Combinatorial properties of graphs and groups of physico-chemical interest

Combinatorial properties of graphs and groups of physico-chemical interest are described. A type of mathematical modeling is applied which involves "translating" algebraic expressions into graphs. The idea is applied to both graph theory and group theory. The former topic includes objects of importance in physics and chemistry such as trees, polyomino graphs, king boards, etc. Our study along these lines emphasizes nonadjacency relations, graph-generation, quasicrystals, continued fractions, fractals, and general ordering schemes of graphs. The second part of the paper considers certain colored graphs as models of several group-theoretical concepts including coset representations of groups, subduction of groups, character tables, and mark tables which are essential to the understanding of recent developments of combinatorial enumeration in chemistry.     

A list-processing approach to quantum mechanics

On the basis of several earlier papers undiuview current availability of logic programming facilities, the authors propose a list-processing approach to the modelling of algebraic quantum field theory methods in which the noncommutative algebra of quantum -mechanical operators is emulated by lists. The processing produces reordered sequences of elements of a ring with a unit commutator and generates dynamic structures which for some initial arrangements correspond to partially ordered graphs characterized by resources relations and combinatorial identities. The approach is illustrated by reviewing the simple case of a forced harmonic oscillator. The programming aspects are briefly described.     

Combinatorial models and algorithms in chemistry. Search for isomorphisms and automorphisms of molecular graphs

An algorithm for the recognition of all isomorphisms for any pair of labeled graphs as well as for generation of the graph group is described. Some results obtained with computer realization of the suggested algorithm are briefly discussed.     

Combinatorial chemistry

Rapid progress in molecular biology and the resulting ability to determine the activity of new compounds extremely efficiently have led to an enormously increased demand for test substances which cannot be satisfied by conventional synthesis methods. Combinatorial chemistry is a method that enables the efficient generation of large numbers of structurally diverse products. These products can be obtained as single compounds or in the form of defined mixtures. The synthesis is performed according to combinatorial principles (“produce all possible combinations of the reactants used”). The techniques and methods applied in combinatorial synthesis give rise to analytical problems: monitoring of reactions that take place on solid supports, structure elucidation with only minute amounts of material available or the characterization of substance mixtures. Examples from the authors’ laboratory illustrate how some of these problems can be approached. Received: 26 October 1996 / Revised: 24 February 1997 / Accepted: 26 February 1997     

Combinatorial chemistry

Rapid progress in molecular biology and the resulting ability to determine the activity of new compounds extremely efficiently have led to an enormously increased demand for test substances which cannot be satisfied by conventional synthesis methods. Combinatorial chemistry is a method that enables the efficient generation of large numbers of structurally diverse products. These products can be obtained as single compounds or in the form of defined mixtures. The synthesis is performed according to combinatorial principles (“produce all possible combinations of the reactants used”). The techniques and methods applied in combinatorial synthesis give rise to analytical problems: monitoring of reactions that take place on solid supports, structure elucidation with only minute amounts of material available or the characterization of substance mixtures. Examples from the authors’ laboratory illustrate how some of these problems can be approached. Received: 26 October 1996 / Revised: 24 February 1997 / Accepted: 26 February 1997     

Nonlocal,noncommutative diagrammatics and the linked cluster theorems

Recent developments in quantum chemistry, perturbative quantum field theory, statistical physics or stochastic differential equations require the introduction of new families of Feynman-type diagrams. These new families arise in various ways. In some generalizations of the classical diagrams, the notion of Feynman propagator is extended to generalized propagators connecting more than two vertices of the graphs. In some others (introduced in the present article), the diagrams, associated to noncommuting product of operators inherit from the noncommutativity of the products extra graphical properties. The purpose of the present article is to introduce a general way of dealing with such diagrams. We prove in particular a “universal” linked cluster theorem and introduce, in the process, a Feynman-type “diagrammatics” that allows to handle simultaneously nonlocal (Coulomb-type) interactions, the generalized diagrams arising from the study of interacting systems (such as the ones where the ground state is not the vacuum but e.g. a vacuum perturbed by a magnetic or electric field, by impurities...) or Wightman fields (that is, expectation values of products of interacting fields). Our diagrammatics seems to be the first attempt to encode in a unified algebraic framework such a wide variety of situations. In the process, we promote two ideas. First, Feynman-type diagrammatics belong mathematically to the theory of linear forms on combinatorial Hopf algebras. Second, linked cluster-type theorems rely ultimately on Möbius inversion on the partition lattice. The two theories should therefore be introduced and presented accordingly. Among others, our theorems encompass the usual versions of the theorem (although very different in nature, from Goldstone diagrams in solid state physics to Feynman diagrams in QFT or probabilistic Wick theorems).     

Combinatorial Materials Science and Catalysis

After forever changing the drug discovery process in the pharmaceutical industry, combinatorial chemistry methodologies are increasingly being applied to the discovery and optimization of more efficient catalysts and materials (see picture). With the advent of new combinatorial synthesis and screening technologies, coupled with integrated data management systems, the application of these technologies to materials science and catalyst research holds tremendous potential and brings high expectations to this new and exciting field.     

