Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a truth table indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.     

Feedback loops for chaos in activator-inhibitor systems

Previous investigations have revealed that special constellations of feedback loops in a network can give rise to saddle-node and Hopf bifurcations and can induce particular bifurcation diagrams including the occurrence of various codimension-two points. To elucidate the role of feedback loops in the generation of more complex dynamics, a minimal prototype for these networks will be taken as purely periodic starting model which will be extended by an additional species in different feedback loops. The dynamics of the resulting systems will be analyzed numerically for the occurrence of chaotic attractors. Especially, the consequences of codimension-two bifurcations and the role of homoclinic orbits in view of the emergence of Shil'nikov chaos will be discussed.     

Enumeration of internal rotation reactions and their reaction graphs

Threefold and twofold internal rotation reactions and their reaction graphs are enumerated using the generalized wreath product method developed by the author in an earlier paper. The correspondence between reaction directed graphs (digraphs) and finite topologies on isomers is established. It is shown that the reaction digraphs can be represented by Borel fields. Atropisomerism in polyphenyl compounds is discussed. Applications to spontaneous generation of optical activity and NMR spectroscopy are considered. Borel fields are enumerated by bumping squares of the upper rows of Young diagrams starting from the Young diagram containing just one row.     

On the centrality of vertices of molecular graphs

For acyclic systems the center of a graph has been known to be either a single vertex of two adjacent vertices, that is, an edge. It has not been quite clear how to extend the concept of graph center to polycyclic systems. Several approaches to the graph center of molecular graphs of polycyclic graphs have been proposed in the literature. In most cases alternative approaches, however, while being apparently equally plausible, gave the same results for many molecules, but occasionally they differ in their characterization of molecular center. In order to reduce the number of vertices that would qualify as forming the center of the graph, a hierarchy of rules have been considered in the search for graph centers. We reconsidered the problem of “the center of a graph” by using a novel concept of graph theory, the vertex “weights,” defined by counting the number of pairs of vertices at the same distance from the vertex considered. This approach gives often the same results for graph centers of acyclic graphs as the standard definition of graph center based on vertex eccentricities. However, in some cases when two nonequivalent vertices have been found as graph center, the novel approach can discriminate between the two. The same approach applies to cyclic graphs without additional rules to locate the vertex or vertices forming the center of polycyclic graphs, vertices referred to as central vertices of a graph. In addition, the novel vertex “weights,” in the case of acyclic, cyclic, and polycyclic graphs can be interpreted as vertex centralities, a measure for how close or distant vertices are from the center or central vertices of the graph. Besides illustrating the centralities of a number of smaller polycyclic graphs, we also report on several acyclic graphs showing the same centrality values of their vertices. © 2013 Wiley Periodicals, Inc.     

Algorithm for topological correction of lists of simplexes of different dimensions for polyhedration of multicomponent systems

A new algorithm for polyhedration of quaternary and quaternary reciprocal systems is presented. The algorithm is based on checking all the links between vertices of a graph describing the composition diagram and selecting the polyhedration variants that correspond to the relations between the numbers of geometric elements of the complex undergoing polyhedration (graph vertices, links between them, and two-and three-dimensional complexes). Unlike Kraeva’s algorithm based on the decomposition of the graph in terms of zero elements of the adjacency matrix (absent links between vertices), the new algorithm can control the entire polyhedration process, accelerates the search for internal diagonals in the polyhedron, and takes into account their possible competition.     

