On the evaluation of the characteristic polynomial via symmetric function theory

The use of power sum symmetric functions leads to Newton's identities, which relate the traces of various powers ofA, the adjacency matrix of a graph, and the coefficients of the characteristic polynomials. While it is possible to solve Newton's identities and generate the coefficients by recursion or, alternatively, to derive them by sequential manipulations (yielding the explicit formulas), we show how the results can be expressed using a combinatorial approach and relate the evaluation of the coefficients to selected Young diagrams.     

Critical behaviour of the compressible magnet with exchange anisotropy

Then-component magnet with exchange anisotropy on a compressible lattice, with isotropic elastic properties, is studied. The renormalization group method is applied ind =4 — dimensions. The fixed points and the stability regions are explored to the order ², and the analysis is concentrated upon the casen<4—2 +O( ²). Investigation of the fixed points reveals various crossover phenomena which are not present in the corresponding rigid model. Renormalization of the anisotropy crossover exponent is demonstrated. It is shown that macroscopic instabilities, leading to the first order phase transition, may appear.     

Raman scattering in SnSe

Zone center optical phonons in SnSe were investigated using Raman scattering data obtained here and previously reported far infrared reflectivity measurements. The values of the ratio of the pairs of interlayer force constants were calculated te be between 3·3 and 4·5. Thus it can be concluded that SnS is a layer like semiconductor but less layer like than GeS, GeSe or SnS.     

Intermolecular potential energy surface and spectra of He-HCl with generalization to other rare gas-hydrogen halide complexes

A two-dimensional (rigid monomer) intermolecular potential energy surface (PES) of the He-HCl complex has been obtained from ab initio calculations utilizing the symmetry-adapted perturbation theory (SAPT) and an spdfg basis set including midbond functions. The bond length in HCl was chosen to be equal to the expectation value in the ground vibrational state of isolated HCl. The rigid-monomer potential should be a very good approximation to the complete (three-dimensional) potential for H-Cl distances corresponding to the lowest vibrational levels of the monomer since the He-HCl interaction energy was found to be only weakly dependent on the HCl bond length in this region, at least as compared to systems such as Ar-HF. The calculated points were fitted using an analytic function with ab initio computed asymptotic coefficients. As expected, the complex is loosely bound, with the dispersion energy providing the majority of the attraction. Our SAPT PES agrees with the semiempirical PES of Willey et al. [J. Chem. Phys. 96, 898 (1992)], in finding that, atypically for rare gas-hydrogen halide complexes including the lighter halide atoms, the global minimum is on the Cl side (with intermonomer separation 3.35 A and depth of 32.8 cm(-1)), rather than on the H side, where there is only a local minimum (3.85 A, 30.8 cm(-1)). The ordering of the minima was confirmed by single-point calculations in larger basis sets and complete basis set extrapolations, and also using higher levels of theory. We show that the opposite findings in the recent calculations of Zhang and Shi [J. Mol. Struct: THEOCHEM 589, 89 (2002)] are due to the lack of midbond functions in their basis set. Despite the closeness in depth of the two linear minima, the existence of a relatively high barrier between them invalidates the assumption of isotropy, a feature of some literature potentials. The trends concerning the locations of minima within the family of rare gas-hydrogen halide complexes are rationalized in terms of the physical components of the intermolecular forces and related to monomer properties. The accuracy of the SAPT PES was tested by performing calculations of rovibrational levels. The transition frequencies obtained were found to be in excellent agreement (to within 0.02 cm(-1)) with the measurements of Lovejoy and Nesbitt [J. Chem. Phys. 93, 5387 (1990)]. The SAPT PES predicts a dissociation energy for the complex of 7.74 cm(-1) which is probably more accurate than the experimental value of 10.1+/-1.2 cm(-1). Our analysis of the ground-state rovibrational wave function shows that the He-HCl configuration is favored over the He-ClH configuration despite the ordering of minima. This is due to the greater volume of the well in the former case. We have also determined positions and widths of three low-lying resonance states through scattering calculations. These predictions are expected to be more accurate than values derived from experiment.     

Sorption of trace concentrations of gallium(III) and iodide ions on tin(II) hydroxide

Summary The results of sorption measurements for gallium (III) and iodide ion traces onto tin(II) hydroxide from aqueous heterogeneous systems are given. Since only tagged sorbate was used (⁶⁷Ga and 1311), in the determination of sorption by radioactive tracer method, it was necessary to establish the pH interval of tin(II) hydroxide in/stability. This was done by a turbidimetric method and the pH region of instability between 3 and 9 was found.The sorption results indicate a difference in sorption ability of gallium(III) and iodide as it appears from the dependence of the amount sorbed on contact time between heterogeneous reactants (sorbentsorbate). The amounts sorbed increase with increasing contact times at higher pH values for Ga(III) but remain unaffected for iodide sorption. Thus the sorption of iodide ions seems to be restricted to the solid surface while the sorption results for gallium(III) indicate the diffusion of sorbate into sorbent as a possible parallel mechanism. Those processes could be taken as compatible with the porous-double-layer mechanism which has been proposed in literature for aqueous heterogeneous oxide systems.

