M. Hargittai, I. Hargittai - Symmetry through the Eyes of a Chemist (793765)
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Symmetry through the Eyes of a ChemistMagdolna Hargittai · István HargittaiSymmetry through the Eyesof a ChemistThird Edition123Magdolna HargittaiIstván HargittaiBudapest University of Technology and EconomicsP. O. Box 91H-1521 BudapestHungaryhargittaim@gmail.comistvan.hargittai@gmail.comISBN: 978-1-4020-5627-7e-ISBN: 978-1-4020-5628-4DOI 10.1007/978-1-4020-5628-4Library of Congress Control Number: 2008926635c Springer Science+Business Media B.V. 2009No part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recordingor otherwise, without written permission from the Publisher, with the exceptionof any material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work.Printed on acid-free paper9 8 7 6 5 4 3 2 1springer.comPrefaceIt is gratifying to launch the third edition of our book.
Its coming tolife testifies about the task it has fulfilled in the service of the community of chemical research and learning. As we noted in the Prefacesto the first and second editions, our book surveys chemistry from thepoint of view of symmetry. We present many examples from chemistry as well as from other fields to emphasize the unifying nature ofthe symmetry concept. Our aim has been to provide aesthetic pleasure in addition to learning experience. In our first Preface we paidtribute to two books in particular from which we learned a great deal;they have influenced significantly our approach to the subject matterof our book. They are Weyl’s classic, Symmetry, and Shubnikov andKoptsik’s Symmetry in Science and Art.The structure of our book has not changed.
Following the Introduction (Chapter 1), Chapter 2 presents the simplest symmetriesusing chemical and non-chemical examples. Molecular geometryis discussed in Chapter 3. The next four chapters present grouptheoretical methods (Chapter 4) and, based on them, discussions ofmolecular vibrations (Chapter 5), electronic structures (Chapter 6),and chemical reactions (Chapter 7). For the last two chapters wereturn to a qualitative treatment and introduce space-group symmetries (Chapter 8), concluding with crystal structures (Chapter 9).For the third edition we have further revised and streamlined ourtext and renewed the illustrative material.
We have expanded thesections dealing with biopolymers and quasicrystals in particular. Wehave added an Epilogue.We dedicated the first edition to the memory of József Pollák(1901–1973), who was the stepfather of one of us (IH). The thirdedition we dedicate to our children and grandchildren, and to thememory of our parents.vviPrefaceWe note with pleasure our joint interest in both chemistry andsymmetry for the past forty years that is behind this book. Our jointwriting efforts have been an important facet of our professional aswell as married life for these forty years.Budapest, January 2008Magdolna HargittaiIstván HargittaiAcknowledgmentsWe thank our colleagues and our students who have helped thecreation of this book over the years, especially at the University of Connecticut (Storrs); Eötvös Loránd University (Budapest);University of Texas (Austin); University of Hawaii (Honolulu);Budapest University of Technology and Economics; University ofNorth Carolina (Wilmington); and elsewhere.
We also appreciate thehelpful comments and suggestions from the reviewers of our bookand from its users and readers from all over the world. We wouldlike to express our gratitude to Professor Emil Molnár for helpfulconsultations.In connection with the preparation of the third edition of this book,we owe special thanks to Ms. Mária Kolonits, Ms. Judit Szücs, andMr. Zoltán Varga for their most careful technical help in many aspectsof the work.For over forty years our research in structural chemistry has beengenerously funded by the Hungarian Academy of Sciences and latelyalso by the Hungarian National Scientific Research Funds.
We arealso grateful for support to Eötvös University and especially to theBudapest University of Technology and Economics.viiContents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1References . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 202 Simple and Combined Symmetries . . . . . . . . . . . . . . . . . . . .2.1. Bilateral Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2. Rotational Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3. Combined Symmetries . . . . .
. . . . . . . . . . . . . . . . . . . . . .2.3.1. A Rotation Axis with Intersecting SymmetryPlanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.3.2. Snowflakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4. Inversion . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .2.5. Singular Point and Translational Symmetry . . . . . . . . .2.6. Polarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7. Chirality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.7.1. Asymmetry and Dissymmetry . . . . .
. . . . . . . .2.7.2. Vital Importance . . . . . . . . . . . . . . . . . . . . . . . .2.7.3. La coupe du roi . . . . . . . . . . . . . . . . . . . . . . . . .2.8. Polyhedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2525333737395355576066697476913 Molecular Shape and Geometry . . . . . . . . . . . . . . . . . . . . . . .3.1. Isomers . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2. Rotational Isomerism . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3. Symmetry Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4. Establishing the Point Group . . . . . . . . . . . . . . . . . . . . . .3.5. Examples . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.6. Consequences of Substitution . . . . . . . . . . . . . . . . . . . . .3.7. Polyhedral Molecular Geometries . . . . . . . . . . . . . . . . .9798100104105107115119ixxContents3.7.1. Boron Hydride Cages . . . . . . . . . . . . . . . . . .
. .3.7.2. Polycyclic Hydrocarbons . . . . . . . . . . . . . . . . .3.7.3. Structures with Central Atom . . . . . . . . . . . . . .3.7.4. Regularities in Nonbonded Distances . . . . . . .3.7.5. The VSEPR Model . . . . . . . . . . . . . . . . . . . . . .3.7.6. Consequences of Intramolecular Motion . . . . .References . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1231251331361391521614 Helpful Mathematical Tools . . . . . . . . . . . . . . . . . . . . . . . . . .4.1. Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2. Matrices . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3. Representation of Groups . . . . . . . . . . . . . . . . . . . . . . . .4.4. The Character of a Representation . . . . . . . . . . . . . . . . .4.5. Character Tables and Properties of IrreducibleRepresentations . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .4.6. Antisymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.7. Shortcut to Determine a Representation . . . . . . . . . . . . .4.8. Reducing a Representation . . . . . . . . . . . . . . . . . . . . . . .4.9. Auxiliaries . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .4.9.1. Direct Product . . . . . . . . . . . . . . . . . . . . . . . . . .4.9.2. Integrals of Product Functions . . . . . . . . . . . . .4.9.3. Projection Operator . . . . . . . . . . . . . . . . . . . . . .4.10. Dynamic Properties . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .4.11. Where Is Group Theory Applied? . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1691691761831895 Molecular Vibrations . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1. Normal Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.1. Their Number . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1.2. Their Symmetry . . . . . . . . . . . . . . . . . . . . . . . . .5.1.3. Their Types . . . . . . . . .
. . . . . . . . . . . . . . . . . . . .5.2. Symmetry Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . .5.3. Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.4. Examples . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2172172182202242252272292371911972042062082092092112122132146 Electronic Structure of Atoms and Molecules . . . . . . .
. . . . 2396.1. One-Electron Wave Function . . . . . . . . . . . . . . . . . . . . . 2416.2. Many-Electron Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Contentsxi6.3.Molecules . . . . . . . . . . . . . . .
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