Remarkable Size Effect on Photophysical and Nonlinear Optical Properties of All-Carboatomic Rings,Cyclo[18]carbon and Its Analogues

Inspired by recent experimental observation of molecular morphology and theoretical predictions of multiple properties of cyclo[18]carbon, we systematically studied the photophysical and nonlinear optical properties of cyclo[2N]carbons (N=3–15) allotropes through density functional theory. This work unveils the unusual optical properties of the sp-hybridized carbon rings with different sizes. The remarkable size dependence of the optical properties of these systems and their underlying nature are profoundly explored, and the relevance between aromaticity and optical properties are highlighted. The extrapolation curves fitted for energy level of frontier molecular orbitals, maximum absorption wavelength, and (hyper)polarizability of considered carbon rings are presented, which can be used to reliably predict corresponding properties for arbitrarily large carbon rings. The findings in this study will facilitate the exploration of potential application of cyclocarbons in the field of optical materials.     

2,2′‐Bipyridine‐Based Dendritic Structured Compounds for Second Harmonic Generation

Parallel alignment of dipolar electron‐donor–π‐bridge‐electron‐acceptor entities can strongly enhance their nonlinear optical properties. This favorable arrangement can be in principle achieved by linking these units covalently or through metal coordination. Four dipolar single‐strand chromophores decorated with a 5‐electron‐donor–5′‐electron‐acceptor‐modified 2,2′‐bipyridine functionality were synthesized. For two of these chromophores triple‐stranded dendritic structures were successfully formed. All of the compounds were characterized with respect to their linear and nonlinear optical properties. For the aldehyde derivatives an enhancement of the first hyperpolarizability of 4.5 rather than 3 was obtained when going from single to triple strands. Theoretical calculations with density functional theory suggest that interstrand transitions contribute to the optical properties of the dendritic structures.     

超实数系统及其一致连续问题

基于模型论的观点与方法介绍超实数系统的构造及其公理体系,以说明非标准分析.由于超实数系统是普通实数系统的一个真扩张,所以,实数系统中的一致连续问题可推广至超实数系统.     

A theoretical study of topomerization of imine systems: Inversion,rotation or mixed mechanisms?

The different mechanisms, rotation, inversion, or intermediate mechanism, by which occur the topomerization of imine systems R₂ CN X have been studied by applying ab initio, B3LYP, and MP2 methods. The effect of a wide variety of substituents R and X on the isomerization pathway have been examined by computing fully optimized structures of the ground and transition states (136 isomers belonging to different imine families were studied and more than 300 transition structures were determined at various levels of theory). Energy barriers have been also obtained and it was found that the groups R and X have a strong influence on the type of mechanism involved and the activation energies. Thus, and depending on the type of substituents, transition state structures related to the following kinds of processes were found: pure inversion, intermediate mechanisms, rotation, and enhanced rotation (hyper‐rotation). In turn, the corresponding activation energies range between very low (<10 kcal/mol) and extremely high (> 70 kcal/mol) values. A simple index that allows us to quantify the percentage of inversion or rotation mechanism is proposed. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

基于Fluent的超高压撞击流乳化喷嘴的优化分析

高压液体通过喷嘴加速,形成高速射流,与相反方向的另一股射流相互撞击,发生强烈的相互作用,产生强烈的径向和轴向湍流速度分量以及狭窄的高压高速湍流区,在此区域内,相间或液滴间的碰撞互磨产生的挤压力和剪切力使流体被细化。本文从液体连续相撞击流的两个特征：微观混合和压力波动入手,逐一分析了撞击速度与微观混合、压力波动的关系,得出了压力波动与撞击流速度乱U0成正比关系,微观混合与U^3 0成正比的规律。同时,用流体模拟软件Fluent对喷嘴的结构和尺寸进行优化,并得出最合理的喷嘴结构和尺寸。模拟认为：在相同压力下,采用矩形槽,出口孔径为0．2mm,槽的深度为0．27mm的结构时撞击速度达到最大,并通过实验验证了这一结论。     

Expansion of potential 1/r12 of c‐spherical harmonics

The expansion coefficient C^D_|L| of Coulomb potential 1/r₁₂ of atomic system in hyper‐spherical harmonics is derived and the explicit expression is given.     

Cell Tracking with Caged Xenon: Using Cryptophanes as MRI Reporters upon Cellular Internalization

Caged xenon has great potential in overcoming sensitivity limitations for solution‐state NMR detection of dilute molecules. However, no application of such a system as a magnetic resonance imaging (MRI) contrast agent has yet been performed with live cells. We demonstrate MRI localization of cells labeled with caged xenon in a packed‐bed bioreactor working under perfusion with hyperpolarized‐xenon‐saturated medium. Xenon hosts enable NMR/MRI experiments with switchable contrast and selectivity for cell‐associated versus unbound cages. We present MR images with 10³‐fold sensitivity enhancement for cell‐internalized, dual‐mode (fluorescence/MRI) xenon hosts at low micromolar concentrations. Our results illustrate the capability of functionalized xenon to act as a highly sensitive cell tracer for MRI detection even without signal averaging. The method will bridge the challenging gap for translation to in vivo studies for the optimization of targeted biosensors and their multiplexing applications.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.