic graph. A self-assembly formed by alternately linking two types of molecules becomes a biholomorphic graph when the molecules are considered as points and the connections as edges.

[0118] Below, in order to narrow down the self-assembling structures, we consider biholomorphic planar graphs. From Theorems 1 and 2, we can show that the following equations hold.

[0119] Theorem 3 (Number of vertices and edges of a biholomorphic planar graph) Among (p,q)-biholomorphic graphs G=(V,E) having m vertices of degree p and n vertices of degree q, the number of vertices and edges of a planar graph can be expressed using a natural number x as follows. A planar graph is a graph that can be drawn on a plane without its edges intersecting.

[0120] Proof Theorem 1 and Theorem 2, Therefore, since G is a biholomorphic graph, pm = qn. Thus, |E| = pm = qn (11) holds. Since |E| is a multiple of p and a multiple of q, it can be written as |E| = lcm(p, q) * x (12) using a natural number x. From equations (11) and (12) We obtain, and from |V| = m + n This can be obtained.

[0121] Next, let's consider the possible ranges of p and q. For simplicity, we will only consider simple graphs.

[0122] Theorem 4 (Properties of Biholomorphic Planar Simple Graphs) Among (p,q)-biholomorphic graphs obtained by alternately connecting p-degree vertices and q-degree vertices, planar simple graphs satisfy the following inequalities: 2 / p + 2 / q > 1 (15) p ≤ 5, q ≤ 5 (16)

[0123] ・Proof From the properties of a bipartite plane graph, we can say that all faces are even-sided, and at the very least, quadrilaterals. Therefore, by Theorem 1 and Theorem 2, the following equations hold: |E| - |V| = -2 + a + b + c + ... (17) 2|E| = 4a + 6b + 8c + ... (18) (a, b, c are the number of sides of 4, 6, 8, ... in that order) (19) Eliminating a, we get 2|V| - |E| = 4 + b + 2c + ... (20)

[0124] Since all terms on the right-hand side are non-negative, 2|V|-|E| must be > 0. On the other hand, by Theorem 3, we can write 2V-E = lcm(p,q)(2 / p+2 / q-1)x (21), so 2 / p+2 / q-1>0 (22), which gives equation (15). When p≦3 and q≦3, the only combinations that satisfy this are (p,q)=(3,3), (3,4), (3,5), (4,3) and (5,3). Therefore, equation (16) is satisfied.

[0125] When p = 2, equation (15) is always satisfied, but in that case, it has a minor q-degree holomorphic planar graph. Since a planar graph always has vertices of degree 5 or less, q ≤ 5 is required. The same applies when q = 2. In either case, equation (16) is satisfied.

[0126] 3.2 From the minimum construct equations (20) and (21) of the planar biholomorphic graph, the following holds: lcm(p,q)(2 / p + 2 / q - 1)x = 4 + b + 2c + ... ≥ 4 (23) Thus, the lower bound of x is given.

[0127] When (p, q) = (3, 3), x ≥ 4, and the lower limit x = 4 corresponds to a cube with 8 vertices and 12 edges. When (p, q) = (3, 4), x ≥ 2, and the lower limit x = 2 corresponds to a rhombic dodecahedron with 14 vertices and 24 edges. When (p, q) = (3, 5), x ≥ 4, and the lower limit x = 4 corresponds to a rhombic triacontahedron with 32 vertices and 60 edges. However, this is limited to planar graphs (for example, K ３，５ This is a binormal graph with 8 vertices, but it is not planar.

[0128] 3.3 Existence conditions for planar biholomorphic graphs According to P. Adams and Y. Nikolayevsky, Discrete Mathematics 342 (2019) 433–440, the following theorem holds.

[0129] Theorem 5 (Conditions for the existence of a planar biholomorphic graph) Let G be a (p,q)-biholomorphic graph (1≦p≦q), and let m and n be the number of p-th order vertices and q-th order vertices, respectively. The conditions for the existence of a planar graph G are as follows: 1. p=1, m=nq 2. p=2, m=qk, n=2k (k≧1) 3. p=q=3, m=n=k (k≧4, k≠5) 4. p=3, q=4, m=4k, n=3k (k≧2) 5. p=3, q=5, m=5k, n=3k (k≧4, k≠5)

[0130] However, the conditions for k in Theorem 5 3, 4, and 5 (k≧4, k≧2, and k≧4, respectively) are as shown in 3.2.

[0131] 3.4 Ratio of edges to vertices in a planar biholomorphic graph In a biholomorphic graph, the ratio of edges to vertices |E| / |V| is constant for each (p, q). In fact, by Theorem 3, Therefore, This can be obtained.

[0132] 3.5 Isolation Radius of Planar Biholomorphic Graphs When self-assembling, it is considered more stable if there are no structures with a similar number of vertices around them. Therefore, the isolation radius of a planar biholomorphic graph is defined as follows.

[0133] Definition 5 (Isolation radius of a planar biholomorphic graph) When G = (V, E) is a planar (p, q)-biholomorphic graph, the largest natural number S that satisfies the following is called the isolation radius of G: There are no planar (p, q)-biholomorphic graphs with a number of vertices greater than |V|-S and less than |V|+S other than those with a number of vertices of |V|.

[0134] Examples are shown below (see also Figure 2). The notation from Theorem 5 is used as is. • Example: (3,3) - A biholomorphic graph exists for k = 4, 6, 7, 8, 9, ..., and the number of vertices |V| = 8, 12, 14, 16, 18, ..., so S = 4 only when k = 4, and S = 2 for all others. • Example: (3,4) - A biholomorphic graph exists for k = 2, 3, 4, 5, ..., and the number of vertices |V| = 14, 21, 28, 35, ..., so S = 7 in all cases. • Example: (3,5) - A biholomorphic graph exists for k = 4, 6, 7, 8, 9, ..., and the number of vertices |V| = 32, 48, 56, 64, 72, ..., Therefore, S=16 only when k=4, and S=8 otherwise. Figure 3 shows examples of three-dimensional shapes of bimorphic graphs other than the (3,4)-bimorphic graph with 14 vertices (rhombic dodecahedron).

[0135] The ratio of edges to vertices and the radius of isolation can have chemical significance when considering self-assemblies. First, when unit molecules (constructing elements) self-assemble, a smaller number of unit molecules (vertices) required to construct the target stereomolecule is entropically advantageous. On the other hand, since the energy decreases proportionally to the number of bonds by the amount of bond energy, a larger number of bonds is energetically advantageous. As a result of this competition, stereomolecules are constructed, and it is thought that a higher ratio of edges to vertices is advantageous for constructing larger stereomolecules. This is because, even if the construction of large stereomolecules is entropically disadvantageous, the contribution of bond energy per stereomolecule becomes relatively higher. In this regard, we assumed stereomolecules constructed from two types of unit molecules corresponding to bi-regular planar simple graphs and calculated the average chemical bond density per unit molecule (Figure 4). The case where (p,q) = (3,5) has the highest chemical bond density, suggesting that the constructed stereomolecule is stable and easily constructed.

[0136] Furthermore, a large isolation radius can also be important for constructing large stereomolecules. This is because if there are other convergent structures with a similar number of vertices, the yield of the desired stereomolecule may decrease.

[0137] (Example 2: Design of constructing elements for constructing the target stereomolecule) Example 1 showed a suitable stereomolecule shape and the vertex order of the constructing elements for its construction. This example provides details on the design of the chemical structure of the constructing elements. Consider the case where a constructing element has no intervertex linkers (or all bonding parts in the molecule are located on approximately the same circumference).

[0138] First, here is an example of the procedure for converting a graphical representation into a three-dimensional shape.

[0139] (Using the graph Laplacian and eigenvectors) The graph Laplacian matrix L is defined as L = D - A (D: degree matrix, A: adjacency matrix). The Laplacian matrix has the following characteristics: - The sum of each row (column) is 0. - Off-diagonal elements are either -1 (if there is a connection) or 0 (if there is no connection). - Diagonal elements represent the degree of their vertices.

[0140] For example, the following graph The graph Laplacian matrix L for can be written as follows:

[0141] Next, we calculate the eigenvalues ​​and eigenvectors of the Laplacian matrix. We use the second to fourth smallest eigenvalues ​​and their corresponding eigenvectors to determine the vertex arrangement. For bipartite graphs, the procedure is as follows: ・Assign coordinates to each vertex using the elements of the eigenvectors. ・Divide the vertices into groups and arrange vertices belonging to the same group on the same sphere. ・For each edge, divide the edge into groups according to the groups to which the vertices at both ends belong. ・Match the centers of the spheres. ・The position of each vertex is represented as a point on the sphere, using the eigenvector value as the direction vector from the center of the sphere. (Reference: Fiedler, M. "Algebraic Connectivity of Graphs", Czechoslovak Mathematical Journal, 1973)

[0142] Although this is just one example of a graph, the following illustrates the procedure for assigning coordinates to a triregular graph (regular tetrahedron). If the vertices of the graph are labeled 0, 1, 2, and 3, the adjacency matrix A will be as follows. This matrix represents the connection relationships between vertices, A ｉｊ = 1 means that vertex i and vertex j are connected, A ｉｊ =0 indicates that it is not connected.

[0143] In the case of a regular tetrahedron, the degree of all vertices is 3, so the degree matrix D is as follows:

[0144] Therefore, the Laplacian matrix L is calculated as follows:

[0145] Next, we calculate the eigenvalues ​​and eigenvectors. The eigenvalues ​​λ and eigenvectors v of the Laplacian matrix L are defined as satisfying the following equation: Lv = λv Calculating the eigenvalues ​​and eigenvectors for the above graph yields the following results (rounded to four decimal places): ・Eigenvalues: • Eigenvectors (displayed as column vectors) (v ０ λ is an eigenvalue ０ This is an eigenvector corresponding to 0, where all elements are equal. This represents a "stationary distribution" and reflects the basic structure of the graph.

[0146] We use the eigenvectors corresponding to the second to fourth smallest eigenvalues. In the case of a regular tetrahedron, λ １ = λ ２ = λ ３ v corresponds to 4.0000 １ ,v ２ and v ３ It is. １ ,v ２ ,v ３ Using these as x, y, and z coordinates respectively, it can be expressed as follows. Converting this to a vertex-by-vertex display results in the following:

[0147] In this way, we can obtain the coordinates of each vertex (which can be used as vectors of equal length from the center of the sphere).

