Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equation

Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.Active Member of the European Academy of Sciences and Arts     

Nanoaggregates of ABC-type triple hydrophilic block copolymers by binding of cationic surfactant

A triple hydrophilic block copolymer comprised of poly(ethylene oxide), poly(sodium 2-acrylamido-2-methylpropanesulfonate), and poly(methacrylic acid) (PEO–PAMPS–PMAA) does not form a micelle by itself when it is dissolved in water. However, in the previous paper, we fabricated the nanoaggregates of PEO–PAMPS–PMAA and cationic surfactant, such as cetyltrimethylammonium chloride (CTAC), by insolubilizing the anionic PAMPS and/or PMAA blocks of the polymer with CTAC only at high pH. In this paper, we fabricated the nanoaggregates of dodecyltrimethylammonium chloride (DTAC) and PEO–PAMPS–PMAA in a wide range of pH to examine the effect of ionization of the PMAA blocks of the polymer on the aggregates formation of PEO–PAMPS–PMAA. The properties of the nanoaggregates are affected by the ionization of PMAA block of the polymer. DTAC (C12 alkyl chain) was employed instead of CTAC (C16 alkyl chain) to reveal the effect of alkyl chain length of surfactant on the aggregate formation of PEO–PAMPS–PMAA. The properties of PEO–PAMPS–PMAA nanoaggregates also depend on the structure of surfactant. The binding of DTAC to PEO–PAMPS–PMAA was monitored by electrophoresis measurements, while the formation of DTAC/PEO–PAMPS–PMAA nanoaggregates was confirmed by scanning electron microscopy, dynamic light scattering measurements and fluorescence spectroscopy.     

Neutron Activation Analysis of Bottom and Fly Oil Ash Leachates

Seven samples of oil fly and bottom ashes were leached with water using a Canadian standard test method for shake extraction of solid waste. The concentrations of 20 elements in the leachates were determined by the computerized systematic instrumental absolute neutron activation analysis. The ranges of concentrations (in ppm) found for the elements in the leachates were: Al (3–526), Ba (0.5–6), Ca (100–695), Cl (13–59), Co (1–6.3), Cr (0.2–6.6), Cs (0.03–0.4), Eu (0.003–0.01), Fe (28–690), K (42–464), La (0.3–49), Mg (214–3150), Mn (1.2–20), Na (88–4050), Sb (0.04–0.4), Sc (0.003–0.07), Sr (1.2–23), U (0.07–1), V (1.2–4540) and Zn (2.3–200). These findings were compared with the maximum concentrations allowed for these elements by Canadian regulations. The concentrations of Cr and U were found to be higher than their permissible limits on 7 occasions. The purpose of this study was to determine the background levels of different elements in oil ash leachates, in order to evaluate their potential impact on underground water.     

Structure and torsional flexibility of the linkage between guanine and fluorene residues in the deoxyguanosine–aminofluorene and deoxyguanosine–acetylaminofluorene carcinogenic adducts

Potential energy surfaces for rotations around two central CN bonds in N-(deoxyguanosin-8-yl)-2-acetylaminofluorene (AAF–dG) and its deacetylated derivative (AF–dG) were studied using Amber 95 molecular mechanics. Both of these adducts are known to be strong mutagens and carcinogens. New Amber 95 force field parameters were derived for the linkage connecting guanine and fluorene moieties in AAF–dG and AF–dG. For this purpose, we determined ab initio MP2/cc-pVDZ//B3-LYP/6-31G* and polarized continuum model Hartree–Fock/6-31G* potential energy surfaces of smaller model systems that included the N-methylimidazole–acetylaniline and N-methylimidazole–aniline adducts. The molecular mechanics parameters were adjusted to minimize differences between the gas-phase ab initio and molecular mechanics surfaces of these model systems. The resulting parameters were transferred to AF–dG and AAF–dG. The barrier for the rotation of the fluorene residue in AF–dG was found to be less than 2 kcal/mol. Such a small barrier renders the fluorene moiety freely rotatable at room temperature. In contrast, the fluorene rotation in AAF–dG is hindered by a significantly larger barrier of 10 kcal/mol. This barrier corresponds to conformations in which the fluorene and acetyl groups lie in the same plane, and is largely due to steric repulsion. Similarly, the coplanar arrangement of guanine and the bridging amino or acetyl groups is disfavored by 5–10 kcal/mol, with AAF–dG again being the more rigid of the two molecules. Energy minima for a rotation around a bond between guanine and the bridging nitrogen are found at ±80° in AAF–dG, and at 120° and –90° for AF–dG. Overall, the fluorene–dG linkages in AF–dG and AAF–dG adducts have significantly different equilibrium structures and torsional flexibilities. These differences may be contributing factors for the observed disparity in mutagenic effects of these adducts.Electronic Supplementary Material: Supplementary material is available in the online version of this article at Acknowledgements. This work was supported by the NSF REU grant no. CHE-0243825 to Loyola University Chicago. We thank to Tom Ellenberger and Shuchismita Dutta for providing us with their results prior to publication.     

