This book, divided into two parts, now in its second edition, presents the basic principles of group theory and their applications in chemical theories. While retaining the thorough coverage of the previous edition, the book in Part I, discusses the symmetry elements, point groups and construction of character tables for different point groups. In Part II, it describes the concept of hybridization to explain the shapes of molecules and analyzes the character tables to predict infrared and Raman active vibrational modes of molecules. It also brings into fore the molecular orbital theory and the techniques of group theory to interpret bonding in transition metal complexes and their electronic spectra. Finally, the book describes the crystal symmetry in detail as well as the Woodward–Hoffmann rules to determine the pathways of electrocyclic and cycloaddition reactions. NEW TO THE SECOND EDITION • New sections on Direct Product, Group–sub-group Relationships, Effect of Descent in Octahedral Symmetry on Degeneracy, Jahn–Teller Distortion, Group–sub-group Relationships and Electronic Spectra of Complexes and Influence of Coordination on the Infrared Spectra of Oxoanionic Ligands, Space Groups • Revised sections on Projection Operator, SALC Molecular Orbitals of Benzene and π-Molecular Orbitals of 1, 3-Butadiene KEY FEATURES • Provides mathematical foundations to understand group theory. • Includes several examples to illustrate applications of group theory. • Presents chapter-end exercises to help the students check their understanding of the subject matter. The book is designed for the senior undergraduate students and postgraduate students of Chemistry. It will also be of immense use to the researchers in the fields where group theory is applied.

The mathematical fundamentals of molecular symmetry and group theory are comprehensibly described in this book. Applications are given in context of electronic and vibrational spectroscopy as well as chemical reactions following orbital symmetry rules. Exercises and examples compile and deepen the content in a lucid manner.

Group Theory and its Applications, Volume III covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory. This volume contains five chapters and begins with an introduction to Wedderburn's theory to establish the structure of semisimple algebras, algebras of quantum mechanical interest, and group algebras. The succeeding chapter deals with Dynkin's theory for the embedding of semisimple complex Lie algebras in semisimple complex Lie algebras. These topics are followed by a review of the Frobenius algebra theory, its centrum, its irreducible, invariant subalgebras, and its matric basis. The discussion then shifts to the concepts and application of the Heisenberg-Weyl ring to quantum mechanics. Other chapters explore some well-known results about canonical transformations and their unitary representations; the Bargmann Hilbert spaces; the concept of complex phase space; and the concept of quantization as an eigenvalue problem. The final chapter looks into a theoretical approach to elementary particle interactions based on two-variable expansions of reaction amplitudes. This chapter also demonstrates the use of invariance properties of space-time and momentum space to write down and exploit expansions provided by the representation theory of the Lorentz group for relativistic particles, or the Galilei group for nonrelativistic ones. This book will prove useful to mathematicians, engineers, physicists, and advance students.

The aIm of the present article is to give a critical exposition of the theory of the symmetry properties of rigid and nonrigid molecules. Despite the fact that several accounts of the subject, both technical and didactic, are now available, and despite the extensive discussion of nonrigid molecule symmetry that has been going on since the classic papers of Hougen and Longuet-Higgins, there remains a need for a unifying survey of the problem. Previous treatments have tended to emphasize one or the other particular viewpoint at the expense of a broader view. Renewed interest in the details of the symmetry classification of rotation vibration states of highly symmetric (octahedral) molecules has led to a reexam ination of the relation between conventional point group operations and permutations of identical nuclei in rigid molecules, together with a clarification of the fundamental role of the Eckart constraints and associated Eckart frame. As is shown below, analogous insights can also be obtained in the case of nonrigid molecule symmetry, where the Eckart-Sayvetz conditions provide a natural generalization of the Eckart constraints. The importance of particular definitions of the 'molecule-fixed' frame in the theory of molecular symmetry can be better appreciated by examining their dynamical origin. Chapter 1 is therefore devoted to a description of the derivation of the usual Wilson-Howard-Watson form of the molecular Hamiltonian, together with its generalization to nonrigid molecules. Particular attention is given to the intro duction of molecular models and use of the Eckart and Eckart-Sayvetz constraints.

