Topological methods for complex intermetallics

We show how the topological methods realized in the so-called nanocluster approach can be applied to elucidating extremely complex intermetallic compounds. We have constructed the nanocluster models for the most complicated cubic structures and collected the motifs of their nanocluster assembling. These motifs are revealed to be similar to the most typical motifs in simple intermetallics. The most complicated nanoclusters up to 4273-atom nine-shell building unit in Al55.4Cu5.4Ta39.1 (ACT-71) are isolated and deposited in the topological types of nanoclusters collection.

Synthesis, structure and gas adsorption properties of a stable microporous Cu-based metal–organic framework assembled from a T-shaped pyridyl dicarboxylate ligand

A three-dimensional microporous metal–organic framework assembled from a T-shaped pyridyl dicarboxylate ligand has been synthesized. It possesses high stability and adsorption capacities for CO₂ (114 cm³ g⁻¹, 273 K) under ambient pressure.

A series of five-coordinated copper coordination polymers for efficient degradation of organic dyes under visible light irradiation

Five-coordinated copper(ii) coordination polymers 1–5 are highly efficient and universal photocatalysts for the degradation of the organic dyes methylene blue (MB), rhodamine B (RhB) and methyl orange (MO) under visible light irradiation.

A series of Cd(ii) coordination polymers based on flexible bis(triazole) and multicarboxylate ligands: topological diversity, entanglement and properties

Eight Cd(ii) coordination polymers with diverse topologies based on 1,4-bis(1,2,4-triazol-4-ylmethyl)benzene and multicarboxylate ligands were synthesized and characterized. The 3D topologies of 1, 2 and 3 are unprecedented.

Non-interpenetrated Cu-based MOF constructed from a rediscovered tetrahedral ligand

A stable non-interpenetrated MOF, UOF-1 (UOF = University of Otago framework), was made by combining the rigid tetrahedral tetrakis(4-carboxyphenyl)adamantane (L) ligand and copper(ii) paddle-wheel SBU. This low-density open framework displayed excellent selectivity for CO₂ over N₂ at practical operating conditions.

Ultrasound irradiation effect on morphology and size of two new potassium coordination supramolecule compounds

Two new potassium coordination supramolecular compounds (2D and 1D), [K(H₃L)(H₂L)(H₂O)]_n·H₂O (1) and [K(H₂L')(HL')(H₂O)₂]·H₂O (2), (L=1,3,5-tricarboxylic acid, L'=2,6-pyridinedicarboxylic acid), have been synthesized under different experimental conditions. Micrometric crystals (bulk) or nano-sized materials have been obtained depending on using the branch tube method or sonochemical irradiation. All materials have been characterized by field emission scanning electron microscopy (FE-SEM), scanning electron microscopy (SEM), powder X-ray diffraction (PXRD), FT-IR spectroscopy and elemental analyses. Single crystal X-ray analyses on compounds 1 and 2 show that K⁺ ions are 3- and 7-coordinated, respectively. Additionally, H-bonds incorporate the layers and chains in 1 and 2 into 3D and 2D (along (0,0,1) direction) frameworks. Topological analysis shows that the compound 1 and 2 are 3,6-coordinated kgd and 2,4-coordinated 2,4C4 net. The thermal stability of compounds 1 and 2 in bulk and nano-size has been studied by thermal gravimetric (TG) and differential thermal analyses (DTA) and compared each other. The role of different parameters like temperature, reaction time and ultrasound irradiation power on the growth and morphology of the nano-structures are studied. Results suggest that an increase of temperature, sonication power and reduction of reaction time led to a particle size decrease.

Two novel metal–organic coordination polymers based on ligand 1,4-diazabicyclo[2.2.2]octane N,N′-dioxide with phase transition, and ferroelectric and dielectric properties

The synthesis of two low-temperature structural phase transition compounds {[Ag₃(dabcodo)(NO₃)₃]·H₂O}n (1) and [Ca(Dabcodo)(H₂O)₄Cl₂]_n (2) are described. Compound 1 displayed ferroelectric–ferroelectric phase transition.

Novel amine templated three-dimensional zinc-organophosphonates with variable pore-openings

Amine templated three-dimensional zinc-organophosphates with different ring sizes have been obtained by varying the organic amine molecules. The figure shows the various net structures obtained during the study.