Readily available phosphine–imine ligands from α-phenylethylamine for highly efficient Pd-catalyzed asymmetric allylic alkylation

A series of novel chiral phosphine–imine ligands have been prepared by a two-step transformation from chiral α-phenylethylamine. The resulting chiral ligands were found to be effective for the palladium-catalyzed asymmetric allylic alkylation of 1,3-diphenylprop-2-en-1-yl pivalate with dimethyl malonate, in which up to 94% ee and 99% conversions were obtained. The results demonstrate that the chirality resided on the chelate ring of P–Pd–N complex is more effective for the transfer of the stereochemical information by comparison with the result obtained by Hashimoto and coworkers’ phosphine–imine ligand, in which the chirality lay in the outside of P–Pd–N chelate ring. The effect of solvent, base and substitutent in phosphine–imine ligand on this catalytic reaction is also described.     

Lithium complexes and the kinetics of interactions of zinc ions with tetra(N-methyl-4–pyridyl)porphyrins in basic solution

The acidity of the free base (H2–P(X)) forms of the tetra- (N-methyl-4–(3 or 2)pyridyl)porphyrins were studied in basic solutions at 25 C, I=0.50. Equilibrium constants for both the H2– P(X)=P(X)2–+2H+ and the Li++ P(X)2–=Li- P(X)– reactions are reported. Log (KS) values for the Mn++P(4)2–=M- P(4)(n–2) reactions are 2.6 for Li+, 17.6 for Cd2+, 17.8 for Pb2+, 19.6 for (OH)2Hg, 25.9 for Zn2+ and 19.6 for the formation of Hg2–P(4)2+. Zn(OH)3– shows similar kinetic reactivity with both H2–P(4) and P(4)2– to form Zn- P(4) and HO-Zn- P(4)–,whileZn(OH)42– is unreactive with either species. For Zn2+, Zn(OH)+ and Zn(OH)3– with H2–P(4) the relative kinetic order for this tetrapositive macrocycle was ca. 1:300:20,000, while the trend Zn(OH)+>Zn2+>Zn(OH)3– is the usual pattern for peripherally negatively charged porphyrins.     

Researches on 2, 1, 3-thia- and selenadiazole

4-Hydroxy-, 4-hydroxy-5-methyl-, 4-hydroxy-7-methylbenzo-2,1,3-thiadiazoles are polymorphous.4-Hydroxybenzo-2,1,3-thiadiazole (I), 4-hydroxy-5-methyl- and 4-hydroxy-7-methylbenzo-2, 1, 3-thiadiazoles (II and III) melt at 114–115°, 110–112°, 100–102° C, respectively, after recrystallization from water [2–4], but after recrystallization from petrol ether [5] they melt at 128–129°, 124–125°, and 119–120° C [5]. In this connection we recrystallized these phenols repeatedly from petrol ether after recrystallizing them from water, and their melting points rose as expected [5]. On the other hand, the compounds with melting points 128–129°, 124–125°, 119–120° C (ex petrol ether), after repeated crystallization from water melted at 114–115°, 110–112°, 100–102° C, respectively.For Part XXXVIII see [1].     

Redox-iodometry: a new potentiometric method

A new iodometric method for quantifying aqueous solutions of iodide-oxidizing and iodine-reducing substances, as well as plain iodine/iodide solutions, is presented. It is based on the redox potential of said solutions after reaction with iodide (or iodine) of known initial concentration. Calibration of the system and calculations of unknown concentrations was performed on the basis of developed algorithms and simple GWBASIC-programs. The method is distinguished by a short analysis time (2–3 min) and a simple instrumentation consisting of pH/mV meter, platinum and reference electrodes. In general the feasible concentration range encompasses 0.1 to 10^–6 mol/L, although it goes down to 10^–8 mol/L (0.001 mg Cl₂/L) for oxidants like active chlorine compounds. The calculated imprecision and inaccuracy of the method were found to be 0.4–0.9% and 0.3–0.8%, respectively, resulting in a total error of 0.5–1.2%. Based on the experiments, average imprecisions of 1.0–1.5% at c(Ox)>10^–5 M, 1.5–3% at 10^–5 to 10^–7 M, and 4–7% at <10^–7 M were found. Redox-iodometry is a simple, precise, and time-saving substitute for the more laborious and expensive iodometric titration method, which, like other well-established colorimetric procedures, is clearly outbalanced at low concentrations; this underlines the practical importance of redox-iodometry.

