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.

---

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.

---

---

With 4 figures     

On the influence of size, zeta potential, and state of motion of dispersed particles on the conductivity of a colloidal suspension

The dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of the dispersed particles is analyzed both theoretically and numerically. It is shown that the simple formula that represents the conductivity as a sum of products: charge times mobility, taken over all the carriers present in the suspension, is only valid for exceedingly low values of the product kappaa. In contrast, the formulation based on the value of the dipolar coefficient of the suspended particles seems to be valid for all the range of particle sizes. This assertion is only true if the dipolar coefficient is calculated taking into account the electrophoretic motion of the particles. For very low values of the product kappaa, the dipolar coefficient of particles free to move can be several orders of magnitude larger than that of immobile particles.     

Structure activity relationship by NMR and by computer: a comparative study

There has recently been considerable interest in using NMR spectroscopy to identify ligand binding sites of macromolecules. In particular, a modular approach has been put forward by Fesik et al. (Shuker, S. B.; Hajduk, P. J.; Meadows, R. P.; Fesik, S. W. Science 1996, 274, 1531-1534) in which small ligands that bind to a particular target are identified in a first round of screening and subsequently linked together to form ligands of higher affinity. Similar strategies have also been proposed for in silico drug design, where the binding sites of small chemical groups are identified, and complete ligands are subsequently assembled from different groups that have favorable interactions with the macromolecular target. In this paper, we compare experimental and computational results on a selected target (FKBP12). The binding sites of three small ligands ((2S)1-acetylprolinemethylester, 1-formylpiperidine, 1-piperidinecarboxamide) in FKBP12 were identified independently by NMR and by computational methods. The subsequent comparison of the experimental and computational data showed that the computational method identified and ranked favorably ligand positions that satisfy the experimental NOE constraints.     

Kinetic models for the chemisorption of organic compounds on oxide surfaces

A kinetic equation for chemisorption on amorphous oxide surfaces is proposed, and activation energies, pre-exponential factors for reactions of various organosilicon compounds with Si, Ti and Al oxide active sites are calculated. Relationships between the kinetic parameters and reagent structure were established.     

Hydrogen‐bonded frameworks of bis(2‐carboxypyridinium) hexafluorosilicate and bis(2‐carboxyquinolinium) hexafluorosilicate dihydrate

In bis(2‐carboxypyridinium) hexafluorosilicate, 2C₆H₆NO₂⁺·SiF₆²⁻, (I), and bis(2‐carboxyquinolinium) hexafluorosilicate dihydrate, 2C₁₀H₈NO₂⁺·SiF₆²⁻·2H₂O, (II), the Si atoms of the anions reside on crystallographic centres of inversion. Primary inter‐ion interactions in (I) occur via strong N—H...F and O—H...F hydrogen bonds, generating corrugated layers incorporating [SiF₆]²⁻ anions as four‐connected net nodes and organic cations as simple links in between. In (II), a set of strong N—H...F, O—H...O and O—H...F hydrogen bonds, involving water molecules, gives a three‐dimensional heterocoordinated rutile‐like framework that integrates [SiF₆]²⁻ anions as six‐connected and water molecules as three‐connected nodes. The carboxyl groups of the cation are hydrogen bonded to the water molecule [O...O = 2.5533 (13) Å], while the N—H group supports direct bonding to the anion [N...F = 2.7061 (12) Å].     

Furan ring opening-furan ring closure: cascade rearrangement of novel 4-acetoxy-9-furylnaphtho[2,3-b]furans

The cascade rearrangement of novel 4-acetoxy-9-furylnaphtho[2,3-b]furans leading to tetracyclic naphthodifurans derivatives has been developed. The reaction proceeds via double recyclization of both furan rings of the initial molecule, one of the furan rings serving as a 1,3-dicarbonyl compound equivalent.