Combinatorial and high-throughput materials science

There is increasing acceptance of high-throughput technologies for the discovery, development, and optimization of materials and catalysts in industry. Over the years, the relative synchronous development of technologies for parallel synthesis and characterization has been accompanied by developments in associated software and information technologies. This Review aims to provide a comprehensive overview on the state of the art of the field by selected examples. Technologies developed to aid research on complex materials are covered as well as databases, design of experiment, data-mining technologies, modeling approaches, and evolutionary strategies for development. Different methods for parallel synthesis provide single sample libraries, gradient libraries for electronic or optical materials, similar to polymers and catalysts, and products produced through formulation strategies. Many examples illustrate the variety of isolated solutions and document the barely recognized variety of new methods for the synthesis and analysis of almost any material. The Review ends with a summary of success stories and statements on still-present problems and future tasks.     

液相组合化学

综述了液相组合化学的研究进展,重点介绍了液相组合合成中的分离纯化方法和合成方法策略,基本分离纯化方法包括利用固相载体协助分离纯化法,相萃取分离纯化法和色谱法,主要合成方法策略有平行合成策略和索引合成策略。     

Combinatorial Knoevenagel reactions

Chlorotrimethylsilane (TMSCl) has been utilized as an efficient promoter and water scavenger in the Knoevenagel condensations of aromatic aldehydes with various methylene active compounds. High yields and a simple workup of target compounds enables the facile generation of combinatorial libraries comprising 11,000 compounds of high structural and functional diversity.     

化合物库的组合技巧和组合合成

从化合物库的组合技巧和组合合成方法两个方面探讨了组合化学及其在药物开发中的应用。     

红霉素的生物合成与组合生物合成

组合生物合成在筛选和发展新型药物方面日益被生物、化学和医药界所关注.红霉素作为组合生物合成发展的模式化合物一直是人们研究的热点.概述了红霉素的生物合成机制及近年来在此基础上采用组合生物合成获得红霉素衍生物的研究进展,并对此方面存在的问题、应用前景作了展望.     

寡糖组合合成

寡糖是许多生物过程的重要协调物质,其结构与功能的关系正成为人们感兴趣的研究课题。然而传统的寡糖合成很复杂且费时费力,随着组合化学方法在寡糖合成领域的应用,方便快捷地制备各种各样的寡糖成为一种可能。本文从液相和固相反应两个方面综述了组合化学在寡糖合成领域的研究进展。     

Combinatorial liquid-phase synthesis of

A new method for the synthesis of [1,4]oxazepin-7-ones from readily available aldehydes and alpha-amino alcohols was developed using the Baylis-Hillman reaction as the key step. To determine the scope and limitations of the method, a mixture library was synthesized from six aldehydes and six alpha-amino alcohols on the soluble polymer support poly(ethylene glycol) 5000 monomethyl ether (MeOPEG) via split synthesis and analyzed by GC-EIMS. Those oxazepines that were formed predominantly were resynthesized in a parallel synthesis and fully characterized. Thus, we have shown that split synthesis on MeOPEG can be an efficient method to rapidly screen the substrate spectrum of a newly developed reaction sequence.     

Combinatorial Clar sextet theory

Clar structures recently used as basis-set to compute resonance energies [9] are identified as maximal independent sets of benzenoid hydrocarbons colored in a special way. Binomial properties of such objects are induced for several catafusenes and perifusenes (Eqs. 2–31). Novel polynomials, called Clar polynomials, are given for perifusens in terms of units of catafusenes which allow display and enumeration of the populations of their Clar structures. The work is particularly pertinent to that of [8] and [9].This paper is dedicated to Professor Eric Clar; the Doyen of aromatic chemistry.     

Combinatorial chemistry in glycobiology

The application of combinatorial chemistry to glycobiology historically has proven challenging due to numerous synthetic hurdles. The advent of novel methodologies has enabled the production of natural as well as mimetic analogues for proof-of-concept experiments and SAR. This review highlights some of the recent synthetic advances in combinatorial carbohydrate synthesis. The application of carbohydrate libraries in glycobiology is also discussed.     

Dyad algebra and multiplication of graphs. II. Undirected graphs

In paper I abstract vectors |e>, their adjoints <e|, dyads such as |e><e|, and abstract linear operators were related to graphs which are in general directed. With an Hermitian operator one gets equivalence classes of undirected graphs with or without loops and multi-lines. The present paper II gives rules for the multiplication of such graphs based on their underlying dyad algebra. The results may be used in the evaluation of the outcome of successive applications of operators for observables as in the case of the powers of a one-electron Hamiltonian in the method of moments, or in using projection operators, electron density, and the like.     

Isospectral graphs and molecules

Isospectral molecules are nonidentical species whose molecular graphs have the same set of eigenvalues within HMO calculations. Several new concepts and methods for constructing pairs of isospectral graphs are discussed. Some possible experimental and theoretical applications of isospectral molecular pairs are outlined.