An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Preliminary X-ray diffraction analysis of YqjH from Escherichia coli: a putative cytoplasmic ferri-siderophore reductase

YqjH is a cytoplasmic FAD-containing protein from Escherichia coli; based on homology to ViuB of Vibrio cholerae, it potentially acts as a ferri-siderophore reductase. This work describes its overexpression, purification, crystallization and structure solution at 3.0 A resolution. YqjH shares high sequence similarity with a number of known siderophore-interacting proteins and its structure was solved by molecular replacement using the siderophore-interacting protein from Shewanella putrefaciens as the search model. The YqjH structure resembles those of other members of the NAD(P)H:flavin oxidoreductase superfamily.

Twists and turns: a tale of two shikimate-pathway enzymes

We are studying two enzymes from the shikimate pathway, dehydroquinate synthase (DHQS) and 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS). Both enzymes have been the subject of numerous studies to elucidate their reaction mechanisms. Crystal structures of DHQS and EPSPS in the presence and absence of substrates, cofactors and/or inhibitors are now available. These structures reveal movements of domains, rearrangements of loops and changes in side-chain positions necessary for the formation of a catalytically competent active site. The potential for using complementary small-angle X-ray scattering (SAXS) studies to confirm the presence of these structural differences in solution has also been explored. Comparative analysis of crystal structures, in the presence and absence of ligands, has revealed structural features critical for substrate-binding and catalysis. We have also analysed these structures by generating GRID energy maps to detect favourable binding sites. The combination of X-ray crystallography, SAXS and computational techniques provides an enhanced analysis of structural features important for the function of these complex enzymes.

Modelling small angle neutron scattering data from electrospun fibres

Electrospinning is a technique employed to produce nanoscale to microscale sized fibres by the application of a high voltage to a spinneret containing a polymer solution. Here we examine how small angle neutron scattering data can be modelled to analyse the polymer chain conformation. We prepared 1:1 blends of deuterated and hydrogenated atactic-polystyrene fibres from solutions in N, N-Dimethylformamide and Methyl Ethyl Ketone. The fibres themselves often contain pores or voiding within the internal structure on the length scales that can interfere with scattering experiments. A model to fit the scattering data in order to obtain values for the radius of gyration of the polymer molecules within the fibres has been developed, that includes in the scattering from the voids. Using this model we find that the radius of gyration is 20% larger than in the bulk state and the chains are slightly extended parallel to the fibre axis.

Synthesis, X-ray crystal structures and properties of complex salts and sterically crowded heteroleptic complexes of group 10 metal ions with aromatic sulfonyl dithiocarbimates and triphenylphosphine ligand

Two new complex salts of the form (Bu4N)(2)[Ni(L)(2)] (1) and (Ph4P)(2)[Ni(L)(2)] (2) and four heteroleptic complexes cis-M(PPh3)(2)(L) [M = Ni(II) (3), Pd(II) (4), L = 4-CH3OC6H4SO2N=CS2] and cis-M(PPh3)(2)(L') [M = Pd(II) (5), Pt(II) (6), L' = C6H5SO2N=CS2] were prepared and characterized by elemental analyses, IR, H-1, C-13 and P-31 NMR and UV-Vis spectra, solution and solid phase conductivity measurements and X-ray crystallography. A minor product trans-Pd(PPh3)(2)(SH)(2), 4a was also obtained with the synthesis of 4. The NiS4 and MP2S2 core in the complex salts and heteroleptic complexes are in the distorted square-plane whereas in the trans complex, 4a the centrosymmetric PdS2P2 core is perforce square planar. X-ray crystallography revealed the proximity of the ortho phenyl proton of the PPh3 ligand to Pd(II) showing rare intramolecular C-H center dot center dot center dot Pd anagostic binding interactions in the palladium cis-5 and trans-4a complexes. The complex salts with sigma(rt) values similar to 10 (5) S cm (1) show semi-conductor behaviors. The palladium and platinum complexes show photoluminescence properties in solution at room temperature.