A novel 3-D photoluminescent cuprous chloride polymer based on bifunctional imidazolate/tetrazolate bridges

The interconnection of rare [Cu₂Cl]⁺cations and multidentate 1-tetrazole-4-imidazole-benzene bridging ligands gives a novel 3-D cuprous chloride polymer with a bimodalfsc-3,5-Cmce-2 topological type (L⁻ligand and Cu⁺ion: orange and blue).

Site-selective Eu(iii) spectroscopy of highly efficient luminescent mixed-metal Pb(ii)/Eu(iii) coordination polymers

Novel coordination polymers based on Pb_1−xEu_x–BDC (x = 0.05–0.50, BDC = 1,4-benzenedicarboxylic acid) are reported with a maximum emission quantum yield of 69 ± 7%.

An unusual porous cationic metal–organic framework based on a tetranuclear hydroxyl-copper(ii) cluster for fast and highly efficient dichromate trapping through a single-crystal to single-crystal process

An unusual porous cationic metal–organic framework based on a tetranuclear hydroxy-copper(ii) cluster displays fast and highly efficient dichromate trapping through a SC–SC transformation.

Crystal structure of a compact three-dimensional metal-organic framework based on Cs+ and (4,5-di-cyano-1,2-phenyl-ene)bis-(phospho-nic acid)

A new metal-organic framework compound, poly[[μ7-dihydrogen (4,5-di-cyano-1,2-phenyl-ene)diphospho-nato]-(oxonium)caesium], [Cs(C8H4N2O6P2)(H3O)] n (I), based on Cs+ and the organic linker 4,5-di-cyano-1,2-phenyl-ene)bis-(phospho-nic acid, (H4cpp), containing two distinct coordinating functional groups, has been prepared by a simple diffusion method and its crystal structure is reported. The coordination polymeric structure is based on a CsO8N2 complex unit comprising a monodentate hydro-nium cation, seven O-atom donors from two phospho-nium groups of the (H2cpp)2- ligand, and two N-atom donors from bridging cyano groups. The high level of connectivity from both the metal cation and the organic linker allow the formation of a compact and dense three-dimensional network without any crystallization solvent. Topologically (I) is a seven-connected uninodal network with an overall Schäfli symbol of {417.64}. Metal cations form an undulating inorganic layer, which is linked by strong and highly directional O-H⋯O hydrogen-bonding inter-actions. These metallic layers are, in turn, connected by the organic ligands along the [010] direction to form the overall three-dimensional framework structure.

Structures of Metal-Organic Frameworks with Rod Secondary Building Units

Rod MOFs are metal-organic frameworks in which the metal-containing secondary building units consist of infinite rods of linked metal-centered polyhedra. For such materials, we identify the points of extension, often atoms, which define the interface between the organic and inorganic components of the structure. The pattern of points of extension defines a shape such as a helix, ladder, helical ribbon, or cylinder tiling. The linkage of these shapes into a three-dimensional framework in turn defines a net characteristic of the original structure. Some scores of rod MOF structures are illustrated and deconstructed into their underlying nets in this way. Crystallographic data for all nets in their maximum symmetry embeddings are provided.

Homo Citans and Carbon Allotropes: For an Ethics of Citation

Cite we must, cite we do. We cite because we are links in a chain, using properties and methods validated by others. We also cite to negotiate the anxiety of influence. And to be fair. After outlining the reasons for citation, we use two case studies of citation amnesia in the field of hypothetical carbon allotropes to present a computer-age search tool (SACADA) in that subsubfield. Finally, we advise on good search practice, including what to do if you miss a citation.

A two-dimensional mixed-valence Cu(II)/Cu(I) coordination polymer constructed from 2-(pyridin-3-yl)-1H-imidazole-4,5-dicarboxylate

