Applications Of Graph Theory And Topology In Inorganic Cluster And Coordination Chemistry
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Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry by R. Bruce King Pdf
Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry is a text-reference that provides inorganic chemists with a rudimentary knowledge of topology, graph theory, and related mathematical disciplines. The book emphasizes the application of these topics to metal clusters and coordination compounds. The book's initial chapters present background information in topology, graph theory, and group theory, explaining how these topics relate to the properties of atomic orbitals and are applied to coordination polyhedra. Subsequent chapters apply these ideas to the structure and chemical bonding in diverse types of inorganic compounds, including boron cages, metal clusters, solid state materials, metal oxide derivatives, superconductors, icosahedral phases, and carbon cages (fullerenes). The book's final chapter introduces the application of topology and graph theory for studying the dynamics of rearrangements in coordination and cluster polyhedra.
From Chemical Topology to Three-Dimensional Geometry by Alexandru T. Balaban Pdf
Even high-speed supercomputers cannot easily convert traditional two-dimensional databases from chemical topology into the three-dimensional ones demanded by today's chemists, particularly those working in drug design. This fascinating volume resolves this problem by positing mathematical and topological models which greatly expand the capabilities of chemical graph theory. The authors examine QSAR and molecular similarity studies, the relationship between the sequence of amino acids and the less familiar secondary and tertiary protein structures, and new topological methods.
This volume addresses a number of topological themes of direct relevance to chemists. Topological concepts are now regularly applied in wide areas of chemistry including molecular engineering and design, chemical toxicology, the study of molecular shape, crystal and surface structures, chemical bonding, macromolecular species such as polymers and DNA, and environmental chemistry. Currently, the design and synthesis of new drugs and agrochemicals are of especial importance. The book's prime focus is on the role played by topological indices in the description and characterisation of molecular species. The Wiener index along with a variety of other major topological indices, are discussed with particular reference to the powerful and much used connectivity indices. In this book an international team of leading experts review their respective fields and present their findings.The considerable benefits offered by topological indices in the investigation of chemical problems in science, medicine, and industry are highlighted. The volume records proceedings of the Harry Wiener Memorial Conference on the Role of Topology in Chemistry, held at the University of Georgia in March 2001, and serves as a fitting tribute to the chemical contributions of the late Harry Wiener. Focuses on the role played by topological indices in the description and characterisation of molecular species Records the proceedings of the Harry Weiner Memorial Conference on the Role of Topology in Chemistry, held at the University of Georgia in March 2001 Along with a variety of other major topological indices, the Wiener index is discussed with particular reference to the powerful and much-used connectivity indices
Graph Theoretical Approaches to Chemical Reactivity by Danail D. Bonchev,O.G. Mekenyan Pdf
The progress in computer technology during the last 10-15 years has enabled the performance of ever more precise quantum mechanical calculations related to structure and interactions of chemical compounds. However, the qualitative models relating electronic structure to molecular geometry have not progressed at the same pace. There is a continuing need in chemistry for simple concepts and qualitatively clear pictures that are also quantitatively comparable to ab initio quantum chemical calculations. Topological methods and, more specifically, graph theory as a fixed-point topology, provide in principle a chance to fill this gap. With its more than 100 years of applications to chemistry, graph theory has proven to be of vital importance as the most natural language of chemistry. The explosive development of chemical graph theory during the last 20 years has increasingly overlapped with quantum chemistry. Besides contributing to the solution of various problems in theoretical chemistry, this development indicates that topology is an underlying principle that explains the success of quantum mechanics and goes beyond it, thus promising to bear more fruit in the future.
