Self-assembly Of Crystal Structures Research Articles

C–H⋯NC hydrogen bonding in cyanobenzene-ethylenedithio-tetrathiafulvalene compounds

The importance of C–H⋯NC interactions, which although generally considered weak, are effective in the self-assembly of crystal structures.

Precursor Clusters K3, K4, and K6 for the Self-Assembly of Crystal Structures of Li20Ca28Sn44-oS92, Li2CaSn-cF16, and LiCaSn-hP9

Precursor Clusters K3, K4, and K6 for the Self-Assembly of Crystal Structures of Li20Ca28Sn44-oS92, Li2CaSn-cF16, and LiCaSn-hP9

Cluster Self-Organization of Intermetallic Systems: Role of K5 = 0@5, K9 = 1@8 and K11 = 0@11 Clusters in the Self-Assembly of Crystal Structures

The combinatorial-topological analysis and simulation of self-assembly of the Na96Hg36-hR132 (space group R-3c, a = b = 9.228 A, c = 52.6380 A, V = 3881.91 A3) and Na12Hg8-tP20 (space group P42/mnm, a = b = 8.520, c = 7.800 A, V = 566.2 A3) crystal structures are conducted by computer-based methods (ToposPro program package). Polyhedral cluster precursors K11 = 0@11(Na8Hg3) and K9 = Hg@Na8 are first determined for the intermetallic compound Na96Hg36-hR132, while polyhedral cluster precursors K5 = 0@Na3Hg2 are determined for the intermetallic compound Na12Hg8-tP20. The symmetry and topology code of the self-assembly processes of the 3D structure Na96Hg36-hR132 from the nanocluster precursors K11 and K9, and of the 3D structure Na12Hg8-tP20 from the K5 clusters are reconstructed as the primary chain $$S_{{\text{3}}}^{1}$$ → layer $$S_{{\text{3}}}^{2}$$ → frame $$S_{{\text{3}}}^{3}.$$ The structural analysis of all known intermetallic compounds is conducted, and numerous examples of the assembly of their structures from the K5, K9, and K11 clusters are found.

Cluster Self-Organization of Intermetallic Systems: Cs6 and Cs4 Metal Clusters and Cs11O3 Metal–Oxygen Cluster for the Self-Assembly of the (Cs4)(Cs6)(Cs11O3) Crystal Structure

A geometric and topological analysis of the Cs21O3 metal oxide with the minimal known oxygen content, which is formed from an oxygen-containing melt of metallic Cs, is performed. To identify clusters that are precursors of the crystal structures, special algorithms (ToposPro software package) for decomposing structural graphs into cluster substructures are used. The following precursor clusters involved in the self-assembly of the crystal structures are determined: Cs11O3 three-octahedral clusters; Cs6 octahedral clusters; and Cs4 tetrahedral clusters. The symmetry and topological code of the processes of self-assembly of crystal structures from precursor clusters is reconstructed in the following form: primary chain → microlayer → microframework.

Modeling Self-Organization Processes in Crystal Forming Systems. Symmetry and Topology Codes of Cluster Self-Assembly of Crystal Structure of Na44Tl7 (Na6Tl)

The geometrical and topological analysis of the crystal structure of intermetallide Na44Tl7 (Na6Tl, a = 24.154 A, V = 14091.8 A3, space group F-43m) is carried out. The algorithms of the combinatorial-topological analysis, which ensure the recovery of the symmetrical and topological code (program) of the cluster self-assembly of the crystal structure of an intermetallide, are developed. The topological type of the basic 3D network for two types of cluster precursors corresponds to a simple cubic 3D network P c with CN = 6 and basic 2D network of type 44. There are eight cluster precursors in the unit cell: four K86 and four K50. The cluster precursor K86 made from 86 atoms is formed from eight icosahedra i-TlNa12 linked by the apices. The center of the cluster precursor K86 is at the position 4a (0, 0, 0) with the point symmetry g = –43m. The 50-atomic cluster precursor K50 consists of six i-TlNa12 icosahedra. The center of the cluster precursor K50 is in the partial position 4b (0, 0, 0) with the point symmetry g = –43m. The symmetrical and topological codes of the self-assembly of 3D structures from nanocluster precursors K86 and K50 are reconstructed in the following form: primary chain → microlayer → microframework.

