Author: David Willock
Publisher: John Wiley & Sons
Symmetry and group theory provide us with a rigorous method for the description of the geometry of objects by describing the patterns in their structure. In chemistry it is a powerful concept 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, leading to a predictive understanding of the absorption properties of molecules and hence their spectra. Molecular Symmetry lays out the formal language used in the area, with illustrative examples of particular molecules throughout. It then applies the ideas of symmetry and group theory to describe molecular structure, bonding in molecules and to 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 Molecular orbital theory of chemical bonding Molecular Symmetry is designed to introduce the subject by combining symmetry with spectroscopy and bonding 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 operations and cover key aspects of the material in depth. 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.
Author: P.R. Bunker,P. Jensen
Publisher: CRC Press
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.
Author: Philip Bunker
Molecular Symmetry and Spectroscopy deals with the use of group theory in quantum mechanics in relation to problems in molecular spectroscopy. It discusses the use of the molecular symmetry group, whose elements consist of permutations of identical nuclei with or without inversion. After reviewing the permutation groups, inversion operation, point groups, and representation of groups, the book describes the use of representations for labeling molecular energy. The text explains an approximate time independent Schrödinger equation for a molecule, as well as the effect of a nuclear permutation or the inversion of E* on such equation. The book also examines the expression for the complete molecular Hamiltonian and the several groups of operations commuting with the Hamiltonian. The energy levels of the Hamiltonian can then be symmetrically labeled by the investigator using the irreducible representations of these groups. The text explains the two techniques to change coordinates in a Schrödinger equation, namely, (1) by using a diatomic molecule in the rovibronic Schrödinger equation, and (2) by a rigid nonlinear polyatomic molecule. The book also explains that using true symmetry, basis symmetry, near symmetry, and near quantum numbers, the investigator can label molecular energy levels. The text can benefit students of molecular spectroscopy, academicians, and investigators of molecular chemistry or quantum mechanics.
Author: Yngve Öhrn
Publisher: John Wiley & Sons
A unique, much-needed introduction to molecular symmetry and group theory Elements of Molecular Symmetry takes the topic of group theory a step further than most books, presenting a quantum chemistry treatment useful for computational, quantum, physical, and inorganic chemists alike. Clearly explaining how general groups and group algebra describe molecules, Yngve Ohrn first develops the theory, then provides coverage not only for point groups, but also permutation groups, space groups, and Lie groups. With over three decades of teaching experience, Dr. Ohrn brings to the discussion unprecedented depth and clarity, incorporating rigorous topics at a level accessible to anyone with basic knowledge of calculus and algebra. This unique and timely book: * Extends coverage to molecular orbital theory, * Utilizes powerful examples to illustrate basic concepts * Contains introductory material on space groups and continuous groups, including point-group character tables * Provides a solid background for exploring the theoretical literature
A Programmed Introduction to Chemical Applications
Author: Alan Vincent
Publisher: John Wiley & Sons
This substantially revised and expanded new edition of the bestselling textbook, addresses the difficulties that can arise with the mathematics that underpins the study of symmetry, and acknowledges that group theory can be a complex concept for students to grasp. Written in a clear, concise manner, the author introduces a series of programmes that help students learn at their own pace and enable to them understand the subject fully. Readers are taken through a series of carefully constructed exercises, designed to simplify the mathematics and give them a full understanding of how this relates to the chemistry. This second edition contains a new chapter on the projection operator method. This is used to calculate the form of the normal modes of vibration of a molecule and the normalised wave functions of hybrid orbitals or molecular orbitals. The features of this book include: * A concise, gentle introduction to symmetry and group theory * Takes a programmed learning approach * New material on projection operators, and the calcultaion of normal modes of vibration and normalised wave functions of orbitals This book is suitable for all students of chemistry taking a first course in symmetry and group theory.
Author: Robert L. Carter
This comprehensive text provides readers with a thorough introduction to molecular symmetry and group theory as applied to chemical problems. Its friendly writing style invites the reader to discover by example the power of symmetry arguments for understanding otherwise intimidating theoretical problems in chemistry. A unique feature demonstrates the centrality of symmetry and group theory to a complete understanding of the theory of structure and bonding." Fundamental Concepts." Representations of Groups." Techniques and Relationships for Chemical Applications." Symmetry and Chemical Bonding." Equations for Wave Functions." Vibrational Spectroscopy." Transition Metal Complexes.