[0148] (Molecular arrangement) Now that the three-dimensional shape corresponding to the graph has been obtained above, the constructing element molecules are arranged based on this. ・Plot the center positions of the newly generated chemical bonds based on the bonding parts of the constructing element molecules. ・Construct a two-dimensional circle that includes all of these plots on its circumference. ・Place the center of this two-dimensional circle on the coordinates obtained from the graph above. Here, the two-dimensional circle A based on constructing element molecule A corresponds to the coordinates on sphere A corresponding to vertex group A, and the two-dimensional circle B based on constructing element molecule B corresponds to the coordinates on sphere B corresponding to vertex group B, and are arranged so that the center of the sphere is perpendicular to the plane of the two-dimensional circle. ・While maintaining the diameters of two-dimensional circles A and B, multiply the coordinates by a constant so that the circumferences of two-dimensional circles A and B are tangent to each other (the same constant for vertex group A and vertex group B). ・Align the plots of the center positions of the chemical bonds on the circumferences of two-dimensional circles A and B. ・Reconstruct the molecular model of the constructing element molecules in accordance with the two-dimensional circle.

[0149] Subsequently, the structure of the three-dimensional molecule can be adjusted as follows: • If chemical bonds are rotatable or multiple bonds exist, select a configuration where the restored molecules do not come into steric contact. • Optimize the configuration by considering bond angles and degrees of rotational freedom to avoid intermolecular steric hindrance. • Confirm the overall structural stability and energy minimization using molecular dynamics simulations, etc.

[0150] Based on the stability of the overall structure, the yield of the desired stereomolecule can be predicted. Furthermore, the building blocks can be designed to have a structure that fits the above-mentioned two-dimensional circle and chemical bond center position plot.

[0151] The coordinates of each vertex of a three-dimensional shape can be obtained through mechanical simulation. For example, the following parameters can be set for each vertex and the simulation can be performed: • Setting virtual charges: Assign virtual charges of the same sign to vertices of the same group, creating a repulsive force between them. • Setting virtual springs: Place virtual springs with spring constants corresponding to the group to which each edge belongs, generating an attractive force. Using dynamic simulations or energy minimization techniques, the equilibrium state of the forces is determined, and the simulation is considered to have converged when the change in energy falls below a certain threshold. This simulation is called a "graph plotting method based on a mechanical model (dynamical system)" or a "spring model (Spring Layout)," and algorithms such as the "Fruchterman-Reingold algorithm" and the "Kamada-Kawai algorithm" are publicly known.

[0152] (Example 3: Design Strategy for Vertex-Deficient Bodies) Following the concepts described in Examples 1 and 2, stereomolecules having the shape of a (p,q) bipartite bihedra and their building elements can be designed. Vertex-deficient bodies can also be designed by deleting one or more vertices from such (p,q) bipartite bihedra. Stereomolecules having vertex-deficient bodies may also be subject to entropic and energetic construction driving forces, similar to stereomolecules having the shape of a bipartite bihedra.

[0153] While some vertex-defect polyhedra can be designed simply by removing (inactivating) some of the bonding parts of the constructing elements, a wider variety of vertex-defect polyhedra can be designed by linking constructing elements corresponding to the same type of vertices via intervertex linkers. Typical design guidelines for vertex-defect polyhedra using intervertex linkers are shown in Figures 5 and 6. By extracting only the p-th order vertices or q-th order vertices from a (p,q) bipartite biholomorphic polyhedron, the p-th order vertex polyhedra and the q-th order vertex polyhedra can be defined, respectively. The intervertex linkers are designed to be positioned along the edges of these p-th order or q-th order vertex polyhedra. It is preferable to design the constructing elements such that, even when the three-dimensional molecules are assembled, no intervertex linkers are positioned along any edges surrounding a particular face (face A) of these p-th order or q-th order vertex polyhedra. In this case, vertices outside face A from the center of the polyhedron can be removed.

[0154] Constructing elements, including intervertex linkers, can also be expressed in terms of the number of binding sites per molecule. For vertex-deficient structures, they are expressed in terms of the number of binding sites per constructing element molecule. In notations such as (3, (4, 5)), (4, 5) represents a mixture of quaternary vertex constructing elements and quintic vertex constructing elements. A construction strategy for vertex-deficient structures using such a mixture probabilistically yields the desired stereomolecule, but does not compete with the construction of stereomolecules of completely different shapes. Therefore, it is not affected by the decrease in yield of the desired stereomolecule due to the presence of other convergent structures, as described in Example 1, and can still be subject to entropic and energetic construction driving forces (however, purification is required to obtain a stereomolecule of a single shape).

[0155] The following shows the design strategies for an exemplary rhombic icosahedron and its vertex-missing form. The edges corresponding to the intervertex linkers are also shown. • trc-A series ・trc-B series ・trc-C series ・trc-D series

[0156] In the examples, a carborane derivative was used as the fifth vertex, but it is thought that vertex-deficient compounds of the trc-B series can also be suitably formed using structural elements that have pyrrole and thiophene as the vertex skeleton.

[0157] The following shows the design strategies for an exemplary rhombic dodecahedron and its vertex-missing form. The edges corresponding to the intervertex linkers are also shown. • rdo-A series ・rdo-B series

[0158] The following are design strategies for an exemplary (2,5) bipartite biregular polyhedron and its vertex-missing solid (where a quadratic vertex is shown as a single edge along with the two edges extending from it): • trc-A series

[0159] (Example 4: Synthesis of Constructing Elements) Following the strategy of Example 3, each constructing element for the construction of the stereomolecule was synthesized.

[0160] - Combination scheme of construction element 3c

[0161] - Synthesis of S1 To a solution of 1,3,5-tris(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzene (456 mg, 1.00 mmol, 1 equivalent) and methyl 3-bromo-4-methylbenzoate (514 μL, 3.30 mmol, 3.3 equivalents) in 1,4-dioxane (10 mL), an aqueous solution of tripotassium phosphate (637 mg, 3.00 mmol, 3 equivalents) (5 mL) was added, and the mixture was degassed by nitrogen bubbling for 15 minutes. Next, Pd(PPh) ３ ) ４(116 mg, 0.100 mmol, 10 mol%) was added, and the mixture was stirred at 100°C under nitrogen for 18 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The organic layer was washed twice with brine, dried over sodium sulfate, and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-20%) to obtain dimethyl 5'-(5-(methoxycarbonyl)-2-methylphenyl)-6,6''-dimethyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S1) (382 mg, yield 73%) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ7.96 (d, J=1.8Hz, 3H), 7.92 (dd, J=7.9, 1.8Hz, 3H), 7.34 (d, J=8. 1Hz, 3H), 7.24 (d, J=0.9Hz, 3H), 3.88 (d, J=0.9Hz, 9H), 2.39 (s, 9H).

[0162] ・3c synthesis S1 (261 mg, 0.500 mmol, 1 equivalent) was dissolved in a mixed solvent of methanol (5 mL) and tetrahydrofuran (5 mL). An aqueous solution (2.5 mL) of lithium hydroxide monohydrate (315 mg, 7.50 mmol, 15 equivalents) was added. The mixture was then refluxed at 80°C for 27 hours. After cooling, organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substance was dissolved. Insoluble substances were roughly removed by filtration using a cotton-lined funnel. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate obtained by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. After drying under reduced pressure overnight, 5'-(5-carboxy-2-methylphenyl)-6,6''-dimethyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylic acid (3c) (231 mg, yield 96%) was obtained as a white solid. １ H NMR (500MHz, DMSO) δ12.90 (s, 3H), 7.88-7.84 (m, 6H), 7.46 (d, J=8.5Hz, 3H), 7.38 (s, 3H), 2.41 (s, 9H).

[0163] - Composition scheme for construction element 6c

[0164] - Synthesis of S2 A suspension mixture of 2,6-dibromophenol (756 mg, 3.00 mmol, 1 equivalent), methyl 3-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzoate (3.15 g, 12.0 mmol, 4 equivalents), sodium carbonate (1.27 g, 12.0 mmol, 4 equivalents), N,N-dimethylformamide (10 mL), and water (10 mL) was degassed by nitrogen bubbling for 15 minutes. Next, palladium acetate (33.7 mg, 0.150 mmol, 5 mol%) was added, and the mixture was stirred under nitrogen at 60°C for 3 hours. After cooling, the reaction mixture was diluted with ethyl acetate and hexane, and most of the inorganic salts were removed by filter paper filtration. The filtrate was washed three times with brine, dried over sodium sulfate, and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-25%) to obtain dimethyl 2'-hydroxy-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S2) (732 mg, yield 67%) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ8.25 (t, J=1.8Hz, 2H), 8.07 (dt, J=7.8, 1.4Hz, 2H), 7.76 (dt, J=7.8, 1.5Hz, 2H), 7.56 ( t, J=7.8Hz, 2H), 7.31 (d, J=7.6Hz, 2H), 7.10 (t, J=7.6Hz, 1H), 5.27 (s, 1H), 3.94 (s, 6H).

[0165] - Synthesis of S3 To a 60 mL solution of S2 (2.17 g, 6.00 mmol, 1 equivalent) in dichloromethane, N-bromosuccinimide (1.17 g, 6.60 mmol, 1.1 equivalents) was added at 0°C, and the mixture was stirred at room temperature for 40 minutes. The reaction mixture was diluted with chloroform and washed with saturated ammonium chloride solution, saturated sodium thiosulfate solution, and brine. The organic layer was dried over sodium sulfate and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-30%) to obtain dimethyl 5'-bromo-2'-hydroxy-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S3) (2.28 g, yield 86%) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ8.21 (s, 2H), 8.09 (d, J=7.7Hz, 2H), 7.73 (d, J=7.6Hz, 2H), 7.57 (t, J=7.8Hz, 2H), 7.44 (s, 2H), 5.26 (s, 1H), 3.95 (s, 6H).

