Skew codes of prescribed distance or rank

In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40, 23, 10]₄ code by imposing a distance and a [42,14,21]₈ code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal length and dimension over those fields. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section.      

Highly Efficient Transition Metal Nanoparticle Catalysts in Aqueous Solutions

A ligand design is proposed for transition metal nanoparticle (TMNP) catalysts in aqueous solution. Thus, a tris(triazolyl)‐polyethylene glycol (tris‐trz‐PEG) amphiphilic ligand, 2 , is used for the synthesis of very small TMNPs with Fe, Co, Ni, Cu, Ru, Pd, Ag, Pt, and Au. These TMNP‐ 2 catalysts were evaluated and compared for the model 4‐nitrophenol reduction, and proved to be extremely efficient. High catalytic efficiencies involving the use of only a few ppm metal of PdNPs, RuNPs, and CuNPs were also exemplified in Suzuki–Miyaura, transfer hydrogenation, and click reactions, respectively.     

17O solid-state NMR and first-principles calculations of sodium trimetaphosphate (Na3P3O9), tripolyphosphate (Na5P3O10), and pyrophosphate (Na4P2O7)

The assignment of high-field (18.8 T) (17)O MAS and 3QMAS spectra has been completed by use of first-principles calculations for three crystalline sodium phosphates, Na 3P 3O 9, Na 5P 3O 10, and Na 4P 2O 7. In Na 3P 3O 9, the calculated parameters, quadrupolar constant ( C Q), quadrupolar asymmetry (eta Q), and the isotropic chemical shift (delta cs) correspond to those deduced experimentally, and the calculation is mandatory to achieve a complete assignment. For the sodium tripolyphosphate Na 5P 3O 10, the situation is more complex because of the free rotation of the end-chain phosphate groups. The assignment obtained with ab initio calculations can however be confirmed by the (17)O{ (31)P} MAS-J-HMQC spectrum. Na 4P 2O 7 (17)O MAS and 3QMAS spectra show a complex pattern in agreement with the computed NMR parameters, which indicate that all of the oxygens exhibit very similar values. These results are related to structural data to better understand the influence of the oxygen environment on the NMR parameters. The findings are used to interpret those results observed on a binary sodium phosphate glass.     

Parametrization of analytic interatomic potential functions using neural networks

A generalized method that permits the parameters of an arbitrary empirical potential to be efficiently and accurately fitted to a database is presented. The method permits the values of a subset of the potential parameters to be considered as general functions of the internal coordinates that define the instantaneous configuration of the system. The parameters in this subset are computed by a generalized neural network (NN) with one or more hidden layers and an input vector with at least 3n-6 elements, where n is the number of atoms in the system. The Levenberg-Marquardt algorithm is employed to efficiently affect the optimization of the weights and biases of the NN as well as all other potential parameters being treated as constants rather than as functions of the input coordinates. In order to effect this minimization, the usual Jacobian employed in NN operations is modified to include the Jacobian of the computed errors with respect to the parameters of the potential function. The total Jacobian employed in each epoch of minimization is the concatenation of two Jacobians, one containing derivatives of the errors with respect to the weights and biases of the network, and the other with respect to the constant parameters of the potential function. The method provides three principal advantages. First, it obviates the problem of selecting the form of the functional dependence of the parameters upon the system's coordinates by employing a NN. If this network contains a sufficient number of neurons, it will automatically find something close to the best functional form. This is the case since Hornik et al., [Neural Networks 2, 359 (1989)] have shown that two-layer NNs with sigmoid transfer functions in the first hidden layer and linear functions in the output layer are universal approximators for analytic functions. Second, the entire fitting procedure is automated so that excellent fits are obtained rapidly with little human effort. Third, the method provides a procedure to avoid local minima in the multidimensional parameter hyperspace. As an illustrative example, the general method has been applied to the specific case of fitting the ab initio energies of Si(5) clusters that are observed in a molecular dynamics (MD) simulation of the machining of a silicon workpiece. The energies of the Si(5) configurations obtained in the MD calculations are computed using the B3LYP procedure with a 6-31G(**) basis set. The final ab initio database, which comprises the density functional theory energies of 10 202 Si(5) clusters, is fitted to an empirical Tersoff potential containing nine adjustable parameters, two of which are allowed to be the functions of the Si(5) configuration. The fitting error averaged over all 10 202 points is 0.0148 eV (1.43 kJ mol(-1)). This result is comparable to the accuracy achieved by more general fitting methods that do not rely on an assumed functional form for the potential surface.     

