Polyhedral symmetry and quantum mechanics

A thorough study of regular and quasi-regular polyhedra shows that the symmetries of these polyhedra identically describe the quantization of orbital angular momentum, of spin, and of total angular momentum, a fact which permits one to assign quantum states at the vertices of these polyhedra assumed as the average particle positions. Furthermore, if the particles are fermions, their wave function is anti-symmetric and its maxima are identically the same as those of repulsive particles, e.g., on a sphere like the spherical shape of closed shells, which implies equilibrium of these particles having average positions at the aforementioned maxima. Such equilibria on a sphere are solely satisfied at the vertices of regular and quasi-regular polyhedra which can be associated with the most probable forms of shells both in Nuclear Physics and in Atomic Cluster Physics when the constituent atoms possess half integer spins. If the average sizes of the constituent particles are known, then the average sizes of the resulting shells become known as well. This association of Symmetry with Quantum Mechanics leads to many applications and excellent results.

Notes on Quantitative Structure-Properties Relationships （QSPR） Part Four： Quantum Multimolecular Polyhedra, Collective Vectors, Quantum Similarity, and Quantum QSPR Fundamental Equation

The nature and origin of a fundamental quantum QSPR （QQSPR） equation are discussed. In principle, as any molecular structure can be associated to quantum mechanical density functions （DF）, a molecular set can be reconstructed as a quantum multimolecular polyhedron （QMP）, whose vertices are formed by each molecular DF. According to QQSPR theory, complicated kinds of molecular properties, like biological activity or toxicity, of molecular sets can be calculated via the quantum expectation value of an approximate Hermitian operator, which can be evaluated with the geometrical information contained in the attached QMP via quantum similarity matrices. Practical ways of solving the QQSPR problem from the point of view of QMP geometrical structure are provided. Such a development results into a powerful algorithm, which can be implemented within molecular design as an alternative to the current classical QSPR procedures.

Enhancing photoresponsiveness of metal-organic polyhedra by modifying microenvironment

Photoresponsiveness of materials is critical to their tunability and efficiency in terminal applications.Photoresponsive metal-organic polyhedra(PMOPs)feature intrinsic pores and remote controllability,but aggregation of PMOPs in solid state hampers their photoresponsiveness seriously.Herein,we report the construction of a new PMOP(Cu_(24)(C_(16)H_(12)N_(2)O_(4))_(12)(C_(18)H_(22)O_(5))12,denoted as MOP-PR-LA),where long alkyl(LA)chains act as the intermolecular poles,propping against adjacent PMOP molecules to create individual microenvironment benefiting the isomerization of photoresponsive(PR)moieties.Upon ultraviolet(UV)-and visible-light irradiation,MOP-PR-LA is much easier to isomerize than the counterpart MOP-PR without LA.For propylene adsorption,MOP-PR has a low change of adsorption capacity(9.9%),while that of MOP-PR-LA reaches 58.6%.Density functional theory calculations revealed that PR in the cis state has a negative effect on adsorption,while the trans state of PR favors adsorption.This work might open an avenue for the construction of photoresponsive materials with high responsiveness and controllability.

Carbon polyhedra encapsulated Si derived from Co-Mo bimetal MOFs as anode materials for lithium-ion batteries

Silicon(Si)holds promise as an anode material for lithium-ion batteries(LIBs)as it is widely avail-able and characterized by high specific capacity and suitable working potential.However,the relatively low electrical conductivity of Si and the significantly high extent of volume expansion realized dur-ing lithiation hinder its practical application.We prepared N-doped carbon polyhedral micro cage en-capsulated Si nanoparticles derived from Co-Mo bimetal metal-organic framework(MOFs)(denoted as Si/CoMo@NCP)and explored their lithium storage performance as anode materials to address these prob-lems.The Si/CoMo@NCP anode exhibited a high reversible lithium storage capacity(1013 mAh g^(−1)at 0.5 A g^(−1)after 100 cycles),stable cycle performance(745 mAh g^(−1)at 1 A g^(−1)after 400 cycles),and excellent rate performance(723 mAh g^(−1)at 2 A g^(−1)).Also,the constructed the full-cell NCM 811//Si/CoMo@NCP exhibited well reversible capacity.The excellent electrochemical performances of Si/CoMo@NCP were at-tributed to two unique properties.The encapsulation of NCP with doped nitrogen and porous structural carbon improves the electrical conductivity and cycling stability of the molecules.The introductions of metallic cobalt and its oxides help to improve the rate capability and lithiation capacity of the materials following multi-electron reaction mechanisms.