[0166] - Synthesis of S4 A mixture of 1,2-bis(chloromethyl)benzene (87.5 mg, 0.500 mmol, 1 equivalent), S3 (552 mg, 1.25 mmol, 2.5 equivalents), dried potassium carbonate (346 mg, 2.50 mmol, 5 equivalents), and N,N-dimethylformamide (5 mL) was stirred at 60°C for 9 hours. After cooling, the reaction mixture was diluted with ethyl acetate and washed three times with brine. The organic layer was dried over sodium sulfate and concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-25%) to obtain tetramethyl 2',2''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5'-bromo-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate) (S4) (437 mg, yield 89%) as a white solid. １ H NMR (500 MHz, CDCl ３δ 8.01 (s, 4H), 7.91 (d, J = 7.8 Hz, 4H), 7.56 (d, J = 7.8 Hz, 4H), 7.42 (s, 4H), 7.29 (t, J = 7.7 Hz, 4H), 6.89 (dd, J = 5.6, 3.3 Hz, 2H), 6.20 (dd, J = 5.6, 3.4 Hz, 2H), 3.95 (s, 12H), 3.21 (s, 4H).

[0167] ・Synthesis of S5 Aqueous solution (1 mL) of tripotassium phosphate (255 mg, 1.20 mmol, 4 equivalents) was added to a 1,4-dioxane solution (3 mL) of S4 (295 mg, 0.300 mmol, 1 equivalent) and methyl 4-methyl-3-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzoate (182 mg, 0.660 mmol, 2.2 equivalents), and the mixture was degassed by nitrogen bubbling for 15 minutes. Next, Pd(PPh ３ )( ４ (34.7 mg, 0.0300 mmol, 10 mol%) was added, and the mixture was stirred at 100 °C for 5 hours under nitrogen. After cooling, the reaction mixture was diluted with ethyl acetate. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0 - 40%) to obtain tetramethyl 4',4''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5'-(3-(methoxycarbonyl)phenyl)-6-methyl-[1'''',1''':3''',1'''''-terphenyl]-3,3''-dicarboxylate) (S5) (282 mg, yield 84%) as a white solid. １ 1H NMR (500 MHz, CDCl ３ ) δ 8.04 (s, 4H), 8.00 (d, J = 2.0 Hz, 2H), 7.93 (dd, J = 7.9, 2.0 Hz, 2H), 7.90 (dt, J = 7.8, 1.4 Hz, 4H), 7.62 (d, J = 7.8 Hz, 4H), 7.35 (d, J = 8.1 Hz, 2H), 7.31 (t, J = 7.7 Hz, 4H), 7.24 (s, 4H), 6.86 (dd, J = 5.6, 3.4 Hz, 2H), 6.23 (dd, J = 5.6, 3.4 Hz, 2H), 3.91 (s, 6H), 3.89 (s, 12H), 3.50 (s, 4H), 2.39 (s, 6H).

[0168] - Synthesis of 6c To S5 (247 mg, 0.220 mmol, 1 equivalent) dissolved in a mixed solvent of methanol (5 mL) and tetrahydrofuran (5 mL), an aqueous solution (3 mL) of lithium hydroxide monohydrate (277 mg, 6.60 mmol, 30 equivalents) was added. Next, the mixture was refluxed at 80 °C for 24 hours. After cooling, the organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substances dissolved. The insoluble substances were roughly removed by filtration using a funnel packed with cotton. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. It was dried overnight under reduced pressure to obtain 4′,4′′′′-((1,2-phenylenebis(methylene))bis(oxy))bis(5′-(3-carboxyphenyl)-6-methyl-[1,1′:3′,1′′-terphenyl]-3,3′′-dicarboxylic acid) (6c) (203 mg, yield 89%) as a white solid. １ 1H NMR (500 MHz, DMSO) δ 12.90 (s, 6H), 8.00 (s, 4H), 7.92 (d, J = 2.0 Hz, 2H), 7.89 - 7.82 (m, 6H), 7.69 (d, J = 7.8 Hz, 4H), 7.47 (d, J = 8.1 Hz, 2H), 7.41 (t, J = 7.7 Hz, 4H), 7.35 (s, 4H), 6.94 (dd, J = 5.6, 3.3 Hz, 2H), 6.25 (dd, J = 5.6, 3.4 Hz, 2H), 3.23 (s, 4H), 2.45 (s, 6H).

[0169] - Synthesis scheme of building block 5c

[0170] - Synthesis of S6 A suspension mixture of S3 (325 mg, 0.736 mmol, 1 equivalent), methyl 4-methyl-3-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzoate (610 mg, 2.21 mmol, 3 equivalents), sodium carbonate (234 mg, 2.21 mmol, 3 equivalents), N,N-dimethylformamide (2.5 mL), and water (2.5 mL) was degassed by nitrogen bubbling for 15 minutes. Next, palladium acetate (3.9 mg, 0.037 mmol, 5 mol%) was added, and the mixture was stirred under nitrogen at 60°C for 3 hours. After cooling, the reaction mixture was diluted with ethyl acetate and hexane, and most of the inorganic salts were removed by vacuum filtration through a Celite® pad. The filtrate was washed three times with brine, dried over sodium sulfate, and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-28%) to obtain dimethyl 4'-hydroxy-5'-(3-(methoxycarbonyl)phenyl)-6-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S6) (293 mg, yield 78%) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ8.28 (s, 2H), 8.08 (dd, J=8.0, 1.3Hz, 2H), 7.97 (s, 1H), 7.92 (dd, J=8.1, 1.7Hz, 1H), 7.80 (dd, J=7.8, 1.2Hz, 2H) ), 7.58 (t, J=7.8Hz, 2H), 7.35 (d, J=8.1Hz, 1H), 7.28 (s, 2H), 5.33 (s, 1H), 3.94 (s, 6H), 3.91 (s, 3H), 2.42 (s, 3H).

[0171] - Synthesis of S7 Diisopropyl azodicarboxylate (583 μL, 3.00 mmol, 1 equivalent) was added to a tetrahydrofuran solution (30 mL) of 2,6-dibromo-4-(tert-butyl)phenol (924 mg, 3.00 mmol, 1 equivalent), 1,2-phenylenedimethyl (1.24 g, 9.00 mmol, 3 equivalents), and triphenylphosphine (787 mg, 3.00 mmol, 1 equivalent) over 2 minutes at 0°C under nitrogen. The mixture was stirred at room temperature for 1.5 hours and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-20%) to obtain (2-((2,6-dibromo-4-(tert-butyl)phenoxy)methyl)phenyl)methanol (S7) (1.20 g, 94% yield) as a clear viscous oil. １ H NMR (500 MHz, CDCl ３ ) δ7.63 (dd, J=7.2, 1.3Hz, 1H), 7.53 (s, 2H), 7.48 (d, J=7.3Hz, 1H), 7.43-7.35 (m, 2H), 5.12 (s, 2H), 4.93 (s, 2H), 1.30 (s, 9H).

[0172] - Synthesis of S8 To a 1,4-dioxane solution (15 mL) of S7 (1.07 g, 2.50 mmol, 1 equivalent) and (3-(methoxycarbonyl)phenyl)boronic acid (1.80 g, 10.0 mmol, 4 equivalents), an aqueous solution (5 mL) of tripotassium phosphate (2.12 g, 10.0 mmol, 4 equivalents) was added, and the solution was degassed by nitrogen bubbling for 15 minutes. Next, Pd (PPh ３ ) ４ (289 mg, 0.250 mmol, 10 mol%) was added, and the mixture was stirred under nitrogen at 100°C for 7 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The organic layer was washed with brine, dried over sodium sulfate, and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-25%) to obtain dimethyl 5'-(tert-butyl)-2'-((2-(hydroxymethyl)benzyl)oxy)-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S8) (1.21 g, 90% yield) as a white solid.１ H NMR (500 MHz, CDCl ３ ) δ8.21 (s, 2H), 8.02 (dd, J=7.8, 1.4Hz, 2H), 7.77 (dd, J=7.7, 1.3Hz, 2H), 7.46 (t, J=7.7Hz, 2H), 7.36 (s, 2H), 7.17-7 .10 (m, 2H), 6.96 (dt, J=8.1, 4.5Hz, 1H), 6.40 (d, J=7.9Hz, 1H), 4.28 (s, 2H), 4.07 (s, 2H), 3.93 (s, 6H), 1.39 (s, 9H).

[0173] - S9 synthesis Triphenylphosphine (393 mg, 1.50 mmol, 1.5 equivalents) was added to a 5 mL dichloromethane solution of S8 (539 mg, 1.00 mmol, 1 equivalent) and carbon tetrabromide (497 mg, 1.50 mmol, 1.5 equivalents) under nitrogen at 0°C. The mixture was stirred at room temperature for 2.5 hours and diluted with cyclohexane. The resulting suspension was directly subjected to silica gel column chromatography (eluent: hexane / ethyl acetate = 5-15%) to obtain dimethyl 2'-((2-(bromomethyl)benzyl)oxy)-5'-(tert-butyl)-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S9) (470 mg, 78% yield) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ8.21 (s, 2H), 8.05 (d, J = 7.8Hz, 2H), 7.79 (d, J = 7.6Hz, 2H), 7.48 (t, J = 7.8Hz, 2H), 7.37 (s, 2H), 7.10 (t, J = 7.5Hz, 1H), 7.03 (d, J=7.6Hz, 1H), 6.98 (t, J=7.5Hz, 1H), 6.38 (d, J=7.6Hz, 1H), 4.28 (s, 2H), 3.94 (s, 6H), 3.79 (s, 2H), 1.39 (s, 9H).

[0174] - Synthesis of S10 A mixture of S9 (60.2 mg, 0.100 mmol, 1 equivalent), S6 (51.1 mg, 0.110 mmol, 1.1 equivalents), dried potassium carbonate (69.1 mg, 0.500 mmol, 5 equivalents), and N,N-dimethylformamide (1 mL) was stirred at 60°C for 3 hours. After cooling, the reaction mixture was diluted with ethyl acetate and washed three times with brine. The organic layer was dried over sodium sulfate and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-28%) to obtain dimethyl 4'-((2-(((5'-(tert-butyl)-3,3''-bis(methoxycarbonyl)-[1,1':3',1''-terphenyl]-2'-yl)oxy)methyl)benzyl)oxy)-5'-(3-(methoxycarbonyl)phenyl)-6-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate (S10) (97.6 mg, 95% yield) as a white solid. １ H NMR (500MHz, DMSO) δ7.98-7.93 (m, 5H), 7.89 (dd, J = 7.9, 2.0Hz, 1H), 7.84-7.79 (m, 4H), 7.69 (d, J=7.6Hz, 2H), 7.66 (d, J=7.6Hz, 2H), 7.50 (d, J=8.1Hz, 1H), 7.46-7.3 7 (m, 4H), 7.36 (s, 2H), 7.35 (s, 2H), 6.98-6.90 (m, 2H), 6.27-6.18 (m, 2H), 3.85 (s, 3H), 3.80 (s, 6H), 3.79 (s, 6H), 3.22 (s, 2H), 3.18 (s, 2H), 2.42 (s, 3H), 1.38 (s, 9H).