Evaluation of a new matrix-free laser desorption/ionization method through statistic studies: comparison of the DIAMS (desorption/ionization on self-assembled monolayer surface) method with the MALDI and TGFA-LDI techniques

This work demonstrates that the desorption/ionization on self-assembled monolayer surface (DIAMS) mass spectrometry, a recent matrix-free laser desorption/ionization (LDI) method based on an organic target plate, is as statistically repeatable and reproducible as matrix assisted laser desorption ionization (MALDI) and thin gold film-assisted laser desorption/ionization (TGFA-LDI) mass spectrometries. On lipophilic DIAMS of target plates with a mixture of glycerides, repeatability/reproducibility has been estimated at 15 and 30% and the relative detection limit has been evaluated at 0.3 and 3 pmol, with and without NaI respectively. Salicylic acid and its d(6)-isomer analysis confirm the applicability of the DIAMS method in the detection of compounds of low molecular weight.     

Structural and spectroscopic characterization of copper(II) complexes of a new bisamide functionalized imidazole tripod and evidence for the formation of a mononuclear end-on Cu-OOH species

A new polyimidazole tripod N,N-bis((1-methyl-4-pivalamidoimidazol-2-yl)methyl)-N'-((1-methylimidazol-2-yl)methyl)amine (L2) has been synthesized and shown to form intramolecular hydrogen bonds with different axial ligands bonded to Cu(II) in the solid state. The same hydrogen-bonding property of L2 appears responsible for the stabilization of a Cu(II)-OOH species in solution. The crystal structures of L2 and three of its Cu(II) complexes are reported. The [Cu(L2)X]ClO4 complexes, 4-6 (X- = Cl-, OH-, or N3-) have distorted trigonal bipyramidal geometries in the solid state and have been characterized further by UV-vis absorption, electron paramagnetic resonance (EPR) spectroscopy, and cyclic voltammetry. The reaction of [Cu(L2)OH](ClO4) (5) with H2O2 and tert-butyl hydroperoxide in methanol generates [Cu(L2)OOH](ClO4) (7) and [Cu(L2)OO(t)Bu](ClO4) (8) which have been characterized by different spectroscopic methods. The compound [Cu(L2)OO(t)Bu]+ displays a band at 395 nm (epsilon = 950 M(-1) cm(-1)) assigned to an alkylperoxo pi*(sigma) --> Cu ligand-to-metal charge transfer (LMCT) transition, while [Cu(L2)OOH]+ displays a peroxo pi*(sigma) --> Cu charge-transfer transition at 365 nm with epsilon = 1300 M(-1) cm(-1), a mass ion at m/z 593.4, and nu(O-O) stretch (resonance Raman) at 854 cm(-1) that shifts to lower energy by 46 cm(-1) upon 18O substitution.     

High-spin to low-spin relaxation kinetics in the [Fe(TRIM)2]Cl2 complex

A quasi-quantitative photo-induced low-spin (LS)-->high-spin (HS) conversion of FeII ions has been observed in the [Fe(TRIM)2]Cl2 complex by irradiating the sample with blue light (488 nm) at 10 K. The time dependence of the HS-->LS relaxation has been studied between 10 K and 44 K by means of magnetic susceptibility measurements. These relaxation curves could be satisfactorily fitted by mono-exponential decays including tunnelling effect except for temperatures below 30 K. The introduction of a distribution of vibrational frequencies into this model improved significantly the fits in the low-temperature range and gave a good agreement with the experimental data in the whole temperature range suggesting a multi-rate relaxation process in this complex.     

Photoionization dynamics in pure helium droplets

The photoionization and photoelectron spectroscopy of pure He droplets were investigated at photon energies between 24.6 eV (the ionization energy of He) and 28.0 eV. Time-of-flight mass spectra and photoelectron images were obtained at a series of molecular beam source temperatures and pressures to assess the effect of droplet size on the photoionization dynamics. At source temperatures below 16 K, where there is significant production of clusters with more than 10(4) atoms, the photoelectron images are dominated by fast electrons produced via direct ionization, with a small contribution from very slow electrons with kinetic energies below 1 meV arising from an indirect mechanism. The fast photoelectrons from the droplets have as much as 0.5 eV more kinetic energy than those from atomic He at the same photon energy. This result is interpreted and simulated within the context of a "dimer model", in which one assumes vertical ionization from two nearest-neighbor He atoms to the attractive region of the He2+ potential energy curve. Possible mechanisms for the slow electrons, which were also seen at energies below IE(He), are discussed, including vibrational autoionizaton of Rydberg states comprising an electron weakly bound to the surface of a large HeN+ core.     

