Polynuclear complexes with bridging pyrophosphate ligands: synthesis and characterisation of {[(bipy)Cu(H2O)(mu-P2O7)Na2(H2O)6] x 4H2O}, {[(bipy)Zn-(H2O)(mu-P2O7)Zn(bipy)]2 x 14H2O} and {[(bipy)(VO)2]2(mu-P2O7)] x 5H2O}

The reaction in water of M(II) ions (M = Cu, 1; Zn, 2; VO, 3) with 2,2'-bipyridine (bipy) followed by Na4P2O7 leads to the formation of three new complexes which feature the pyrophosphate anion, P2O7(4-), as a bridging ligand. Single crystal X-ray diffraction revealed 1 to be {[(bipy)Cu(H2O)(micro-P2O7)Na2(H2O)6] x 4H2O}, and 2 as a tetranuclear Zn(II) complex, {[(bipy)Zn(H2O)(micro-P2O7)Zn(bipy)]2 x 14H2O}. The structure of 1 consists of a mononuclear [(bipy)Cu(H2O)(P2O7)]2- unit that links via a pyrophosphate bridge to two Na atoms. The hydrated six-coordinate Na atoms themselves join together through bridging water molecules to generate a 2D Na-water sheet. The structure of 2 consists of a tetranuclear Zn(II) cluster (dimer-of-dimers) with two pyrophosphate ligands bridging between four metal centres. Adjacent clusters interact through face-to-face pi-pi interactions via the bipy ligands to yield a 2D sheet. Adjacent sheets pack in register to create channels, which are filled by the water molecules of crystallisation. An intricate 2D H-bonded water network separates adjacent sheets and encapsulates the tetranuclear clusters. Aspects of the pyrophosphate coordination modes in 1 and 2 are of structural relevance to those found within the inorganic pyrophosphatases. Compound 3, {[(bipy)(VO)2]2(micro-P2O7)] x 5H2O}, was isolated as an insoluble lime-green powder. Its dinuclear structure was elucidated from elemental and thermal analysis, magnetic susceptibility measurement and IR spectroscopy. The latter displayed characteristic bridging pyrophosphate and signature V=O stretches, which were corroborated by contrast to the IR spectra of 1 and 2 and through comparison with those found in the structurally characterised dinuclear complex, {[(bipy)Cu(H2O)]2(micro-P2O7) x 7H2O}, 4.     

Optically active diaryl tetrahydroisoquinoline derivatives

In (1R,3S)‐6,7‐dimethoxy‐3‐(methoxydiphenylmethyl)‐1‐phenyl‐1,2,3,4‐tetrahydroisoquinoline, C₃₁H₃₁NO₃, (I), and (1R,3S)‐2‐benzyl‐3‐[diphenyl(trimethylsiloxy)methyl]‐6,7‐dimethoxy‐1‐phenyl‐1,2,3,4‐tetrahydroisoquinoline, C₄₀H₄₃NO₃Si, (II), the absolute configurations have been confirmed to be R and S at the isoquinoline 1‐ and 3‐positions, respectively, by NMR spectroscopy experiments. Both structures have monoclinic (P2₁) symmetry and the N‐containing six‐membered ring assumes a half‐chair conformation. The asymmetric unit of (I) contains one molecule, while (II) has two molecules within the asymmetric unit. These structures are of interest with respect to the conformation around the exocyclic C—C bond: (I) displays an ap (antiperiplanar) conformation, while (II) displays an sc‐exo (synclinal) conformation around this bond. These conformations are significant for stereocontrol when these compounds are used as catalysts. Various C—H...π and C—H...O bonds link the molecules together in the crystal structure of (I). In the crystal structure of (II), three intermolecular C—H...π hydrogen bonds help to establish the packing.     

Synthesis and NMR elucidation of homoisoflavanone analogues

A series of five homoisoflavanone analogues have been synthesized from the corresponding 3,5-methoxy phenols via chroman-4-one in three steps. The complete NMR elucidation of these homoisoflavanone analogues is reported. The use of 2D NMR techniques (COSY, NOESY, HSQC and HMBC) proved to be very useful tools in the elucidation of homoisoflavanone analogues. The homoisoflavanone analogues exhibit an AA′BB′ spin pattern in the ring B of the homoisoflavanone. These homoisoflavanone analogues are potential antifungal and anti-inflammatory agents.     

Europium-directed self-assembly of a luminescent supramolecular gel from a tripodal terpyridine-based ligand

Eu(III), the last piece in the puzzle: Europium-induced self-assembly of ligands having a C(3)-symmetrical benzene-1,3,5-tricarboxamide core results in the formation of luminescent gels. Supramolecular polymers are formed through hydrogen bonding between the ligands. The polymers are then brought together into the gel assembly through the coordination of terpyridine ends by Eu(III) ions (blue dashed arrow: distance between two ligands in the strand direction).     

Some Remarks on Stability of Generalized Equations

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C ² inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian–Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.     

A simple and environmentally benign synthesis of polypyridine-polycarboxylic acids

An oxidation method using dilute nitric acid solutions under solvothermal conditions has been developed to synthesise a series of polypyridine-polycarboxylic acids. It has been successfully applied to a range of methyl substituted polypyridines including symmetrical and asymmetrical 2,2′-bipyridines; 2,2′:6′,2″-terpyridines and; 2,2′:6′,2″:6″,2?-tetra-pyridines and yields crystalline polypyridine-polycarboxylic acids in a single step. Simple product recovery through filtration yields a recyclable filtrate. More forcing conditions led to demethylation of the polypyridine ligand most probably via decarboxylation. This simple approach avoids potentially harmful metal-based oxidants and negates any issues associated with the disposal of their resultant (hazardous) waste.     

On relaxing the Mangasarian–Fromovitz constraint qualification

For the classical nonlinear program, two new relaxations of the Mangasarian–Fromovitz constraint qualification are discussed and their relationship with some standard constraint qualifications is examined. In particular, we establish the equivalence of one of these constraint qualifications with the recently suggested by Andreani et al. Constant rank of the subspace component constraint qualification. As an application, we make use of this new constraint qualification in the local analysis of the solution map to a parameterized equilibrium problem, modeled by a generalized equation.