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Zusammenfassung In der Arbeit werden Ergebnisse von Sorptionsmessungen für Ga³⁺- und j-Spuren an Zinn(II)-Hydroxid aus wäßrigen heterogenen Systemen berichtet. Zur analytischen Erfassung wurden radioaktives⁶⁷Ga und 131 J verwendet. Die Stabilität von Zinn(II)-Hydroxid wurde durch Trübungsmessungen untersucht. Im pH-Bereich von 3–9 ist das Zinn(II)-Hydroxid als kolloide Suspension instabil.Ga³⁺ und J^– verhalten sich bei der Adsorption unterschiedlich. Die adsorbierte Menge steigt mit zunehmender Kontaktzeit bei hohen pH-Werten von Gallium, bleibt jedoch für Jod unverändert. Die Unterschiede werden gedeutet durch die Annahme, daß Jod nur an der festen Oberfläche adsorbiert wird, während die Galliumionen auch in das Sorbens diffundieren können. Man könnte die Ergebnisse als verträglich mit einem porösen Doppelschichtmechanismus ansehen; ein solcher Mechanismus ist in der Literatur für wäßrige heterogene Oxidsysteme vorgeschlagen worden.

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With 4 figures     

Zur komplexometrischen Bestimmung des Natriums

Zusammenfassung Bei der Titration von Zink aus dem Niederschlag von Natrium-Zinkuranylacetat wird statt des früher vorgeschlagenen Indikators Eriochromschwarz T der Indikator Dithizon verwendet. Dadurch wird auch bei Titrationen mit 0,001-m Lösungen ein scharfer Umschlag erzielt.

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Summary Dithizone is used in place of Eriochrome black T previously suggested as indicator in the titration of zinc contained in the precipitate of sodium-zinc-uranyl acetate. A sharper change is thus observed even with 0.001M solutions.

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Résumé Lors du titrage du zinc dans le précipité d'acétate d'uranyle de zinc et de sodium, les auteurs emploient comme indicateur la dithizone au lieu du Noir Eriochrome T qui avait été précédemment recommandé. Il est ainsi possible d'obtenir un virage très net, même pour des titrages effectués avec des solutions 0,001M.

     

The effect of ligand field on the excitation luminescence spectra of some complex compounds of manganese (II)

The excitation and emission luminescence spectra of the complex compounds of manganese (II) chloride with the hydrochlorides of pyridine, 2-methyl- and 2-ethylpiperidine have been studied. It has been established that the crystals of these complex compounds appear in tetrahedral and octahedral configurations. The excitation spectra in both configurations contain bands originating from the⁴G,⁴P,⁴D and⁴F terms, the position of which is determined by configuration. From the excitation spectra the Racah parametersB andC and the ligand field strength parameter 10Dq have been determined.The emission luminescence spectra also depend on configuration of the complex compound. The character of these spectra is expressed in terms of the following characteristic parameters: the position of the maximum of the functionG(v), the half-width of the emission luminescence band, and the constants andm. From the excitation and emission luminescence spectra it has been established that the emission in both configurations is due to the⁴T₁(G)⁶A₁ transition.     

Excitation of adsorbed molecule vibrations in low energy electron scattering

We develop a theory of low energy electron loss spectroscopy of vibrational modes of molecules adsorbed on metal surfaces. Differential and total cross sections are calculated in the Distorted Wave Born Approximation, assuming i) strong elastic scattering on the metal surface, ii) direct electron-molecule interaction via the electric dipole field associated with the molecular vibration. The angular distributions are calculated and discussed for molecules adsorbed at various distances above the metal surface and for several electron energies and impact angles. The influence of electronic screening of dipolar oscillations is discussed and the consequences of the classical induced image dipoles are explored. It is shown that the metal surface selection rule known in IR spectroscopy is only approximately valid in electron scattering. Finally, we give numerical estimates of the inelastic scattering cross sections for the stretching vibrations of CO molecule adsorbed on transition metal surfaces, in reasonable agreement with experiments.     

Adsorption configuration and local ordering of silicotungstate anions on Ag(100) electrode surfaces

X-ray reflectivity, cyclic voltammetry, and scanning tunneling microscopy (STM) are used to examine the structure of alpha-SiW12O4(4-) or silicotungstic acid (STA) adsorbed on Ag(100) in acid solution. The voltammetry shows that STA passivates the Ag surface relative to electron transfer to a solution redox species. STM images reveal the formation of a series of lattice structures, one of which can be associated with a commensurate ( radical13x radical13)R33.69 degrees structural model. X-ray reflectivity measurements show uniquely that STA orients with its four-fold axis perpendicular to the Ag(100) surface and that the center of the STA molecule is 4.90 A above the top layer of the Ag substrate. Analysis of bond lengths leads to a footprint of STA on Ag(100), in which the four terminal O atoms are located near the hollow sites and have a Ag-O bond length of 2.06 A. This bond length is consistent with a strong covalent interaction between STA and the Ag surface.     

Distribution of fallout radionuclides through soil surface layer

The distribution of¹³⁷Cs through soil layers has been investigated by field sampling. The investigation deals with¹³⁷Cs concentration found after the Chernobyl accident. The relationship between important soil characteristics, total precipitation and cesium distribution are analyzed. Cesium is strongly sorbed in the top soil layer and its migration downward is limited. Measurements performed over a 3-year period revealed that approximately 20–38 per cent of total¹³⁷Cs is located in the upper soil layer.