A Modified Perturbation Technique Depending Upon an Artificial Parameter

In this paper, a modified perturbation method is proposed to search for analytical solutions of nonlinear oscillators without possible small parameters. An artificial perturbation equation is carefully constructed by embedding an artificial parameter, which is used as expanding parameter. It reveals that various traditional perturbation techniques can be powerfully applied in this theory. Some examples, such as the Duffing equation and the van der Pol equation, are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weak nonlinear systems, but also for strongly nonlinear systems. In applying the new method, some special techniques have been emphasized for different problems.     

Van der Waals Radii of Hydrogen in Gas-Phase and Condensed Molecules

Van der Waalsa radii of hydrogen in the different gas-phase and condensed molecules are determined and shown that a value of the van der Waals radius depends on the effective charge of the H atom. Is described also the van der Waals anisotropy of H in some molecules.     

Global Coupling of an Interface Problem in an Activator-inhibitor System

An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling.     

Synthesis and crystal structure of 5,7-diallyloxy-4-methylcoumarin

The title compound, 5,7-diallyloxy-4-methyl-2H-[1]-benzopyran-2-one, (C₁₆H₁₆O₄), was prepared by condensation of ethyl acetoacetate with phloroglucinol followed by allylation of the 5,7-dihydroxy-4-methylcoumarin thus obtained. The compound crystallizes into monoclinic space group P2₁/c with unit cell parameters a = 7.531(1) Å, b = 22.596(4) Å, c = 8.090(1) Å, β = 92.74(2)°, Z = 4. The crystal structure was solved by direct methods using single crystal X-ray diffraction data and refined to R = 0.0596 for 2166 observed reflections. The coumarin moiety is perfectly planar, with dihedral angle between the two fused rings of 0.46(5)°. The two allyloxy groups have different behaviour, one of them being disordered. Molecules form chains of weak C–HO and C–Hπ hydrogen bonds.     

Effects of van Hove Singularities on Transport of Quantum Dot Systems in Kondo Regime

In the present paper, we study the effect of van Hove singularities of conduction electron on the transport of a single quantum dot system in the Kondo regime. By using both the equation-of-motion and the noncrossing approximation techniques, we show that the corrections caused by these singularities are actually minor. It can be explained by observing that the singularities in the equations, which determine the electronic DOS on the dot, are integrable. Furthermore, we find that, although each line width function is divergent at van Hove singular points, the total divergence is canceled out in the final formula to calculate the current through the system. Therefore, as far as the qualitative properties of the system is concerned, these singularities can be ignored and the wide-band approximation can be safely used in calculation.     

理想气体与范氏气体在任意准静态过程中的摩尔热容

导出了理想气体与范氏气体在任意准静态过程中的摩尔热容公式。     

Modeling chemical reactions on surfaces: The roles of chemical bonding and van der Waals interactions

Chemical reactions on surfaces play central roles in heterogeneous catalysis, and most reactions involve the formation and/or the cleavage of bonds. At present, density functional theory (DFT) has become the workhorse for computational investigation of reaction mechanisms, but its predictive power has been severely limited by the lack of appropriate exchange-correlation functionals. Here, we show that there are many cases where the chemical bonding and van der Waals (vdW) interactions both play a key role in chemical reactions on surfaces. After briefly introducing some DFT methods and basic theory in chemical reactions, we first demonstrate that DFT can help to understand the mechanisms of “classic” reactions that mainly dominated by covalent bonding and vdW forces, as exemplified in electrocatalytic reduction of CO₂ and the fabrication of 2D materials on metal substrates. We next show that DFT calculations can help to uncover the tautomerization reactions of molecules on metal surfaces, wherein the hydrogen bonding and vdW forces would largely affect the reaction process. More importantly, we show that in some cases, the vdW interactions can become the decisive effect that determines the adsorption configuration, energy hierarchy, and the potential-energy surface of chemical reactions, yielding distinct pathways and products. Additionally, we highlight the importance of more realistic conditions, such as surface defects, finite coverage, and temperature effects, in accurate modeling of chemical reactions. Finally, we summarize some challenges in modeling catalysis, which include many-body dispersive correction, strong correlation effect, and non-adiabatic approximations.     

Multiple surface conduction channels via topological insulator and amorphous insulator thin film multi-stacks

Multi-channel Bi₂Se₃ thin films were grown by combining molecular beam epitaxy and atomic layer deposition. High-resolution transmission electron microscope images showed that c-axis oriented Bi₂Se₃ grew on amorphous Al₂O₃ even after multiple stacking. While the surface morphology degraded for the upper layers, each layer was electrically similar. The electrical transport measurements showed that the weak anti-localization effect was quantitatively enhanced upon increasing the number of Bi₂Se₃ channels. Our results provide a promising approach to exploit diverse combinations of layered topological insulator films vertically stacked with amorphous insulator films.     

Surface chemistry and catalysis of oxide model catalysts from single crystals to nanocrystals

Fundamental understandings of surface chemistry and catalysis of solid catalysts are of great importance for the developments of efficient catalysts and corresponding catalytic processes, but have been remaining as a challenge due to the complex nature of heterogeneous catalysis. Model catalysts approach based on catalytic materials with uniform and well-defined surface structures is an effective strategy. Single crystals-based model catalysts have been successfully used for surface chemistry studies of solid catalysts, but encounter the so-called “materials gap” and “pressure gap” when applied for catalysis studies of solid catalysts. Recently catalytic nanocrystals with uniform and well-defined surface structures have emerged as a novel type of model catalysts whose surface chemistry and catalysis can be studied under the same operational reaction condition as working powder catalysts, and they are recognized as a novel type of model catalysts that can bridge the “materials gap” and “pressure gap” between single crystals-based model catalysts and powder catalysts. Herein we review recent progress of surface chemistry and catalysis of important oxide catalysts including CeO₂, TiO₂ and Cu₂O acquired by model catalysts from single crystals to nanocrystals with an aim at summarizing the commonalities and discussing the differences among model catalysts with complexities at different levels. Firstly, the complex nature of surface chemistry and catalysis of solid catalysts is briefly introduced. In the following sections, the model catalysts approach is described and surface chemistry and catalysis of CeO₂, TiO₂ and Cu₂O single crystal and nanocrystal model catalysts are reviewed. Finally, concluding remarks and future prospects are given on a comprehensive approach of model catalysts from single crystals to nanocrystals for the investigations of surface chemistry and catalysis of powder catalysts approaching the working conditions as closely as possible.     

An accurate three-dimensional potential energy surface for the He-Na<Subscript>2</Subscript> complex

An accurate three-dimensional potential energy surface (PES) for the He-Na₂ van der Waals complex was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connected triple (CCSD(T)) level of theory. A mixed basis set, aug-cc-pVQZ for the He atom and cc-pCVQZ for the sodium atom, and an additional (3s3p2d1f) set of midbond functions were used. The computed interaction energies in 819 configurations were fitted to a 96-parameter analytic potential model by least squares fitting. The PES has two shallow wells corresponding to the T-shaped structure and the linear configuration, which are located at 12.5a ₀ and 14 a ₀ with depths of 1.769 and 1.684 cm⁻¹, respectively. The who potential energy surface exhibits weak anisotropy. Based on the fitted PES, state-to-state differential cross sections were calculated. Supported by the Natural Science Foundation of Anhui Educational Committee (Grant No. 2006kj072A) and the Natural Science Foundation of Anhui Province (Grant No. 070416236)