Automatic X-ray screening of aircraft hold luggage

R. Benjamin (1995) addressed the application of the “object 3D” X ray reconstruction technique for electronically “unpacking” suspect items, when screening aircraft luggage. However, there is no satisfactory solution to the mass screening of hold luggage. Computed Tomography, CT, entails excessive radiation dosages, and its rate of throughput is quite inadequate. A novel variant of “object 3D” is therefore put forward, adapting some of the technology of existing cabin luggage screening systems-but on a substantially larger scale-which does achieve the required throughput at an acceptable radiation dosage and cost.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Puroindoline-a, a lipid binding protein from common wheat, spontaneously forms prolate protein micelles in solution

The self-assembly in solution of puroindoline-a (Pin-a), an amphiphilic lipid binding protein from common wheat, was investigated by small angle neutron scattering, dynamic light scattering and size exclusion chromatography. Pin-a was found to form monodisperse prolate ellipsoidal micelles with a major axial radius of 112 +/- 4.5 A ˚ and minor axial radius of 40.4 +/- 0.18 A ˚ . These protein micelles were formed by the spontaneous self-assembly of 38 Pin-a molecules in solution and were stable over a wide pH range (3.5–11) and at elevated temperatures (20–65 degC). Pin-a micelles could be disrupted upon addition of the non-ionic surfactant dodecyl-b-maltoside, suggesting that the protein self-assembly is driven by hydrophobic forces, consisting of intermolecular interactions between Trp residues located within a well-defined Trp-rich domain of Pin-a.

Nickel(II) and copper(II) complexes of Schiff base ligands containing N4O2 and N4S2 donors with pyrrole terminal binding groups: synthesis, characterization, X-ray structures, DFT and electrochemical studies

A series of hexadentate ligands, H2Lm (m = 1−4), [1H-pyrrol-2-ylmethylene]{2-[2-(2-{[1H-pyrrol-2-ylmethylene]amino}phenoxy)ethoxy]phenyl}amine (H2L1), [1H-pyrrol-2-ylmethylene]{2-[4-(2-{[1H-pyrrol-2-ylmethylene]amino}phenoxy)butoxy]phenyl}amine (H2L2), [1H-pyrrol-2-ylmethylene][2-({2-[(2-{[1H-pyrrol-2-ylmethylene]amino}phenyl)thio]ethyl}thio)phenyl]amine (H2L3) and [1H-pyrrol-2-ylmethylene][2-({4-[(2-{[1H-pyrrol-2-lmethylene]amino}phenyl)thio]butyl}thio) phenyl]amine (H2L4) were prepared by condensation reaction of pyrrol-2-carboxaldehyde with {2-[2-(2-aminophenoxy)ethoxy]phenyl}amine, {2-[4-(2-aminophenoxy)butoxy]phenyl}amine, [2-({2-[(2-aminophenyl)thio]ethyl}thio)phenyl]amine and [2-({4-[(2-aminophenyl)thio]butyl}thio)phenyl]amine respectively. Reaction of these ligands with nickel(II) and copper(II) acetate gave complexes of the form MLm (m = 1−4), and the synthesized ligands and their complexes have been characterized by a variety of physico-chemical techniques. The solid and solution states investigations show that the complexes are neutral. The molecular structures of NiL3 and CuL2, which have been determined by single crystal X-ray diffraction, indicate that the NiL3 complex has a distorted octahedral coordination environment around the metal while the CuL2 complex has a seesaw coordination geometry. DFT calculations were used to analyse the electronic structure and simulation of the electronic absorption spectrum of the CuL2 complex using TDDFT gives results that are consistent with the measured spectroscopic behavior of the complex. Cyclic voltammetry indicates that all copper complexes are electrochemically inactive but the nickel complexes with softer thioethers are more easily oxidized than their oxygen analogs.

