On a characterization of polynomials by divided differences

Summary We consider the functional equationf[x ₁,x ₂,, x _n ] =h(x ₁ + +x _n ) (x ₁,,x _n K, x _j x _k forj k), (D) wheref[x ₁,x ₂,,x _n ] denotes the (n – 1)-st divided difference off and prove Theorem. Let n be an integer, n 2, let K be a field, char(K) 2, with # K 8(n – 2) + 2. Let, furthermore, f, h: K K be functions. Then we have that f, h fulfil (D) if, and only if, there are constants a_j K, 0 j n (a := a_n, b := a_{n – 1}) such thatf = ax ⁿ +bx ^{n – 1} + +a ₀ and h = ax + b.     

The relative importance of temperature and isotope effects on the dipole oscillator strength distribution of H2

Summary The calculation of the effects of temperature and isotopic composition on the energy weighted moments of the dipole oscillator strength distribution of H₂ in the random phase approximation to the polarization propagator are reported. It is seen that the effect of isotopic composition is small, while that of temperature is of an order accessible to experiment. We find that all the mean excitation energiesI , for =–1, 0, 1, decrease with temperature as does the dipole oscillator strength momentS() for >0, while the opposite is true for <0. These effects are interpreted in terms of the bond length dependence of the excitation energies.     

The structure of magnesium alanate

Mg(AlH(4))(2) was produced as a nanocrystalline powder by metathesis of NaAlH(4) and MgCl(2). Starting with a structure estimation which was developed from an evaluation of FTIR data and comparison of structural properties of two solvent adducts, quantum chemical calculations were performed on the density functional theory (DFT) level. The calculated atomic positions were used to simulate an X-ray powder diffraction pattern, based on a trigonal unit cell. The simulated pattern was congruent to experimental data. Thus, magnesium alanate exhibits a CdI(2) layer structure, the layers being formed by Mg atoms occupying the Cd sites and AlH(4) tedrahedra occupying the sites of the iodine atoms in CdI(2).     

Diastereoselective synthesis of 2-aminoalkyl-3-sulfonyl-1,3-oxazolidines on solid support

Herein we report our investigation on the oxidation of solid-support-bound amino alcohols to their corresponding aldehydes. These aldehydes were converted into diastereomerically pure (>10:1) 2,4-cis-2-aminoalkyl-3-sulfonyl-1,3-oxazolidines using optically pure 1,2-amino alcohols. The relative configuration was determined using the nuclear Overhauser effect (NOE). The synthesized oxazolidines, which were obtained in high purities, represent a new, diverse scaffold for the solid-phase synthesis of libraries directed toward a pharmacological target.     

Synthesis of quinolines, 2-quinolones, phenanthridines, and 6(5h)-phenanthridinones via palladium[0]-mediated Ullmann cross-coupling of 1-bromo-2-nitroarenes with beta-halo-enals, -enones, or -esters

Palladium[0]-mediated Ullmann cross-coupling of 1-bromo-2-nitrobenzene (1 R = H) and its derivatives with a range of beta-halo-enals, -enones, or -esters readily affords the corresponding beta-aryl derivatives, which are converted into the corresponding quinolines, 2-quinolones, phenanthridines, or 6(5H)-phenanthridinones on reaction with dihydrogen in the presence of Pd on C or with TiCl(3) in aqueous acetone. [reaction: see text]     

Thioacetylacetone: structural and vibrational assignments.

Thioacetylacetone and its variously deuterated isotopomers have been investigated using electronic and vibrational spectroscopy combined with quantum chemical calculations. Thioacetylacetone is known for its photochromic properties, but the structures of the initial and final forms have been the subject of a long debate. Analysis of the IR spectra recorded in low-temperature argon and xenon matrices, room-temperature solutions, and in the gas phase has allowed us to establish the nature of the photochromic species and of its precursor. Similar to the case of another beta-thioxoketone, monothiodibenzoylmethane, the photo-product has been assigned to the nonchelated SH exo-rotamer of the (Z)-enethiol tautomeric form, whereas the dominant ground-state species corresponds to the chelated (Z)-enol tautomeric form. Detailed vibrational assignments have been proposed for both forms based on quantum chemical calculations and polarization experiments. In the case of the chelated (Z)-enol species prevailing in the ground state, a second-order perturbative anharmonic analysis at the B3LYP/cc-pVTZ level indicated strong anharmonic effects associated with the intramolecular hydrogen bond, leading to a shift of more than 600 cm-1 of the wavenumber of the OH-stretching vibration. A small fraction of the SH endo-rotameric chelated (Z)-enethiol form was also detected under unperturbed conditions. The (Z)-enethiol form can be converted into the (Z)-enol form by irradiation at 290 nm.     