Coordination polymers are a thriving class of functional solid-state materials and there have been noticeable efforts and progress toward designing periodic functional structures with desired geometrical attributes and chemical properties for targeted applications. Self-assembly of metal ions and organic ligands is one of the most efficient and widely utilized methods for the construction of CPs under hydro(solvo)thermal conditions. 2-(Pyridin-3-yl)-1H-imidazole-4,5-dicarboxylate (HPIDC(2-)) has been proven to be an excellent multidentate ligand due to its multiple deprotonation and coordination modes. Crystals of poly[aquabis[μ3-5-carboxy-2-(pyridin-3-yl)-1H-imidazole-4-carboxylato-κ(5)N(1),O(5):N(3),O(4):N(2)]copper(II)dicopper(I)], [Cu(II)Cu(I)2(C10H5N3O4)2(H2O)]n, (I), were obtained from 2-(pyridin-3-yl)-1H-imidazole-4,5-dicarboxylic acid (H3PIDC) and copper(II) chloride under hydrothermal conditions. The asymmetric unit consists of one independent Cu(II) ion, two Cu(I) ions, two HPIDC(2-) ligands and one coordinated water molecule. The Cu(II) centre displays a square-pyramidal geometry (CuN2O3), with two N,O-chelating HPIDC(2-) ligands occupying the basal plane in a trans geometry and one O atom from a coordinated water molecule in the axial position. The Cu(I) atoms adopt three-coordinated Y-shaped coordinations. In each [CuN2O] unit, deprotonated HPIDC(2-) acts as an N,O-chelating ligand, and a symmetry-equivalent HPIDC(2-) ligand acts as an N-atom donor via the pyridine group. The HPIDC(2-) ligands in the polymer serve as T-shaped 3-connectors and adopt a μ3-κ(2)N,O:κ(2)N',O':κN''-coordination mode, linking one Cu(II) and two Cu(I) cations. The Cu cations are arranged in one-dimensional -Cu1-Cu2-Cu3- chains along the [001] direction. Further crosslinking of these chains by HPIDC(2-) ligands along the b axis in a -Cu2-HPIDC(2-)-Cu3-HPIDC(2-)-Cu1- sequence results in a two-dimensional polymer in the (100) plane. The resulting (2,3)-connected net has a (12(3))2(12)3 topology. Powder X-ray diffraction confirmed the phase purity for (I), and susceptibilty measurements indicated a very weak ferromagnetic behaviour. A thermogravimetric analysis shows the loss of the apical aqua ligand before decomposition of the title compound.

A Chiral 3 D Net with 2 D Cairo Pentagonal Tiling Projection in Site-Modified CuCN/CuSCN Networks

A novel isohedral 3-periodic net (i.e. a net with one kind of tile), showing a Cairo pentagonal tiling projection on the Euclidean plane, has been identified in a series of site-modified CuCN/CuSCN networks, namely, [Cu₆ (SCN)₂ (CN)₆ ⋅Ni(tpy)₂ ]_n (1), [Cu₆ (SCN)(CN)₇ ⋅Ni(tpy)₂ ]_n (2) and [Cu₆ (CN)₈ ⋅Ni(tpy)₂ ]_n (3) (tpy=2,2':6'',2''-terpyridine). These infinite inclusion compounds were prepared via a solvothermal sulfur migration reaction with subtle modification to fine-tune the sulfur content. The chiroptical activity of single crystals, which arises from the intrinsically chiral net, was confirmed by X-ray diffraction and solid-state circular dichroism spectra.

Vertex-connectivity in periodic graphs and underlying nets of crystal structures

Periodic nets used to describe the combinatorial topology of crystal structures have been required to be 3-connected by some authors. A graph is n-connected when deletion of less than n vertices does not disconnect it. n-Connected graphs are a fortiari n-coordinated but the converse is not true. This article presents an analysis of vertex-connectivity in periodic graphs characterized through their labelled quotient graph (LQG) and applied to a definition of underlying nets of crystal structures. It is shown that LQGs of p-periodic graphs (p ≥ 2) that are 1-connected or 2-connected, but not 3-connected, are contractible in the sense that they display, respectively, singletons or pairs of vertices separating dangling or linker components with zero net voltage over every cycle. The contraction operation that substitutes vertices and edges, respectively, for dangling components and linkers yields a 3-connected graph with the same periodicity. 1-Periodic graphs can be analysed in the same way through their LQGs but the result may not be 3-connected. It is claimed that long-range topological properties of periodic graphs are respected by contraction so that contracted graphs can represent topological classes of crystal structures, be they rods, layers or three-dimensional frameworks.

Monoclinic sphere packings. I. Invariant, univariant and bivariant lattice complexes

All homogeneous sphere packings were derived that refer to the two invariant, the four univariant and the three bivariant lattice complexes belonging to the monoclinic crystal system. In total, sphere packings of 29 types have been found. Only for five types is the maximal inherent symmetry of their sphere packings monoclinic whereas the inherent symmetry is orthorhombic for nine types, tetragonal for five types, hexagonal for six types and cubic for four types.