While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.

Volume 2 of the Handbook of Colorant Chemistry focuses on paints, painting and drawing systems used by the painter and craftsman. It describes in detail structure of oil, watercolor, acrylic and ceramic paints, inks, toners, and other drawing systems. From presenting molecular compositions of common paints and inks to a historical look at color chemistry, the author offers an in-depth look at the world of color. The complementary “Volume 1: Dyes and Pigments Fundamentals” (ISBN 978-3-11-077699-7) focuses on paints, painting and drawing systems used by the painter and craftsman. The book is supplemented by a comprehensive bibliography with references to standard works, monographs, and original papers. The reader is provided with a unique overview of the fi eld of color chemistry.

Mathematical Tools for Physicists is a unique collection of 18 carefully reviewed articles, each one written by a renowned expert working in the relevant field. The result is beneficial to both advanced students as well as scientists at work; the former will appreciate it as a comprehensive introduction, while the latter will use it as a ready reference. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic/ analytic / geometric methods - Symmetries and conservation laws - Mathematical modeling - Quantum computation The emphasis throughout is ensuring quick access to the information sought, and each article features: - an abstract - a detailed table of contents - continuous cross-referencing - references to the most relevant publications in the field, and - suggestions for further reading, both introductory as well as highly specialized. In addition, a comprehensive index provides easy access to the vast number of key words extending beyond the range of the headlines.

Discrete mathematics is used in the design and analysis of data structures, which are ways of storing and organizing data in computers. The data structures taught in this book are fundamental to computer science because they allow for the efficient and effective storage and manipulation of data. Applying discrete mathematics to the study of data structures allows for their construction, analysis, and the investigation of algorithm complexity. The data structures taught in this book are fundamental to computer science because they allow for the efficient and effective storage and manipulation of data. Applying discrete mathematics to the study of data structures allows for their construction, analysis, and the investigation of algorithm complexity. Discrete mathematics is used for the design and analysis of digital circuits, which are used to build computers and other electrical devices. Digital circuits rely on logic gates, which execute logical operations such as AND, OR, and NOT. Digital circuit design and analysis rely on discrete mathematics, a fundamental tenet of computer engineering theory.

Comprehensive Inorganic Chemistry II, Nine Volume Set reviews and examines topics of relevance to today’s inorganic chemists. Covering more interdisciplinary and high impact areas, Comprehensive Inorganic Chemistry II includes biological inorganic chemistry, solid state chemistry, materials chemistry, and nanoscience. The work is designed to follow on, with a different viewpoint and format, from our 1973 work, Comprehensive Inorganic Chemistry, edited by Bailar, Emeléus, Nyholm, and Trotman-Dickenson, which has received over 2,000 citations. The new work will also complement other recent Elsevier works in this area, Comprehensive Coordination Chemistry and Comprehensive Organometallic Chemistry, to form a trio of works covering the whole of modern inorganic chemistry. Chapters are designed to provide a valuable, long-standing scientific resource for both advanced students new to an area and researchers who need further background or answers to a particular problem on the elements, their compounds, or applications. Chapters are written by teams of leading experts, under the guidance of the Volume Editors and the Editors-in-Chief. The articles are written at a level that allows undergraduate students to understand the material, while providing active researchers with a ready reference resource for information in the field. The chapters will not provide basic data on the elements, which is available from many sources (and the original work), but instead concentrate on applications of the elements and their compounds. Provides a comprehensive review which serves to put many advances in perspective and allows the reader to make connections to related fields, such as: biological inorganic chemistry, materials chemistry, solid state chemistry and nanoscience Inorganic chemistry is rapidly developing, which brings about the need for a reference resource such as this that summarise recent developments and simultaneously provide background information Forms the new definitive source for researchers interested in elements and their applications; completely replacing the highly cited first edition, which published in 1973