New analytical expressions,symmetry relations and numerical solutions for the rotational overlap integrals

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Experimental and molecular modeling investigation of (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide

The Schiff base compound (E)-N-{2-[(2-hydroxybenzylidene)amino]phenyl}benzenesulfonamide has been synthesized and characterized by IR, NMR and Uv-vis spectroscopies, and single-crystal X-ray diffraction technique. In addition, quantum chemical calculations employing density functional theory (DFT) method with the 6–311++G(d,p) basis set were performed to study the molecular, spectroscopic and some electronic structure properties of the title compound, and the results were compared with the experimental findings. There exists a good correlation between experimental and theoretical data. Enol-imine/keto-amine tautomerization mechanism was investigated in the gas phase and in solution phase using the polarizable continuum model (PCM) approximation. The energetic and thermodynamic parameters of the enol-imine?→?keto-amine transfer process show that the single proton exchange is thermodynamically unfavored both in the gas phase and in solution phase. However, the reverse reaction seems to be feasible with a low barrier height and is supported by negative values in enthalpy and free energy changes both in the gas phase and in solution phase. The solvent effect is found to be sizable with increasing polarity of the solvents for the reverse reaction. The predicted nonlinear optical properties of the compound are found to be much greater than those of urea.     

Investigations for Modification of Polyacrylamide-Bentonite by Phytic Acid and its Usability in Fe3+, Zn2+ and UO2 2+ Adsorption

Composite of polyacrylamide-bentonite (PAA-B) was prepared by direct polymerisation of PAA in a suspension of bentonite (B). Adsorption and thermodynamic features of phytic acid (Phy) adsorption onto B, PAA and PAA-B, and those of Fe³⁺, Zn²⁺, UO₂ ²⁺ adsorption onto PAA-B and its modification by Phy (PAA-B-Phy) have been investigated. The reusability, storagability, ion selectivity and recoverability of sorbed ions with 1 M HCl have also been considered.The chemical and physical structure of adsorbents has been characterised by means of FT-IR and XRD. All adsorption isotherms for Phy and the ions were L-type of the Giles classification except, the one which is S type for adsorption of Phy onto PAA. The maximum adsorption capacities for the ions adsorbed were in order of UO₂ ²⁺ > Fe³⁺ > Zn²⁺ for PAA-B and Zn²⁺ > Fe³⁺ > UO₂ ²⁺ for PAA-B-Phy. Langmuir equilibrium constants for the adsorption of ions onto PAA-B-Phy were significantly higher than those found for PAA-B; the magnitude of increase for UO₂ ²⁺ was about 100. The thermodynamic parameters indicated that adsorption reactions are spontaneous in terms of adsorption free enthalpy.The chemical structure of PAA-B-Phy was not changed at the end of the studies of reusability and storagability. The composite was selective for UO₂ ²⁺ of the ions of interest.The composite of PAA-B and its modification by Phy have been used for the first time in this investigation. It is proposed that the composites can be practically used in the investigations and applications of adsorption.     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

The taxicab space group

It is shown that the group of isometries of the 3-dimensional space with respect to taxicab metric is the semi-direct product of octahedral group O _h and T(3), where O _h is the (Euclidean) symmetry group of the regular octahedron and T(3) is the group of all translations of the 3-dimensional space.     

The distribution of the domination number of class cover catch digraphs for non-uniform one-dimensional data

For two or more classes of points in R^d with d≥1, the class cover catch digraphs (CCCDs) can be constructed using the relative positions of the points from one class with respect to the points from one or all of the other classes. The CCCDs were introduced by Priebe et al. [C.E. Priebe, J.G. DeVinney, D.J. Marchette, On the distribution of the domination number of random class catch cover digraphs. Statistics and Probability Letters 55 (2001) 239-246] who investigated the case of two classes, X and Y. They calculated the exact (i.e., finite sample) distribution of the domination number of the CCCDs based on X points relative to Y points both of which were uniformly distributed on a bounded interval. We investigate the distribution of the domination number of the CCCDs based on data from non-uniform X points on an interval with end points from Y. Then we extend these calculations for multiple Y points on bounded intervals.     

Chow groups of the moduli spaces of weighted pointed stable curves of genus zero

The moduli space of weighted pointed stable curves of genus zero is stratified according to the degeneration types of such curves. We show that the homology groups of are generated by the strata of and give all additive relations between them. We also observe that the Chow groups and the homology groups are isomorphic. This generalizes Kontsevich-Manin's and Losev-Manin's theorems to arbitrary weight data A.     

Synthesis,characterization and electrochemical properties of novel metal free and zinc(II) phthalocyanines of ball and clamshell types

The phthalodinitrile derivative 1 was prepared by the reaction of 4-nitrophthalonitrile and 1,3-dimethoxy-4-tert-butylcalix[4]arene in dry dimethylsulfoxide as the solvent, in the presence of the base K₂CO₃, by nucleophilic substitution of an activated nitro group in an aromatic ring. The tetramerization of compound 1 gave a binuclear zinc(II) phthalocyanine and a metal-free phthalocyanine of the ball type, 2 and 3, respectively. Its condensation with 4,5-bis(hexylthio)phthalonitrile results in a binuclear phthalocyanine of the clamshell type, 4. The newly synthesized compounds were characterized by elemental analysis, UV–Vis, IR, MS and ¹H NMR spectra. The electronic spectra exhibit an intense π → π^∗ transition with characteristic Q and B bands of the phthalocyanine core. The electrochemical properties of 2–4 were examined by cyclic voltammetry in non-aqueous media. The voltammetric results showed that while there is no considerable interaction between the two phthalocyanine rings in 4, the splitting of a molecular orbital occurs as a result of the strong interaction between the phthalocyanine rings in 2 and 3.     

Preparation and thermal characterization of poly(2‐vinylpyridine) copolymers coordinated to Cr nanoparticles

In this study, polystyrene‐block‐poly(2‐vinylpyridine), PS‐b‐P2VP, polyisoprene‐block‐poly(2‐vinylpyridne), PI‐b‐P2VP and poly(methyl metacrylate)‐block‐poly(2‐vinylpyridine), PMMA‐b‐P2VP, coordinated to Cr metal were synthesized and characterized by Fourier transform infrared, transmission electron microscopy and direct pyrolysis mass spectrometry techniques. Both thermal degradation mechanism and thermal stability of P2VP blocks were affected by the coordination of Cr nanoparticles to nitrogen of pyridine rings. Thermal decomposition of P2VP blocks was started by loss of pyridine units leaving an unsaturated and/or crosslinked polymer backbone that degraded at relatively high temperatures. Incorporation of Cr metal did not noticeably influence thermal behavior of PS and PI blocks. However, increase in thermal stability of PMMA block was detected and associated with inhibition of the interactions between carbonyl groups of MMA chains with nitrogen atom of pyridine ring as a consequence of coordination to metal. Copyright © 2015 John Wiley & Sons, Ltd.