Metal-organic framework-derived, Zn-doped porous carbon polyhedra with enhanced activity as bifunctional catalysts for rechargeable zinc-air batteries

Zinc-air batteries have recently attracted considerable interest owing to the larger storage capacity and lower cost compared to their lithium-ion counterparts. Electrode catalysts for the oxygen reduction reaction （ORR） and oxygen evolution reaction （OER） play a critical role in the operation of rechargeable zinc-air batteries. Herein, we report a simple and scalable strategy to fabricate porous carbon polyhedra using Zn-doped Co-based zeolitic imidazolate frameworks （ZnCo-ZIFs） as precursors. Strikingly, Zn doping leads to smaller Co nanoparticles and higher nitrogen content, which in turn enhances the ORR and OER activities of the obtained porous carbon polyhedra. The synergistic effect of the N-doped carbon and cobalt nanoparticles in the composite, the improved conductivity resulting from the high graphitization of carbon, and the large surface area of the porous polyhedral structure resulted in porous carbon polyhedra with excellent ORR and OER electrocatalytic activity in alkaline media. More importantly, air cathodes based on the optimal porous carbon polyhedra further exhibited superior performance to Pt/C catalysts in primary and rechargeable zinc-air batteries.

Synthesis and Enhanced Photocatalytic Activity of Regularly Shaped Cu2O Nanowire Polyhedra

A series of unique nanowire superstructures, Cu2O nanowire polyhedra, have been synthesized through a cost-effective hydrothermal route. Three types of nanowire polyhedra, namely octahedra, concave octahedra, and hexapods, were formed in high morphological yields （90%） by reducing cupric acetate with o-anisidine or o-phenetidine in the presence of carboxylic acids. The architectures of these Cu2O nanowire polyhedra were examined by electron microscopy, which revealed ordered, highly aligned CU2O nanowires within the polyhedral outlines. The growth of the Cu2O nanowire polyhedra is controlled by the orientation and growth rates of the nanowire branches which are adjusted by addition of carboxylic acids. Compared to the Cu2O samples reported in the recent literature, the Cu2O nanowire octahedra exhibit notably enhanced photocatalytic activities for dye degradation in the presence of H202 under visible light, probably due to the high-density charge carriers photoexcited from the branched nanowires with their special structures. Additionally, the discussion in the recent literature of the photocatalytic activity of Cu2O in the absence of H2O2 for direct photodegradation of dyes seems questionable.

Single-atom Pd catalyst anchored on Zr-based metal-organic polyhedra for Suzuki-Miyaura cross coupling reactions in aqueous media

The challenge for single-atom catalysts in various C-C cross coupling reaction exists in the development of solid supporting materials.It has been desired tofind a supporting material designed in molecular level to anchor a single-atom catalyst and provide high degree of dispersion and substrate access in aqueous media.Here,we prepared discrete cages of metal-organic polyhedra anchoring single Pd atom(MOP-BPY(Pd))and successfully performed a Suzuki-Miyaura cross coupling reaction with various substrates in aqueous media.It was revealed that each tetrahedral cage of MOP-BPY(Pd)has 4.5 Pd atoms on average and retained its high degree of dispersion up to 3 months in water.The coupling efficiencies of the Suzuki-Miyaura cross coupling reaction exhibited more than 90.0%for various substrates we have tested in the aqueous media,which is superior to those of the molecular Pd complex and metal-organic framework(MOF)anchoring Pd atoms.Moreover,MOP-BPY(Pd)was successfully recovered and recycled without performance degradation.

Pseudo minimum translational distance between convex polyhedra(Ⅰ)——Definition and properties

Based on the concept of gauge function, the pseudo minimum translational distance (PMTD) between two convex objects is defined in this paper. PMTD not only provides a measure of the clearance between two separating objects, but also quantifies the penetration of two objects intersecting each other. It is proved that the PMTD is differentiate almost everywhere w. r.t. the configuration variable of the objects. Algorithms for calculating PMTD and its derivative are also presented.

Central Circuit Coverings of Octahedrites and Medial Polyhedra

An octahedrite is a 4-valent polyhedron with only 3-faces and 4-faces. We study edge-partitions of some octahedrites, medial and related polyhedra into central circuits.