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An erratum to this article is available at .     

Generalized Christoffel–Darboux formulae and the frontier Kohn–Sham molecular orbitals

The Christoffel–Darboux formula for classical orthogonal polynomials is generalized to arbitrary sets of orthogonal functions in three dimensions, yielding an explicit link between frontier Kohn–Sham molecular orbitals and the Kohn–Sham density matrix. Methods using this result could significantly accelerate Kohn–Sham density functional theory calculations, as only a subset of the Kohn–Sham equations would need to be addressed. The result can also be seen as an explicit justification for the utility of frontier molecular orbital theory.     

A Laboratory Investigation of the Reduction of Chromium Oxide by a Reverse-Polarity DC Plasma-Driven Molten Oxide Electrolysis Process

A method for producing chromium metal/chromium alloys using a reverse-polarity DC plasma-driven molten oxide electrolysis process was investigated. A laboratory-scale 50 kW DC plasma-crucible system was designed and built to investigate the feasibility of this process. Experiments on molten oxide electrolysis were successfully conducted to produce chromium metal from chromic oxide. Two starting slag systems, SiO₂–CaO–Al₂O₃–Cr₂O₃–Na₂O and SiO₂–CaO–Cr₂O₃–Na₂O, were used in this study. It was found that in each case chromic oxide was successfully reduced to metallic chromium. Aluminum was also reduced with the presence of alumina in the starting slag. Small amounts of carbon monoxide gas were introduced to the electrolysis system to study oxygen evolution rates from the plasma/slag interface. For the SiO₂–CaO–Al₂O₃–Cr₂O₃–Na₂O system, the oxygen evolution rate showed a maximum during the electrolysis process. For the SiO₂–CaO–Cr₂O₃–Na₂O system, the oxygen evolution rates displayed a declining trend with processing time. These two reduction behaviors were apparently controlled by different mechanisms. The significance of this process is that it might be used to produce carbon-free chromium metal/chromium alloys without carbon containing reducing agent and since no carbon based reactants are used for heating or reduction there are no carbon dioxide emissions.     

New Layered Double Hydroxide, Zn–Ti LDH : Preparation and Intercalation Reactions

The layered double hydroxide (LDH) well known for its abilityto intercalate anionic compounds has been prepared conventionallyonly with bivalent and trivalent cations. In this study, Zn–Ti LDH consisting of bivalent and tetravalent cations was prepared, andreacted with organic monocarboxylic, dicarboxylic and aromatic acidsat high or room temperature. XRD patterns of the prepared LDH(Zn–Ti-CO₃) showed that interlayer spacing of the LDH was 0.67 nm. The value was small compared to the usual LDH (Zn–Al–CO₃)of 0.76 nm in the case of carbonate anion as the guest. Also, DTA,TG and DTG analysis indicated that the electrostatic force betweenthe layers and carbonate anions increased where the carbonate anionsin Zn–Ti LDH decomposed at 255 °C while those inZn–Al–CO₃ decomposed at 230–240 °C.     

Application of isotope-dilution laser ablation ICP–MS for direct determination of Pu concentrations in soils at pg g<Superscript>−1</Superscript> levels

The methods available for determination of environmental contamination by plutonium at ultra-trace levels require labor-consuming sample preparation including matrix removal and plutonium extraction in both nuclear spectroscopy and mass spectrometry. In this work, laser-ablation inductively coupled plasma mass spectrometry (LA–ICP–MS) was applied for direct analysis of Pu in soil and sediment samples. Application of a LINA-Spark-Atomizer system (a modified laser ablation system providing high ablation rates) coupled with a sector-field ICP–MS resulted in detection limits as low as 3×10^–13 g g^–1 for Pu isotopes in soil samples containing uranium at a concentration of a few g g^–1. The isotope dilution (ID) technique was used for quantification, which compensated for matrix effects in LA–ICP–MS. Interferences by UH⁺ and PbO₂⁺ ions and by the peak tail of ²³⁸U⁺ ions were reduced or separated by use of dry plasma conditions and a mass resolution of 4000, respectively. No other effects affecting measurement accuracy, except sample inhomogeneity, were revealed. Comparison of results obtained for three contaminated soil samples by use of -spectrometry, ICP–MS with sample decomposition, and LA–ICP–IDMS showed, in general, satisfactory agreement of the different methods. The specific activity of ^239+240Pu (9.8±3.0 mBq g^–1) calculated from LA–ICP–IDMS analysis of SRM NIST 4357 coincided well with the certified value of 10.4±0.2 mBq g^–1. However, the precision of LA–ICP–MS for determination of plutonium in inhomogeneous samples, i.e. if "hot" particles are present, is limited. As far as we are aware this paper reports the lowest detection limits and element concentrations yet measured in direct LA–ICP–MS analysis of environmental samples.Sergei F. Boulyga is on leave from The Radiation Physics and Chemistry Problems Institute, 220109 Sosny, Minsk, Belarus.     

