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In chapter 1, after an outline of some historical aspects of the use of symmetry in chemistry is given, the scene is set by introducing a number of group theoretical techniques that have been employed by chemists. Chapter 2 considers in detail the nature and the differing types of groups that have been employed by chemists and others in their description of chemical systems. In chapter 3 a comparatively new mathematical formalism is presented that is now being increasingly used for the interpretation of stereochemical phenomena. The symmetry of molecules is analyzed from a group-theoretical perspective in chapter 4, while in chapter 5 the symmetry of the chemical graphs that are commonly used to represent both organic and inorganic molecules is addressed. Chapters 4 and 5 together encompass applications such as the enumeration of many different chemical isomers and analysis of the symmetry characteristics of a variety of recently synthesized molecules such as the fullerenes.
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CHEMICAL GROUP THEORY
Mathematical Chemistry A series of books edited by:
Danail Bonchev, Department of Physical Chemistry, Higher Institute of Chemical Technology, Burgas, Bulgaria
Dennis H. Rouvray, Department of Chemistry, University of Georgia, Athens, Georgia, USA
Volume 1 CHEMICAL GRAPH THEORY: Introduction and Fundamentals
Volume 2 CHEMICAL GRAPH THEORY: Reactivity and Kinetics
Volume 3 CHEMICAL GROUP THEORY: Introduction and Fundamentals
Additional Volume in Preparation Volume 4 CHEMICAL GROUP THEORY: Reactivity and Kinetics
This book is part of a series. The publisher will accept continuation orders which may be cancelled at any time and which provide for automatic billing and shipping of each title in the series upon publication. Please write for details.
CHEMICAL GROUP THEORY Introduction and Fundamentals Edited by
Danail Bonchev Department of Physical Chemistry, Higher Institute of Technology, Burgas, Bulgaria and
Dennis H. Rouvray Department of Chemistry, University of Georgia, Athens, USX
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Library of Congress Cataloging-in-Publication Data
Chemical group theory: introduction and fundamentals / edited by Danail Bonchev and Dennis H. Rouvray. p. cm.- ( Mathematical chemistry; v. 3) Includes bibliographical references and index. 1. Group theory. 2. Chemistry, Physical and theoretical. I. Bonchev. Danail. II. Rouvray, D.H. III. Series. QD455.3.G75C48 1994 5407F5122—dc20 93-38653 CIP
CONTENTS
INTRODUCTION TO THE SERIES
vii
PREFACE
xi
1.
SYMMETRY IN CHEMISTRY
R.B. King 1. 2. 3. 4. 5. 6. 7. 8. 9. 2.
3.
1
Introduction Symmetry Operations Symmetry Point Groups Symmetry of Crystals and Quasicrystals: Lattices and Space Groups Matrix Representations of Symmetry Groups Permutation Groups Framework Groups Symmetry, Isomerism and Enumeration References
1 5 6 11 15 18 23 25 29
BIG GROUPS, SMALL GROUPS AND THEIR CONNECTIONS
R. L. Flurry, Jr.
31
1. 2. 3. 4. 5. 6. 7. 8.
31 43 47 60 66 73 79 79
Introduction Rotation