Cluster and periodic DFT calculations of adsorption and activation of CO2 on the Cu(hkl) surfaces

The adsorption behavior and thermal activation of carbon dioxide on the Cu(1 1 1), Cu(1 0 0), and Cu(1 1 0) surfaces have been investigated by means of density functional theory calculations and cluster models and periodic slabs. According to the cluster models, the optimized results indicate that the basis set of C and O atoms has a distinct effect on the adsorption energy, but an indistinct one on the equilibrium geometry. For the CO₂/Cu(hkl) adsorption systems studied here, the final structure of adsorbed CO₂ is near linear and the preferred modes for the adsorption of CO₂ onto the Cu(1 1 1), Cu(1 0 0), and Cu(1 1 0) surfaces are the side-on adsorption at the cross bridge site with an adsorption energy of 13.06 kJ/mol, the side-on adsorption at the short bridge site (13.54 kJ/mol), and the end-on adsorption on the on-top site with C–O bonds located along the short bridge site (26.01 kJ/mol), respectively. However, the calculated adsorption energies from periodic slabs are lower as compared to the experimental data as well as the cluster model data, indicating that the periodic slab approach of generalized gradient approximation in the density function theory may be not suitable to obtain quantitative information on the interaction of CO₂ with Cu(hkl) surfaces.     

Density functional theory investigation of CN on Cu(1 1 1), Ni(1 1 1) and Ni(1 0 0)

The adsorption of CN on Cu(1 1 1), Ni(1 1 1) and Ni(1 0 0) has been investigated using density functional theory (DFT). While experimental studies of CN on Cu(1 1 1) show the molecular axis to be essentially parallel to the surface, the normally-preferred DFT approach using the generalised gradient approximation (GGA) yields a lowest energy configuration with the C-N axis perpendicular to the surface, although calculations using the local density approximation (LDA) do indicate that the experimental geometry is energetically favoured. The same conclusions are found for CN on Ni(1 1 1); on both surfaces bonding through the N atom is always unfavourable, in contrast to some earlier published results of ab initio calculations for Ni(1 1 1)/CN and Ni(1 0 0)/CN. The different predictions of the GGA and LDA approaches may lie in subtly different relative energies of the CN 5σ and 1π orbitals, a situation somewhat similar to that for CO adsorbed on Pt(1 1 1) which has proved challenging for DFT calculations. On Ni(1 0 0) GGA calculations favour a lying-down species in a hollow site in a geometry rather similar to that found experimentally and in GGA calculations for CN on Ni(1 1 0).     

The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

石墨炉原子吸收光谱法直接测定血样中硒

用石墨炉原子吸收光谱法，以硝酸铜和硝酸铵为基体改进剂，塞曼效应扣背景，采用标准加入法可直接测定血样中硒，回收率为95％～105％，相对标准偏差为5．8％，检出限为96pg，测定结果准确可靠。     

Comparative studies of static dipole polarizabilities of ionic crystals on the basis of different self-consistent potentials

The static dipole polarizabilities, ^D , have been studied for the ions O^2–, F^–, Na⁺, Mg²⁺, Cl^–, K⁺ and Ca²⁺ in the crystals NaF, KF, NaCl, KC1, MgO and CaO. The starting zero-order wave functions have been generated using various exchange- and exchange-correlation potentials in order to study the effect of these potentials on ^D . The direct contribution to the dipole polarizability, _o ^D , has been determined by the uncoupled Hartree-Fock method. Self-consistency effects have been included by the geometric approximation. The crystal potential is incorporated using the Watson sphere model. Good agreement between theoretical and experimental results are found for those self-consistent potentials which exclude self-interaction.     

两种计算吸光光度法同时测定钙镁

研究了在pH10．5的硼砂-氢氧化钾缓冲溶液和乙醇的增敏作用条件下，偶氮氯膦Ⅰ与钙、镁的吸收特性，建立了多波长光度法同时测定钙和镁的方法。采用两种矩阵算法对试验数据进行处理，并对结果进行比较和分析。钙和镁含量在0～25μg／25ml范围内用计算法Ⅱ能得到准确结果。     

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.     

M-矩阵平方根的一类迭代法

矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.     

Molecular Structures from Density Functional Calculations with Simulated Annealing

The geometrical structure of any aggregate of atoms is one of its basic properties and, in principle, straightforward to predict. One chooses a structure, determines the total energy E of the system of electrons and ions, and repeats the calculation for all possible geometries. The ground state structure is that with the lowest energy. A quantum mechanical calculation of the exact wave function Ψ would lead to the total energy, but this is practicable only in very small molecules. Furthermore, the number of local minima in the energy surface increases dramatically with increasing molecular size. While traditional ab initio methods have had many impressive successes, these difficulties have meant that they have focused on systems with relatively few local minima, or have used experiment or experience to limit the range of geometries studied. On the other hand, calculations for much larger molecules and extended systems are often forced to use simplifying assumptions about the interatomic forces that limit their predictive capability. The approach described here avoids both of these extremes: Total energies of predictive value are calculated without using semi-empirical force laws, and the problem of multiple minima in the energy surface is addressed. The density functional formalism, with a local density approximation for the exchange-correlation energy, allows one to calculate the total energy for a given geometry in an efficient, if approximate, manner. Calculations for heavier elements are not significantly more difficult than for those in the first row and provide an ideal way to study bonding trends. When coupled with finite-temperature molecular dynamics, this formalism can avoid many of the energetically unfavorable minima in the energy surface. We show here that the method leads to surprising and exciting results.     

Effects of Strong Ion‐Pairing on the Electrochemical Reduction of Cyclooctatetraene in Tetrahydrofuran in the Presence of Lithium Ion. Peak Coalescence Does Not Imply Potential Inversion

The first study of the voltammetric reduction of cyclooctatetraene (COT) in tetrahydrofuran (THF) in the presence of lithium ion is reported. A single wave is observed at ?2.23 V vs. Ag/0.1 M AgNO₃. Density functional calculations have been carried out on a variety of COT/Li/THF species in order to clarify the nature and role of ion pairing in this system. The dominant species in solution are the COT/Li/(THF)₂ anion radical and the COT/Li₂/(THF)₄ dianion. Computer simulations have been carried out to further understand the effects of ion pairing on the reduction. The simulations show that coalescence of two waves into one can occur in the presence of strong ion pairing even when the second reduction potential is negative of the first.