Author: J. S. Ogden
Publisher: Oxford University Press on Demand
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
A new kind of tutorial book
Author: William McClain
Publisher: Springer Science & Business Media
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.
New Ideas for Solving Old Problems
Author: Hanno Schmiedt
This book presents a range of fundamentally new approaches to solving problems involving traditional molecular models. Fundamental molecular symmetry is shown to open new avenues for describing molecular dynamics beyond standard perturbation techniques. Traditional concepts used to describe molecular dynamics are based on a few fundamental assumptions, the ball-and-stick picture of molecular structure and the respective perturbative treatment of different kinds of couplings between otherwise separate motions. The book points out the conceptual limits of these models and, by focusing on the most essential idea of theoretical physics, namely symmetry, shows how to overcome those limits by introducing fundamentally new concepts. The book begins with an introduction to molecular symmetry in general, followed by a discussion of nuclear spin symmetry. Here, a new correlation between identical particle exchange and spin angular momentum symmetry of nuclei is exhibited. The central part of the book is the discussion of extremely floppy molecules, which are not describable in the framework of traditional theories. The book introduces a fundamentally new approach to describing the molecular dynamics of these molecules - the super-rotor model, which is based on a five-dimensional symmetry that has never been observed in molecules before. By applying the super-rotor theory to the prototype of floppy molecules, protonated methane, this model can consistently predict the symmetry and energy of low-energy states, which were characterized experimentally only a few years ago. The theoretical predictions agree with the experimental results, which makes the prospect of further developing the super-rotor theory and applying it to other molecules a promising one. In the final section, the book also covers the topic of ultrafast rotations, where usual quantum calculations reach their natural limits. A semi-classical method for determining rotational energies, developed in the early 1990s, is shown to be attachable to quantum calculations of the vibrational states. This new combined method is suitable for efficiently calculating ro-vibrational energies, even for molecular states with large angular momentum.
An Introduction to Vibrational and Electronic Spectroscopy
Author: Daniel C. Harris,Michael D. Bertolucci
Publisher: Courier Corporation
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.
Author: Melvin Lax
Publisher: Courier Corporation
High-level text applies group theory to physics problems, develops methods for solving molecular vibration problems and for determining the form of crystal tensors, develops translational properties of crystals, more. 1974 edition.
Author: G. S. Ezra
Publisher: Springer Science & Business Media
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.
Author: Carlo di Lauro
Recent advances in infrared molecular spectroscopy have resulted in sophisticated theoretical and laboratory methods that are difficult to grasp without a solid understanding of the basic principles and underlying theory of vibration-rotation absorption spectroscopy. Rotational Structure in Molecular Infrared Spectra fills the gap between these recent, complex topics and the most elementary methods in the field of rotational structure in the infrared spectra of gaseous molecules. There is an increasing need for people with the skills and knowledge to interpret vibration-rotation spectra in many scientific disciplines, including applications in atmospheric and planetary research. Consequently, the basic principles of vibration-rotation absorption spectroscopy are addressed for contemporary applications. In addition to covering operational quantum mechanical methods, spherical tensor algebra, and group theoretical methods applied to molecular symmetry, attention is also given to phase conventions and their effects on the values of matrix elements. Designed for researchers and PhD students involved in the interpretation of vibration-rotation spectra, the book intentionally separates basic theoretical arguments (in the appendices), allowing readers who are mainly concerned with applications to skip the principles while at the same time providing a sound theoretical basis for readers who are looking for more foundational information. Reviews basic theory and contemporary methods of vibration rotation absorption spectroscopy, including operational quantum mechanical methods, spherical tensor algebra, and group theoretical methods applied to molecular symmetry Covers sophisticated mathematical topics in simple, easy-to-read language Discusses methods and applications separately from basic theoretical arguments for quick reference
An Introduction to Group Theory and Its Applications
Author: R. McWeeny
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.