Synthesis and immobilization of quaternary ammonium cations in acidic zeolites

A general method for the synthesis of quaternary ammonium cations in acidic zeolites by a direct reaction of tertiary amines and alcohols is described.     

Charge recombination fluorescence in photosystem I reaction centers from Chlamydomonas reinhardtii

The fluorescence kinetics of photosystem I core particles from Chlamydomonas reinhardtii have been measured with picosecond resolution in order to test a previous hypothesis suggesting a charge recombination mechanism for the early electron-transfer steps and the fluorescence kinetics (Müller et al. Biophys. J. 2003, 85, 3899-3922). Performing global target analyses for various kinetic models on the original fluorescence data confirms the "charge recombination" model as the only acceptable one of the models tested while all of the other models can be excluded. The analysis allowed a precise determination of (i) the effective charge separation rate constant from the equilibrated reaction center excited state (438 ns(-1)) confirming our previous assignment based on transient absorption data (Müller et al. Biophys. J. 2003, 85, 3899-3922), (ii) the effective charge recombination rate constant back to the excited state (52 ns(-1)), and (iii) the intrinsic secondary electron-transfer rate constant (80 ns(-1)). The average energy equilibration lifetime core antenna/RC is about 1 ps in the "charge recombination" model, in agreement with previous transient absorption data, vs the 18-20 ps energy transfer lifetime from antenna to RC within "transfer-to-the-trap-limited" models. The apparent charge separation lifetime in the recombination model is about three times faster than in the "transfer-to-the-trap-limited" model. We conclude that the charge separation kinetics is trap-limited in PS I cores devoid of red antenna states such as in C. reinhardtii.     

Conformational analysis of a stereochemically complete set of cis-enediol peptide analogues

A conformational analysis of a stereochemically complete set of peptide analogues based on a cis-enediol unit is presented. The cis-enediol unit, which can replace a two or a three amino acid segment of a peptide, contains two "side chains", four asymmetrical carbon atoms, and six free dihedral angles. To determine the accessible conformational space, the molecules are divided into three fragments, each containing two free dihedral angles. The energy surfaces are computed for all dihedral angle values, and the possible conformations of the cis-enediol unit analogues are built using all combinations of the surface minima. Such a "build-up" procedure, which is very fast, is able to reproduce 75% of the minima obtained from a full dihedral angle exploration of the conformational space. The cis-enediol unit minima are compared with the corresponding di- and tripeptide minima; all peptide minima can be closely matched by a cis-enediol unit minimum of low energy (less than 2.2 kcal/mol above the lowest energy conformer). However, there are low energy minima of the cis-enediol unit that have no corresponding minima in peptides. The results are shown to depend strongly on the chirality of the analogues. The ability of each of the stereoisomers to mimic natural peptides, evaluated by the present approach, is correlated with its experimental activity in a renin inhibition assay.     

Ionene–surfactant complexes: temperature and humidity sensitive materials

Solid stoichiometric complexes of [3,12]-ionene and dodecyl sulfate form upon reaction of the bromide of the ionene and the silver salt of dodecyl sulfate in methanol. IR, DSC, and TG investigations indicated that the solid complexes are stable between 30 and 120 °C. TG and DSC also showed that the complexes easily take up water at ambient conditions. These samples are optically isotropic. When exposed to an increased humidity they exhibit optical anisotropy, i.e., birefringence, which is caused by the formation of a hexagonal mesogenic phase. Mesogenicity is necessarily accompanied by a further uptake of water (4–5 H₂O molecules per ionic unit), which is dependent on the relative humidity. The phase behavior as a function of temperature and controlled relative humidity was studied using birefringence measurements and polarizing microscopy.