High-order nonlinear initial-value problems countably determined

We give a numerical approximation of the solution of a high-order nonlinear initial-value problem by making use of certain properties of an adequate Schauder basis.     

Free-Standing,Flexible Nanofeatured Polymeric Films Prepared by Spin-Coating and Anodic Polymerization as Electrodes for Supercapacitors

Flexible and self-standing multilayered films made of nanoperforated poly(lactic acid) (PLA) layers separated by anodically polymerized poly(3,4-ethylenedioxythiophene) (PEDOT) conducting layers have been prepared and used as electrodes for supercapacitors. The influence of the external layer has been evaluated by comparing the charge storage capacity of four- and five-layered films in which the external layer is made of PEDOT (PLA/PEDOT/PLA/PEDOT) and nanoperforated PLA (PLA/PEDOT/PLA/PEDOT/PLA), respectively. In spite of the amount of conducting polymer is the same for both four- and five-layered films, they exhibit significant differences. The electrochemical response in terms of electroactivity, areal specific capacitance, stability, and coulombic efficiency was greater for the four-layered electrodes than for the five-layered ones. Furthermore, the response in terms of leakage current and self-discharge was significantly better for the former electrodes than for the latter ones.     

Structure and properties of a new double-stranded tetranuclear [Cu(II)2]2 helicate

A novel double-stranded tetranuclear helicate composed of a pair of [Cu(II)(2)] dimers has been prepared and characterized by exploiting the flexibility, chelating ability and bridging potential of a hexadentate bis-oximate ligand.     

Unique asymmetric (CuII4) double-stranded helicate from a hexadentate piperazine-based ligand: ligand conformation isomerism upon coordination

In methanol, the reaction of Cu(ClO(4))(2).6H(2)O and a sterically constrained piperazine imine phenol ligand (H(2)L), in the presence of NEt(3), affords a novel tetranuclear copper(II) complex of formula [Cu(II)(4)(mu(3)-L)(2)(mu-OH)(2)(H(2)O)(2)](ClO(4))(2).H(2)O (1). The X-ray structure of this complex shows an elongated Cu(4) quasi-tetrahedron coordinated to two hexadentate chair-(e,a)-mu(3)-piperazine bridging ligands. Variable-temperature magnetic studies show an S(t) = 0 spin ground state resulting from antiferromagnetic interactions between Cu(II) ions within the complex.     

Polynuclear vanadium complexes from thermal decomposition of [V3O(O2CPh)6(H2O)3]Cl

Solid-state decomposition of [V3O(O2CPh)6(H2O)3]Cl at 300 degrees C followed by alcoholysis of the product gives the new vanadium complexes [V6O6(PhCO2)6(CH3O)6(CH3OH)3] (1), [V6O6(PhCO2)6(C2H5O)6(C2H5OH)3] (2), [V6O6(PhCO2)6(C3H7O)6(C3H7OH)3] (3), [V6O6(PhCO2)6(C4H9O)6(C4H9OH)3] (4) and [V4O4(OCH3)6(O2CPh)2(HOCH3)2] (5). Complexes 2, 3 and 5 have been crystallographically characterised. DC magnetic susceptibility studies on complex shows antiferromagnetic coupling leading to a S = 0 spin ground state.     

Synthetic and structural studies of cobalt-pivalate complexes

The synthesis and characterisation of a range of cobalt pivalate cage complexes are reported. The cages include: a dinuclear Co(II) complex; an oxo-centred Co(III) triangle; tetranuclear Co(II) heterocubanes and butterflies; tetranuclear heterovalent cobalt butterflies and hexanuclear edge-sharing bitetrahedra; heterovalent penta-, hexa- and hepta-nuclear cages based on [M(4)O(4)] heterocubane cores; and a tetradecanuclear cage based on heterocubanes sharing edges and vertices. Spectroscopic studies suggest that some of these cores are retained in solution, but that only in the Co(III) triangle is the structure including ligands retained. A scheme is proposed to account for the many structures observed, which may be applicable to other polymetallic cage complexes.     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Squaramido-based receptors: applicability of molecular interaction potential to molecular recognition of polyalkylammonium compounds

 A computational study of the mechanism of host–guest complexation between quaternary ammonium compounds and squaramido-based tripodal receptors has been carried out. Semiempirical molecular orbital calculations, which are in qualitative agreement with experimental results have been performed using the PM3 Hamiltonian. Molecular interaction potential (MIP) maps were used to analyze the suitability of both host and guest binding units for a high-affinity recognition process. MIP calculations were computed from PM3 wavefunctions of the corresponding ammonium cations and dimethyl squaramide as a model compound for the hydrogen-bond-acceptor unit of the receptors. MIP analyses are helpful for understanding the host–guest process from the point of view of the double-complementarity principle. Received: 23 June 1999 / Accepted: 22 September 1999 / Published online: 17 January 2000     

Synthesis and studies of a tetradecanuclear manganese(II)/(III) cage

A novel Mn14 cluster is reported; this is a new nuclearity for manganese cages and highly unusual in that the ligands are not exclusively oxygen donors.     

A versatile series of nickel(II) complexes derived from tetradentate imine/pyridyl ligands and various pseudohalides: azide and cyanate compared

The chemical reactions of a family of tetradentate pyridyl/imine ligands, L1, L2, and L3 (L1=[ N, N'-bis(2-pyridinylmethylene)]ethane-1,2-diamine; L2=[ N, N'-bis(pyridin-2-yl)benzylidene]ethane-1,2-diamine; L3=[ N, N'-bis(2-pyridinylmethylene)]propane-1,3-diamine), with Ni (II) in the presence of various pseudohalides (N3(-), SCN(-), and NCO(-)) have served to prepare six different complexes, [Ni 2(L1)2(N3)2](ClO4)2.H2O (1), [Ni 2(L2)2(N3)2](ClO4)2 (2), [Ni2(L2)2(NCS)4] (3), [Ni2(L2)2(NCO) 2](ClO4)2 (4), [Ni2(L3)2(NCO)2](ClO4)2 (5), and [Ni(L3)(N 3)2] (6), which have been characterized by X-ray crystallography. Interestingly, four of these complexes are dinuclear and exhibit end-on (EO) pseudohalide bridges (1, 2, 4, and 5), one is dinuclear and bridged exclusively by the tetradentate ligand (3), and one is mononuclear (6). The bulk magnetization of the complexes bridged by EO pseudohalides has been studied, revealing these ligands to mediate ferromagnetic coupling between the Ni(II) ions, with modeled coupling constants, J, of +31.62 (1), +28.42 (2), +2.81 (4), and +1.72 (5) cm(-1) (where the convention H=-2JS1S2 was used). The striking difference in the coupling intensity between N3(-) and NCO(-) has prompted an investigation by means of density functional theory calculations, which has confirmed the experimental results and provided insight into the reasons for this observation.