[0175] ・5c synthesis S10 (309 mg, 0.300 mmol, 1 equivalent) was dissolved in a mixed solvent of methanol (5 mL) and tetrahydrofuran (5 mL). An aqueous solution of lithium hydroxide monohydrate (315 mg, 7.50 mmol, 25 equivalents) (3 mL) was added. The mixture was then refluxed at 80°C for 18 hours. After cooling, organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substance was dissolved. Insoluble substances were roughly removed by filtration using a cotton-lined funnel. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. The mixture was dried overnight under reduced pressure to obtain 4'-((2-(((5'-(tert-butyl)-3,3''-dicarboxy-[1,1':3',1''-terphenyl]-2'-yl)oxy)methyl)benzyl)oxy)-5'-(3-carboxyphenyl)-6-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylic acid (5c) (250 mg, yield 87%) as a white solid. １ H NMR (500MHz, DMSO) δ12.89 (s, 5H), 7.96 (d, J = 14.0Hz, 4H), 7.92 (s, 1H), 7.87 (d, J = 8.5Hz, 1H), 7.81 (t, J = 9.3Hz, 4H), 7.67 (d, J = 7.6Hz, 2H), 7.64 (d, J = 7.6Hz, 2H) ), 7.47 (d, J=8.1Hz, 1H), 7.39 (t, J=7.7Hz, 2H), 7.37-7.31 (m, 6H), 6.92 (q, J=3. 9Hz, 2H), 6.28-6.22 (m, 2H), 3.23 (s, 2H), 3.19 (s, 2H), 2.44 (s, 3H), 1.39 (s, 9H).

[0176] - Combination scheme of construction element 4c-A1

[0177] - Synthesis of S11 Diisopropyl azodicarboxylate (1.28 mL, 6.60 mmol, 2.2 equivalents) was added to a tetrahydrofuran solution (20 mL) of 2,6-dibromo-4-methylphenol (1.76 g, 6.60 mmol, 2.2 equivalents), 1,2-phenylenedi methanol (415 mg, 3.00 mmol, 1 equivalent), and triphenylphosphine (1.73 g, 6.60 mmol, 2.2 equivalents) under nitrogen at 0°C over 3 minutes. The mixture was stirred at room temperature for 22 hours, and then concentrated under reduced pressure. A methanol suspension of the crude product (80 mL) was sonicated and stirred for several hours. A fine white precipitate was collected by vacuum filtration using a membrane filter and washed twice with methanol. Upon drying under reduced pressure, 1,2-bis((2,6-dibromo-4-methylphenoxy)methyl)benzene (S11) (1.67 g, yield 88%) was obtained as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ7.76 (dd, J=5.5, 3.7Hz, 2H), 7.42 (dd, J=5.3, 3.7Hz, 2H), 7.34 (s, 4H), 5.27 (s, 4H), 2.29 (s, 6H).

[0178] - Synthesis of S12 To a 1,4-dioxane solution (15 mL) of S11 (1.27 g, 2.00 mmol, 1 equivalent) and (3-(methoxycarbonyl)phenyl)boronic acid (2.16 g, 12.0 mmol, 6 equivalents), an aqueous solution (5 mL) of tripotassium phosphate (2.55 g, 12.0 mmol, 6 equivalents) was added, and the solution was degassed by nitrogen bubbling for 15 minutes. Next, Pd (PPh ３ ) ４ (347 mg, 0.300 mmol, 15 mol%) was added, and the mixture was stirred under nitrogen at 100°C for 6.5 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-22%) to obtain tetramethyl 2',2''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5'-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate) (S12) (1.16 g, yield 68%) as a white solid. １H NMR (500 MHz, CDCl ３ ) δ8.04 (s, 4H), 7.85 (d, J = 7.9Hz, 4H), 7.59 (d, J = 7.8Hz, 4H), 7.24 (d, J = 7.8Hz, 4H), 7.10 (s, 4H), 6.87 (dd, J=5.6, 3.3Hz, 2H), 6.25 (dd, J=5.6, 3.4Hz, 2H), 3.92 (s, 12H), 3.27 (s, 4H), 2.41 (s, 6H).

[0179] - Synthesis of 4c-A1 S12 (855 mg, 1.00 mmol, 1 equivalent) was dissolved in a mixed solvent of methanol (10 mL) and tetrahydrofuran (10 mL). An aqueous solution (5 mL) of lithium hydroxide monohydrate (1.05 g, 25.0 mmol, 25 equivalents) was added to this solution. The mixture was then refluxed at 80°C for 24 hours. After cooling, organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substance was dissolved. Insoluble substances were roughly removed by filtration using a cotton-lined funnel. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. After drying under reduced pressure overnight, 2',2''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5'-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylic acid) (4c-A1) (719 mg, yield 90%) was obtained as a white solid. １ H NMR (500MHz, DMSO) δ12.89 (s, 4H), 7.95 (s, 4H), 7.80 (d, J = 7.6Hz, 4H), 7.59 (d, J = 7.6Hz, 4H), 7.34 (t, J = 7. 8Hz, 4H), 7.14 (s, 4H), 6.92 (dd, J=5.6, 3.3Hz, 2H), 6.23 (dd, J=5.6, 3.4Hz, 2H), 3.05 (s, 4H), 2.41 (s, 6H).

[0180] - Combination scheme of construction element 4c-A2

[0181] - Synthesis of S13 Diisopropyl azodicarboxylate (1.28 mL, 6.60 mmol, 2.2 equivalents) was added to a tetrahydrofuran solution (40 mL) of 2,6-dibromo-4-(tert-butyl)phenol (2.03 g, 6.60 mmol, 2.2 equivalents), 1,3-phenylenedimethyl (415 mg, 3.00 mmol, 1 equivalent), and triphenylphosphine (1.73 g, 6.60 mmol, 2.2 equivalents) over 3 minutes at 0°C under nitrogen. The mixture was stirred at room temperature for 18 hours and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-30%) to obtain 1,3-bis((2,6-dibromo-4-(tert-butyl)phenoxy)methyl)benzene (S13) (2.13 g, yield 99%) as a clear viscous solid. １ H NMR (500 MHz, CDCl ３ ) δ7.85 (s, 1H), 7.61 (d, J=7.6Hz, 2H), 7.52 (s, 4H), 7.46 (t, J=7.6Hz, 1H), 5.06 (s, 4H), 1.30 (s, 18H).

[0182] - Synthesis of S14 To a 1,4-dioxane solution (20 mL) of S13 (2.10 g, 2.92 mmol, 1 equivalent) and (3-(methoxycarbonyl)phenyl)boronic acid (3.15 g, 17.5 mmol, 6 equivalents), an aqueous solution (10 mL) of tripotassium phosphate (3.71 g, 17.5 mmol, 6 equivalents) was added, and the solution was degassed by nitrogen bubbling for 15 minutes. Next, Pd (PPh ３ ) ４ (506 mg, 0.438 mmol, 15 mol%) was added, and the mixture was stirred at 100°C under nitrogen for 5 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-15%) to obtain tetramethyl 2',2''''-((1,3-phenylenebis(methylene))bis(oxy))bis(5'-(tert-butyl)-[1'''',1'''':3'''',1''''''-terphenyl]-3,3''-dicarboxylate) (S14) (1.75 g, yield 61%) as a white solid. １H NMR (500 MHz, CDCl ３ ) δ8.17 (s, 4H), 7.96 (d, J = 7.8Hz, 4H), 7.76 (d, J = 7.6Hz, 4H), 7.39-7.33 (m, 8H), 6.77 (t, J =7.6Hz, 1H), 6.43 (d, J = 7.4Hz, 2H), 5.85 (s, 1H), 3.92 (s, 4H), 3.88 (s, 12H), 1.38 (s, 18H).

[0183] - Synthesis of 4c-A2 S14 (1.52 g, 1.62 mmol, 1 equivalent) was dissolved in a mixed solvent of methanol (25 mL) and tetrahydrofuran (25 mL). To this, an aqueous solution (10 mL) of lithium hydroxide monohydrate (1.36 g, 32.4 mmol, 20 equivalents) was added. The mixture was then refluxed at 80°C for 24 hours. After cooling, organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substance was dissolved. Insoluble substances were roughly removed by filtration using a cotton-lined funnel. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. The mixture was dried overnight under reduced pressure to obtain 2',2''''-((1,3-phenylenebis(methylene))bis(oxy))bis(5'-(tert-butyl)-[1'''',1'''':3'''',1''''''-terphenyl]-3,3''-dicarboxylic acid) (4c-A2) (1.38 g, yield 96%) as a white solid. １ H NMR (500MHz, DMSO) δ12.95 (s, 4H), 8.07 (s, 4H), 7.89 (d, J = 7.6Hz, 4H), 7.77 (d, J = 7.9Hz, 4H), 7.47 (t, J = 7.7 Hz, 4H), 7.39 (s, 4H), 6.80 (t, J=7.8Hz, 1H), 6.46 (d, J=7.2Hz, 2H), 5.78 (s, 1H), 3.88 (s, 4H), 1.36 (s, 18H).