Immobilization of foreign protein into polyhedra of Bombyx mori nucleopolyhedrovirus(BmNPV)

In the late phase of Bombyx mori nucleopolyhedrovirus(BmNPV)infection,a large amount of polyhedra appear in the infected cell nucleolus,these polyhedra being dense protein crystals protecting the incorporated virions from the harsh environment.To investigate whether the foreign protein could be immobilized into the polyhedra of BmNPV,two recombinant baculoviruses were generated by a novel BmNPV polyhedrin-plus(polh +)Bac-to-Bac system,designated as vBmBac(polh +)-enhanced green fluorescent protein(EGFP)and vBmBac(polh +)-LacZ,which can express the polyhedrin and foreign protein simultaneously.Light microscopy analysis showed that all viruses produced polyhedra of normal appearance.Green fluorescence can be apparently detected on the surface of the vBmBac(polh +)-EGFP polyhedra,but not the BmNPV polyhedra.Fluorescence analysis and anti-desiccation testing confirmed that EGFP was embedded in the polyhedra.As expected,the vBmBac(polh +)-LacZ polyhedra contained an amount of LacZ and had a higherβ-galactosidase activity.Sodium dodecyl sulfate polyacrylamide gel electrophoresis(SDS-PAGE)and Western blotting were also performed to verify if the foreign proteins were immobilized into polyhedra.This study provides a new inspiration for efficient preservation of useful proteins and development of new pesticides with toxic proteins.

Breathing Metal-Organic Polyhedra Controlled by Light for Carbon Dioxide Capture and Liberation

Metal-organic polyhedra(MOPs)have emerged as versatile platforms for artificial models of biological systems due to their discrete structure and modular nature.However,the design and fabrication of MOPs with special functionality for mimicking biological processes are challenging.Inspired by the breathing mechanism of lungs,we developed a new type of MOP(a breathing MOP,denoted as NUT-101)by directly using azobenzene units as the pillars of the polyhedra to coordinate with Zr-based metal clusters.In addition to considerable thermal and chemical stability,the obtained MOP exhibits photocontrollable breathing behavior.Upon irradiation with visible or UV light,the configuration of azobenzene units transforms,leading to reversible expansion or contraction of the cages and,correspondingly,capture or liberation of CO_(2)molecules.Such a breathing behavior of NUT-101 is further confirmed by density functional theory(DFT)calculation.This system might establish an avenue for the construction of new materials with particular functionality that mimic biological processes.

Constructing Isosurfaces from 3D Data Sets Taking Account of Depth Sorting of Polyhedra

Creating and rendering intermediate geometric primitives is one of the approaches to visualize data sets in 3D space. Some algorithms have been developed to construct isosurface from uniformly distributed 3D data sets. These algorithms assume that the function value varies linearly along edges of each cell. But to irregular 3D data sets, this assumption is inapplicable. Moreover, the depth sorting of cells is more complicated for irregular data sets, which is indispensable for generating isosurface images or semitransparent isosurface images, if Z-buffer method is not adopted.In this paper, isosurface models based on the assumption that the function value has nonlinear distribution within a tetrahedroll are proposed. The depth sorting algorithm and data structures are developed for the irregular data sets in which cells may be subdivided into tetrahedra. The implementation issues of this algorithm are discussed and experimental results are shown to illustrate potentials of this technique.

Sulfonate-Functionalized Polyoxovanadate-Based Metal-Organic Polyhedra for Enhanced Proton Conduction via the Synergy of Linker and Metal Cluster Vertex

Metal-organic polyhedra(MOPs)have emerged as novel porous platforms for proton conduction,however,the concerted employment of both linker and metal cluster vertex is rarely applied for the fabrication of MOPs-based high conducting materials.Herein we report the synthesis of sulfonate-functionalized polyoxovanadate-based MOPs for enhanced proton conduction via the synergistic effect from linker and metal cluster node.MOPs 1 and 2 exhibit octahedral cage configuration constructed from{V_(5)O_(9)Cl}vertex and 5-sulfoisophthalate linker.Owing to the ordered packing of octahedral cages along three axes,3D interpenetrated open channels that are lined with high-density sulfonates are thus formed within 2.Coupled with the proton-conductive{V_(5)O_(9)Cl}vertexs as well as protonated counterions,an extensive H-bonded network is therefore generated for facile proton transfer.2 exhibits high proton conductivity of 3.02×10^(-2)S cm^(-1)at 65℃under 90%RH,recording the highest value for MOPs pellet sample.This value is enhanced~1order of magnitude compared with that of carboxylate-functionalized analogue 3,clearly illustrating the advantage of combining linker and metal cluster node for enhanced proton conduction.This work will further promote the exploitation of high proton conductive MOPs-based materials by the synergy design strategy.

