Multianvil high-pressure/high-temperature preparation, crystal structure, and properties of the new oxoborates Dy4B6O14(OH)2 and Ho4B6O14(OH)2

This paper reports about two new hydrogen-containing rare-earth oxoborates RE₄B₆O₁₄(OH)₂ (RE=Dy, Ho) synthesized under high-pressure/high-temperature conditions from the corresponding rare-earth oxides, boron oxide, and water using a Walker-type multianvil equipment at 8 GPa and 880 °C. The single crystal structure determination of Dy₄B₆O₁₄(OH)₂ showed: Pbcn, a=1292.7(2), b=437.1(2), , Z=2, R1=0.0190, and wR2=0.0349 (all data). The isotypic holmium species revealed: Pbcn, a=1292.8(2), b=436.2(2), , Z=2, R1=0.0206, and wR2=0.0406 (all data). The compounds exhibit a new type of structure, which is built up from layers of condensed BO₄-tetrahedra. Between the layers, the rare-earth cations are coordinated by 7+2 oxygen atoms. Furthermore, we report about temperature-resolved in situ powder diffraction measurements, DTA/TG, and IR-spectroscopic investigations into RE₄B₆O₁₄(OH)₂ (RE=Dy, Ho).     

Reactivity of monolayer-protected gold nanoclusters at dye-sensitized liquid/liquid interfaces

Hexanethiolate monolayer-protected gold nanoclusters (MPCs) were used as redox quenchers at the polarizable water/1,2-dichloroethane (DCE) interface. Photocurrent responses originating from the heterogeneous quenching of photoexcited water soluble porphyrin complexes by MPCs dissolved in the DCE phase were observed. As MPCs can function as both electron acceptors and donors, the photocurrent results from the superposition of two simultaneous processes, which correspond to the oxidation and reduction of MPCs. The magnitude of the net photocurrent is essentially determined by the balance of the kinetics of these two processes, which can be controlled by tuning the Galvani potential difference between the two phases. We show that, within the available potential window, the apparent electron-transfer rate constants follow classical Butler-Volmer dependence on the applied potential difference.     

The virial theorem in relativistic quantum mechanics

For a class of potentials including the Coulomb potential q = μr^?1 with ¦ μ ¦ < 1 (1) (i.e., atomic numbers Z ? 137), the virial theorem $\text{(u, α ·}\text{p}\text{u) = (u, r(}\text{?q}\text{?r}\text{)u)}$ is shown to hold, u being an eigenfunction of the operator

$\text{Hu = TU : = (α ·}\text{p}\text{+ β + q)u}$

,

$\text{D(H) = {u ¦ u ∈ [H}{}_{\mathrm{loc}}{}^1\text{(}\text{R}\text{+}{}^3\text{)]}{}^4\text{, r}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{u, TU ∈ [L}{}^2\text{(R)}{}^3\text{]}{}^4\text{}}$

($\text{R}$₊³ := $\text{R}$?{0}). The result implies in particular that H with (1) does not have any eigenvalues embedded in the continuum. The proof uses a scale transformation.     

Coexistence of Two Different Distorted Octahedral [MnF6]3− Sites in K3[MnF6]: Manifestation in Spectroscopy and Magnetism

As a consequence of the static Jahn-Teller effect of the ⁵E ground state of Mn^III in cubic structures with octahedral parent geometries, their octahedral coordination spheres become distorted. In the case of six fluorido ligands, [MnF₆]³⁻ anions with two longer and four shorter Mn−F bonds making elongated octahedra are usually observed. Herein, we report the synthesis of the compound K₃[MnF₆] through a high-temperature approach and its crystallization by a high-pressure/high-temperature route. The main structural motifs are two quasi-isolated, octahedron-like [MnF₆]³⁻ anions of quite different nature compared to that met in ideal octahedral Mn^III Jahn-Teller systems. Owing to the internal electric field of C_i symmetry dominated by the next-neighbour K⁺ ions acting on the Mn^III sites, both sites, the pseudo-rhombic (site 1) and the pseudo-tetragonally elongated (site 2) [MnF₆]³⁻ anions are present in K₃[MnF₆]. The compound was characterized by single-crystal and powder X-ray diffraction, and magnetometry as well as by FTIR, Raman, and ligand field spectroscopy. A theoretical interpretation of the electronic structure and molecular geometry of the two Mn sites in the lattice is given by using a vibronic coupling model with parameters adjusted from multireference ab-initio cluster calculations.     

Two-Scale Convergence of Integral Functionals with Convex, Periodic and Nonstandard Growth Integrands

We study the periodic homogenization for a family of functionals defined on Orlicz-Sobolev spaces. One fundamental in this topic is to extend the classical compactness results of the two-scale convergence method to this type of spaces.     

Degradation of cellulosic key chromophores by ozone: a mechanistic and kinetic study

Cellulose - Chromophores, colored substances of rather high stability that reduce brightness, are present in all kinds of cellulosic products, such as pulp, fibers, aged cellulosic material, and...     

1,2,5,6-Tetrakis(guanidino)-Naphthalenes: Electron Donors,Fluorescent Probes and Redox-Active Ligands

New redox-active 1,2,5,6-tetrakis(guanidino)-naphthalene compounds, isolable and storable in the neutral and deep-green dicationic redox states and oxidisable further in two one-electron steps to the tetracations, are reported. Protonation switches on blue fluorescence, with the fluorescence intensity (quantum yield) increasing with the degree of protonation. Reactions with N-halogenosuccinimides or N-halogenophthalimides led to a series of new redox-active halogeno- and succinimido-/phthalimido-substituted derivatives. These highly selective reactions are proposed to proceed via the tri- or tetracationic state as the intermediate. The derivatives are oxidised reversibly at slightly higher potentials than that of the unsubstituted compounds to dications and further to tri- and tetracations. The integration of redox-active ligands in the transition-metal complexes shifts the redox potentials to higher values and also allows reversible oxidation in two potentially separated one-electron steps.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.