Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Metal-free phthalocyanine single crystal: Solvothermal synthesis and near-infrared electroluminescence

A metal-free purple H₂Pc single crystal was synthesized by a facile solvothermal method, and its solubility and near-infrared (NIR) optical properties were also investigated due to its potential applications as a light-emitting layer for OLEDs. The H₂Pc single crystal is insoluble in 1-chlorine naphthalene and other organic solvents. It gives a wide absorption in the range from 620 nm to 679 nm and a wide emission in near 922 nm. As an active light-emitting layer, H₂Pc was employed to fabricate electroluminescent (EL) devices with a structure of ITO/NPB (30 nm)/Alq₃:H₂Pc (30 nm)/BCP (20 nm)/Alq₃ (20 nm)/Al. The emission center is at 936 nm when the H₂Pc doping concentration is 20 wt%. The doping concentration strongly governs the emission intensity. When doping concentration decreases from 10 wt% to 1 wt%, the emission intensity remarkably fades, and simultaneously the emission center undergoes a blue shift.     

Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function

Results in Mathematics - In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial n! and the gamma function Γ in terms of the tri-gamma function...     

Graphdiyne-actinyl complexes as potential catalytic materials: A DFT perspective from their structural,bonding, electronic and redox properties

Versatile graphdiyne (GDY) substrate has been modified by numerous transition metals and resulting composites showed excellent photo/electro-catalytic performance. However, GDY materials modified by actinides that are stockpiled waste product due to large-scale use in nuclear industry, are particularly scarce and remains great challenge. To deeply understand the structural properties, GDY complexating actinyl (An^mO₂)ⁿ⁺ (An = U, Np, Pu; m = VI, V) species with its atomistic pore was investigated by relativistic density functional theory (DFT). The GDY pore was found suitable to hold actinyl species, by forming organometallic AnC dative bonds. This chemical coupling interaction was further confirmed by quantum theory of atoms-in-molecule and electronic structure calculations. The GDY-uranyl(V), for instance, shows a π(UC) bonding HOMO, which is anticipated to improve electron transfer between ligand and metal. Orbital structures and compositions of complexes suggest their implication towards catalysis, which were further corroborated by calculations on redox potentials of GDY-actinyl complexes. Hence, our results show the potential applications of GDY complexating actinyl species towards novel catalytic surfaces.     

粉末晶体(ZrO2)x(Bi2O3)1-x(x=1.0, 0.97) 晶体结构分析

为了确定ZrO2和(ZrO2)0.97(Bi2O3)0.03的晶体结构和原子热振动各向同性温度因子B，对该粉末晶体进行X射线衍射实验，建立了晶体结构模型，进行晶体结构分析。首先，采用共沉淀法和高温固相烧结法制备了纳米氧化锆ZrO2和(ZrO2)0.97(Bi2O3)0.03粉末晶体，接着，使用X射线测试仪对两种样品进行了衍射实验（XRD），利用Rietveld 精修方法的 RIETAN-2000程序对所得实验结果进行了晶体结构分析，获得了晶体结构参量和原子热振动各向同性温度因子B。通过Maximum Entropy Method（MEM）解析得到了粉末晶体(ZrO2)x(Bi2O3)1-x(x=1.0，0.97)的等高电子密度分布可视化图谱。结果表明，(ZrO2)0.97(Bi2O3)0.03的晶胞体积比ZrO2的晶胞体积大分别为140.6850 Å3和140.5637Å3；ZrO2晶体的原子热振动各向同性温度因子B(Zr)、BO(1)、BO(2)和 B（Bi）分别为0.690、0.269、 0.178 和 0 Å2，(ZrO2)0.97(Bi2O3)0.03晶体的分别为0.460 、0.583 、0.121 和0.581 Å2。 确定了(ZrO2)0.97(Bi2O3)0.03的晶体结构属于单斜晶系，实现了等高电子密度分布三维（3D）和二维（2D）的可视化，进一步确定了晶体结构和原子位置。     

基于Rietveld精修方法解析Bi2O3的原子热振动

三氧化二铋(Bi₂O₃)是氧离子导电体,为了获得它的原子热振动各向同性温度因子,对该粉末晶体进行X射线衍射实验,建立了晶体结构模型,利用Rietveld 精修方法的RIETAN-2000 程序对所得实验结果进行了晶体结构精修,通过最大熵方法(MEM)解析得到了粉末晶体的等高电子密度分布三维(3D) 和二维(2D)可视化图谱。结果表明,各原子Bi₍₁₎、Bi₍₂₎、O₍₁₎、O₍₂₎和O₍₃₎的原子热振动各向同性温度因子分别为0.004 938 nm²、0.004 174 nm²、0.007 344 nm²、0.007 462 nm²、和0.007 857 nm²,等高电子密度分布的可视化,进一步验证了晶体结构模型和原子位置的准确性,这些参数对研究晶体材料的热性质具有一定参考意义。     

Comparative Analysis of Hydration Layer Reorientation Dynamics of Antifreeze Protein and Protein Cytochrome P450

Antifreeze proteins (AFPs) inhibit ice recrystallization by a mechanism remaining largely elusive. Dynamics of AFPs' hydration water and its involvement in the antifreeze activity have not been identified conclusively. We herein, by simulation and theory, examined the water reorientation dynamics in the first hydration layer of an AFP from the spruce budworm, Choristoneura fumiferana, compared with a protein cytochrome P450 (CYP). The increase of potential acceptor water molecules around donor water molecules leads to the acceleration of hydrogen bond exchange between water molecules. Therefore, the jump reorientation of water molecules around the AFP active region is accelerated. Due to the mutual coupling and excitation of hydrogen bond exchange, with the acceleration of hydrogen bond exchange, the rearrangement of the hydrogen bond network and the frame reorientation of water are accelerated. Therefore, the water reorientation dynamics of AFP is faster than that of CYP. The results of this study provide a new physical image of antifreeze protein and a new understanding of the antifreeze mechanism of antifreeze proteins.