Group Theory for Chemists

Group Theory for Chemists

Fundamental Theory and Applications

2nd Edition - December 21, 2010

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  • Author: Kieran Molloy
  • eBook ISBN: 9780857092410
  • Paperback ISBN: 9780857092403

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Description

The basics of group theory and its applications to themes such as the analysis of vibrational spectra and molecular orbital theory are essential knowledge for the undergraduate student of inorganic chemistry. The second edition of Group Theory for Chemists uses diagrams and problem-solving to help students test and improve their understanding, including a new section on the application of group theory to electronic spectroscopy.Part one covers the essentials of symmetry and group theory, including symmetry, point groups and representations. Part two deals with the application of group theory to vibrational spectroscopy, with chapters covering topics such as reducible representations and techniques of vibrational spectroscopy. In part three, group theory as applied to structure and bonding is considered, with chapters on the fundamentals of molecular orbital theory, octahedral complexes and ferrocene among other topics. Additionally in the second edition, part four focuses on the application of group theory to electronic spectroscopy, covering symmetry and selection rules, terms and configurations and d-d spectra.Drawing on the author’s extensive experience teaching group theory to undergraduates, Group Theory for Chemists provides a focused and comprehensive study of group theory and its applications which is invaluable to the student of chemistry as well as those in related fields seeking an introduction to the topic.

Key Features

  • Provides a focused and comprehensive study of group theory and its applications, an invaluable resource to students of chemistry as well as those in related fields seeking an introduction to the topic
  • Presents diagrams and problem-solving exercises to help students improve their understanding, including a new section on the application of group theory to electronic spectroscopy
  • Reviews the essentials of symmetry and group theory, including symmetry, point groups and representations and the application of group theory to vibrational spectroscopy

Readership

Professionals and academics

Table of Contents

  • Part I: Symmetry and Groups

    Chapter 1: Symmetry

    1.1 SYMMETRY

    1.2 POINT GROUPS

    1.3 CHIRALITY AND POLARITY

    1.4 SUMMARY

    PROBLEMS

    Chapter 2: Groups and Representations

    2.1 GROUPS

    2.2 TRANSFORMATION MATRICES

    2.3 REPRESENTATIONS OF GROUPS

    2.4 CHARACTER TABLES

    2.5 SYMMETRY LABELS

    2.6 SUMMARY

    PROBLEMS

    Part II: Application of Group Theory to Vibrational Spectroscopy

    Chapter 3: Reducible Representations

    3.1 REDUCIBLE REPRESENTATIONS

    3.2 THE REDUCTION FORMULA

    3.3 THE VIBRATIONAL SPECTRUM OF SO2

    3.4 CHI PER UNSHIFTED ATOM

    3.5 SUMMARY

    PROBLEMS

    Chapter 4: Techniques of Vibrational Spectroscopy

    4.1 GENERAL CONSIDERATIONS

    4.2 INFRARED SPECTROSCOPY

    4.3 RAMAN SPECTROSCOPY

    4.4 RULE OF MUTUAL EXCLUSION

    4.5 SUMMARY

    PROBLEMS

    Chapter 5: The Vibrational Spectrum of Xe(O)F4

    5.1 STRETCHING AND BENDING MODES

    5.2 THE VIBRATIONAL SPECTRUM OF Xe(O)F4

    5.3 GROUP FREQUENCIES

    PROBLEMS

    Part III: Application of Group Theory to Structure and Bonding

    Chapter 6: Fundamentals of Molecular Orbital Theory

    6.1 BONDING IN H2

    6.2 BONDING IN LINEAR H3

    6.3 LIMITATIONS IN A QUALITATIVE APPROACH

    6.4 SUMMARY

    PROBLEMS

    Chapter 7: H2O – Linear or Angular ?

    7.1 SYMMETRY-ADAPTED LINEAR COMBINATIONS

    7.2 CENTRAL ATOM ORBITAL SYMMETRIES

    7.3 A MOLECULAR ORBITAL DIAGRAM FOR H2O

    7.4 A C2v/D∞h MO CORRELATION DIAGRAM

    7.5 SUMMARY

    PROBLEMS

    Chapter 8: NH3 – Planar or Pyramidal ?

    8.1 LINEAR OR TRIANGULAR H3 ?

    8.2 A MOLECULAR ORBITAL DIAGRAM FOR BH3

    8.3 OTHER CYCLIC ARRAYS

    8.4 SUMMARY

    PROBLEMS

    Chapter 9: Octahedral Complexes

    9.1 SALCS FOR OCTAHEDRAL COMPLEXES

    9.2 d-ORBITAL SYMMETRY LABELS

    9.3 OCTAHEDRAL P-BLOCK COMPLEXES

    9.4 OCTAHEDRAL TRANSITION METAL COMPLEXES

    9.5 π-BONDING AND THE SPECTROCHEMICAL SERIES

    9.6 SUMMARY

    PROBLEMS

    Chapter 10: Ferrocene

    10.1 CENTRAL ATOM ORBITAL SYMMETRIES

    10.2 SALCS FOR CYCLOPENTADIENYL ANION

    10.3 MOLECULAR ORBITALS FOR FERROCENE

    PROBLEMS

    Part IV: Application of Group Theory to Electronic Spectroscopy

    Chapter 11: Symmetry and Selection Rules

    11.1 SYMMETRY OF ELECTRONIC STATES

    11.2 SELECTION RULES

    11.3 THE IMPORTANCE OF SPIN

    11.4 DEGENERATE SYSTEMS

    11.5 EPILOGUE – SELECTION RULES FOR VIBRATIONAL SPECTROSCOPY

    11.6 SUMMARY

    PROBLEMS

    Chapter 12: Terms and Configurations

    12.1 TERM SYMBOLS

    12.2 THE EFFECT OF A LIGAND FIELD – ORBITALS

    12.3 SYMMETRY LABELS FOR dn CONFIGURATIONS – AN OPENING

    Table 12.5 Direct product table for octahedral symmetry

    12.4 WEAK LIGAND FIELDS, TERMS AND CORRELATION DIAGRAMS

    12.5 SYMMETRY LABELS FOR dn CONFIGURATIONS – CONCLUSION

    12.6 SUMMARY

    PROBLEMS

    Chapter 13: d-d Spectra

    13.1 THE BEER-LAMBERT LAW

    13.2 SELECTION RULES AND VIBRONIC COUPLING

    13.3 THE SPIN SELECTION RULE

    13.4 d-d SPECTRA – HIGH-SPIN OCTAHEDRAL COMPLEXES

    13.5 d-d SPECTRA – TETRAHEDRAL COMPLEXES

    13.6 d-d SPECTRA – LOW-SPIN COMPLEXES

    13.7 DESCENDING SYMMETRY

    13.8 SUMMARY

    PROBLEMS

    Appendices

    Appendix 1: Projection Operators

    APPENDIX 2: Microstates and Term Symbols

    Appendix 3: Answers to SAQs

    APPENDIX 4: Answers to Problems

    Appendix 5: Selected Character Tables

    Index

Product details

  • No. of pages: 232
  • Language: English
  • Copyright: © Woodhead Publishing 2010
  • Published: December 21, 2010
  • Imprint: Woodhead Publishing
  • eBook ISBN: 9780857092410
  • Paperback ISBN: 9780857092403

About the Author

Kieran Molloy

Kieran C. Molloy is Professor of Inorganic Chemistry at the University of Bath.

Affiliations and Expertise

University of Bath, UK

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