物理化学课程中相平衡理论的教学策略

针对物理化学相平衡章节体系多变、知识点繁多、相图抽象等问题提出了一套系统的教学策略。首先对相平衡中的基本概念和定律进行论述,并强调重、难点;随后对章节知识点进行总结归纳,通过表格系统罗列相图的体系、相律、应用和术语;最后提出相图解读通行方法,并结合具体例子讲解这些方法、相律以及杠杆规则如何使用。     

Oblate deltahedra in dimetallaboranes: geometry and chemical bonding

A new series of nonspherical and very oblate deltahedra, conveniently called the oblatocloso deltahedra, is found in dimetallaboranes among which the dirhenaboranes Cp2Re2B(n-2)H(n-2) (8 相似文献   

X-Ray Mapping and Interpretation of Scatter Diagrams

Electron beam induced quantitative X-ray mapping has become a very useful characterisation tool for determining the elemental distribution in materials, whether using energy dispersive spectroscopy or wavelength dispersive spectroscopy. The X-ray intensity distributions of the elements from an X-ray map allow us to generate two dimensional and ternary scatter diagrams thus converting spatial information into concentration dimensions, which is an important tool for displaying the spatial relationships of elements or correlated elements (phases) in materials. To best understand how to use this tool, we need to understand the production and features of the scatter diagram. The type of clustering observed in the scatter diagram, whether oval, linear or spherical, can give the major and trace element distributions within phases as well as qualitative and quantitative phase information. This paper demonstrates the generation of scatter diagrams, properties of scatter diagrams, interpretation of scatter diagrams and the advantages of scatter diagrams through the use of examples.     

Semiempirical dynamic phase diagrams of nanocrystalline products during copper (II) acetylacetonate vapour decomposition

Nanoparticle production by Cu(acac)₂ vapour decomposition was studied. The composition of the produced particles varied from Cu to Cu₂O depending on experimental conditions. In order to explain the crystalline phase behaviour, a kinetic model to build a semiempirical dynamic phase diagram of the products was proposed. Prevailing role of copper dimers in the processes of copper and copper (I) oxide particle growth was demonstrated. The composition of products was determined by reactions on the surface of growing particles and depended on the ratio of gaseous species. The calculated dynamic phase diagrams were in excellent agreement with the experimental results.     

Feedback loops for Shil'nikov chaos: The peroxidase-oxidase reaction

Special structures in a chemical reaction network can give rise to bistability, oscillations, and chaos. It has been shown recently [A. Sensse and M. Eiswirth, J. Chem. Phys. 122, 044516 (2005)] that the introduction of an additional species in a supplementary feedback loop to a minimal autocatalytic oscillator gives rise to chaotic dynamics in a certain range of parameters, independent of the particular realization of the additional loop. This provides a possibility to decide if chaos may occur just by analyzing the network structure of an existing model. Here, we apply this concept to analyze the complex dynamics in several essential subsystems of the peroxidase-oxidase reaction system. The aim of the present paper is to determine the nature of the occurring chaos and its location in the parameter space by numerical bifurcation analysis and simulations.     

From the two-component system CBrCl3+CBr4 to the high-pressure properties of CBr4

The experimental phase diagram of the CBrCl3+CBr4 system has been determined by means of X-ray powder diffraction and thermal analysis techniques from 200 K to the liquid state. Before melting, the two components have the same orientationally disordered (OD) face-centered cubic phase, and solid-liquid equilibrium is explained by simple isomorphism. The application of multiple crossed isopolymorphism formalism to the low-temperature solid-solid equilibria has enabled the inference of an OD rhombohedral metastable (at normal pressure) phase for CBr4. Experimental determination of the pressure-volume-temperature and construction of the pressure-temperature phase diagrams for CBr4 reveal the existence of a high-pressure phase, the rhombohedral symmetry of which is inferred by means of the thermodynamic assessment of the experimental phase diagram and demonstrated by means of high-pressure neutron diffraction measurements. The procedure used in this work confirms the connection between the appearance of metastable phases at normal pressure and their existence at high-pressure.     