Assembly of face-rotating molecular polyhedra

Supported by the National Natural Science Foundation of China,the research team led by Dr.Cao Xiaoyu(曹晓宇)at the State Key Laboratory of Physical Chemistry of Solid Surfaces and College of Chemistry and Chemical Engineering,Collaborative Innovation Centre of Chemistry for Energy Materials,Xiamen University,assembled a new series of molecular polyhedra,the face-rotating polyhedra(FRP).This

Unique Ligand Exchange Dynamics of Metal-Organic Polyhedra for Vitrimer-like Gas Separation Membranes

Metal-organic polyhedra(MOPs)possess a microporous framework and impose hierarchical constraints on their surface ligands,leading to the long-ignored,logarithmic ligand exchange dynamics.Herein,polymer networks with MOP as nanoscale cross-linkers(MOP-CNs)can integrate unique ligand exchange dynamics and microporosity,affording vitrimer-like gas separation membranes with promising mechanical performance and(re)processability.All the ligands on the MOP surfaces are confined and correlated via a 3D coordination framework and their neighboring spaces,giving rise to a high energy barrier for ligand exchange.Therefore,MOP-CNs demonstrate high mechanical strengths at room temperature due to their negligible ligand dynamics.The thermo-activated ligand exchange process with integrated network topology enables facile(re)processing and high solvo-resistance at high temperatures.This facilitates Arrhenius type temperature dependence of flowability and stress relaxation,giving rise to the simultaneous achievement of promising mechanical strengths and(re)processability.Finally,the cage topologies of MOPs endow the materials with a bonus microporous feature and spur their applications as gas separation membranes.

金属有机多面体材料的制备及应用进展

金属有机多面体(MOPs)是由无机金属离子和具有特定结构的有机配体通过自组装的形式合成的。MOPs是一种高度有序和离散分子结构的无机有机杂化材料,具有高孔隙率、可调节的孔径、化学稳定性以及可定制的功能等特点,应用前景广阔。总结了MOPs的制备方法及应用进展,指出了MOPs材料发展的制约因素及未来MOPs材料的发展方向。

金属玻璃切削中原子结构演化分子动力学研究

金属玻璃具有中短程有序、长程无序的结构特性,这些中短程有序结构对金属玻璃的加工过程极为敏感。为研究金属玻璃原子结构的特点,分析在纳米切削过程中金属玻璃原子结构的演化趋势,应用分子动力学方法,以0.1 K/s的冷却速率制备Zr52Cu20Ti16Ni12金属玻璃模型,并对模型进行室温纳米切削模拟。采用径向分布函数分析法和Voronoi多面体分析法对纳米切削过程中原子组态的演化进行分析,分析结果表明,配位数为12的原子结构是局域应变的主要承担者。

形成多角体的杆状病毒载体系统的建立

用具有多聚A信号、不带翻译起始密码子ATG或含三种读码框ATG的寡聚核苷酸为聚合接头,构建了含多角体蛋白基因、并能利用人工合成启动序列和多角体蛋白XIV启动子表达外源基因的转移载体质粒pSXIVVI^+X_3系列。为便于重组毒株的筛选,还组建了含合成启动子和β-半乳糖苷酶基因的无包含体粉纹夜蛾核型多角体病毒株TnNPV-SVI^-G,并由此建立起以上述质粒为转移载体,形成多角体及能在X-gal半固体培养基中呈白斑,具有易于辨认遗传标志的TnNP V表达载体系统。

一种面向地理信息系统的空间索引方法

空间检索技术是有效地管理和操纵空间数据的一种必要手段。本文分析了目前常用的空间检索方法在地理信息系统应用上的局限性 ,提出了一种基于凸多边形的空间索引技术。本文首先介绍了目前常用的几类空间索引技术及其特点 ,接着讨论了面向地理信息的空间索引技术面临的基本问题 ,提出了基于凸多边形的空间索引结构—— CP-树 ,并侧重分析了其空间运算算法及时空效率 ,最后指出了空间索引技术所存在的问题及下一步的研究方向。

硫酸盐类晶体中[SO_4]^(2-)四面体的结晶方位与晶体的形貌

本文从硫酸盐类晶体中负离子配位多面体的结晶方位和相互联结的稳定性出发，探讨了硫酸盐类晶体中[SO4]2-结晶方位与晶体结晶形貌之间的关系;认为[SO4]2-四面体与金属阳离子（Ba2+、Ca2+、Mg2+…）结合时，由于晶体结构和生长条件（如温度、过饱和度等）的不同，在晶体各族晶面上的叠合速率和取向不同;晶体的结晶形貌迥然有别.晶体的结晶形貌与[SO4]2-四面体在晶体中的结晶方位密切相关，四面体的面和棱的法线（L2）所对向的晶面，生长速率慢，顽强显露，均属晶体的板面;四面体的顶角所指向的晶面，生长速率快，显露面积小，经常消失.