Point Group Theory Tables
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| Author | : Simon L. Altmann |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 740 |
| Release | : 1994 |
| Genre | : Literary Criticism |
| ISBN | : |
This book--a unique reference for all those who use point groups--presents tables much improved over those previously available. They are more extensive, providing 75 point groups and their double groups. And they are more precise and complete--all symmetry operations are uniquely parameterized and their multiplication tables (including the double groups) are given. Full matrix representations are provided and particular attention has been paid to keeping phase factors constant on subduction along group chains. A theoretical introduction contains an extensive list of the subject's important results, a very clear statement of all conventions required, and detailed instructions--with examples--showing how to use the tables. Solved problems appear throughout the book. Besides being an indispensable reference tool for anyone who uses point groups, this book is an ideal resource for students taking group theory, chemistry, and physics courses.
| Author | : Philip H. Butler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 564 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1461331412 |
The mathematical apparatus of group theory is a means of exploring and exploiting physical and algebraic structure in physical and chemical prob lems. The existence of structure in the physical processes leads to structure in the solutions. For group theory to be useful this structure need not be an exact symmetry, although as examples of exact symmetries we have that the identity of electrons leads to permutation symmetries in many-electron wave functions, the spatial structure of crystals leads to the Bloch theory of crystal eigenfunctions, and the rotational invariance of the hydrogenic Hamiltonian leads to its factorization into angular and radial parts. In the 1930's Wigner extended what is known to mathematicians as the theory of group representations and the theory of group algebras to study the coupling coefficients of angular momentum, relating various properties of the coefficients to the properties of the abstract group of rotations in 3-space. In 1949 Racah, in a paper on rare earth spectra, showed that similar coefficients occur in other situations. Immediately a number of studies of the coefficients were begun, notably by Jahn, with his applications in nuclear physics. In the years since then a large number of physicists and chemists have added to the development of a general theory of the coefficients, or have produced specialized tables for a specific application. Applications now range from high-energy physics to biology.
| Author | : J. A. Salthouse |
| Publisher | : CUP Archive |
| Total Pages | : 100 |
| Release | : 1972-06-22 |
| Genre | : Science |
| ISBN | : 9780521081399 |
| Author | : M Ladd |
| Publisher | : Elsevier |
| Total Pages | : 424 |
| Release | : 1998-09-01 |
| Genre | : Mathematics |
| ISBN | : 0857099779 |
A comprehensive discussion of group theory in the context of molecular and crystal symmetry, this book covers both point-group and space-group symmetries. Provides a comprehensive discussion of group theory in the context of molecular and crystal symmetry Covers both point-group and space-group symmetries Includes tutorial solutions
| Author | : Mildred S. Dresselhaus |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 576 |
| Release | : 2007-12-18 |
| Genre | : Science |
| ISBN | : 3540328998 |
This concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.
| Author | : R. McWeeny |
| Publisher | : Elsevier |
| Total Pages | : 263 |
| Release | : 2013-09-03 |
| Genre | : Mathematics |
| ISBN | : 1483226247 |
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
| Author | : Christopher Bradley |
| Publisher | : Oxford University Press |
| Total Pages | : 758 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0199582580 |
This classic book gives, in extensive tables, the irreducible representations of the crystallographic point groups and space groups. These are useful in studying the eigenvalues and eigenfunctions of a particle or quasi-particle in a crystalline solid. The theory is extended to the corepresentations of the Shubnikov groups.
| Author | : Brian W. Pfennig |
| Publisher | : John Wiley & Sons |
| Total Pages | : 761 |
| Release | : 2015-03-30 |
| Genre | : Science |
| ISBN | : 1118859103 |
Aimed at senior undergraduates and first-year graduate students, this book offers a principles-based approach to inorganic chemistry that, unlike other texts, uses chemical applications of group theory and molecular orbital theory throughout as an underlying framework. This highly physical approach allows students to derive the greatest benefit of topics such as molecular orbital acid-base theory, band theory of solids, and inorganic photochemistry, to name a few. Takes a principles-based, group and molecular orbital theory approach to inorganic chemistry The first inorganic chemistry textbook to provide a thorough treatment of group theory, a topic usually relegated to only one or two chapters of texts, giving it only a cursory overview Covers atomic and molecular term symbols, symmetry coordinates in vibrational spectroscopy using the projection operator method, polyatomic MO theory, band theory, and Tanabe-Sugano diagrams Includes a heavy dose of group theory in the primary inorganic textbook, most of the pedagogical benefits of integration and reinforcement of this material in the treatment of other topics, such as frontier MO acid--base theory, band theory of solids, inorganic photochemistry, the Jahn-Teller effect, and Wade's rules are fully realized Very physical in nature compare to other textbooks in the field, taking the time to go through mathematical derivations and to compare and contrast different theories of bonding in order to allow for a more rigorous treatment of their application to molecular structure, bonding, and spectroscopy Informal and engaging writing style; worked examples throughout the text; unanswered problems in every chapter; contains a generous use of informative, colorful illustrations
| Author | : William McClain |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 672 |
| Release | : 2010-03-12 |
| Genre | : Science |
| ISBN | : 0387734708 |
Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.
| Author | : Sidney F. A. Kettle |
| Publisher | : John Wiley & Sons |
| Total Pages | : 436 |
| Release | : 2008-03-11 |
| Genre | : Science |
| ISBN | : 9780470516188 |
Building on the foundation of the Second Edition, Symmetry and Structure: Readable Group Theory for Chemists, Third Edition turns the complex and potentially difficult subject of group theory into an accessible and readable account of this core area of chemistry. By using a diagrammatical approach and demonstrating the physical principles involved in understanding group theory, the text provides a non-mathematical, yet thorough, treatment of this broad topic. This new edition has been fully revised and updated to include a much more three-dimensional and accurate visualization of many of the key topics. The chapter on octahedral molecules is extended to cover the important topic of the ligand field theory of octahedral transition metal complexes. Problems and summaries are included at the end of each chapter, the book provides detailed answers to frequently asked questions, and numerous diagrams and tables are featured for ease of reading and to enhance student understanding. Symmetry and Structure: Readable Group Theory for Chemists, Third Edition is an essential textbook for all students, researchers and lecturers in chemistry, biochemistry, chemical engineering, physics and material science.