[0184] - Combination scheme of construction element 4c-B1

[0185] - Synthesis of S15 A suspension mixture of 2-bromo-6-methylphenol (1.87 g, 10.0 mmol, 1 equivalent), methyl 3-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzoate (5.24 g, 20.0 mmol, 2 equivalents), sodium carbonate (2.12 g, 20.0 mmol, 2 equivalents), N,N-dimethylformamide (20 mL), and water (20 mL) was degassed by nitrogen bubbling for 15 minutes. Next, palladium acetate (112 mg, 0.500 mmol, 5 mol%) was added, and the mixture was stirred under nitrogen at 60°C for 3 hours. After cooling, the reaction mixture was diluted with ethyl acetate and hexane, and most of the inorganic salts were removed by filtration through filter paper. The filtrate was washed three times with saline solution, dried over sodium sulfate, and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-12%) and recrystallization from thermal cyclohexane to obtain methyl 2'-hydroxy-3'-methyl-[1,1'-biphenyl]-3-carboxylate (S15) (1.64 g, 68% yield) as white crystals. １ H NMR (500 MHz, CDCl ３ ) δ8.16 (s, 1H), 8.07 (d, J = 7.8Hz, 1H), 7.68 (d, J = 7.6Hz, 1H), 7.56 (t, J = 7.7Hz, 1H), 7.16 (d, J = 7 .3Hz, 1H), 7.09 (d, J=7.6Hz, 1H), 6.92 (t, J=7.5Hz, 1H), 5.05 (s, 1H), 3.93 (s, 3H), 2.32 (s, 3H).

[0186] - Synthesis of S16 To a 60 mL solution of S15 (1.45 g, 6.00 mmol, 1 equivalent) in dichloromethane, N-bromosuccinimide (1.17 g, 6.60 mmol, 1.1 equivalents) was added at 0°C, and the mixture was stirred at room temperature for 50 minutes. The reaction mixture was diluted with chloroform and washed with saturated ammonium chloride solution, saturated sodium thiosulfate solution, and brine. The organic layer was dried over sodium sulfate and then concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-15%) and recrystallization from hot toluene to obtain methyl 5'-bromo-2'-hydroxy-3'-methyl-[1,1'-biphenyl]-3-carboxylate (S16) (994 mg, 52% yield) as white crystals. １ H NMR (500 MHz, CDCl ３ ) δ8.12 (t, J=1.7Hz, 1H), 8.09 (dt, J=7.8, 1.5Hz, 1H), 7.64 (dt, J=7.6, 1.5Hz, 1H), 7.57 (t, J=7 .7Hz, 1H), 7.28 (d, J=2.7Hz, 1H), 7.22 (d, J=2.6Hz, 1H), 5.02 (s, 1H), 3.94 (s, 3H), 2.29 (s, 3H).

[0187] - Synthesis of S17 A mixture of 1,2-bis(chloromethyl)benzene (140 mg, 0.800 mmol, 1 equivalent), S16 (642 mg, 2.00 mmol, 2.5 equivalents), dried potassium carbonate (552 mg, 4.00 mmol, 5 equivalents), and N,N-dimethylformamide (8 mL) was stirred at 60°C for 23 hours. After cooling, the reaction mixture was diluted with ethyl acetate and washed three times with brine. The organic layer was dried over sodium sulfate and concentrated under reduced pressure. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 0-10%) to obtain dimethyl 2',2'''-((1,2-phenylenebis(methylene))bis(oxy))bis(5'-bromo-3'-methyl-[1,1'-biphenyl]-3-carboxylate) (S17) (563 mg, yield 94%) as a white solid. １ H NMR (500MHz, CD ２ Cl ２) δ8.01 (t, J=1.8Hz, 2H), 7.84 (dt, J=7.8, 1.4Hz, 2H), 7.56 (dt, J=7.6, 1.6Hz, 2H), 7.34 (d, J=2.7Hz, 2H), 7.32 -7.26 (m, 4H), 7.13 (dd, J=5.6, 3.4Hz, 2H), 6.94 (dd, J=5.6, 3.4Hz, 2H), 4.15 (s, 4H), 3.87 (s, 6H), 2.16 (s, 6H).

[0188] - Synthesis of S18 To a 1,4-dioxane solution (6 mL) of S17 (427 mg, 0.574 mmol, 1 equivalent) and methyl 4-methyl-3-(4,4,5,5-tetramethyl-1,3,2-dioxaborolan-2-yl)benzoate (475 mg, 1.72 mmol, 3 equivalents), an aqueous solution (2 mL) of tripotassium phosphate (487 mg, 2.30 mmol, 4 equivalents) was added, and the solution was degassed by nitrogen bubbling for 15 minutes. Next, Pd (PPh ３ ) ４ (66.3 mg, 0.0574 mmol, 10 mol%) was added, and the mixture was stirred under nitrogen at 100°C for 6 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-35%) to obtain tetramethyl 4',4''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5',6-dimethyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate) (S18) (430 mg, yield 85%) as a white solid. １ H NMR (500 MHz, CDCl ３ ) δ8.13 (t, J=1.8Hz, 2H), 7.95 (d, J=2.0Hz, 2H), 7.92 (dd, J=7.9, 2.0H z, 2H), 7.89 (d, J = 7.8Hz, 2H), 7.69 (d, J = 7.6Hz, 2H), 7.34 (d, J = 7.9Hz, 2H), 7.31 (t, J = 7.7Hz, 2H), 7.16-7.11 (m, 6H), 6.99 (dd, J = 5.6, 3.4Hz, 2H), 4.35 (s, 4H), 3.91 (s, 6H), 3.87 (s, 6H), 2.37 (s, 6H), 2.24 (s, 6H).

[0189] ・Synthesis of 4c-B1 To S18 (385 mg, 0.436 mmol, 1 equivalent) dissolved in a mixed solvent of methanol (8 mL) and tetrahydrofuran (8 mL), an aqueous solution (4 mL) of lithium hydroxide monohydrate (366 mg, 8.72 mmol, 20 equivalents) was added. Next, the mixture was refluxed at 80 °C for 20 hours. After cooling, the organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substances dissolved. The insoluble substances were roughly removed by filtration using a funnel packed with cotton. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. It was dried overnight under reduced pressure to obtain 4',4''''-((1,2-phenylenebis(methylene))bis(oxy))bis(5',6-dimethyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylic acid) (4c-B1) (320 mg, yield 92%) as a white solid. １ 1H NMR (500 MHz, DMSO) δ 12.91 (s, 4H), 8.02 (s, 2H), 7.86 - 7.80 (m, 4H), 7.78 (d, J = 7. Hz, 2H), 7.69 (d, J = 7.8 Hz, 2H), 7.44 (d, J = 7.9 Hz, 2H), 7.37 (t, J = 7.8 Hz, 2H), 7.27 (d, J = 1.9 Hz, 2H), 7.20 (dd, J = 5.7, 3.3 Hz, 2H), 7.15 (d, J = 2.0 Hz, 4H), 7.09 (dd, J = 5.6, 3.5 Hz, 2H), 4.24 (s, 4H), 2.36 (s, 6H), 2.20 (s, 6H).

[0190] ・Synthesis scheme of building block 4c-B2

[0191] ・Synthesis of S19 Diisopropyl azodicarboxylate (642 μL, 3.30 mmol, 2.2 equivalents) was added to a tetrahydrofuran solution (20 mL) of 2,4-dibromo-6-methylphenol (878 mg, 3.30 mmol, 2.2 equivalents), 1,3-phenylenedi methanol (207 mg, 1.50 mmol, 1 equivalent), and triphenylphosphine (866 mg, 3.30 mmol, 2.2 equivalents) under nitrogen at 0°C for 3 minutes. The mixture was stirred at room temperature for 16 hours, and then concentrated under reduced pressure. The methanol suspension of the crude product was sonicated and stirred for several hours. A fine white precipitate was collected by vacuum filtration using a membrane filter and washed twice with methanol. Upon drying under reduced pressure, 1,3-bis((2,4-dibromo-6-methylphenoxy)methyl)benzene (S19) (929 mg, yield 98%) was obtained as a white solid. １ H NMR (500MHz, CD ２ Cl ２ ) δ7.67 (s, 1H), 7.59 (d, J = 2.6Hz, 2H), 7.51 (d, J = 8.4Hz, 2H), 7.45 (dd , J=8.5, 6.6Hz, 1H), 7.32 (d, J=3.2Hz, 2H), 4.95 (s, 4H), 2.29 (s, 6H).

[0192] - Synthesis of S20 To a 1,4-dioxane solution (10 mL) of S19 (634 mg, 1.00 mmol, 1 equivalent) and (3-(methoxycarbonyl)phenyl)boronic acid (1.08 g, 6.00 mmol, 6 equivalents), an aqueous solution (5 mL) of tripotassium phosphate (1.27 g, 6.00 mmol, 6 equivalents) was added, and the mixture was degassed by nitrogen bubbling for 15 minutes. Next, Pd (PPh ３ ) ４(173 mg, 0.150 mmol, 15 mol%) was added, and the mixture was stirred under nitrogen at 100°C for 6.5 hours. After cooling, the reaction mixture was diluted with ethyl acetate. The crude product was purified by silica gel column chromatography (eluent: hexane / ethyl acetate = 5-35%) to obtain tetramethyl 4',4''''-((1,3-phenylenebis(methylene))bis(oxy))bis(5'-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylate) (S2O) (780 mg, yield 91%) as a white solid. １ H NMR (500MHz, DMSO) δ8.22 (s, 2H), 8.17 (s, 2H), 8.02 (d, J = 7.8Hz, 2H), 7.95 (t, J =7.7Hz, 4H), 7.89 (d, J = 7.9Hz, 2H), 7.66 (d, J = 2.2Hz, 2H), 7.62 (t, J = 7.8Hz, 2H ), 7.57 (t, J=7.8Hz, 2H), 7.54 (d, J=2.6Hz, 2H), 7.17 (t, J=7.6Hz, 1H), 7.01 (d, J=7.4Hz, 2H), 6.75 (s, 1H), 4.38 (s, 4H), 3.89 (s, 6H), 3.81 (s, 6H), 2.38 (s, 6H).

