Excellent fluorescence properties are exhibited by d 10 metal compounds. The novel three-dimensional ZnII coordination framework, poly[[{μ2-bis[4-(2-methyl-1H-imidazol-1-yl)phenyl] ether-κ2 N 3:N 3′}(μ2-furan-2,5-dicarboxylato-κ2 O 2:O 5)zinc(II)] 1.76-hydrate], {[Zn(C6H2O5)(C20H18N4O)]·1.76H2O} n , has been prepared and characterized using IR spectroscopy, elemental analysis and single-crystal X-ray diffraction. The crystal structure analysis revealed that the compound exhibits a novel fourfold interpenetrating diamond-like network. This polymer also displays a strong fluorescence emission in the solid state at room temperature.

A novel three-dimensional (3D) CdII coordination polymer, namely, poly[[μ2-4,4′-bis(2-methylimidazol-1-yl)-[1,1′-biphenyl]](μ2-5-methylisophthalato)cadmium(II)], [Cd(C9H6O4)(C20H18N4)] n or [Cd(MIP)(4,4′-BMIBP)] n , (I), was synthesized by the hydrothermal method using 5-methylisophthalic acid (H2MIP), 4,4′-bis(2-methylimidazol-1-yl)-[1,1′-biphenyl] (4,4′-BMIBP) and Cd(NO3)2·6H2O, and characterized by single-crystal X-ray diffraction, elemental analysis, IR spectroscopy and thermogravimetric analysis. Compound (I) exhibits a novel fivefold interpenetrating 3D diamondoid framework. Additionally, it shows fluorescence emission in the solid state and promising photocatalytic activities for the degradation of methylene blue (MB) in water at room temperature.

A three-dimensional metal–organic framework, namely, poly[[bis(μ3-benzene-1,3,5-tricarboxylato)bis[μ3-1,3,5-tris(2-methylimidazol-1-yl)benzene]tricopper(II)] hexahydrate], {[Cu3(C9H3O6)2(C18H18N6)2]·6H2O} n or {[Cu(BTC)2/3(TMIB)2/3]·2H2O} n , (I) [TMIB is 1,3,5-tris(2-methylimidazol-1-yl)benzene and H3BTC is benzene-1,3,5-tricarboxylic acid], has been synthesized under solvothermal conditions and structurally characterized by elemental analysis, IR spectroscopy, single-crystal X-ray diffraction and thermogravimetric analysis (TGA). Compound (I) features an unusual three-dimensional (3,4)-connected 2-nodal net with {83}4{86}3 topology. Photocatalytic investigations indicate that (I) affords good photocatalytic capabilities in the degradation of methylene blue (MB). Furthermore, the possible photocatalytic mechanism is discussed.

A solution for least square generalised inverse Ai- is found by elementary transformation of block matrix, and is further used to solve the contradictory equations set in Article [1].