Groups 3 and 4 single-site catalysts for styrene–ethylene and styrene–α-olefin copolymerization

Styrene–ethylene and styrene–α-olefin copolymers are relatively new materials that were developed since the early 1990s thanks to homogeneous single-site catalysts. A wide range of copolymers, differing in their compositions, microstructures and properties have been prepared by using several types of early transition (groups 3 and 4) metal catalysts, which are critically reviewed in this contribution. Structure–activity–control relationships are also discussed.     

Neutron activation analysis of asbestos from Canada

Concentrations of Al, Au, Br, Ce, Cl, Co, Cr, Fe, K, La, Mg, Mn, Na, Ni, Sb, Sc, Sm, Srm and V were determined in 6 samples of asbestos from Canada. They were equal to (in ppm): Al 1660–3430; Au 0.03–0.04; Br 3.1–11.7; Ce 1.7–4.8; Cl 116–331; Co 35–83; Cr 200–2060; Fe 29300–42200; K 125–867; La 0.28–1.03; Mg 24–25.9%; Mn 418–545; Na 364–1610; Sb 0.65–1.46; Sc 3.73–5.57; Sm 0.09–0.3; Sr 26.7–41.4; V 8.4–14.3. Five toxic elements were found in asbestos; Cr, Mn, Ni, Sb and V.     

Mechanism of the Effect of Thermal Treatment on the Formation of Strong Acid Sites in the Surface Layers of Sulfated Metal Oxides

Strong acid catalysts were synthesized by the impregnation of hydrated ZrO₂ and TiO₂ with sulfuric acid followed by thermal treatment at different temperatures. The surface acidity and crystallochemical characteristics of the catalysts were studied by potentiometry and X-ray diffraction analysis, respectively. It was found that the surface acidity gradually increased as the temperature of thermal treatment was increased from 350 to 600°C for SO^2– ₄/ZrO₂ or to 200°C for SO^2– ₄/TiO₂; this increase correlated with the degrees of crystallinity of the samples. A hypothesis was proposed to explain the gradual accumulation of acid sites in the surface layer in the course of thermal treatment. It was assumed that, because of crystallographic changes that caused the weakening or even rupture of Zr–O–S and Ti–O–S bonds in modified surface layers, these layers exhibited an enhanced reactivity in contact with water vapor. Subsequently, this resulted in the formation of strongly acidic grafted M–O–SO₃–H⁺ groups.     

Mechanism of lactic acid formation catalyzed by tetraamine rhodium(III) complexes

The transformation of methylglyoxal and of 1,3–dihydroxyacetone and glyceraldehyde into lactic acid can be catalyzed by cis- tetraaminediaquarhodium(III) complexes of ethane-1,2–diamine and of the macrocyclic racemic 5,5,7,12,12,14–hexamethyl-1,4,8,11– tetraazacyclotetradecane ligand. The detailed stoichiometry of this process has been investigated by isotopic labelling studies and 1H and 13C-n.m.r. spectroscopy.The suggested mechanism of the methylglyoxal transformation process involves bidentate substrate coordination, followed by an intramolecular 1,2–hydride shift in a resonance stabilized carbocation. The transformations of 1,3–dihydroxyacetone and glyceraldehyde are stoichiometrically more complicated, and rhodium(III) catalyzed conversion of 1,3–dihydroxyacetone into glyceraldehyde is observed. Ultimately both substrates are converted into coordinated lactate in which one hydrogen atom in the methyl group originates from the solvent water.     

