Molecular Symmetry and Group Theory

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.

Die Symmetrie der Moleküle gehört zu den Grundpfeilern der modernen Chemie. Viele Studenten haben Schwierigkeiten mit der Mathematik, die den Symmetriebetrachtungen zugrunde liegt - der Gruppentheorie. Bei der Lösung dieser Probleme hilft der hier verfolgte Ansatz des "programmierten Lernens": Sorgfältig erarbeitete, geschickt kommentierte Übungen führen Schritt für Schritt von Symmetrieelement und Charaktertafel bis zur Berechnung von Molekülschwingungen. Besonders geeignet für das gezielte Selbststudium! (10/00)

Preface to the Second Edition vii

How to use the Programmes ix

Programme 1: Symmetry Elements and Operations 1

Programme 2: Point Groups 22

Programme 3: Non-degenerate Representations 46

Programme 4: Matrices 65

Programme 5: Degenerate Representations 85

Programme 6: Applications to Chemical Bonding 102

Programme 7: Applications to Molecular Vibration 122

Programme 8: Linear Combinations 139

Bibliography 173

Mathematical Data for use with Character Tables 174

Character Tables for Chemically Important Symmetry Groups 176

Index 186

"the best introduction to the subject, especially for those whose mathematics is weak." (Chemistry and Industry, 2nd April 2001)

".I recommend this book..." (Education in Chemistry, September 2002)

Alan Vincent is the author of Molecular Symmetry and Group Theory: A Programmed Introduction to Chemical Applications, 2nd Edition, published by Wiley.

The new edition of this best-selling 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. Molecular Symmetry and Group Theory is based around a series of programmes that help students learn at their own pace and enable them to 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. The second edition has been revised and expanded and includes 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.

Features:

• A concise, gentle introduction to symmetry and group theory
• Takes a programmed learning approach
• New material on projection operators, and the calculation of normal modes of vibration and normalised wave functions of orbitals