简立方格点自避行走所模拟的高分子链吸附和塌缩

采用复合Markov链法 ,针对简立方格点上的自避行走模型 ,研究了同时具有对壁的吸附作用ε1 和最近邻相互作用ε2 的高分子链的热力学性质 .相互作用能量参数ε1 和ε2 分别联系于参数α和 β .令链长N=10 0 ,由这种MonteCarlo方法可得出链的自由能FN(α ,β) ,热容2 FN(α ,β) /2 α和2 FN(α ,β) /2 β ,吸附点平均数〈m〉/N ,最近邻相互作用对平均数〈n〉/N和均方末端距对壁的垂直分量RZ2 .除已有方法由热容数据可绘出α β相图外 ,建议由结构参数〈m〉/N ,〈n〉/N和RZ2 绘制相图 ,并发现二者基本一致 .所得相图表明 ,存在 4个相区 ,分别是解吸 膨胀相 (DE) ,吸附 膨胀相 (AE) ,解吸 紧密相 (DC)和吸附 紧密相 (AC) .在伸展区和塌缩区 ,随着吸附作用的增强 ,会出现吸附相转变 .在解吸区和吸附区 ,随着自相互作用的增大 ,也将出现塌缩相转变 .相图出现了两个三相点 ,即AE AC DC三相点和AE DE DC三相点     

V-H2O体系的溶解组分优势区域图和电势-pH 图

运用浓度比较法, 对25 ℃时V-H2O体系进行热力学分析和电化学分析, 编程计算出各溶解组分浓度, 以及固相和液相、各固相间边界线, 确定固相区和液相区的位置. 在此基础上, 绘制出了总V浓度cT(V)=1.0×10-5 mol·L-1时V-H2O体系的溶解组分优势区域图和电势-pH图以及cT(V)=1.0×10-7 mol·L-1时V-H2O体系的电势-pH图. 电势-pH图结果表明在一定温度和压力下, 各相稳定区取决于体系中溶液态物质的总浓度. 随cT(V)的减小, 溶液稳定区增大, 各固相稳定区均不同程度减小.     

Predominance zone diagrams and their application to solvent extraction techniques

Predominance zone diagrams have been useful tools in solving problems in analytical chemistry. They can be used to establish the best conditions for separation of mixtures or to optimize recovery procedures for a given species. The few reports on predominance zone diagrams for the participant species in liquid-liquid extraction systems, describe their construction as diagrams of the Pourbaix type (epsilon/pH). With the generalized species and equilibria method (GSEM) it is possible to elaborate Predominance zone diagrams for extraction (PZDE) in proper spaces and with parameters strictly related to these processes such as pH and the volume ratio, r. Therefore, using the GSEM, PZDE that allow us to determine the best conditions for the extraction of a given substance have been elaborated. The stoichiometry of the species been extracted can also be determined from the experimental conditions. It has been demonstrated that with the GSEM, PZDE can be constructed for systems of one and two components. In this work, we intend to demonstrate that the algorithm is valid for the elaboration of PZDE in systems of three and four components. Examples of analytical interest are presented such as lead (II) extraction with diphenyltiocarbazone (dithizone) and that for cadmium (II) with 8-hydroxyquinolein (oxine) in chloroform. The influence of a masking agent, the etilendiaminotetraacetic acid (EDTA) over the extraction of both metals was also assessed.     

Application of chemical graph theory for automated mechanism generation

We present an application of the chemical graph theory approach for generating elementary reactions of complex systems. Molecular species are naturally represented by graphs, which are identified by their vertices and edges where vertices are atom types and edges are bonds. The mechanism is generated using a set of reaction patterns (sub-graphs). These subgraphs are the internal representations for a given class of reaction thus allowing for the possibility of eliminating unimportant product species a priori. Furthermore, each molecule is canonically represented by a set of topological indices (Connectivity Index, Balaban Index, Schulz TI Index, WID Index, etc.) and thus eliminates the probability for regenerating the same species twice. Theoretical background and test cases on combustion of hydrocarbons are presented.     

