First systematic investigation of C-H...Cl hydrogen bonding using inorganic supramolecular synthons: lamellar, stitched stair-case, linked-ladder, and helical structures

Using a group of six neutral M(II)Cl(2)-containing coordination compounds as building blocks, the first systematic investigation of C-H...Cl hydrogen-bonding interactions was performed. Single-crystal X-ray structural analyses of four new compounds (pseudo-tetrahedral Co(II) and Zn(II); distorted trigonal bipyramidal Zn(II)) authenticate the metal coordination geometry. To provide a unified view of the presence of noncovalent interactions in this class of compounds, we have re-examined the packing diagram of two previously reported compounds (a distorted square-pyramidal Cu(II) complex and a trans-octahedral Co(II) complex). The organic ligands of our choice comprise bidentate/tridentate pyrazolylmethylpyridines and an unsymmetrical tridentate pyridylalkylamine. This systematic investigation has allowed us to demonstrate the existence of versatile C-H...Cl(2)M interactions and to report the successful application of such units as inorganic supramolecular synthons. Additional noncovalent interactions such as C-H...O and O-H...Cl hydrogen bonding and pi-pi stacking interactions have also been identified. Formation of novel supramolecular architectures has been revealed: 2D lamellar (p-cyclophane) and 3D lamellar, 3D "stitched staircase" (due to additional hydrogen-bonding interactions by water tetramers, with an average O-O bond length in the tetramer unit of 2.926 A, acting as "molecular clips" between staircases), 3D linked ladder, and single-stranded 1D helix.     

Supramolecular architectures with ladder and lamellar topologies using metal-ligand coordination units via C–H···Cl and O–H···Cl hydrogen bonding

New Mn^II/Cu^II/Zn^II complexes [(L¹)MnCl₂] (1), [(L²)CuCl₂]·0.5H₂O (2) and [(L²)ZnCl(H₂O)][ClO₄] (3), containing (2-pyridyl)alkylamine ligands, N-methyl-N,N-bis(2-pyridylmethyl)amine (L¹) and methyl[2-(2-pyridyl)ethyl](2-pyridylmethyl)amine (L²), have been prepared and characterized, including X-ray crystallography. The most striking feature of the structures of these complexes is the formation of molecular ladder and lamellar topology through the crystal packing arrangement, determined by both strong O–H···Cl and weak (however, multiple) C–H···Cl hydrogen-bonding interactions, to maintain the neutral/cationic metal-ligand coordination units linked to each other. In 3, additional secondary interactions are observed involving coordinated solvent and the counter-ion. The results presented here demonstrate that (i) the choice of organic ligands to provide flexibility and inherent potential to participate in hydrogen-bonding interactions, (ii) the coordination geometry preferences of metal ions, (iii) the number of metal-bound chloride ion and (iv) the presence of solvent/counter-anion have a great influence on supramolecular network topology.     

The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the “convex feasibility” problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the “angles” between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the “norm” of the product of the (nonlinear) metric projections onto related convex sets.In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the “linear regularity property” of Bauschke and Borwein, the “normal property” of Jameson (as well as Bakan, Deutsch, and Li’s generalization of Jameson’s normal property), the “strong conical hull intersection property” of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well.     

Diorganotin(IV) and triorganotin(IV) derivatives of diphenic acid

The diorganotin(IV) and triorganotin(IV) derivatives R₂SnA (R = Me, n-Pr, n-Bu, n-Oct) and (R₃Sn)₂A [R = Me, Ph, cyclohexyl (Cyh); A = an anion of diphenic acid] have been prepared and characterized by elemental analysis, IR, ¹H and ¹³C NMR spectroscopies. Tetrahedral tin forms a part of a diphenate cyclic ring in the diorganotin complexes with unidentate carboxylates, which have further been used for the synthesis of cyclic acid anhydrides. The soluble dinuclear triorganotin complexes (Me, Ph) possess symmetrically bonded carboxylates while the less soluble compound (Cyh₃Sn)₂A has two asymmetrically bonded carboxylates. All have a trigonal bipyramidal structure with R₃Sn units remote from each other.