Molecular Symmetry and Group Theory E-Book

Alan Vincent

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 143

Veröffentlichungsjahr: 2013

Beschreibung

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.

Leseprobe

Contents

Preface to the Second Edition

How to use the Programmes

Programme 1: Symmetry Elements and Operations

Objectives

Assumed Knowledge

Symmetry Elements and Operations

Symmetry Elements and Operations Test

Symmetry Elements and Operations

Programme 2: Point Groups

Objectives

Assumed Knowledge

Point Groups

Point Groups Test

Answers

Point Groups

Systematic Classification of Molecules into Point Groups

Programme 3: Non-degenerate Representations

Objectives

Assumed Knowledge

Non-degenerate Representations

Non-degenerate Representations Test

Answers

Non-degenerate Representations

Programme 4: Matrices

Objectives

Assumed Knowledge

Matrices

Matrices Test

Answers

Matrices

Programme 5: Degenerate Representations

Objective

Assumed Knowledge

Note

Degenerate Representations

Degenerate Representations Test

Answers

Degenerate Representations

Programme 6: Applications to Chemical Bonding

Objectives

Assumed Knowledge

Applications to Chemical Bonding

Applications to Chemical Bonding Test

Answers

Applications to Chemical Bonding

Programme 7: Applications to Molecular Vibration

Objectives

Assumed Knowledge

Applications to Molecular Vibration

Applications to Molecular Vibration Test

Answers

Applications to Molecular Vibration

Programme 8: Linear Combinations

Objectives

Assumed Knowledge

A Simplified Procedure

Conclusion

Linear Combinations Test

Answers

Results of theTetrahedral Case

Linear Combinations

Bibliography

Mathematical Data for use with Character Tables

Character Tables for Chemically Important Symmetry Groups

Index

First edition © 1977 by John Wiley & Sons, Ltd

Reprinted 1978, 1979, 1981, 1983, 1985, 1987, 1988, 1990, 1992, 1993, 1996 (twice), 1997, 1998.

Second Edition copyright © 2001 by John Wiley & Sons Ltd,

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Reprinted 2003, 2005 (twice), 2006, 2008, 2009, 2010

All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, UK W1P OLP, without the permission in writing of the Publisher.

Other Wiley Editorial Offices

New York, Weinheim, Brisbane, Singapore, Toronto

Library of Congress Cataloging in Publication Data

Vincent, Alan

Molecular symmetry and group theory

Bibliography: p.

Includes index.

1. Molecular theory—Programmed instruction.

2. Symmetry (Physics)—Programmed instruction.

3. Groups, Theory of—Programmed instruction. I. Title.

QD461.V52 2000-10-16

541.2′2′077–dc21

00–043363

British Library Cataloging in Publication Data

A catalogue record for this book is available from the British Library

ISBN-13 978-0471-48939-9 (P/B)

Preface to the Second Edition

The first edition of this book was well received by both students and teachers. The second edition, therefore, has required only minor changes to the first seven chapters. In these I have put more emphasis on the idea of the basis of a reducible representation and have clarified a few small ambiguities which reviewers have pointed out. The diagrams have also been completely re-drawn. The major addition in this edition is a completely new chapter on linear combinations. This not only introduces the projection operator method as the rigorous approach to finding the form of vibrations, wave functions, etc., but goes on to develop a simplified approach to the subject making direct use of the character table. Again the emphasis is on the application of the techniques to real chemical problems rather than on the mathematics of the method. I hope that this will give readers an enthusiasm for symmetry methods and encourage them to learn more via the excellent advanced texts cited in the bibliography. 

Finally I would like to thank the (often anonymous) reviewers whose comments have been helpful in the process of revision and all the staff at John Wiley & Sons for their patience as I failed to meet various deadlines.

Alan Vincent

Kingston University

2000

How to use the Programmes

Each programme starts with a list of learning objectives, and a summary of the knowledge you will need before starting. You should study these sections carefully and make good any deficiencies in your previous knowledge. You may find it helpful at this stage to look at the revision notes at the end of the programme which give a summary of the material covered. The test, also at the end, will show you the sort of problems you should be able to tackle after working through the main text (but don’t at this stage look at the answers!). 

The body of each programme consists of information presented in small numbered sections termed frames. Each frame ends with a problem or question and then a line. You should cover the page with a sheet of paper or card and pull it down until you come to the line at the end of the frame. Read the frame and write down your answer to the question. This is most important - your learning will be much greater if you commit yourself actively by writing your answer down. You can check immediately whether or not your answer is right because each frame starts with the correct answer to the previous frame’s question. 

If you work through the whole programme in this way you will be learning at your own pace and checking on your progress as you go. If you are working at about the right pace you should get most of the questions right, but if you get one wrong you should read the frame again, look at the question, its answer, and any explanation offered, and try to understand how the answer was obtained. When you are satisfied about the answer go on to the next frame. 

Learning a subject (as opposed to just reading a book about it) can be a long job. Don’t get discouraged if you find the programmes taking a long time. Some students find this subject easy and work through each programme in about an hour or even less. Others have been known to take up to four hours for some programmes. Provided the programme objectives are achieved the time spent is relatively unimportant. 

After completing each programme try the test at the end and only proceed to the next programme if your test score is up to the standard indicated. 

Each programme finishes with a page of revision notes which should be helpful either to summarise the programme before or after use, or to serve as revision material later. 

I hope you find the programmes enjoyable and useful.

Programme 1

Symmetry Elements and Operations

Objectives

After completing this programme, you should be able to:

1. Recognise symmetry elements in a molecule.

2. List the symmetry operations generated by each element.

3. Combine together two operations to find the equivalent single operation.