One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model

We consider the Skyrme model using the explicit parameterization of the rotation group through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of is . We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces .     

Multiresolution Analysis and Radon Measures on a Locally Compact Abelian Group

A multiresolution analysis is defined in a class of locally compact abelian groups G. It is shown that the spaces of integrable functions and the complex Radon measures M(G) admit a simple characterization in terms of this multiresolution analysis.     

Experimental and theoretical study of the structure of N,N-dimethyl-4-nitroaniline derivatives as model compounds for non-linear optical organic materials

Molecular and crystal structure of a series of derivatives of N,N-dimethyl-4-nitroaniline has been studied by both X-ray diffraction method and high-level ab initio calculations. According to these data, the dimethylamino groups were found to have a trigonal-pyramidal configuration and are considerably turned with respect to the ring plane in all molecules having a substituent in the ortho-position; on the contrary, this group is planar in the meta-substituted molecules. Topological analysis of the electron density function for all molecules studied within the framework of Bader's ‘atoms in molecules’ (AIM) theory revealed that introduction of a substituent into the ortho- or meta-position of the ring results in increasing of the contribution of the resonance forms different from the quinoid one. Contribution of the latter form is predominant for the structure of N,N-dimethyl-4-nitroaniline (1). Topological analysis of the electron density distribution was used to explain a decreasing of the molecular hyperpolarisabilites of the ortho- and meta-substituted compounds as compared with those for 1.     

OCS,CO2,N2O与烯、炔烃之间π…π作用的电子密度拓扑研究

采用MP2/aug-cc-pVDZ方法对氧硫化碳(OCS)、二氧化碳(CO2)、一氧化二氮(N2O)与乙烯(C2H4)、乙炔(C2H2)、2-丁炔(C4H6)之间形成的平行构型复合物中的分子间相互作用进行了理论研究.复合物的相互作用能按照B…C2H4B…C2H2>B…C4H6(B=OCS,CO2,N2O)的顺序依次减小.采用电子密度拓扑分析理论方法,讨论了复合物中π…π作用的成键特性.电子密度拓扑分析表明复合物中形成了弱的分子间相互作用,且以静电作用为主;π电子密度分子图与全电子密度分子图中键径方向是一致的,说明π…π作用在本文所讨论的体系中起着很重要的作用.NBO分析表明净电荷迁移从电子给体C2H4,C2H2,C4H6到电子受体OCS,CO2,N2O,迁移数按照B…C2H4相似文献   

A Combined Experimental and Theoretical Electron Density Study of Intra‐ and Intermolecular Interactions in Thiourea S,S‐Dioxide

The thiourea S,S‐dioxide molecule is recognized as a zwitterion with a high dipole moment and an unusually long C? S bond. The molecule has a most interesting set of intermolecular interactions in the crystalline state—a relatively strong O???H? N hydrogen bond and very weak intermolecular C???S and N???O interactions. The molecule has C_s symmetry, and each oxygen atom is hydrogen‐bonded to two hydrogen atoms with O???H? N distances of 2.837 and 2.826 Å and angles of 176.61 and 158.38°. The electron density distribution is obtained both from Xray diffraction data at 110 K and from a periodic density functional theory (DFT) calculation. Bond characterization is made in terms of the analysis of topological properties. The covalent characters of the C? N, N? H, C? S, and S? O bonds are apparent, and the agreement on the topological properties between experiment and theory is adequate. The features of the Laplacian distributions, bond paths, and atomic domains are comparable. In a systematic approach, DFT calculations are performed based on a monomer, a dimer, a heptamer, and a crystal to see the effect on the electron density distribution due to the intermolecular interactions. The dipole moment of the molecule is enhanced in the solid state. The typical values of ρ_b and H_b of the hydrogen bonds and weak intermolecular C???S and N???O interactions are given. All the interactions are verified by the location of the bond critical point and its associated topological properties. The isovalue surface of Laplacian charge density and the detailed atomic graph around each atomic site reveal the shape of the valence‐shell charge concentration and provide a reasonable interpretation of the bonding of each atom.     

On a new semi‐empirical electrotopological index for QSRR models

A new semi‐empirical electrotopological index, I_SET, for quantitative structure–retention relationships (QSRR) models was developed based on the refinement of the previously published semi‐empirical topological index, I_ET. We demonstrate that the values of C_i fragments that were firstly attributed from the experimental chromatographic retention and theoretical deductions have an excellent relationship with the net atomic charge of the carbon atoms. Thus, the values attributed to the vertices in the hydrogen‐suppressed graph of carbon atoms (C_i) are calculated from the correlation of the net atomic charge in each carbon atom, which is obtained from quantum chemical semi‐empirical calculations, and the C_i fragments for primary, secondary, tertiary and quaternary carbon atoms (1.0, 0.9, 0.8 and 0.7, respectively) obtained from the experimental values. This shows that I_ET encoded this quantum physical reality and that it is possible to calculate a new I_SET (the semi‐empirical electrotopological index) through the net atomic charge values obtained from a Mulliken population analysis using the semi‐empirical AM1 method and their correlation with the values attributed to the different types of carbon atoms. This demonstrates that the I_SET encodes information on the charge distribution of the solute on which dispersive and electrostatic interactions between the solute (alkanes and alkenes) and the stationary phase strongly depend. Thus, this new method can be considered as an initial step towards forthcoming QSRR/QSAR studies. Copyright © 2008 John Wiley & Sons, Ltd.     

HNCX (X＝O,S)和F反应机理及电子密度拓扑分析

采用G3B3//B3LYP/6-311＋＋G(d,p)方法研究了HNCX (X＝O, S)与F原子的反应机理. 找到了六条可能的反应通道, 计算结果表明, 该反应的主产物为HF＋NCX (X＝O, S). 对反应过程进行了电子密度拓扑分析, 讨论了反应过程中化学键的断裂和生成规律, 找到了HNCX (X＝O, S)和F反应过程中的T型结构过渡态、三元环状结构过渡区和四元环状结构过渡区.     

化合物结构／性质相关的研究／拓扑指数法（Ⅰ）

本文提出一种新的拓扑指数－ＥＡ系列指数，它是从表示分子图形的邻接矩阵出发，结合图形中顶点的度构造成ＥＡ矩阵，计算ＥＡ矩阵的本征值，求出本征值绝对值和指数ＥＡΣ及本征值绝对值最大值指数ＥＡｍａｘ，实验表明，ＥＡ系列指数具有良好的唯一性和相关性。     

Unexpected Room‐Temperature Ferromagnetism in Nanostructured Bi2Te3

There is an urgent need for the development in the field of the magnetism of topological insulators, owing to the necessity for the realization of the quantum anomalous Hall effect. Herein, we discuss experimentally fabricated nanostructured hierarchical architectures of the topological insulator Bi₂Te₃ without the introduction of any exotic magnetic dopants, in which intriguing room‐temperature ferromagnetism was identified. First‐principles calculations demonstrated that the intrinsic point defect with respect to the antisite Te site is responsible for the creation of a magnetic moment. Such a mechanism, which is different from that of a vacancy defect, provides new insights into the origins of magnetism. Our findings may pave the way for developing future Bi₂Te₃‐based dissipationless spintronics and fault‐tolerant quantum computation.