This is the first edited volume that features two important frameworks, Hückel and quantum chemical topological analyses. The contributors, which include an array of academics of international distinction, describe recent applications of such topological methods to various fields and topics that provide the reader with the current state-of-the-art and give a flavour of the wide range of their potentialities.

"The second step is to determine constitution, Le. which atoms are bonded to which and by what types of bond. The result is ex pressed by a planar graph (or the corresponding connectivity mat rix) •••• In constitutional formulae, the atoms are represented by letters and the bonds by lines. They describe the topology of the molecule." VLADIMIR PRELOG, Nobel Lecture, December l2;h 1975. In the present notes we describe the topological approach to the che mistry of conjugated molecules using graph-theoretical concepts. Con jugatedstructures may be conveniently studied using planar and connec ted graphs because they reflect in the simple way the connectivity of their pi-centers. Connectivity is important topological property of a molecule which allows a conceptual qualitative understanding, via a non numerical analysis, of many chemical phenomena or at least that part of phenomenon which depends on topology. This would not be possible sole ly by means of numerical (molecular orbital) analysis.

Introduces a new method and language, based on finite topological spaces, for investigating molecular structure. Eschews the ``theorem-proof-remarks'' format of mathematics in favor of a more readable style commonly used in physical science. Part I develops the mathematical machinery which can serve as an analytical tool to investigate nonmetric aspects of chemical structure. Specific topics covered include set theory, lattices, graph theory, connectivity, classification of spaces, combinatorics, and functions and continuity. Part II explains the application of the above concepts to molecular structure. Chapters cover the bond topology, the graph topology, duplex spaces, and the topology of chemical reactions. Eight appendixes cover ancillary topics.

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

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.

Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology includes peer-reviewed contributions based on carefully selected presentations given at the 17th International Workshop on Quantum Systems in Chemistry, Physics, and Biology. New trends and state-of-the-art developments in the quantum theory of atomic and molecular systems, and condensed matter (including biological systems and nanostructures) are described by academics of international distinction.

Advances in Quantum Chemical Topology Beyond QTAIM provides a complete overview of the field, starting with traditional methods and then covering key steps to the latest state-of-the-art extensions of QTAIM. The book supports researchers by compiling and reviewing key methods, comparing different algorithms, and providing computational results to show the efficacy of the approaches. Beginning with an introduction to quantum chemistry, QTAIM and key extensions, the book goes on to discuss interacting quantum atoms and related energy properties, explores partitioning methods, and compares algorithms for QTAIM. Partitioning schemes are them compared in more detail before applications are explored and future developments discussed. Drawing together the knowledge of key authorities in the area, this book provides a comprehensive, pedogeological guide to this insightful theory for all those interested in modelling, exploring and understanding molecular properties. - Provides a contemporary review of the extensions and application of QTAIM methods - Compiles all extensions of QTAIM in one place for easy reference - Includes a chapter with an Introduction to Quantum Chemistry - Presents complex information at a level accessible to those engaged in theoretical/computational chemistry

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Observing computational chemistry's proven value to the introduction of new medicines, Computational Medicinal Chemistry for Drug Discovery offers the techniques most frequently utilized by industry and academia for ligand design. Featuring contributions from more than 50 preeminent scientists, this book surveys molecular structure computation, intermolecular behavior, ligand-receptor interaction, and modeling. It also examines molecular mechanics, semi-empirical methods, wave function-based quantum chemistry, density functional theory, 3-D structure generation, and hybrid methods.

Topology is becoming increasingly important in chemistry because of its rapidly growing number of applications. Here, its many uses are reviewed and the authors anticipate what future developments might bring. This work shows how significant new insights can be gained by representing molecular species as topological structures known as topographs. The text explores carbon structures, establishing how the stability of fullerene species can be accounted for and also predicting which fullerenes will be most stable. It is pointed out that molecular topology, rather than molecular geometry, characterizes molecular shape and various tools for shape characterization are described. Several of the fascinating ideas that arise from regarding topology as a unifying principle in chemical bonding theory are discussed, and in particular, the novel concept of the molecular topoid is shown to have numerous uses. The topological description of polymers is examined and the reader is gently guided through the realms of branched and tangled polymers. Overall, this work outlines the fact that topology is not only a theoretical discipline but also one that has practical applications and high relevance to the whole domain of chemistry.