弯曲振动引致的过渡态的混沌

Molecular vibration is correlated to the motion of a pendulum and the lowly excited states are corresponding to that of the pendulum around its stable fixed point while the highly excited states are to the unstable fixed point. Specifically,the transitional state due to internal rotation is also corresponding to the unstable fixed point of the pendulum. As for a perturbed pendulum,chaos occurs first around its unstable fixed point,which is a reasonable consequence that the highly excited state and the transitional state are full with intrinsic chaotic motion. With this conjecture,HCN,its isomer HNC and the excited delocalized transitional state due to the internal rotation of H-C around the skeleton of C-N are interpreted with Morse oscillators in resonance. It is stressed that the delocalized transitional state is in multiple resonances between the H - C stretch and the bending due to that the classical bending frequency is lowered as the transitional state is approached. Multiple resonances,or the overlapping of resonances,lead to chaos as noted by Chirikov. Hence,the delocalzed transitional state can be in a chaotic state. Besides,the internal rotational state of HCP due to H atom is analyzed by this physical picture. For this purpose,an algebraic Hamiltonian for HCN,its isomer HNC and the delocalized transitional state is proposed with its coefficients elucidated by fitting with the quantal levels adopted from the literature by the quantum mechanical algorithm. The result shows that both the transitional state due to the internal rotation of H atom and the highly excited states of HCN and HNC are full of multiple resonances. Therefore,chaos is expected for these systems. Finally,all these ideas are compounded by a proposed model for unfolding the characteristics of chaos in the molecular system.     

Space-time chaos in reactions of NADH with atmospheric oxygen in the presence of copper(II) complexes

In the oxidation of aqueous solutions of NADH by atmospheric oxygen in the presence of certain copper(II) compounds, an irregularly oscillating timewise change has been observed in the potential of a point platinum electrode (PPE), relative to either a silver chloride electrode or a second PPE located in the same solution. Phase portraits have been constructed on the basis of experimental data for all of the systems that have been investigated. It has been shown that the existence of chaotic oscillations, and also the form of the phase portrait of the systems, depend on the magnitude of the redox potential of the CuL²⁺/CuL⁺ pair. For compounds with E₀=0.60–0.64 V, the phase portrait has the form of a screw-type chaos, which then changes over to Lorentz-type chaos. Only for this group of complexes is chaotic behavior observed when the solution is stirred. For compounds with E₀=0.15–0.41 V, screw-type chaos is observed; and for compounds with E₀<0, no chaotic behavior has been detected.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 26, No. 2, pp. 175–184, March–April, 1990.     

Structural Features of Solid Phases and Topology of Phase Diagrams

The paper considers model phase diagrams of binary and ternary systems involving transformations (transitions) of phase equilibria. The relationship between the type of structural solidstate transformation and the type of phase diagram is shown. Topological series of phase diagrams of systems with continuous and limited types of solid solutions are considered, including phase diagrams with polymorphic transitions between intermediate solid phases of variable composition.     

On the application of open circuit relaxation spectroelectrochemistry to the diagnosis and evaluation of the kinetics of succeeding second order chemical reactions

The spectroelectrochemical technique of open circuit relaxation (OCR) has found limited application in the kinetic characterization of systems wherein the electrogenated absorbing species is consumed in a second or higher order reaction. This limited usage arises from the inapplicability of conventional homogeneous kinetic data analysis techniques to the absorbance-time transients observed in the OCR experiment. Treatment of such transients by conventional kinetic expressions (e.g., 1/A vs. t for second order reactions) results in non-linear plots which neither serve as diagnostic criteria for the assignment of kinetic order nor provide meaningful rate constants. This paper presents an empirical method for the treatment of spectroelectrochemical OCR data arising from post-electron transfer kinetic processes which exhibit second order dependence on the concentration of the electrogenerated absorbing species. This procedure, which takes into account the inhomogeneous distribution of the reactant species, affords reduced data plots which not only are linear, hence diagnostic of kinetic order, but also provide a valid measure of the bimolecular rate parameters characteristic of this type of dynamic system. The procedure has been applied to the treatment of OCR data for the reaction of 9,10-diphenylanthracene cation radical with 4-cyanopyridine in acetonitrile. Excellent agreement between the resulting kinetic parameters and those obtained using stopped-flow techniques has been demonstrated.