Search for isotypism in crystal structures by means of the graph theory

Блатов, В. А.

doi:10.1107/s0108767399015512

Cited by 65 publications

(15 citation statements)

References 26 publications

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“…Furthermore, Voronoi-Dirichlet polyhedra [40] were constructed around the pseudo-atoms to find contacts between pseudo-atoms in the crystal and to construct the packing graph. [41] The net of centroids (centres of gravity) of the spherical was created in a similar way, but the net edges between the centroids exist only if there are van der Waals contacts between the units; all contacts shorter than the sum of van der Waals radii [20] of interacting atoms were taken into account. In contrast to the packing graph, which characterizes the spatial arrangement of even disconnected objects, the net of centroids describes the topology of somehow connected molecular moieties.…”

Section: Methodsmentioning

confidence: 99%

Structures and Properties of Spherical 90‐Vertex Fullerene‐Like Nanoballs

Scheer

Schindler

Bai

et al. 2010

Chemistry A European J

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By applying the proper stoichiometry of 1:2 to [Cp(R)Fe(eta(5)-P(5))] and CuX (X=Cl, Br) and dilution conditions in mixtures of CH(3)CN and solvents like CH(2)Cl(2), 1,2-Cl(2)C(6)H(4), toluene, and THF, nine spherical giant molecules having the simplified general formula [Cp(R)Fe(eta(5)-P(5))]@[{Cp(R)Fe(eta(5)-P(5))}(12){CuX}(25)(CH(3)CN)(10)] (Cp(R)=eta(5)-C(5)Me(5) (Cp*); eta(5)-C(5)Me(4)Et (Cp(Et)); X=Cl, Br) have been synthesized and structurally characterized. The products consist of 90-vertex frameworks consisting of non-carbon atoms and forming fullerene-like structural motifs. Besides the mostly neutral products, some charged derivatives have been isolated. These spherical giant molecules show an outer diameter of 2.24 (X=Cl) to 2.26 nm (X=Br) and have inner cavities of 1.28 (X=Cl) and 1.20 nm (X=Br) in size. In most instances the inner voids of these nanoballs encapsulate one molecule of [Cp*Fe(eta(5)-P(5))], which reveals preferred orientations of pi-pi stacking between the cyclo-P(5) rings of the guest and those of the host molecules. Moreover, pi-pi and sigma-pi interactions are also found in the packing motifs of the balls in the crystal lattice. Electrochemical investigations of these soluble molecules reveal one irreversible multi-electron oxidation at E(p)=0.615 V and two reduction steps (-1.10 and -2.0 V), the first of which corresponds to about 12 electrons. Density functional calculations reveal that during oxidation and reduction the electrons are withdrawn or added to the surface of the spherical nanomolecules, and no Cu(2+) species are involved.

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Section: Methodsmentioning

confidence: 99%

Structures and Properties of Spherical 90‐Vertex Fullerene‐Like Nanoballs

Scheer

Schindler

Bai

et al. 2010

Chemistry A European J

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“…Pairs of binary and pseudobinary structures with identical T i values of A and B atoms like NaCl and NaSbF 6 or ZnS and BeSO 4 can be recognized from Table 2. Some related binary and pseudobinary structures with monoclinic or orthorhombic symmetry [1,[12][13][14] are included in Table 2.…”

Section: Analysis Of Binary and Quasibinary Compoundsmentioning

confidence: 99%

Morphological lattice complexes

Hauck

Mika²,

Sager

2005

Cryst. Res. Technol.

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Binary and pseudobinary compounds AB like NaCl and CaCO 3 , with the center of charge at carbon position, are characterized by self-coordination numbers of nearest, second and third neighbors T 1 T 2 T 3 of A and B positions. The maximum Madelung factor of compounds with identical T i values of A and B atoms is obtained for a maximum of B positions at the border of the A-A Dirichlet domain. The A and B positions form a packing with different T i values, if all B positions are on the border of the Dirichlet domain. This packing like the primitive cubic packing of Na and Cl atoms with T i values 6 12 8 or the rhombohedrally distorted packing 6 8 6 of CaCO 3 as morphological lattice complexes can be related to cubic NaCl crystals or the cleaved rhombohedron of calcite. A different habit of crystals is expected for sphere, rod or layered packings. Many well-defined nanoparticles can be obtained from microemulsions at variation of temperature, water content or water partial pressure.

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“…At present, topological description has become a routine procedure in structure investigations. The theoretical basis of the graph representation has also been intensively developed in the last two decades (Chung et al, 1984;Klee, 1987Klee, , 2004Eon, 1998;Winkler et al, 2001); the authors proposed to reduce the three-dimensional graph to a finite labelled quotient graph suitable for computer storage (Blatov, 2000;Delgado-Friedrichs & O'Keeffe, 2003). An intermediate approach that considers both geometrical and topological structure features was first developed for zeolites (Meier, 1968).…”

Section: Introductionmentioning

confidence: 99%

“…Taking into account the large variety even of simple topological motifs found in crystal structures and different chemical ways to separate SBUs in a compound, we need a distinct algorithmic procedure to consider a crystal structure at all allowable levels of its organization. In previous work (Blatov, 2000), we proposed a computer method and developed a program IsoTest to enumerate crystal structure representations and to analyse corresponding topologies. These tools were successfully applied to process various classes of inorganic synthetic compounds and minerals (Blatov, 2001;Ilyushin & Blatov, 2002;Ilyushin et al, 2004;Blatov & Peskov, 2006).…”

Section: Introductionmentioning

confidence: 99%

A method for hierarchical comparative analysis of crystal structures

Блатов

2006

Acta Cryst Sect A

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A geometrical-topological description of crystal structure as a three-dimensional graph with coloured nodes, weighted and coloured edges is used to generate a hierarchical sequence of the structure representations. The solid angles of Voronoi-Dirichlet polyhedra of atoms are used as the edge weights and the nodes and edges are coloured according to chemical reasons. Two operations are defined to derive the representations: contracting an atom to other atoms keeping the local connectivity, and removing an atom together with all its bonds. The atoms of the crystal structure are called origin, removed, contracted or target according to their roles in the operations. Each structure representation is described as a labelled quotient graph and determined by (i) colours of the graph nodes and edges, (ii) some level for edge weights, and (iii) an arrangement of atoms according to their roles. The computer enumeration and topological comparative analysis of all representations for crystal structures of any composition and complexity are implemented into the TOPOS program package. The advantages of the method are shown by the analysis of typical inorganic compounds and a molecular packing.

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Search for isotypism in crystal structures by means of the graph theory

Cited by 65 publications

References 26 publications

Structures and Properties of Spherical 90‐Vertex Fullerene‐Like Nanoballs

Structures and Properties of Spherical 90‐Vertex Fullerene‐Like Nanoballs

Morphological lattice complexes

A method for hierarchical comparative analysis of crystal structures

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