ZnO nanorods decorated calcined Mg–Al layered double hydroxides as photocatalysts with a high adsorptive capacity

The nanocomposites of magnesium–aluminium–carbonate–layered double hydroxides (Mg–Al–CO₃–LDHs) and ZnO nanorods were prepared via a homogeneous precipitation process. The presence of ZnO nanorods made the calcined Mg–Al–CO₃–LDHs, the strong adsorptive adsorbents for anions, have a photocatalytic activity. Both Mg–Al–CO₃–LDHs and the nanocomposites with various ZnO/Mg–Al–CO₃–LDHs mass ratios from 0.5:1 to 3:1 were characterized by X-ray diffraction, transmission electron microscope and UV–vis diffuse reflectance spectra. The nanocomposites quickly adsorbed the anionic dyes such as acid red G (ARG) without the light illumination, and the adsorbed dyes on the recovered nanocomposites were then degraded in a separated photocatalytic reactor. The adsorption ability of the nanocomposites and their photocatalytic activities for the removal of ARG were evaluated by the Fourier transform infrared spectra and UV–vis extinction spectra. The sample at 3:1 ZnO/Mg–Al–CO₃–LDHs mass ratio was shown to have higher photocatalytic efficiencies.     

Effects of Ozone on Catalytic and Physicochemical Properties of Cu–Ce–Al–O Catalysts for Soot Combustion

The elimination of carbon particles at the level of the exhaust line is one of the present challenges of the car manufacturer. In this study, the catalytic combustion of carbon particles has been investigated in the presence of Cu–Ce–Al oxides. The influence of ozonation on the catalytic and physicochemical properties of Cu–Ce–Al oxides at the reaction of diesel soot combustion was examined by thermal analysis and EPR methods.     

Blue-shifted hydrogen-bonded complexes. II. CH3F(HF)1 n 3 and CH2F2(HF)1 n 3

The equilibrium structures, binding energies, and vibrational spectra of the clusters CH₃F(HF)_{1 n 3} and CH₂F₂(HF)_{1 n 3} have been investigated with the aid of large-scale ab initio calculations performed at the Møller–Plesset second-order level. In all complexes, a strong C–FH–F halogen–hydrogen bond is formed. For the cases n = 2 and n = 3, blue-shifting C–HF–H hydrogen bonds are formed additionally. Blue shifts are, however, encountered for all C–H stretching vibrations of the fluoromethanes in all complexes, whether they take part in a hydrogen bond or not, in particular also for n = 1. For the case n = 3, blue shifts of the ν(C–H) stretching vibrational modes larger than 50 cm⁻¹ are predicted. As with the previously treated case of CHF₃(HF)_{1 n 3} complexes (A. Karpfen, E. S. Kryachko, J. Phys. Chem. A 107 (2003) 9724), the typical blue-shifting properties are to a large degree determined by the presence of a strong C–FH–F halogen–hydrogen bond. Therefore, the term blue-shifted appears more appropriate for this class of complexes. Stretching the C–F bond of a fluoromethane by forming a halogen–hydrogen bond causes a shortening of all C–H bonds. The shortening of the C–H bonds is proportional to the stretching of the C–F bond.     

Use of High-Performance Liquid Chromatography–UV and Gas Chromatography–Mass Spectrometry for Determination of the Imidacloprid Content of Honeybees, Pollen, Paper Filters, Grass, and Flowers

Imidacloprid is a new insecticide with a wide range of action. Because honeybees are very sensitive to this substance, two techniques (HPLC–UV and GC–MS) which enable its detection in several matrices of both animal and vegetable origin were used to monitor its possible presence in cultivated land. In the first method quantification of imidacloprid in honeybees was achieved by use of the external standard method; the detection limit was 50 mg kg^–1, the linear range 0.05–1 mg mL^–1, recovery 60–83%, and the imprecision (coefficient of variation) 8.6% for repeatability and 11.8% for reproducibility. Recovery from pollen was 71–98% in the range 0.05–0.5 mg kg^–1. The repeatability was 9.2–13.9%. Imidacloprid can often be found in the environment, not as a simple molecule but as a group of degradation products. The GC–MS method could be used to quantify all these species as oxidation products and to determine the initial quantity of imidacloprid by use of a conversion factor. The liquid chromatographic analysis could be used to detect, in a standard solution, 10 ng mL^–1 derivatized 6-chloronicotinic acid. The linearity was good (R=0.999) over a wide concentration range (10 g mL^–1–10 ng mL^–1). Several samples with different matrices (filter paper placed on an pneumatic corn seed drill, grass, flowers, honeybees, etc.) obtained during the sowing period for imidacloprid-treated corn were analyzed. The quantification limit (LOQ) was 0.005 mg kg^–1 for grass and flowers, 0.002 mg kg^–1 for honeybees, and 0.024 mg kg^–1 for paper filters.