Intermetallic Chemistry by Riccardo Ferro,Adriana Saccone Pdf
Intermetallic science is closely related to physics, chemistry, metallurgy, materials science & technology, and engineering. This book emphasizes the chemical aspects of this science, and therefore the mutual reactivity of metals and the characteristics of intermetallic compounds. Topics included are: • Phase diagrams of alloy systems. Many intermetallic systems form several compounds, generally not obeying common simple stoichiometric rules, which are often homogeneous in a certain range of compositions. The stability and extension of these phases are conveniently presented through phase diagrams. • Selected aspects of intermetallics structural chemistry, with emphasis on the solid state. The general structural characteristics of intermetallic phases are considered, with attention to nomenclature and to alternative and complementary methods of presenting crystal-chemical data. A brief account is given of derivative and degenerate structures, modular aspects of crystal structures, and of a few special groups of alloys such as quasicrystals and amorphous alloys. A number of selected structural prototypes with typical features, their possible grouping in structural “families and their distribution among different types of alloys are provided. • Intermetallic reactivity trends in the Periodic Table. Attention is given to a few selected elemental parameters such as electron configuration and valence electron number and to their changes along the Table, which act as reference factors of the intermetallic behaviour. As an example, the relationships are considered between crystal structure and the number of valence electrons per atom (or per formula) in various classes of compounds or solid solution phases. • Alloying behaviour systematics of intermetallic systems with a description of the intermetallic reactivity of each element, or group of elements, in the order of their position in the Periodic Table. For each pair of metallic elements, their capability to form intermediate phases is summarised by maps and schemes. • A description of small scale preparation methods of intermetallics. A number of interesting and significant peculiarities are, e.g., those related to their high melting points, insolubility in common solvents, etc. · Systematic treatment of alloying behaviour · Wide overview of intermetallic chemistry · Illustrated, with many examples
Quantum Techniques In Stochastic Mechanics by Baez John C,Biamonte Jacob D Pdf
We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets. Contents: Stochastic Petri Nets The Rate Equation The Master Equation Probabilities vs Amplitudes Annihilation and Creation Operators An Example from Population Biology Feynman Diagrams The Anderson–Craciun–Kurtz Theorem An Example of the Anderson–Craciun–Kurtz Theorem A Stochastic Version of Noether's Theorem Quantum Mechanics vs Stochastic Mechanics Noether's Theorem: Quantum vs Stochastic Chemistry and the Desargues Graph Graph Laplacians Dirichlet Operators and Electrical Circuits Perron–Frobenius Theory The Deficiency Zero Theorem Example of the Deficiency Zero Theorem Example of the Anderson–Craciun–Kurtz Theorem The Deficiency of a Reaction Network Rewriting the Rate Equation The Rate Equation and Markov Processes Proof of the Deficiency Zero Theorem Noether's Theorem for Dirichlet Operators Computation and Petri Nets Summary Table Readership: Graduate students and researchers in the field of quantum and mathematical physics. Keywords: Stochastic;Quantum;Markov Process;Chemical Reaction Network;Petri NetReview: Key Features: It's a light-hearted introduction to a deep analogy between probability theory and quantum theory It explains how stochastic Petri nets can be used in modeling in biology, chemistry, and many other fields It gives new proofs of some fundamental theorems about chemical reaction networks
New Edition! Completely Revised and Updated Chemical Graph Theory, 2nd Edition is a completely revised and updated edition of a highly regarded book that has been widely used since its publication in 1983. This unique book offers a basic introduction to the handling of molecular graphs - mathematical diagrams representing molecular structures. Using mathematics well within the vocabulary of most chemists, this volume elucidates the structural aspects of chemical graph theory: (1) the relationship between chemical and graph-theoretical terminology, elements of graph theory, and graph-theoretical matrices; (2) the topological aspects of the Hückel theory, resonance theory, and theories of aromaticity; and (3) the applications of chemical graph theory to structure-property and structure-activity relationships and to isomer enumeration. An extensive bibliography covering the most relevant advances in theory and applications is one of the book's most valuable features. This volume is intended to introduce the entire chemistry community to the applications of graph theory and will be of particular interest to theoretical organic and inorganic chemists, physical scientists, computational chemists, and those already involved in mathematical chemistry.
Fluxional Organometallic and Coordination Compounds by Marcel Gielen,Rudolph Willem,Bernd Wrackmeyer Pdf
This series offers leading contributions by well-known chemists reviewing the state of the art of this wide research area. Physical organometallic chemistry aims to develop new insights and to promote novel interest and investigations applicable to organometallic chemistry. This volume focuses on several important topics on fluxionality in organometallic and coordination chemistry, reviewed by experts in each of the respective fields. It is intended to provide both authoritative concepts and stimulating ideas in order to tackle dynamics from different angles, aiming at an interdisciplinary approach. The fascinating fluxionality of metal-ligand interactions has been in the centre of interest ever since modern coordination and organometallic chemistry started, and has expanded towards bioinorganic chemistry, catalysis and materials sciences. Provides information on some of the most relevant physical methods for studying dynamic processes Presents numerous examples of dynamic behavior, demonstrating the efficiency of the respective method and stimulating further applications Connects main group, transition metal and solid state chemistry in the question for dynamics
This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. Chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches.
Inorganic Chemistry of Main Group Elements by R. Bruce King Pdf
Many chapters include the following: a summary of the typical coordination number, oxidation states, bonding types, etc. found in the elements covered; important properties of the free elements including a discussion of allotropic forms; discussions of halides, oxides, oxyacids, organimetallic derivatives, and other compound types in separate sections.
In a series of reviews on topics including circular DNA and other cyclic biological macromolecules, synthetic polymers and large organic and inorganic ring molecules, internationally renowned authors survey the many important advances in the area of large ring molecules. Large Ring Molecules examines the new and fascinating development of large cyclics including topological aspects such as catenane and rotaxane formation. Current research in large ring molecules is leading to new concepts and ideas which are illustrated by chapters on cyclic molecules formed by self assembly and molecular recognition. Large Ring Molecules will be invaluable for researchers in physical, organic, inorganic, biological, polymer, topological, analytical, theoretical and supramolecular chemistry.
