Atomic & Molecular Symmetry Groups and Chemistry PDF
Preview Atomic & Molecular Symmetry Groups and Chemistry
Atomic & Molecular Symmetry Groups and Chemistry ATOMIC & MOLECULAR SYMMETRY GROUPS AND CHEMISTRY S. C. Rakshit, Ph.D. Formerly Professor of Chemistry, Burdwan University Levant Books Kolkata, India First published 2022 by CRC Press 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN and by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 © 2022 S. C. Rakshit and Levant Books CRC Press is an imprint of Informa UK Limited The right of S. C. Rakshit to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright. com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan). British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record has been requested ISBN: 9781032075310 (hbk) ISBN: 9781003208266 (ebk) To My Teachers Professor B. N. Ghosh who led me through the puzzling areas of research into the inner recess of chemistry Professor P. C. Rakshit ȱȱȱȱȱ ȱěȱȱ Professor S. K. Siddhanta whose scintillating lectures on Group Theory opened the door Preface The book scripted by me namely, Molecular Symmetry Groups and Chemistry had a welcome response from the readers. This emboldened me to have its present incarnation, Atomic & Molecular Symmetry Groups and Chemistry. This is a trimly fattened edition of the old one strengthened by the incorporation of the different aspects of atomic symmetry. Atomic Symmetry groups, being continuous groups, are just a fallout of the Lie Groups and Lie Algebras. The description of Lie Groups, for reasons of complexities, has been confined to the barest minimum so as not to produce much of indentations in the smooth description of atomic symmetry. Atoms are structurally simpler than molecules, but atomic symmetry is more complex than molecular symmetry. In quantum mechanics, we study atoms first and then the molecules. In symmetry studies, we just do the reverse. Apart from the theories, the descriptions of both the symmetry groups are attended with adequate applications. S. C. Rakshit vii Contents 1 Symmetry Elements and Symmetry Operations 1 1.1 Symmetry Elements, Symmetry Operations and Symbols 1 1.2 Symmetry Planes . . 6 1.3 Centre of Symmetry 7 1.4 Roto-reflection Axis of Symmetry . 8 1.5 Multiple Symmetry Operations, Inverse Operations and Simplified Symbols for Symmetry Operations 10 1.6 Choice of Origin and Axes . 12 1.7 Active and Passive Modes . 13 2 Groups and Molecular Point Groups 14 2.1 Groups, Definition, Elucidations and MultiplicationTables 14 2.2 Basic Concepts and Some Theorems 20 2.2.1 Generators 20 2.2.2 Subgroups. 21 2.2.3 Cosets 21 2.2.4 Some Finite Group Theorems . 21 2.2.5 Generators and Generation of Group Elements 23 2.2.6 Conjugate Elements and Classes 24 2.2.7 Invariant Subgroup . . 26 2.2.8 Direct Product Group 26 2.3 Molecular Symmetry Groups (Point Groups) 27 2.3.1 Classification of Point Symmetry Groups and Group Symbols ........................ 30 2.3.2 Generation of Point Symmetry Groups: Axial Point Groups. ....... . .................... 33 ix
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