Metal complexes with atropisomeric sulfur ligands in asymmetric hydroformylation X-ray structure of [Rh2(μ-biphes)(cod)2] (H2biphes = 4,4′-biphenanthrene-3,3′-dithiol)

The addition of the atropisomeric racemic sulfur compound 4,4′-biphenanthrene-3,3′-dithiol (H2 biphes) to a dichloromethane solution of [{M(μ-OMe)(cod)}2] (M = Rh, Ir, cod = cycloocta-1,5-diene) afforded the dithiolate-bridged complexes [{Rh2(μ-biphes)(cod)2}n] (n = 2 5 or n = 1 6) and [{Ir2(μ-biphes)(cod)2}n]·nCH2Cl27. When 1,1′-binaphthalene-2,2′-dithiol (H2 binas) reacted with [{Ir(μ-OMe)(cod)}2], complex [Ir2(μ-binas)(cod)2] 8 was obtained. Complexes 5 and 6 reacted with carbon monoxide to give the dinuclear tetracarbonyl complex [Rh2(μ-biphes)(CO)4] 9. The reaction of 9 with PR3 provided the mixed-ligand complexes [{Rh2(μ-biphes)(CO)2(PR3)2}2] · xCH2Cl2 (R = Ph, x = 2 10, C6H11, x = 1 11) and [{Rh2(μ-biphes)(CO)3(PR3)}2] · CH2Cl212 (R = OC6H4But-o). The crystal structure of 6 was determined by X-ray diffraction. Reaction of the dithioether ligand Me2biphes with [Rh(cod)2]ClO4 in CH2Cl2 solution afforded the cationic complex [Rh(cod)(Me2biphes)]ClO4 · CH2Cl213. Asymmetric hydroformylation of styrene was performed using the complexes described. The extent of aldehyde conversion ranges from 53 to 100%, with selectivities towards branched aldehydes in the range 51 to 96%. The enantioselectivities were quite low and did not exceed 20%.

Synthesis, X-ray crystal structure and reactivity of the polymeric copper(II) dicarboxylic acid complex {Cu2(η1η1μ2-oda)2(py)4(H2O)2}n(odaH2 = octanedioic acid, PY = pyridine)

An aqueous solution of the α-ω-dicarboxylic acid octanedioic acid (odaH2) reacts with [Cu2(μ-O2CCH3)4(H2O)2] in the presence of an excess of pyridine (py) to give the crystalline copper(II) complex {Cu2(η1η1μ2-oda)2(py)4(H2O)2}n (1). structure of 1, as determined by X-ray crystallography, consists of polymeric chains in which bridging oda2− anions link two crystallographically identical copper atoms. The copper atoms are also ligated by two transoidal pyridine nitrogens and an oxygen atom from an apical water molecule, giving the metals an overall N2O3 square-pyramidal geometry. If the blue solid 1 is gently heated, or if it is left to stand in its mother liquor for prolonged periods, it loses one molecule of pyridine and half a molecule of water and the green complex {Cu (oda)(py)(H2O)0.5}n (2) is formed. Spectroscopic and magnetic data for both complexes are given, together with the electrochemical and thermogravimetric measurements for 1.

Synthesis and X-ray crystal structure of the copper(I) dicarboxylic acid complex [Cu(η1-bdoaH)(PPh3)3] (bdoaH2 = benzene-1,2- dioxyacetic acid)

The copper(II) complex [Cu(bdoa)(H2O)2] (bdoaH2 = benzene-1,2-dioxyacetic acid) reacts with triphenylphosphine (1:4 mol ratio) to give the colourless copper(I) complex [Cu(η1-bdoaH)(PPh3)3] (1) in good yield. The X-ray crystal structure of the complex shows the copper atom at the centre of a distorted tetrahedron, and is ligated by the phosphorus atoms of the three triphenylphosphines and one carboxylate oxygen atom of the bdoaH− ligand. Significant intermolecular hydrogen-bonding exists between the pendant carboxylate OH function of one molecule and the uncoordinated “ketonic” oxygen of a neighbouring molecule. Complex 1 is non-conducting in chloroform but ionizes readily in acetonitrile. The cyclic voltammogram of an acetonitrile solution of 1 shows a single irreversible anodic peak for the oxidation of the PPh3 ligands and the copper(I) centre, and a single irreversible cathodic peak for the reduction of the bdoaH− ion. IR and mass spectral data for 1 are given.

