Chemical applications of symmetry and group theory

392 Pages·2017·38.58 MB·English

by  Ameta

CHEMICAL APPLICATIONS
OF SYMMETRY AND
GROUP THEORY

CHEMICAL APPLICATIONS
OF SYMMETRY AND
GROUP THEORY
Rakshit Ameta, PhD
Suresh C. Ameta, PhD
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Library and Archives Canada Cataloguing in Publication
Ameta, Rakshit, author
Chemical applications of symmetry and group theory / Rakshit Ameta, PhD, Suresh C. Ameta,
PhD.
Includes bibliographical references and index.
Issued in print and electronic formats.
ISBN 978-1-77188-398-6 (hardcover).--ISBN 978-1-77188-399-3 (pdf).
1. Group theory. 2. Symmetry (Physics). 3. Chemistry, Physical and theoretical. I. Ameta,
Suresh C., author II. Title.
QD455.3.G75A44 2016 541'.2 C2016-905082-3 C2016-905083-1
Library of Congress Cataloging-in-Publication Data
Names: Ameta, Rakshit. | Ameta, Suresh C.
Title: Chemical applications of symmetry and group theory / Rakshit Ameta, PhD, Suresh C.
Ameta, PhD.
Description: Toronto : Apple Academic Press, 2017. | Includes bibliographical references and
index.
Identifiers: LCCN 2016032885 (print) | LCCN 2016035313 (ebook) | ISBN 9781771883986
(hardcover : alk. paper) | ISBN 9781771883993 ()
Subjects: LCSH: Chemistry, Physical and theoretical--Mathematics. | Group theory. | Symmetry
(Physics)
Classification: LCC QD455.3.G75 A44 2017 (print) | LCC QD455.3.G75 (ebook)
DDC 541.01/5122--dc23
LC record available at https://lccn.loc.gov/2016032885
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CONTENTS
List of Abbreviations ..................................................................................vii
Preface ........................................................................................................ix
About the Authors ........................................................................................xi
1. Symmetry ....................................................................................................1
2. Point Groups .............................................................................................47
3. Group Theory ...........................................................................................71
4. Matrices .....................................................................................................99
5. Character Tables ....................................................................................133
6. Hybridization ..........................................................................................151
7. Molecular Orbital Theory .....................................................................189
8. Molecular Vibrations .............................................................................243
9. Coordination Compounds and Others .................................................289
Character Tables for Chemically Important Symmetry Groups ..............359
Suggested Further Reading ......................................................................372
Index .........................................................................................................373

LIST OF ABBREVIATIONS
AOs atomic orbitals
CFSE crystal field stabilization energy
ED delocalization energy
GMT group multiplication table
GOT great orthogonality theorem
IR irreducible representation
L ligands
LCAO linear combination of atomic orbitals
LGO ligand group orbitals
LOs ligand orbitals
MOT molecular orbital theory
NUA number of unshifted atom
P pairing energy
R reducible representations
SALC symmetry-adapted linear combination
UA unshifted atom
VBT valence bond theory

PREFACE
Symmetry gives us a sense of beauty, and group theory is a study of symme-
try in molecules. When one is dealing with an object that appears symmetric,
group theory can help us with its analysis. As the structure and behavior
of molecules and crystals depend on their different symmetries, group the-
ory becomes an essential tool in many important areas of chemistry. Group
theory is a part of mathematical sciences. It is a quite powerful theoreti-
cal tool to predict many basics as well as some characteristic properties of
molecules. Where quantum mechanics provide solutions of some chemical
problems on the basis of complicated mathematics, group theory puts for-
ward these solutions in a very simplified and fascinating manner.
Apart from chemical applications of group theory, it has been also applied
to robotics, computers, medical image analysis, crystallography, mathemati-
cal music theory, statistics, cosmological, stellar and atomic particle abstrac-
tions, modeling of vibrational modes of virus, molecular systems biology,
mathematical biology, spectroscopy, etc.
Group theory has been successfully applied to many chemical problems.
Students and teachers of chemical sciences have an invisible fear from this
subject due to inadvertence with the mathematical jugglery and an active
sixth dimension required to understand the concept as well as to apply it to
solve the problems of chemistry. The subject of group theory is difficult to
understand by the readers of chemical sciences lacking strong mathematical
background. The main aim of this book is to avoid mathematical complica-
tions and present it in a form that the student, teacher, as well as researcher
will find friendly.
A number of chemists have helped us in finalizing the script of group
theory at various stages, and worth mentioning are Dr. Jitendra Vardia,
Vadodara, Dr. Dipti Vaya, Delhi, Dr. Aarti Ameta, Udaipur and would-be Dr.
Meenakshi Singh Solanki, Udaipur.
Rakshit Ameta, PhD
Suresh C. Ameta, PhD