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This book presents a comprehensive theoretical basis of symmetry representations of molecular vibrations, matrix representation of symmetries, and the elements of group theory that are relevant to other symmetry elements/operations, crystallographic and molecular point groups. The book helps understand the reducible and irreducible representations of symmetry matrices and then derive the normal modes of vibration of different molecules by using suitable techniques independently. Targeted to graduate students and researchers, this book aims not only to derive the normal modes of vibration of any given molecule themselves but also compares and verifies them with the experimentally found modes by using IR and Raman-related techniques. For the first time in the crystallographic history, this book presents the group multiplication tables of all 32 point groups in both international and Schoenflies notations.
Informal, effective undergraduate-level text introduces vibrational and electronic spectroscopy, presenting applications of group theory to the interpretation of UV, visible, and infrared spectra without assuming a high level of background knowledge. 200 problems with solutions. Numerous illustrations. "A uniform and consistent treatment of the subject matter." — Journal of Chemical Education.
This book presents a comprehensive theoretical basis of symmetry representations of molecular vibrations, matrix representation of symmetries, and the elements of group theory that are relevant to other symmetry elements/operations, crystallographic and molecular point groups. The book helps understand the reducible and irreducible representations of symmetry matrices and then derive the normal modes of vibration of different molecules by using suitable techniques independently. Targeted to graduate students and researchers, this book aims not only to derive the normal modes of vibration of any given molecule themselves but also compares and verifies them with the experimentally found modes by using IR and Raman-related techniques. For the first time in the crystallographic history, this book presents the group multiplication tables of all 32 point groups in both international and Schoenflies notations.
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.
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
This Primer presents an introduction to molecular symmetry and point groups with an emphasis on their applications. The author has adopted a non-mathematical approach as far as possible and the text will supplement those that are too advanced or gloss over important information. Chapter topics include symmetry elements, operations and point groups; matrices, multiplications tables and representations; the reduction formula; molecular vibrations; vibrational spectroscopy and degenerate vibrations; symmetry aspects of chemical bonding and matrices in higher order point groups
Winner of a 2005 CHOICE Outstanding Academic Book Award Molecular symmetry is an easily applied tool for understanding and predicting many of the properties of molecules. Traditionally, students are taught this subject using point groups derived from the equilibrium geometry of the molecule. Fundamentals of Molecular Symmetry shows how to set up symmetry groups for molecules using the more general idea of energy invariance. It is no more difficult than using molecular geometry and one obtains molecular symmetry groups. The book provides an introductory description of molecular spectroscopy and quantum mechanics as the foundation for understanding how molecular symmetry is defined and used. The approach taken gives a balanced account of using both point groups and molecular symmetry groups. Usually the point group is only useful for isolated, nonrotating molecules, executing small amplitude vibrations, with no tunneling, in isolated electronic states. However, for the chemical physicist or physical chemist who wishes to go beyond these limitations, the molecular symmetry group is almost always required.
Symmetry and group theory provide us with a formal method for the description of the geometry of objects by describing the patterns in their structure. In chemistry it is a powerful method that underlies many apparently disparate phenomena. Symmetry allows us to accurately describe the types of bonding that can occur between atoms or groups of atoms in molecules. It also governs the transitions that may occur between energy levels in molecular systems, which in turn allows us to predict the absorption properties of molecules and hence their spectra. Molecular Symmetry lays out the formal language used in the area using illustrative examples of particular molecules throughout. It then applies the ideas of symmetry to describe molecular structure, bonding in molecules and consider the implications in spectroscopy. Topics covered include: Symmetry elements Symmetry operations and products of operations Point groups used with molecules Point group representations, matrices and basis sets Reducible and irreducible representations Applications in vibrational spectroscopy Symmetry in chemical bonding Molecular Symmetry is designed to introduce the subject by combining symmetry with spectroscopy in a clear and accessible manner. Each chapter ends with a summary of learning points, a selection of self-test questions, and suggestions for further reading. A set of appendices includes templates for paper models which will help students understand symmetry groups. Molecular Symmetry is a must-have introduction to this fundamental topic for students of chemistry, and will also find a place on the bookshelves of postgraduates and researchers looking for a broad and modern introduction to the subject.
This is a textbook for advanced undergraduate inorganic chemistry courses, covering elementary inorganic reaction chemistry through to more advanced inorganic theories and topics. The approach integrates bioinorganic, environmental, geological and medicinal material into each chapter, and there is a refreshing empirical approach to problems in which the text emphasizes observations before moving onto theoretical models. There are worked examples and solutions in each chapter combined with chapter-ending study objectives, 40-70 exercises per chapter and experiments for discovery-based learning.
Atomic Symmetry Groups, being continuous groups, are just a fallout of the Lie Groups and Lie Algebras. Atoms are structurally simpler than molecules but atomic symmetry is more complex than molecular symmetry. In quantum mechanics we study atoms first and then the molecules. In symmetry studies, we do just the reverse. In this book, apart from theories, the description of both the symmetry groups – atomic and molecular, are attended with adequate applications. Please note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.