Modeling of self-organization processes in crystal-forming systems: Symmetry and topology code for cluster self-assembly of crystal structures for molecular and framework compounds

This is a review over the state of art in self-organization in crystal-forming systems, where a longrange order appears spontaneously in the arrangement of nanoscale building units of any nature (atomic clusters and molecules), which initially existed in a dynamic state as a chaotic mixture. The focus is on bimolecular compounds where building units are M-octahedra M(O, OH, H2O) and T-tetrahedra T(O, OH)4 bonded by OH–O hydrogen bonds and/or bridging oxygen atoms O. The combinatorial–topological modeling of 1D and 2D packings of suprapolyhedral clusters (MT)n has been carried out. These packings are symmetrically and topologically conceivable types of molecular MT clusters S03, from which chains S13 and 2D microlayers S23 are formed. The theoretically derived model MT-clusters (MT)n are compared with known types of precursor clusters in the molecular and framework MT-structures of polyvalent metal sulfates and their analogues. Combinatorial–topological analysis algorithms are provided to restore, from structure data, the convergent matrix crystal structure self-assembly code in the form of the sequence of significant elementary events. Crystal structure modeling involves combinatorial–topological analysis methods, whose underlying idea is the recogniition of packing-forming precursor nanoclusters and the construction of the relevant basal 2D and 3D networks in the form of graphs where nodes correspond to the positions of their centroids. The model is universal and has first been used to model the cluster self-assembly of molecular MT structures for V(2+)(H2O)4(SO4) (V-Rozenite), V(4+)O(H2O)5(SO4)(H2O) (SYN1), V(4+)O(H2O)5(SO4) (Orthominasragrite, Minasragrite, Anorthominasragrite), V(4+)O(H2O)3(SO4) (Bobjonesite); framework MT structures V(4+)O(SO4)(H2(SO4) (SYN2), V(4+)O(SO4) (Pauflerite and SYN3), V(4+)2O3(SO4)2 (SYN4), V(4+)2O3(SeO4)2 (SYN5), Fe(3+)2(SO4)3 (LIPHOS), and Fe(3+)2(SO4)3 (NASICON); and for templated framework MT structures (NH4)2[Ga2(PO4)2F2] (KTP), (NH4)2[Ga2(PO4)2(HF)F2] (p-KTP), TlMo2(PO4)3 (SYN06), and K2Mg2(SO4)3 (Langbeinite). Frequency analysis of topological and symmetry pathways in the formation and evolution of clusters (from primary chain S13 through microlayer S23 to microframework S33) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.

Modeling of self-organization processes in crystal-forming systems: Symmetry and topology code for cluster self-assembly of crystal structures in MT-structures of polyvalent sulfates and phosphates

We consider the supramolecular chemistry of polyvalent metal sulfates and phosphates built of M(n+)(O, OH, H2O)6 polyhedral clusters with octahedral O-coordination (M-polyhedra) and SO4 and PO4 polyhedral clusters with tetrahedral O-coordination (T-polyhedra). These compounds form molecular (insular), chain, layered, or framework 3D MT structures by means of directed (bridging) hydrogen bonds O–H…O and/or bridging covalent O-bonds. Combinatorial–topological analysis algorithms are provided to restore, from structure data, the convergent matrix crystal structure self-assembly code. Cluster self-assembly modeling has been performed for the following sulfates: MgSO4 (Pnma and Cmcm), MgSO4 ∙ 1H2O (Kieserite), and CuSO4 ∙ 3H2O (Bonattite) having 3D MT strucutres; MgSO4 ∙ 2H2O (Sanderite), MgSO4 · 2.5H2O, MnSO4 · 3H2O, and MnSO4(OH) · 2H2O having 2D MT structures; MgSO4 · 4H2O (Cranswickite) and MgSO4 · 5H2O (Pentahydrite) having 1D MT structures; and MgSO4 · 4H2O (Starkeyite) having a 0D MT structure, for the following phosphates: (VO)(HPO4) (P-1), MgSO4 · H2O (Kieserite), and CuSO4 · 3H2O (Bonattite) having 3D MT structures; (VO)(HPO4)(H2O)0.5 (P121/c1 and Pmmn), (VO)(HPO4)(H2O)2 (P4/nmm and P121/c1), V(3+)(PO4)(H2O)2 (P121/n1), V(3+)(PO4)(H2O)4 (C12/c1), and Mg(HPO4)(H2O)3 (Newberyite, Pbca) having 2D MT structures; phosphite (VO(H2O)2)(HPO3)(H2O)3 (P41) and phosphate (VO)(HPO4)(H2O)4 (P-1) having 1D MT structures. For all compounds, the symmetry and combinatorial codes of cluster self-assembly code in the form of the following sequence: precursor nanocluster S30 → primary chain S31→ microlayer S32→ microframework S33. At the stage of primary chain S31 formation, in all of MT crystal structures considered, precursor clusters are four-polyhedral MTMT chains, transor cis, and their derivatives with additional O-bonds between polyhedra and ring cluster M2T2 (the result of coiling a cis-chain into a ring). Frequency analysis of topological and symmetry pathways in the formation and evolution of MT-clusters (from primary chain S31 through microlayer S32 to microframework S33) elucidates new crystal-formation trends in diverse chemical systems at the microscopic level.