Dicyanometallates as Model Extended Frameworks

We report the structures of eight new dicyanometallate frameworks containing molecular extra-framework cations. These systems include a number of hybrid inorganic–organic analogues of conventional ceramics, such as Ruddlesden–Popper phases and perovskites. The structure types adopted are rationalized in the broader context of all known dicyanometallate framework structures. We show that the structural diversity of this family can be understood in terms of (i) the charge and coordination preferences of the particular metal cation acting as framework node, and (ii) the size, shape, and extent of incorporation of extra-framework cations. In this way, we suggest that dicyanometallates form a particularly attractive model family of extended frameworks in which to explore the interplay between molecular degrees of freedom, framework topology, and supramolecular interactions.

On the group-theoretical approach to the study of interpenetrating nets

Using group–subgroup and group–supergroup relations, a general theoretical framework is developed to describe and derive interpenetrating 3-periodic nets. The generation of interpenetration patterns is readily accomplished by replicating a single net with a supergroupGof its space groupHunder the condition that site symmetries of vertices and edges are the same in bothHandG. It is shown that interpenetrating nets cannot be mapped onto each other by mirror reflections because otherwise edge crossings would necessarily occur in the embedding. For the same reason any other rotation or roto-inversion axes fromG \ Hare not allowed to intersect vertices or edges of the nets. This property significantly narrows the set of supergroups to be included in the derivation of interpenetrating nets. A procedure is described based on the automorphism group of aHopf ring net[Alexandrovet al.(2012).Acta Cryst.A68, 484–493] to determine maximal symmetries compatible with interpenetration patterns. The proposed approach is illustrated by examples of twofold interpenetratedutp,diaandpcunets, as well as multiple copies of enantiomorphic quartz (qtz) networks. Some applications to polycatenated 2-periodic layers are also discussed.

Topological features in crystal structures: a quotient graph assisted analysis of underlying nets and their embeddings

Topological properties of crystal structures may be analysed at different levels, depending on the representation and the topology that has been assigned to the crystal. Considered here is thecombinatorialorbond topologyof the structure, which is independent of its realization in space. Periodic nets representing one-dimensional complexes, or the associated graphs, characterize the skeleton of chemical bonds within the crystal. Since periodic nets can be faithfully represented by their labelled quotient graphs, it may be inferred that their topological features can be recovered by a direct analysis of the labelled quotient graph. Evidence is given for ring analysis and structure decomposition into building units and building networks. An algebraic treatment is developed for ring analysis and thoroughly applied to a description of coesite. Building units can be finite or infinite, corresponding to 1-, 2- or even 3-periodic subnets. The list of infinite units includes linear chains or sheets of corner- or edge-sharing polyhedra. Decomposing periodic nets into their building units relies on graph-theoretical methods classified assurgery techniques. The most relevant operations are edge subdivision, vertex identification, edge contraction and decoration. Instead, these operations can be performed on labelled quotient graphs, evidencing in almost a mechanical way the nature and connection mode of building units in the derived net. Various examples are discussed, ranging from finite building blocks to 3-periodic subnets. Among others, the structures of strontium oxychloride, spinel, lithiophilite and garnet are addressed.

Bis(triethanolamine)bis(μ2-trimesato)dicobalt(II): a Co(II) dimer with an unreported two-dimensional supramolecular topology formed from triethanolamine and trimesic acid ligands

Supramolecular networks are an important subset in the field of coordination polymer (CP) frameworks and are widely encountered in crystal engineering research. The search for novel topologies continues to be a significant goal in CP chemistry. The dimeric compound bis(μ-5-carboxybenzene-1,3-dicarboxylato-κ(2)O(1):O(3))bis[(triethanolamine-κ(4)N,O,O',O'')cobalt(II)], [Co2(C9H4O6)2(C6H15NO3)2], formed from the coligands 5-carboxybenzene-1,3-dicarboxylate (tmaH(2-)) and triethanolamine (teaH3), namely [Co(μ2-tmaH)(teaH3)]2, was synthesized and characterized by single-crystal and powder X-ray diffraction analyses, IR spectroscopy, thermogravimetric analysis (TGA) and magnetic measurements. The crystal structure features a zero-dimensional molecular structure consisting of centrosymmetric macrocyclic dinuclear complexes. Four classical hydrogen bonds between carboxylate groups and hydroxyethyl arms stabilize and extend the molecules into a two-dimensional supramolecular network. The topological analysis indicates that an unreported (3,5)-binodal supramolecular topology with a short Schläfli symbol of (4.5.6)(4.5(5).6(3).7) can be achieved by means of intermolecular hydrogen bonds. The crystal structure accounts for the potential to obtain unique topological types from two excellent hydrogen-bonding candidates, i.e. tmaH3 and teaH3. A variable-temperature magnetic study shows the existence of antiferromagnetic behaviour in the complex.