Jacobi matrices with absolutely continuous spectrum

Let be a Jacobi matrix defined in as , where is a unilateral weighted shift with nonzero weights such that Define the seqences: If and , then has an absolutely continuous spectrum covering . Moreover, the asymptotics of the solution is also given.

     

Probing the wave function of shallow Li and Na donors in ZnO nanoparticles

Electron paramagnetic resonance and electron nuclear double resonance (ENDOR) experiments on ZnO nanoparticles reveal the presence of shallow donors related to interstitial Li and Na atoms. The shallow character of the wave function is evidenced by the multitude of 67Zn ENDOR lines and further by the hyperfine interactions with the 7Li and 23Na nuclei that are much smaller than for atomic lithium and sodium. In the case of the Li-doped nanoparticles, an increase of the hyperfine interaction with the 7Li nucleus and with the 1H nuclei in the Zn(OH)(2) capping layer is observed when reducing the size of the nanoparticles. This effect is caused by the confinement of the shallow-donor 1s-type wave function that has a Bohr radius of about 1.5 nm, i.e., comparable to the dimension of the nanoparticles.     

Overhauser effect of 67Zn nuclear spins in ZnO via cross relaxation induced by the zero-point fluctuations of the phonon field

Hole burning in and displacements of the magnetic-resonance absorption line of the electron spin of the shallow hydrogen-related donor in ZnO are observed upon resonant irradiation with microwaves at 275 GHz and at 4.5 K in a magnetic field of 10 T. These effects arise from an almost complete polarization of the many 67Zn (I=5/2) nuclear spins that have an isotropic hyperfine interaction with the electron spin of the shallow donor. It is proposed that this huge dynamic nuclear polarization is caused by a spontaneous-emission-type cross relaxation in the coupled electron-spin nuclear-spin system induced by the zero-point fluctuations of the phonon field.     

Complexation of Am(III) and Nd(III) by 1,10-Phenanthroline-2,9-Dicarboxylic Acid

The complexant 1,10-phenanthroline-2,9-dicarboxylic acid (PDA) is a planar tetradentate ligand that is more preorganized for metal complexation than its unconstrained analogue ethylendiiminodiacetic acid (EDDA). Furthermore, the backbone nitrogen atoms of PDA are aromatic, hence are softer than the aliphatic amines of EDDA. It has been hypothesized that PDA will selectively bond to trivalent actinides over lanthanides. In this report, the results of spectrophotometric studies of the complexation of Nd(III) and Am(III) by PDA are reported. Because the complexes are moderately stable, it was necessary to conduct these titrations using competitive equilibrium methods, competitive cation complexing between PDA and diethylenetriaminepentaacetic acid, and competition between ligand protonation and complex formation. Stability constants and ligand protonation constants were determined at 0.1 mol·L^?1 ionic strength and at 0.5 mol·L^?1 ionic strength nitrate media at 21 ± 1 °C. The stability constants are lower than those predicted from first principles and speciation calculations indicate that Am³⁺ selectivity over Nd³⁺ is less than that exhibited by 1,10-phenanthroline.     

Theoretical analysis of singlet and triplet excited states of nickel porphyrins

Local density and generalized gradient approximation time-dependent density functional methods have been used for calculation of the singlet and triplet excited states of nickel-porphine, Ni-tetraphenyloporphine, and Ni-octaethyloporphyrine. Special attention is paid to metal-ligand transitions and d-d transitions. It is shown that the lowest exited singlet states of the three compounds can be described as a transfer of an electron from the porphine ring to the d(x2-y2) orbital of the nickel atom. On the other hand, the lowest excited triplet state arises from promotion of an electron between two nickel d orbitals, an occupied d(z2) and an empty d(x2-y2). It is proposed that a rapid quenching of the excited singlet states is due to an ultrafast intersystem crossing between 1Eg)and 3Eg or 3B1g states.     

Tuning rate of the bergman cyclization of benzannelated enediynes with ortho substituents

[reaction: see text] The Bergman cyclization of benzannelated enediynes is highly sensitive to ortho substitution. This finding opens possibilities for the rational design of conformer-specific and pH-dependent DNA-cleaving agents.     