[0193] • Synthesis of 4c-B2 S20 (684 mg, 0.800 mmol, 1 equivalent) was dissolved in a mixed solvent of methanol (10 mL) and tetrahydrofuran (10 mL). An aqueous solution (5 mL) of lithium hydroxide monohydrate (671 mg, 16.0 mmol, 20 equivalents) was added to this solution. The mixture was then refluxed at 80°C for 20 hours. After cooling, organic volatile substances were removed under reduced pressure. The resulting aqueous suspension was diluted with water and sonicated until most of the white substance was dissolved. Insoluble substances were roughly removed by filtration using a cotton-lined funnel. Concentrated hydrochloric acid was added to the resulting aqueous solution to make it acidic. The precipitate formed by acidification was collected by vacuum filtration using a membrane filter and washed twice with water. The mixture was dried overnight under reduced pressure to obtain 4',4''''-((1,3-phenylenebis(methylene))bis(oxy))bis(5'-methyl-[1,1':3',1''-terphenyl]-3,3''-dicarboxylic acid) (4c-B2) (586 mg, yield 92%) as a white solid.１ H NMR (500MHz, DMSO) δ13.04 (s, 4H), 8.22 (s, 2H), 8.18 (s, 2H), 7.99 (d, J = 8.4 Hz, 2H), 7.93 (d, J = 7.6Hz, 4H), 7.87 (d, J = 7.6Hz, 2H), 7.64 (d, J = 2.0Hz, 2H), 7.59 (t, J=7.7Hz, 2H), 7.55 (t, J=7.7Hz, 2H), 7.53 (d, J=2.4Hz, 2H), 7.17 (t, J=7.6Hz, 1H), 7.02 (d, J=7.6Hz, 2H), 6.83 (s, 1H), 4.38 (s, 4H), 2.39 (s, 6H).

[0194] (Example 5: Construction of stereomolecules by self-assembly) Stereomolecules were constructed using the structural elements created above.

[0195] - Synthesis of (3,5)-trc-1 from construction elements 5c-A and 3c-A 5c-A in DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 50 mM solution. A similar 83.3 mM solution of 3c-A was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 200 μL of 5c-A solution and 200 μL of 3c-A solution were mixed in the glass vial, and the solution was mixed with DMSO-d ６ Diluted until the total volume was 2000 μL. 2 μL of TFA-d １ The reaction vessel was sealed with a screw cap after adding the substance. The reaction vessel was heated at 100°C for 72 hours while stirring. The formation of the target product was due to the reaction solution １ The product was confirmed by 1H NMR and mass spectrometry. The solution was filtered using a disposable membrane filter (DISMIC®-13JP) and freeze-dried to obtain the product as a pale yellow solid (5.8 mg, yield 74%) (Figure 7A).

[0196] - Synthesis of (3,5)-trc-2 from construction elements 5c-A and 3c-B 5c-A in DMSO-d ６The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 50 mM solution. A similar 83.3 mM solution of 3c-B was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of 5c-A solution and 100 μL of 3c-B solution were mixed in the glass vial, and the solution was mixed with DMSO-d ６ Diluted until the total volume was 2000 μL. 1 μL of TFA-d １ The reaction vessel was sealed with a screw cap. The reaction vessel was heated at 100°C for 48 hours while stirring. The formation of the target product was observed in the reaction solution. １ This was confirmed by 1H NMR and mass spectrometry (Figure 7B).

[0197] - Synthesis of (3,5)-trc-3 from construction elements 5c-B and 3c-B 5c-B to DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 10 mM solution. A 25 mM solution of 3c-B was prepared in the same manner. A magnetic stirring bar was placed in a 2.0 mL glass microtube. 100 μL of 5c-B solution and 66.8 μL of 3c-B solution were mixed in a glass vial, and the solution was mixed with DMSO-d ６ It was then diluted until the total volume was 400 μL. 0.4 μL of TFA-d １ The reaction vessel was sealed with a polyethylene cap. The reaction vessel was heated at 100°C for 36 hours while stirring. The formation of the target product was observed in the reaction solution. １ This was confirmed by 1H NMR and mass spectrometry (Figure 7C).

[0198] - Synthesis of (3,5)-trc-4 from construction elements 5c-C and 3c-B 5c-C in DMSO-d ６ The solution was dissolved in DMSO-d and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 12.5 mM solution. A 25 mM solution of 3c-B was prepared in the same manner. A magnetic stirring bar was placed in a 2.0 mL glass microtube. 25 μL of the 5c-C solution and 20.8 μL of the 3c-B solution were mixed in a glass vial, and the solution was mixed with DMSO-d ６It was then diluted until the total volume was 500 μL. 0.5 μL of TFA-d １ The reaction vessel was sealed with a polyethylene cap. The reaction vessel was heated at 100°C for 48 hours while stirring. The formation of the target product was confirmed by mass spectrometry of the reaction solution (Figure 7D). In this way, by adjusting the length of the main chain of the arms, it is possible to construct three-dimensional molecules with the same three-dimensional shape but different sizes.

[0199] - Synthesis of (3,4)-T-1 from construction elements 4c-car-A and 3c-C 4c-car-A to DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 25 mM solution. A 41.7 mM solution of 3c-C was prepared in the same manner. A magnetic stirring bar was placed in a 1.0 mL glass microtube. 30 μL of 4c-car-A solution and 24 μL of 3c-C solution were mixed in a glass vial, and the solution was mixed with DMSO-d ６ Diluted until the total volume was 300 μL. 1 μL of TFA-d １ The reaction vessel was sealed with a polyethylene cap. The reaction vessel was heated at 100°C for 48 hours while stirring. The formation of the target product was due to the reaction solution １ This was confirmed by 1H NMR and mass spectrometry. It is thought that even stereomolecules with vertex-defect shapes exhibit the same construction-promoting effect as stereomolecules with bipartite biregular polyhedra.

[0200] - Synthesis of (3,4)-T-2 from construction elements 4c-car-B and 3c-B 4c-car-B to DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 25 mM solution. A 25 mM solution of 3c-B was prepared in the same manner. A magnetic stirring bar was placed in a 2.0 mL glass microtube. 30 μL of 4c-car-B solution and 40 μL of 3c-B solution were mixed in a glass vial, and the solution was mixed with DMSO-d ６ It was then diluted until the total volume was 300 μL. 0.3 μL of TFA-d １The reaction vessel was sealed with a polyethylene cap. The reaction vessel was heated at 100°C for 34 hours while stirring. The formation of the target product was due to the reaction solution １ This was confirmed by 1H NMR and mass spectrometry.

[0201] - (3,4)-O from construction element 3c ｈ synthesis 3c was dissolved in DMF and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 150 mM solution of O was prepared. In a 0.5 mL glass microtube, 10 μL of 3c solution and 10 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and EtOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 4 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-EtOH solution with a solvent ratio of 65:35 (Figure 8).

[0202] - (6,4)-D from construction element 6c ４ｈ synthesis 6c was dissolved in DMF and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In a similar manner, Cu(NO) ３ ) ２ 3H ２ A 300 mM solution of O was prepared. In a 0.5 mL glass microtube, 5 μL of 6c solution and 5 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and ethylene glycol until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 4 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-ethylene glycol solution with a solvent ratio of 85:15.

[0203] - (5,4)-C from construction element 5c ４ｖ synthesis 5c was dissolved in DMF and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In a similar manner, Cu(NO) ３ ) ２ 3H ２ A 250 mM solution of O solution was prepared. In a 0.5 mL glass microtube, 2 μL of 5c solution and 2 μL of Cu(NO) solution were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF until the total volume was 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 3 days to obtain blue crystals of the product suitable for X-ray diffraction analysis.

[0204] - Construction element 4c-A1 to (4,4)-D ４ｈ synthesis 4c-A1 was dissolved in DMF and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In a similar manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 0.5 mL glass microtube, 10 μL of 4c-A1 solution and 10 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and EtOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 6 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-EtOH solution with a solvent ratio of 55:45.

[0205] - Construction element 4c-B1 to (4,4)-D ２ｄ synthesis 4c-B1 was dissolved in DMF and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 0.5 mL glass microtube, 5 μL of 4c-B1 solution and 5 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and MeOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 60°C for 6 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-MeOH solution with a solvent ratio of 50:50.

[0206] - Construction element 4c-B2 to (4,4)-D ２ｈ synthesis 4c-B2 was dissolved in DMA and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 0.5 mL glass microtube, 5 μL of 4c-B2 solution and 5 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMA and EtOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 7 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMA-EtOH solution with a solvent ratio of 95:5.

[0207] - (6,4)-D from construction element 6c ４ｈ synthesis 6c was dissolved in DMF and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In a similar manner, Cu(NO) ３ ) ２ 3H２ A 300 mM solution of O was prepared. In a 0.5 mL glass microtube, 5 μL of 6c solution and 5 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and ethylene glycol until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 4 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-ethylene glycol solution with a solvent ratio of 85:15.

[0208] - (5,4)-C from construction element 5c ４ｖ synthesis 5c was dissolved in DMF and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In a similar manner, Cu(NO ３ ) ２ 3H ２ A 250 mM solution of O was prepared. In a 0.5 mL glass microtube, 2 μL of 5c solution and 2 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF until the total volume was 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 3 days to obtain blue crystals of the product suitable for X-ray diffraction analysis.

[0209] - Construction element 4c-A1 to (4,4)-D ４ｈ synthesis 4c-A1 was dissolved in DMF and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 0.5 mL glass microtube, 10 μL of 4c-A1 solution and Cu(NO) were added. ３ ) ２ 3H ２10 μL of solution O was mixed and diluted with DMF and EtOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 6 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-EtOH solution with a solvent ratio of 55:45.

[0210] - Construction element 4c-B1 to (4,4)-D ２ｄ synthesis 4c-B1 was dissolved in DMF and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 0.5 mL glass microtube, 5 μL of 4c-B1 solution and 5 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF and MeOH until the total volume reached 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 60°C for 6 days to obtain the blue crystal product. Single crystals suitable for X-ray diffraction analysis were prepared under conditions of a DMF-MeOH solution with a solvent ratio of 50:50.

[0211] - Synthesis of ico-(2,5)-1 from the construction elements car-5c-A and ndi-2c-A car-5c-A in DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 50 mM solution. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of car-5c-A solution and ndi-2c-A (3.70 mg, 12.5 μmol) were mixed in the glass vial, and the solution was mixed with DMSO-d ６ Diluted until the total volume was 1000 μL. 1 μL of TFA-d １ The reaction vessel was sealed with a screw cap. The reaction vessel was heated at 100°C for 48 hours while stirring. The formation of the target product was observed in the reaction solution. １This was confirmed by 1H NMR and mass spectrometry.

[0212] - Synthesis of ico-(2,5)-2 from the construction elements car-5c-A and ben-2c-B car-5c-A in DMSO-d ６ The solution was dissolved in DMSO-d and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 50 mM solution. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of car-5c-A solution and ben-2c-B (6.33 mg, 12.5 μmol) were mixed in the glass vial, and the solution was converted to DMSO-d ６ Diluted until the total volume was 1000 μL. 1 μL of TFA-d １ The reaction vessel was sealed with a screw cap. The reaction vessel was heated at 100°C for 48 hours while stirring. The formation of the target product was observed in the reaction solution. １ Confirmed by 1H NMR.