Synthesis and reactions of [Et3NH]4[Mo8O6]: X-ray crystal structure of [Et3NH]3[NaMo8O26]

[Et3NH]4[Mo8O26] (1) was prepared by reacting triethylamine with either molybdenum trioxide dihydrate or with a solution of ammonium molybdate in aqueous HCl. An aqueous solution of complex 1 reacted with an excess of sodium chloride to give a mixture of [Et3NH]3[NaMo8O26] (2) and [Et3NH]2[Mo6O19] (3). Complex 2 was also formed on reacting sodium molybdate with triethylamine in aqueous HCl. In the reaction of 1 with potassium chloride the nature of the product obtained was critically dependent upon reaction time. After a 5.5 h reflux period a mixture of [Et3NH]3[KMo8O26] (4) and 3 was obtained, whereas upon prolonged reflux (24 h) only K4Mo8O26 · H2O (5) was precipitated. The X-ray crystal structure of 2 shows it to be polymeric, with each Na+ ion sandwiched between two β[Mo8O26]4− ions. Four oxygen atoms on one face of each β[Mo8O26]4− ion are coordinated to a Na+ ion, and four oxygens from the opposite face are bonded to the next Na+ ion in the polymer chain. This produces a zig-zag arrangement of Na+ ions throughout the molecular structure. Spectral, conductivity and voltammetry data are given.

Synthesis and properties of tetra-μ-acetatodiruthenium(II,III) phenylphosphinate and phenylphosphonate complexes: X-ray crystal structures of [Ru2(μ-O2CCH3)4(HPhPO2)2]H and [Ru2(μ-O2CCH3)4(PhPO3H)2]H·H2O

Phenylphosphinic acid (HPhPO2H) and phenylphosphonic acid (PhPO3H2) react with a methanolic solution of [Ru2(μ-O2CCH3)4(O2CCH3)2]H·0.7H2O at room temperature to give [Ru2(μ-O2CCH3)4(HPhPO2)2H (1) and [Ru2(μ-O2CCH3)4 (PhPO3H)2]H·H2O (2), respectively. The X-ray crystal structures of 1 and 2 each show the RuRu core to be ligated by four bridging bidentate acetate ligands [RuRu distances: 1 = 2.272(1) Å; 2 = 2.267(2) Å] and two axial phenylphosphinate and phenylphosphonate ligands, respectively. In each complex the individual bimetallic molecules are linked together by a hydrogen ion which bridges the oxygen atoms of neighbouring axial ligands. In 2 the water molecule is also hydrogen-bonded to one of the axial phenylphosphonate groups. Spectroscopic, magnetic and cyclic voltammetric data for the complexes are given.

Synthesis of water-soluble and ether-soluble tetra-μ-acetatodiruthenium(II,III) complexes and X-ray crystal structure of [Ru2(μ-O2CC6H5)4(C2H5OH)2][Ru2(μ-O2CC6H5)4(HSO4)2]

[Ru2(μ-O2CCH3)4Cl] reacts readily with aqueous Ag2SO4 (2: 1 molar ratio) to give the sulphate salt [Ru2(μ-O2CCH3)4(H2O)2]2(SO4) (1). Addition of NaBPh4 to an aqueous solution of 1 produces the ether-soluble tetraphenylborate salt [Ru2(μ-O2CCH3)4(H2O)2][BPh4] (2). A methanolic solution of 1 reacts with Ba(C6H5CCCO2)2 · H2O to give the tetraacetatemonophenylpropynoate complex [Ru2(μ-O2CCH3)4(O2CCCC6H5)] · H2O (3). The reaction of an ethanolic suspension of [Ru2(μ-O2CC6H5)4Cl] with Ag2SO4 and H2SO4 (2 : 1 : 1 molar ratio) leads to the tetra-μ-benzoatodiruthenium(II,III) double complex salt [Ru2(μ-O2CC6H5)4(C2H5OH)2][Ru2(μ-O2CC6H5)4(HSO4)2] (4). Complex 4 is also obtained by reacting an ethanolic solution of 1 with an excess of benzoic acid in the presence of H2SO4. The X-ray crystal structure of 4 shows it to consist of [Ru2(μ-O2CC6H5)4(C2H5OH)2]+ and [Ru2(μ-O2CC6H5)4(HSO4)2]− ions, which are linked together by hydrogen bonds into an infinite polymeric chain. The RuRu distances in the cation and anion are very similar [2.265(2) and 2.272(2) Å, respectively]. Spectroscopic, magnetic, conductivity and cyclic voltammetry data are given for the complexes.