Affinity of An(VI) for N4-Tetradentate Donor Ligands: Complexation of the Actinyl(VI) Ions with N4-Tetradentate Ligands

In this report the affinity of four N₄-tetradentate ligands that incorporate the 2-methylpyridyl functionality with hexavalent actinides $(\mathrm{AnO}_{2}^{2+})$ has been investigated in methanol solution. The ligands studied include N,N??-bis(2-methylpyridyl)diaminoethane (BPMDAE), N,N??-bis(2-methylpyridyl)-1,3-diaminopropane (BPMDAP), N,N??-bis(2-pyridylmethyl)piperazine (BPMPIP), and trans-N,N-bis(2-pyridylmethyl)-1,2-diaminocyclohexane (BPMDAC). Conditional stability constants describing the strength of the interaction were determined by UV?Cvisible spectrophotometry. The log₁₀ K ₁₀₁ values for both U(VI) and Pu(VI) are comparable and show the same trend of stability with ligand structure. Dinuclear complexes are also indicated as being important. The log₁₀ K ₂₀₁ values for Pu(VI) complexation with the N₄-ligands are identical for the four ligands (within experimental error), indicating that the structure of the ligand backbone has little effect on the stability of the (PuO₂)₂L²⁺ complex. The exception to this trend is the behavior of N,N??-bis(2-pyridylmethyl)piperazine (BPMPIP) with Pu(VI). This ligand displays a tendency to reduce Pu(VI) within the experimental time frame of 45 minutes. BPMPIP is the only ligand tested that contains tertiary amines in the ligand backbone. The decomposition of BPMPIP by Pu(VI) suggests a susceptibility of tertiary amines to oxidative degradation.     

Fast spatially localised electrooptical mode in vertically aligned nematic LCs with negative dielectric anisotropy

ABSTRACT

Electro-optical switching and the liquid crystal (LC) director distribution are studied in spatially periodic electric field for vertically aligned LC with negative dielectric anisotropy. Two electro-optical switching modes characterised by different switching times are observed. These modes are well distinguished optically by choosing proper geometry for the polarisers axes orientation. One of these modes is significantly faster as compared to the other. The fast switching is explained in terms of localised near-to-surface director reorientation. The 3D-numerical simulation shows very good agreement with the experiment: it points out the existence of the disclination lines and field-stabilised walls responsible for the localised director field switching and its relaxation. Possibilities of enhancing the fast mode for high-speed light modulators are discussed.     

Tubular aggregates of cyclic oligothiophenes. A theoretical study

The geometries of neutral, mono-, and dioxidized tubular aggregates of cyclo[8]thiophenes containing up to 5 repeating units were fully optimized at the MPWB1K/3-21G* level of theory. Calculated interplane distances between macrocycles were found to be close to 3.1 A for neutral and charged aggregates. The binding energies between macrocycles in neutral intermediates were in the range of 40-45 kcal/mol, increasing for monocations and dropping strongly for dicationic species due to electrostatic repulsion between polarons. It was established that there exists a noticeable interaction between pi-orbitals of individual macrocycles in tubular aggregates as follows from decreasing of the band gap with a number of repeating units in aggregates and the polaron delocalization toward tube axes in oxidized species. A polaron pair is the most stable dicationic state for all studied molecules according to the calculations. A singlet polaron pair is more stable than a triplet one. The energy difference between singlet and triplet states is growing smaller with the size of the system, becoming zero for the pentamer corresponding to a completely dissociated bipolaron.     

Oligothiophene catenanes and knots. Part II. Mono and dications. A theoretical study

Mono- and dications of catenanes and knots containing 16, 22, and 28 thiophene units have been studied at the BHandHLYP/3-21G* level of theory. The polaron localization and relaxation energies of monoionized molecules increase with dihedral angle between thiophene fragments, being higher for catenanes and knots compared to linear oligomers. Monoionization of catenanes results in the polaron localization at one macrocycle leaving another one intact. In all diionized oligomers, polaron pairs were found to be more stable than corresponding bipolarons. The energy difference between bipolaron and polaron pairs increases with the number of repeating units in oligomers for all studied molecular architectures. Singlet polaron pairs are more stable than triplet ones. The energy difference between triplet and singlet states does not exceed 7-8 kcal/mol and decreases with the number of thiophene units in oligomers. Two different singlet minima were found for diionized catenanes. In the first one (the most stable), each macrocycle loses one electron, and in the other one, the polaron pairs are located at one macrocycle, leaving another intact. The energy difference between two minima decreases with the number of repeating units in catenanes.