Modeling of the self-organization processes in crystal-forming systems: Symmetry and topological code of cluster self-assembly of molecular (island) and framework MT structures of vanadyl sulfates

The supramolecular chemistry of vanadyl sulfates, consisting of polyhedral clusters V(O, OH, H2O)6 with octahedral O coordination (M polyhedra) and SO4 tetrahedra (T polyhedra) and forming molecular (island) and framework 3D MT structures, is considered. Algorithms of combinatorial and topological analysis are developed that make it possible to reconstruct (based on known structural data) the symmetry and topological code of the matrix convergent self-assembly of crystal structure. Cluster modeling of the selfassembly of molecular (island) MT structures of the V2O2(H2O)6(SO4)2 · 4H2O (anorthominasragrite (ANM)) and V2O2(H2O)6(SO4)2 (bobjonesite (BBN)) compositions and topologically different framework 3D MT structures with covalent bonds, V2O2(SO4)2 (pauflerite (PAF) and synthetic phase (SYN)), is performed. A 3D reconstruction of the self-assembly mechanism in the form nanocluster precursor S 0 3 → primary chain → S 1 3 microlayer S 2 3 → microframework S 3 3 has revealed an invariant type of cyclic cluster precursor M2T2 (with a symmetry \(g = \overline 1 \)) for all compounds; differences in the self-assembly mechanisms are found for ANM and BBN in the stage of formation of primary chain S 1 3 and for PAF and SYN in the stage of formation of microlayer S 2 3. Basic 2D and 3D nets are presented in the form of graphs, the sites of which correspond to the positions of centroids of cluster precursors M2T2. The same topological type of basic 2D nets (4.4.4.4) is ascertained for all compounds. A basic 3D net corresponding to a simple cubic structure of Po (coordination number (CN) = 6) is established for ANM, SYN, and PAF; the basic 3D net for BBN corresponds to the cubic F structure of Cu (CN = 12).

Combinatorial-topological modeling of the cluster self-assembly of crystal structures of zeolites of the GME, AFX, AFT, and ISC-2 family

Combinatorial-topological 3D modeling of periodic packages from T12 polyhedral clusters has been carried out (t-hpr tiles in the form of hexagonal prisms), most frequent in the crystal zeolite structures. A basic 2D microlayer L is obtained by decoding a single-node 2D grid of the 6.6.6 type of graphite and it contains cyclic hexamers (T12)6. The hexamer is located in a triple hexagonal cell with ahex = 13.90 A; the height of the layer is about 10 A. In theory, the formation of an unlimited number of structures of polytypes with cell parameters of chex = N × 10 A is possible due to the different variants of the complementary communication of the L layers with each other (both with and without a shift). For the three obtained models of skeletons, an analogy is found with the following known zeolites: GME (mineral Gmelinite, P63/mmc, chex = 10 A), which is classified as a single layer 1H-polytype from the translation-related layers L, AFX—2H-polytype (P63/mmc, chex = 20A) and AFT—3H-polytype (P63/mmc, chex = 30 A). A new 3H-polytype ISC-2 is found with parameters a = 13.90 A, c = 30.00 A, V = 5019.7 A3, and P-6m2 (187). Using a TOPOS program pack, a set of tiles Tn is determined characterizing all polyhedral zeolite cavities: t-hpr-12T, t-gme-24T, t-aft-48T, and t-isc-72T (a new type of tile). It is assumed that the synthesis of skeletonized compound Al36P36O144 can be carried out by selecting the corresponding organic structure directing agents (OSDA molecules) in order to stabilize local areas corresponding to the cavities of the largest size (t-isc-72T size).

