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 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.
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.
A unique, much-needed introduction to molecular symmetry and grouptheory Elements of Molecular Symmetry takes the topic of grouptheory a step further than most books, presenting a quantumchemistry treatment useful for computational, quantum, physical,and inorganic chemists alike. Clearly explaining how general groupsand group algebra describe molecules, Yngve Öhrn firstdevelops the theory, then provides coverage not only for pointgroups, but also permutation groups, space groups, and Lie groups.With over three decades of teaching experience, Dr. Öhrnbrings to the discussion unprecedented depth and clarity,incorporating rigorous topics at a level accessible to anyone withbasic knowledge of calculus and algebra. This unique and timelybook: * Extends coverage to molecular orbital theory, * Utilizes powerful examples to illustrate basic concepts * Contains introductory material on space groups and continuousgroups, including point-group character tables * Provides a solid background for exploring the theoreticalliterature
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.
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.
Suitable for advanced undergraduates and graduate students, this text covers V coefficients for symmetry groups, W coefficients, irreducible products, two-electron formulae for the octahedral group, X coefficients, more. 1962 edition.
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.