[0213] - Synthesis of a missing rhombic icosahedron from the construction elements car-5c-A', car-4c-A, and ben-3c-C car-5c-A' in DMSO-d ６ The solution was dissolved in DMSO-d and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 25 mM solution. A 25 mM solution of car-4c-A and a 41.7 mM solution of ben-3c-C were prepared in the same manner. A magnetic stirring bar was placed in a 1.0 mL glass microtube. 22.5 μL of car-5c-A' solution, 7.5 μL of car-4c-A solution, and 28.5 μL of ben-3c-C solution were mixed in a glass vial, and the solution was dissolved in DMSO-d ６ Diluted until the total volume was 300 μL. 1 μL of TFA-d １ The reaction vessel was sealed with a polyethylene cap after adding the substance. The reaction vessel was heated at 100°C for 48 hours while stirring. Mass spectrometry of the reaction solution revealed peaks for one-vertex-defect and two-vertex-defect structures in addition to the rhombic triacontahedron peak, confirming the formation of the target product.

[0214] • Barrel-shaped apex-deficient derivatives: Barrel-shaped stereomolecules, such as those with the following shapes, allow for easy design of derivative shapes.

[0215] As shown in the schematic diagram below, since these barrel-shaped stereomolecules are composed of repeating units, it is possible to design structures by changing the number of repeating units.

[0216] In fact, a derivative composed of three repeating units of a barrel-shaped vertex-defect structure based on a rhombic dodecahedron was synthesized. • Synthesis of (4,4)-D3h from constructor element 4c-A2 4c-A2 was dissolved in DMF and filtered through a disposable membrane filter (DISMIC®-13JP) to obtain a 100 mM solution. In the same manner, Cu(NO) ３ ) ２ 3H ２ A 200 mM solution of O was prepared. In a 1.0 mL glass microtube, 10 μL of 4c-A2 solution and 10 μL of Cu(NO) were added. ３ ) ２ 3H ２ The O solution was mixed and diluted with DMF until the total volume was 200 μL. The reaction vessel was sealed with a polyethylene cap and placed in an incubator (BAS TB-1), where it was heated at 70°C for 2 days to obtain a pale blue solution of the product. Single crystals suitable for X-ray diffraction analysis were prepared from the product solution by vapor diffusion using methanol as a poor solvent.

[0217] (Example 6: Behavior of constructed stereomolecules) The basic physicochemical properties of the constructed stereomolecules were investigated.

[0218] When the DMSO solution of (3,5)-trc-1, immediately after construction from constituent elements 5c-A and 3c-A, was diluted with DMSO or DMF, no precipitate formed, suggesting that it was dissolved. Next, DMSO was added to the (3,5)-trc-1 powder obtained by freeze-drying, and when heated, it dissolved.

[0219] When a DMSO solution of (3,5)-trc-1 was stored at room temperature for 2-3 years in a screw-cap sealed vial without degassing, NMR and MS analysis was performed, the results were almost identical to those obtained immediately after synthesis.

[0220] (5,4)-C with introduced tBu group ４ｖ and (4,4)-D ３ｈ Each of these molecules takes a relatively long time to crystallize and requires vapor diffusion for crystallization; therefore, the solubility of the stereomolecules of this disclosure can be improved by introducing bulky substituents, similar to general organic molecules. In the crystallized state, no change in crystal quality was observed even when stored at room temperature (approximately 25 degrees Celsius).

[0221] Based on the above, the stereomolecules of this disclosure may have high stability.

[0222] (Example 7: Analysis of stereomolecules) The formation of stereomolecules was further confirmed using multiple analytical methods.

[0223] Similar to Example 5, a stereomolecule (Product) with the shape of (3,5)-trc-1 was synthesized from the following constructor 1 (monomer 1) and constructor 2 (monomer 2).

[0224] Gel permeation chromatography (GPC) analysis was performed using a TSKgel G3000HHR column (7.8 mm inner diameter, 30 cm, 5 μm). The results are shown in Figure 9. Compared to each constituent element, the reaction product showed rapid elution with a short retention time, suggesting the formation of a larger complex (stereomolecule). The sharp peak of the reaction product suggests the stable formation of a homogeneous stereomolecule.

[0225] Similar to Example 5, a stereomolecule with the shape of (3,5)-trc-1 was synthesized from the following two structural elements.

[0226] The reaction products were measured by dynamic light scattering (DLS). A Zetasizer μV (Malvern) was used, and measurements were performed in DMSO-d6 solvent at 25°C. The results are shown in Figure 10. From the molecular model, the size of the stereomolecules was expected to be around 5 nm, and the measured particle size was consistent with this. In DLS analysis, the volume-based and intensity-based measurements increase with increasing particle size compared to the number-based measurements. Therefore, the distribution of the three types of measurements consistently indicates that stereomolecules are stably formed according to the design. The absence of the interfering peak around 100 nm, which is frequently observed in intensity-based measurements, also suggests that the target stereomolecules are formed with high efficiency.

[0227] (Example 8: Construction of further stereomolecules) (2,3) Stereomolecules having the stereomorphism of a bipartite biregular polyhedron and its vertex-missing body that satisfy biregularity were designed and synthesized. Specifically, stereomolecules having the following stereomorphisms were designed. Edges corresponding to intervertex linkers are also shown. For ease of drawing, intervertex linkers connecting cubic vertices are shown as being formed outside the stereomorphism.

[0228] Synthesis of tet-(6,2)-1 from constituent element A3 and ethylenediamine A3 is dichloromethane-d ２ It was dissolved in and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 12 mM solution. Similarly, a 36 mM solution of ethylenediamine was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of solution A3 and 100 μL of ethylenediamine solution were mixed in the glass vial, and dichloromethane-d ２ The total volume was diluted to 1000 μL. The reaction solution was stirred for 16 hours. The formation of the target product was observed. １ Confirmed by 1H NMR.

[0229] Synthesis of tet-(6,2)-2 from constituent element A6 and ethylenediamine Aldehyde A6 to dichloromethane-d ２It was dissolved in and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 12 mM solution. Similarly, a 36 mM solution of ethylenediamine was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of solution A6 and 100 μL of ethylenediamine solution were mixed in the glass vial, and dichloromethane-d ２ The total volume was diluted to 1000 μL. The reaction solution was stirred for 19 hours. The formation of the target product was observed. １ Confirmed by 1H NMR.

[0230] Synthesis of tet-(6,2)-3 from constituent element G2 and ethylenediamine G2 is dichloromethane-d ２ It was dissolved in and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 12 mM solution. Similarly, a 36 mM solution of ethylenediamine was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of G2 solution and 100 μL of ethylenediamine solution were mixed in the glass vial, and dichloromethane-d ２ The total volume was diluted to 1000 μL. The reaction solution was stirred for 19 hours. The formation of the target product was observed. １ Confirmed by 1H NMR.

[0231] Synthesis of tet-(5,2)-1 from constituent element E4 and ethylenediamine E4 is dichloromethane-d ２ It was dissolved in [a certain substance] and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 12 mM solution. Similarly, a 30 mM solution of ethylenediamine was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of E4 solution and 100 μL of ethylenediamine solution were mixed in the glass vial, and dichloromethane-d ２ The total volume was diluted to 1000 μL. The reaction solution was stirred for 30 hours. The formation of the target product was observed. １ Confirmed by 1H NMR.

[0232] Synthesis of tet-(5,2)-2 from constituent element F4 and ethylenediamine F4 is dichloromethane-d ２It was dissolved in and filtered using a disposable membrane filter (DISMIC®-13JP) to obtain a 12 mM solution. Similarly, a 30 mM solution of ethylenediamine was prepared. A magnetic stirring bar was placed in a 4.0 mL glass vial. 100 μL of F4 solution and 100 μL of ethylenediamine solution were mixed in the glass vial, and dichloromethane-d ２ The total volume was diluted to 1000 μL. The reaction solution was stirred for 24 hours. The formation of the target product was observed. １ Confirmed by 1H NMR.

[0233] (Example 9: Evaluation using the Jaccard index) The technology of this disclosure also has the aspect of enabling the active design of a stereomolecule having a different stereomorphology that has a high topological (graph) similarity to the stereomorphology of a stereomolecule whose synthesis has been confirmed to be successful. Therefore, the Jaccard index is introduced as a measure for quantifying topological similarity.

[0234] Two graphs (G １ G ２ Let M be the Maximum Common Subgraph (MCS) of these graphs. The vertices and edges of these graphs are represented as follows: G １ = (V １ , E １ ), G ２ = (V ２ , E ２ ), M = (V Ｍ , E Ｍ )

[0235] Furthermore, the number of vertices and edges of these graphs are expressed as follows: n １ = | V １ |, m １ = | E １ |, n ２ = | V ２ |, m ２ = | E ２ |, n Ｍ = | V Ｍ |, m Ｍ = | E Ｍ | (Here, |V| represents the number of vertices in the vertex set V, and |E| represents the number of edges in the edge set E.)

[0236] Based on the above, vertex Jaccard(J Ｖ ), edge Jaccard (J Ｅ ) and harmonic mean (J ｈａｒｍ ) is defined as follows:

[0237] Regarding various three-dimensional shapes in the same series, J ｈａｒｍ The results of the calculation are shown below (structures in brackets indicate MCS). • (3,5) Bipartite biregular polyhedra (rhombic triacontahedron) and its series of polyhedra (3,4) Bipartite biregular polyhedra (rhombic dodecahedron) and related polyhedra (2,3) Bipartite biregular polyhedra and polyhedra of their series

[0238] Stereolites with a graph showing a higher Jaccard index compared to the stereomorphisms of stereomolecules whose synthesis has been confirmed to be successful are considered to have a higher probability of being synthesized and / or to be able to be synthesized under more similar conditions. Approximately 60-70% J ｈａｒｍ Since the synthesis of stereomolecules possessing this property has also been successful, the amount of J exceeding approximately 60% is based on the stereomolecules whose synthesis was confirmed in the examples. ｈａｒｍ Stereomorphs possessing this property are expected to be synthesizable.