Modeling of self-organization processes in crystal-forming systems: Templated precursor nanoclusters T48 and the self-assembly of crystal structures of 15-crown-5, Na-FAU, 18-crown-6, Na-EMT, and Ca,Ba-TSC zeolites

The combinatorial and topological modeling of packings of symmetry-related nanoclusters T48 (diameter: ∼16 A, symmetry $$\bar 43m$$ ) is performed. The packings are 1D claims S 3 1 and 2D microlayers S 3 2 , which give rise to 3D structures S 3 3 . For three of the five framework structures, correspondence was established with zeolite FAU (Faujasite, Fd-3m, Z = 4 T48), EMT (P63/mmc, Z = 2 T48), and TSC (Tschortnerite $$Fm\bar 3m$$ , Z = 8 T48). Combinatorial topological analysis methods (the ToposPro program package) were used to model the steps of zeolite crystal structure self-assembly. The underlying idea of these methods consists in that the basal 3D network of the zeolite structure is designed as a graph, where the nodes correspond to the centroid positions of clusters T48. For FAU, the basal 3D network corresponds to the copper cubic strucutre (CN = 12); for EMT, it corresponds to the hexagonal (H) strucutre of magnesium (CN = 12); and for TSC, to the cubic structure of polonium (CN = 6). The symmetry and topology code of zeolite strucutre formation has been restored in the form of the sequence of significant elementary events that characterize the shortest (rapidest) program of convergent cluster self-assembly. The functional role played by 15-crown-5 and 18-crown-6 template molecules has been established to consist in the stabilization of the primary chains and microlayers of FAU and EMT frameworks and the relevant network of diamond and graphite topological types. The model for 3D structure self-assembly from clusters T48 is capable of explaining the morphogenesis of single crystals to form regular octahedra in FAU, hexagonal prisms in EMT, and regular cubes in TSC.

Icosahedral nanoclusters-precursors and self-assembly of crystal structures of the WAl12 (Im-3, cI26) family and sillenite Bi12 SiO20 (I23, cI66)

The self-assembly of crystal structures of the family WAl12 (Im-3, cI26) and sillenite Bi12SiO20 (I23, cI66) has been simulated. The methods of the combinatorial and topological analysis (TOPOS program package) have been used based on the determination of the type of the cluster-precursor and building the basic 3D net of the structure in the form of a graph, the nodes of which correspond to the position of the centers of gravity of the clusters-precursors, and the edges characterize the bonds between them. The topological type of the basic 3D net corresponds to the body-centered Fe structure (with the 3D net of the BCC type). The symmetric-topological code of the processes of self-assembling 3D structures from nanoclusters-precursors—primary chain → microlayer → micronetwork—has been completely reconstructed. The chemical composition of the icosahedral nanoclusters-precursors of 13 atoms for WAl12 and 33 atoms for Bi12SiO20 corresponds to the chemical composition of the compounds on the whole. The cluster-precursor of the crystal structure WAl12 is an icosahedron of 12 Al atoms with the W atom in the center. The icosahedron occupies position 2a in the unit cell with the highest crystallographically possible symmetry of m-3. In the cluster-precursor of the Bi12SiO20 structure, the location of the 32 atoms in the shell of the nanocluster Bi12SiO20 corresponds to the Bergman icosahedral cluster: the 12 vertices of the icosahedron are occupied by Bi atoms, oxygen atoms, of which four are also coupled with the Si atom located in the center of the cluster, are located above and below the centers of the 20 faces of the icosahedron. Nanoclusters Bi12SiO20 have the symmetry 32 and occupy positions 2a in the unit cell. The crystal structure of WAl12 can be obtained from Bi12SiO20 by the removal of O atoms, and the system of bonds between icosahedra is completely conserved.