A theoretical study of water adsorption on (10-10) and (0001) ZnO surfaces: molecular cluster, basis set and effective core potential dependence

The adsorption of water molecule and hydroxyl ions on the (10-10) and (0001) ZnO surfaces has been studied for (ZnO)₄, (ZnO)₅ and (ZnO)₆ cluster models. Different representations for the atomic basis sets and the effective core potential (ECP) approximations have been employed and the effects of cluster size, conformation and basis sets are analyzed and discussed.     

An investigation of the radial densities in the FeS5−4 cluster as calculated by the multiple scattering X α method

Multiple scattering Xα calculations on the FeS^5?₄ cluster are used to investigate the participation of the radial functions in the bonding mechanisms of the cluster. The total electron density at the iron nucleus is used to interpret Mössbauer isomer shift data and determine the iron isomer shift calibration constant.     

The hopf algebra of linearly recursive sequences

We explain how the space of linearly recursive sequences over a field can be considered as a Hopf algebra. The algebra structure is that of divided-power sequences, so we concentrate on the perhaps lesser-known coalgebra (diagonalization) structure. Such a sequence satisfies a minimal recursive relation, whose solution space is the subcoalgebra generated by the sequence. We discuss possible bases for the solution space from the point of view of diagonalization. In particular, we give an algorithm for diagonalizing a sequence in terms of the basis of the coalgebra it generates formed by its images under the difference-operator shift. The computation involves inverting the Hankel matrix of the sequence. We stress the classical connection (say over the real or complex numbers) with formal power series and the theory of linear homogeneous ordinary differential equations. It is hoped that this exposition will encourage the use of Hopf algebraic ideas in the study of certain combinatorial areas of mathematics.     

Asymmetric 1,4-hydrosilylations of alpha,beta-unsaturated esters

Complexing catalytic amounts of CuH with a nonracemic JOSIPHOS or SEGPHOS ligand, together with stoichiometric PMHS, leads to exceedingly efficient and highly enantioselective 1,4-reductions of beta,beta-disubstituted enoates and lactones. An unprecedented substrate-to-ligand ratio of 7700:1 for this type of reaction is documented.     

An electron transfer mechanism of O4 formation

A resonating valence bond electron transfer mechanism of combining two O₂ molecules to form an O₄ molecule is presented. The predicted molecular states of the reaction path D_∞h→C_2v→D_2h are supported by the present ab initio molecular orbital calculations. The CASPT2 BSSE calculations yield a stable diamagnetic D_2h O₄ molecule with a very weak chemical bond between the monomers, in good agreement with experiments. A low activation barrier energy of 26 cal/mol for the O₄ formation is found.     

Different origins of green-light photoluminescence emission in structurally ordered and disordered powders of calcium molybdate

A strong greenish-light photoluminescence (PL) emission was measured at room temperature for disordered and ordered powders of CaMoO4 prepared by the polymeric precursor method. The structural evolution from disordered to ordered powders was accompanied by XRD, Raman spectroscopy, and TEM imagery. High-level quantum mechanical calculations in the density functional framework were used to interpret the formation of the structural defects of disorder powders in terms of band diagram and density of states. Complex cluster vacancies [MoO3 x V(O(z))] and [CaO7 x V(O(z))] (where V(O(z)) = V(O(X)), V(O(*)), V(O(**))) were suggested to be responsible to the appearance of new states shallow and deeply inserted in the band gap. These defects give rise to the PL in disordered powders. The natural PL emission of ordered CaMoO4 was attributed to an intrinsic slight distortion of the [MoO4] tetrahedral in the short range.     

The use of acids,niobium oxide,and zeolite catalysts for esterification reactions

We have evaluated the influence of alcohol/fatty acid molar ratio (methanol or ethanol), water and catalyst concentrations and temperature by the esterification of palm fatty acids by heterogeneous acid catalysts (varying types, forms, and particle size). Polynaphtalene sulfonic acid (PSA) and niobium oxide (Nb₂O₅) presented better performance than zeolite catalysts. Reaction with methanol presented higher conversion than with ethanol. The experimental design showed that the most relevant variable is the catalyst concentration and all interactions become important in process. A heterogeneous kinetic model was proposed and applied to experimental data. One of the models was adequate for methanol reaction, whereas the homogeneous model was more appropriate for ethanol reaction. Copyright © 2009 John Wiley & Sons, Ltd.     

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.