[0239] (Example 10: Evaluation using discrete Ricci curvature) It was found that there are shapes that are difficult to construct as actual stereomolecules, such as the one on the bottom right of the rdo-A series shown in Example 3. To evaluate the feasibility of constructing stereomolecules, an evaluation using Ollivier-Ricci curvature was performed based on the graph of the stereomorphic shape of the stereomolecules.

[0240] The discrete Ricci curvature is calculated as follows. The derivation of the Ollivier-Ricci curvature described herein is based on a general method.

[0241] For a graph, given a vertex x, its neighborhood set π(x) (the set of vertices connected to x by edges), and a constant α (0 ≤ α ≤ 1), the Lin-Yau distribution is: It is given by a constant. Using this, we generalize as follows to reflect the properties of each edge. (d( , ) represents the graph distance, b (>0) represents the basis, and p (≧0) represents the exponent.)

[0242] In this specification, including in the examples, curvature refers to the value when α = 0.5, p = 2, b = exp, and the graph distance = 1 without weighting, unless otherwise specified. The graph distance can be adjusted within the range of 1 to 100 depending on the weighting.

[0243] Definition 1 (Wasserstein distance; 1-dimensional) In, m ｘ Let and be probability measures, and define the transport distance between the two probability measures as follows: Here, f is, Let the function satisfy the following: • Definition 2 (Discrete Ricci curvature) For any two points x, y ∈ X, the discrete Ricci curvature is defined as follows:

[0244] The derivation of such discrete Ricci curvature can be implemented using the Python library GraphRicciCurvature (v0.5.1).

[0245] For example, the following three-dimensional shape is shown below, along with its graphical representation and the discrete Ricci curvature values ​​of each edge (where α = 0 is used).

[0246] These graphs of three-dimensional shapes do not contain edges with low discrete Ricci curvature, and it is thought that three-dimensional molecules with such shapes can be easily formed. Three-dimensional molecules with the three-dimensional shape of a graph that does not contain edges with low discrete Ricci curvature are thought to exist stably with reversible chemical bonds (bonds between pairs of bonding parts) formed at the positions corresponding to each edge. Note that reversible chemical bonds may be replaced with irreversible covalent bonds (intervertex linkers). Also, irreversible covalent bonds may be replaced with reversible chemical bonds. For example, in the lower diagram of the three-dimensional shape above, the vertical edge located at the very front is (6,4)-D in the actual fabrication example of Example 3. ４ｈIn the synthesis of [the compound], an irreversible covalent bond (vertex linker) is introduced, but a chemical group that forms a reversible chemical bond (for example, an arm having an SH group that forms an S-S bond) may be introduced at the corresponding location.

[0247] On the other hand, the following three-dimensional structures have edges with negative discrete Ricci curvature, and it is considered relatively difficult to construct a three-dimensional molecule with such a shape by forming reversible chemical bonds at the positions corresponding to each edge.

[0248] The following shows the results of weighting the graph edges at the positions corresponding to the vertical edge located at the forefront of the above 3D shape diagram (using graph distance = 3). This operation eliminated edges with negative discrete Ricci curvature.

[0249] While we do not wish to be bound by any particular theory, graph distance can be considered, for example, to be similar to the average lifetime of a bond before it breaks in an actual stereomolecule. Therefore, setting a large value such as 100 as the graph distance may be sufficient to reflect irreversible bonds. In fact, the weighted graph above was calculated with a graph distance of 3, but even when the graph distance is changed to an even larger value, the value of the discrete Ricci curvature (excluding the edges where the graph distance was changed) does not change much across the entire graph, suggesting that in the above example, a graph distance of 3 reflects a sufficiently strong bond. Discrete curvature indicates the coordination of local stability; when the discrete curvature is negative, the surrounding bonds tend to fluctuate independently, leading to a tendency for it to become a break point, while when the discrete curvature is positive, the neighboring bonds are stable in sync, making the bond point stable as well.

[0250] In fact, the following is a structural element designed to form irreversible covalent bonds (intervertex linkers) instead of reversible chemical bonds at the positions corresponding to the weighted edges described above. The enclosed area is the part that reflects the weighting. As a result, the formation of the desired stereomolecule was confirmed (Example 5, (4,4)-D). ２ｄ(See the synthesis section.)

[0251] Thus, even for three-dimensional shapes that are judged from the graph of their three-dimensional shape to contain edges with low discrete Ricci curvature, it is thought that it is possible to form three-dimensional molecules with such shapes by weighting them so that there are no edges with low discrete Ricci curvature, and by designing the molecule so that the chemical bonds at the positions corresponding to the weighted edges become irreversible covalent bonds.

[0252] Furthermore, the lowest discrete Ricci curvature (κ) in the graph min The fact that ) is suitable for evaluating the possibility and stability of stereomolecules can be explained physically (details omitted). Since stereomolecules are thought to break down mainly around the edges with low discrete curvature, κ min Stereomorphs that result in a large value are preferably selected. Also, without weighting, κ min Stereomorphs with large values ​​are given appropriate weightings by κ min Since it is easy to design it so that it exceeds a predetermined value, it can also be chosen as a basis for design.

[0253] This disclosure provides a stereomolecular structure with novel structures and offers a foundation for the development of new chemical products.

Claims

1. A stereomolecule having a polyhedral shape, wherein the polyhedron is a bipartite biregular polyhedron satisfying (p,q) biregularity, or a vertex-deficient polyhedron or a barrel-shaped vertex-deficient derivative thereof, where p and q are each independently selected from integers between 2 and 6.

2. The stereomolecule according to claim 1, wherein the biregular polyhedron satisfies the biregularity of (3,4), (3,5), (2,5), or (2,3).

3. The stereomolecule according to claim 1, wherein the number of vertices of the biregular polyhedron is in the range of 8 to 50.

4. The stereomolecule according to claim 1, wherein the isolated radius of the biregular polyhedron is 4 or more.

5. The stereomolecule according to claim 1, wherein the biregular polyhedron is a rhombic dodecahedron or a rhombic triicosahedron.

6. The stereomolecule according to claim 1, wherein the vertex-defect body is deficient in vertices at symmetrical positions in the biregular polyhedron.

7. The stereomolecule according to claim 1, wherein the polyhedron is a vertex-deficient rhombic dodecahedron or rhombic triicosahedron.

8. The stereomolecule according to claim 1, wherein the polyhedron is one of the vertex-deficient bodies listed in Tables 1 to 4.

9. A stereomolecule according to claim 1, having a three-dimensional shape of a graph that does not contain edges having discrete Ricci curvature values ​​less than -0.5, or having a three-dimensional shape of a weighted graph that does not contain edges having discrete Ricci curvature values ​​less than -0.

5.

10. The polyhedron has a harmonic mean (J) of approximately 60-100% for any of the three-dimensional shapes listed in Tables 1-4. ｈａｒｍ A stereomolecule according to claim 1, having the following characteristics.

11. The stereomolecule according to claim 1, wherein the stereomolecule is constructed of two types of structural elements.

12. The two types of building elements include a first building element and a second building element, where the first building element is a compound having the following formula: where each A is a vertex skeleton having a vertex degree of m independently, each R ２ is independently a first binding moiety, each R １ is independently an arm connecting A and R ２ and each L １ is independently an inter-vertex linker connecting different As and does not exist when p = 1, each m is independently an integer selected from 2 to 6, p is an integer selected from 1 to 4, and the second building element is a compound having the following formula: where each B is a vertex skeleton having a vertex degree of n independently, each R ４ is independently a second binding moiety, each R ３ is independently an arm connecting B and R ４ and each L ２ is independently an inter-vertex linker connecting different Bs and does not exist when q = 1, each n is independently an integer selected from 2 to 6, q is an integer selected from 1 to 4, the three-dimensional molecule according to claim 11.

13. The stereomolecule according to claim 1, having a diameter greater than approximately 6 nm.

14. The stereomolecule according to claim 1, having a diameter of approximately 8 nm to approximately 12 nm.

15. The stereomolecule according to claim 12, wherein for all pairs of A-B distances in the stereomolecule, the A-B distances have a variation of less than 10% from each other.

16. The stereomolecule according to claim 12, wherein the first structural elements and the second structural elements do not form bonds with each other.

17. The stereomolecule according to claim 12, wherein A or B is selected from the group consisting of carborane or a fused ring thereof, a six-membered aromatic ring or a fused ring thereof, a five-membered aromatic ring or a fused ring thereof, colannulene, cyanoster, porphyrin, tetraarylethene, triarylamine, triarylphosphine, triarylmethane, triarylsilyl, and a metal atom (including the case of two metal atoms in a paddlewheel structure).

18. R ２ and R ４ The stereomolecule according to claim 12, wherein the combination has a reaction energy of approximately 10 to 500 kJ / mol.

19. R ２ and R ４ The stereomolecule according to claim 12, wherein the combination is a lone pair of electrons of -COOH and a pair of metal atoms, or a pair of bonding moieties that are bonded by electrophilic or nucleophilic addition reactions.

20. R １ or R ３ The stereomolecule according to claim 12, wherein each arm independently has a main chain composed of 5 to 100 atoms.

21. A method for producing a three-dimensional molecule having a polyhedral shape, the method comprising: (A) a step of preparing a first constructing element, wherein the first constructing element is given by the following formula: The compound has the following characteristics, where each A is an independent vertex skeleton having a vertex degree of m, and each R ２ This is independently the first bonding part, and each R １ A and R are independent of each other. ２ It is an arm that connects to each L １ (B) A is an intervertex linker that connects independently different A's, and does not exist when p = 1, where each m is an integer independently selected from 2 to 6, and p is an integer selected from 1 to 4, (B) a step of preparing a second construction element, where the second construction element is given by the following equation: The compound has the following characteristics, where each B is an independent vertex skeleton having a vertex degree of n, and each R ４ This is an independent second bonding part, and each R ３ B and R are independent of each other. ４ It is an arm that connects to each L ２ (C) a method comprising the steps of (C) a vertex linker that connects independently different Bs, which does not exist when q=1, where each n is an integer independently selected from 2 to 6, and q is an integer selected from 1 to 4, and (D) a method comprising mixing the first and second construction elements to form a plurality of bonds between the first bonding portion and the second bonding portion, thereby forming a stereomolecule having the shape of the polyhedron with A and B positioned at its vertices.

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