Formation of sodium 6-hydroxy-2-naphthoate in the <Emphasis Type="Italic">Kolbe-Schmitt</Emphasis> reaction

This work is an extension of our investigation of the mechanism of the Kolbe-Schmitt reaction of sodium 2-naphthoxide. The carboxylation reaction of sodium 2-naphthoxide in the position 6 is examined by means of the B3LYP/LANL2DZ method. After the initial formation of sodium 2-naphthoxide-CO₂ complex, the carbon of the CO₂ moiety performs an electrophilic attack on the naphthalene ring in position 8. Further transformations lead to the formation of sodium 6-hydroxy-2-naphthoate. Our findings are in good agreement with the experimental results on the carboxylation reaction of sodium 2-naphthoxide. Correspondence: Svetlana Marković, Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia.     

Crystal Growth and Crystal Structures of Gold(V) Compounds: Cu(AuF6)2, Ag(AuF6)2, and O2(CuF)3(AuF6)4 ⋅ HF

Crystal growth from anhydrous hydrogen fluoride solutions of M²⁺ (M=Cu, Ag) and [AuF₆]⁻ gave M(AuF₆)₂ salts (M=Cu, Ag). Similar attempts to prepare single crystals of the corresponding nickel, zinc and magnesium salts failed. The crystal structure of Cu(AuF₆)₂ consists of layers of Cu²⁺ cations connected by [AuF₆]⁻ anions, thus forming slabs. Only van der Waals interactions exist between adjacent slabs. The crystal structure of Ag(AuF₆)₂ consists of a three-dimensional framework in which Ag⁺ cations are linked by [AuF₆]⁻ anions. Both structures are members of the M^II(X^VF₆)₂ family, in which seven different structure types have been observed to date. In the crystal structure of O₂(CuF)₃(AuF₆)₄ ⋅ HF, the bridging AuF₆ units connect [−Cu−F−Cu−F−]_∞ chains to form stacks between which O₂⁺ cations and HF molecules are located.     

Acetylcholinesterase: mechanisms of covalent inhibition of wild-type and H447I mutant determined by computational analyses

The reaction mechanisms of two inhibitors TFK+ and TFK0 binding to both the wild-type and H447I mutant mouse acetylcholinesterase (mAChE) have been investigated by using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) approach and classical molecular dynamics (MD) simulations. In the wild-type mAChE, the binding reactions of TFK+ and TFK0 are both spontaneous processes, which proceed through the nucleophilic addition of the Ser203-Ogamma to the carbonyl-C of TFK+ or TFK0, accompanied with a simultaneous proton transfer from Ser203 to His447. No barrier is found along the reaction paths, consistent with the experimental reaction rates approaching the diffusion-controlled limit. By contrast, TFK+ binding to the H447I mutant may proceed with a different reaction mechanism. A water molecule takes over the role of His447 and participates in the bond breaking and forming as a "charge relayer". Unlike in the wild-type mAChE case, Glu334, a conserved residue from the catalytic triad, acts as a catalytic base in the reaction. The calculated energy barrier for this reaction is about 8 kcal/mol. These predictions await experimental verification. In the case of the neutral ligand TFK0, however, multiple MD simulations on the TFK0/H447I complex reveal that none of the water molecules can be retained in the active site as a "catalytic" water. Furthermore, our alchemical free energy calculation also suggests that the binding of TFK0 to H447I is much weaker than that of TFK+. Taken together, our computational studies confirm that TFK0 is almost inactive in the H447I mutant and also provide detailed mechanistic insights into the experimental observations.     

Polyaniline “Nanotube” Self‐Assembly: The Stage of Granular Agglomeration on Nanorod Templates

The identification and control of a critical stage of polyaniline “nanotube” self‐assembly is presented, namely the granular agglomeration or growth onto nanorod templates. When the synthesis pH is held above 2.5, smooth insulating nanorods exhibiting hydrogen bonding and containing phenazine structures are produced, while below pH 2.5, small 15–30 nm granular polyaniline nanoparticles appear to agglomerate onto the available nanorod surface, apparently improving conductivity of the resulting structures by three orders of magnitude. This finding affects both fundamental theories of polyaniline nanostructure self‐assembly and their practical applications.

     

Lattice energy calculation for quantitatively-modeled Perovskite distortion

In case of reactions, it is a necessary condition that the free energy of formation, Δ_fG, of the product is lower than the total free energies of formation of the reactants. The free energy of all reactions and/or all compounds have not been determined in the literature. In this paper, we report the formation, stability, and reactions for all compounds based on their free energies. However, it also seems possible to discuss them based on their lattice energies, because it can be calculated for many compounds if their composition, structure and their lattice parameters are known. Also, we can discuss the formation, stability, etc., for compounds excluding small effects due to temperature and entropy. As a result of the calculations, the lattice energy correlates with the perovskite distortion.     

Boundary Harnack principle for subordinate Brownian motions

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in κ$\kappa$-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded κ$\kappa$-fat open sets with respect to these processes with their Euclidean boundaries.     

Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)

Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman’s path integral preserves its exact expression for quadratic models. The compact general formalism presented here can be easily illustrated in any particular quadratic case. As an important result of phenomenological interest, we give the path integral for a charged particle in the noncommutative plane with a perpendicular magnetic field. We also present an effective Planck constant ħ _eff which depends on additional noncommutativity.     

Remarks on “Quasi-contraction on a cone metric space”

Recently, D. Ili? and V. Rako?evi? [D. Ili?, V. Rako?evi?, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition.     

Quantitative study of fluorescence excitation and emission spectra of bean leaves

A quantitative and comprehensive knowledge of leaf fluorescence is required for the interpretation of fluorescence signals at the canopy level and also for the modelling of leaf and canopy fluorescence. In this work we present full range fluorescence excitation and emission spectra of intact leaves, expressed in units of apparent spectral fluorescence yield, from both the adaxial and the abaxial sides of the leaves, and for both front-side and back-side geometries. Emission spectra were measured for incident radiations in the blue and the green spectral range. The red/far-red fluorescence ratio depended on the measurement geometry and on the excitation wavelength. Excitation spectra were measured for emissions at 687 and 760 nm. When the abaxial side was illuminated, the measured spectra always had a larger intensity compared to adaxial side that is explained by the higher scattering of the spongy tissues. At 760 nm, the spectra had the same shape for front-side and back-side geometry, indicating that scattering predominated. At 687 nm, the shape of the spectra was very different for front-side and back-side geometry due to re-absorption of red fluorescence within the leaf. The comparison of excitation spectra measured from the adaxial or the abaxial side revealed differences in carotenoid absorption.     

Brachistochrone with limited reaction of constraint in an arbitrary force field

The paper considers brachistochronic motion of a particle along a curve y=y(x) in an arbitrary force field in the vertical plane of Cartesian coordinate system. The curve is treated as a bilateral or unilateral constraint that can be smooth or rough. The projection of the reaction force of the curve onto the normal to the curve is confined to the fixed limits. A control variable u is given as the second derivative of the function y(x) relative to the horizontal coordinate?x of the particle, i.e., u=d ² y/dx ². Applying Pontryagin??s maximum principle and singular optimal control theory, the problem is reduced to numerical solving of the corresponding two-point boundary value problem. The procedure based on the shooting method is used to solve the boundary value problem. Two examples with friction forces of the viscous friction and Coulomb friction type have been solved.