Spectroscopic and electrochemical characterization of an aqua ligand exchange and oxidatively induced deprotonation in diiron complexes

Reaction of the unsymmetrical phenol ligand 2-((bis(2-pyridylmethyl)amino)methyl)-6-(((2-pyridylmethyl)benzylamino)methyl)-4-methylphenol (HL-Bn) or its 2,6-dichlorobenzyl analogue (HL-BnCl(2)) with Fe(H(2)O)(6)(ClO(4))(2) in the presence of disodium m-phenylenedipropionate (Na(2)(mpdp)) followed by exposure to atmosphere affords the diiron(II,III) complexes [Fe(2)(L-Bn)(mpdp)(H(2)O)](ClO(4))(2) and [Fe(2)(L-BnCl(2))(mpdp)(CH(3)OH)](ClO(4))(2), respectively. The latter complex has been characterized by X-ray crystallography. It crystallizes in the monoclinic system, space group P2(1)/n, with a = 13.3095(14) A, b = 20.1073(19) A, c = 19.4997(19) A, alpha = 90 degrees, beta = 94.471(2) degrees, gamma = 90 degrees, V = 5202.6(9) A(3), and Z = 4. The structure of the compound is very similar to that of [Fe(2)(L-Bn)(mpdp)(H(2)O)](BPh(4))(2) determined earlier, except for the replacement of a water by a methanol on the ferrous site. Magnetic measurements of [Fe(2)(L-Bn)(mpdp)(H(2)O)](BPh(4))(2) reveal that the two high-spin Fe ions are moderately antiferromagnetically coupled (J = -3.2(2) cm(-)(1)). Upon dissolution in acetonitrile the terminal ligand on the ferrous site is replaced by a solvent molecule. The acetonitrile-water exchange has been investigated by various spectroscopic techniques (UV-visible, NMR, M?ssbauer) and electrochemistry. The substitution of acetonitrile by water is clearly evidenced by M?ssbauer spectroscopy by a reduction of the quadrupole splitting value from 3.14 to 2.41 mm/s. In addition, it causes a 210 mV downshift of the oxidation potential of the ferrous site and a similar reduction of the stability domain of the mixed-valence state. Exhaustive electrolysis of a solution of [Fe(2)(L-Bn)(mpdp)(H(2)O)](2+) shows that the aqua diferric species is not stable and undergoes a chemical reaction which can be partly reversed by reduction to the mixed-valent state. This and other electrochemical observations suggest that upon oxidation of the diiron center to the diferric state the aqua ligand is deprotonated to a hydroxo. This hypothesis is supported by M?ssbauer spectroscopy. Indeed, this species possesses a large quadrupole splitting value (DeltaE(Q) >or= 1.0 mm.s(-)(1)) similar to that of analogous complexes with a terminal phenolate ligand. This study illustrates the drastic effects of aqua ligand exchange and deprotonation on the electronic structure and redox potentials of diiron centers.     

Theoretical and experimental studies on the carbon-nanotube surface oxidation by nitric acid: interplay between functionalization and vacancy enlargement

The nitric acid oxidation of multiwalled carbon nanotubes leading to surface carboxylic groups has been investigated both experimentally and theoretically. The experimental results show that such a reaction involves the initial rapid formation of carbonyl groups, which are then transformed into phenol or carboxylic groups. At room temperature, this reaction takes place on the most reactive carbon atoms. At higher temperatures a different mechanism would operate, as evidenced by the difference in activation energies. Experimental data can be partially related to first-principles calculations, showing a multistep functionalization mechanism. The theoretical aspects of the present article have led us to propose the most efficient pathway leading to carboxylic acid functional groups on the surface. Starting from mono-vacancies, it ends up with the synergistic formation of dangling -COOH groups and the enlargement of the vacancies.