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Group Theory for Chemists, 2nd Edition

Book 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.

  • 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

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. About the Author
  5. Copyright
  6. Preface
  7. Part I: Symmetry and Groups
    1. Chapter 1: Symmetry
      1. 1.1 SYMMETRY
      2. 1.2 POINT GROUPS
      3. 1.3 CHIRALITY AND POLARITY
      4. 1.4 SUMMARY
      5. PROBLEMS
    2. Chapter 2: Groups and Representations
      1. 2.1 GROUPS
      2. 2.2 TRANSFORMATION MATRICES
      3. 2.3 REPRESENTATIONS OF GROUPS
      4. 2.4 CHARACTER TABLES
      5. 2.5 SYMMETRY LABELS
      6. 2.6 SUMMARY
      7. PROBLEMS
  8. Part II: Application of Group Theory to Vibrational Spectroscopy
    1. Chapter 3: Reducible Representations
      1. 3.1 REDUCIBLE REPRESENTATIONS
      2. 3.2 THE REDUCTION FORMULA
      3. 3.3 THE VIBRATIONAL SPECTRUM OF SO2
      4. 3.4 CHI PER UNSHIFTED ATOM
      5. 3.5 SUMMARY
      6. PROBLEMS
    2. Chapter 4: Techniques of Vibrational Spectroscopy
      1. 4.1 GENERAL CONSIDERATIONS
      2. 4.2 INFRARED SPECTROSCOPY
      3. 4.3 RAMAN SPECTROSCOPY
      4. 4.4 RULE OF MUTUAL EXCLUSION
      5. 4.5 SUMMARY
      6. PROBLEMS
    3. Chapter 5: The Vibrational Spectrum of Xe(O)F4
      1. 5.1 STRETCHING AND BENDING MODES
      2. 5.2 THE VIBRATIONAL SPECTRUM OF Xe(O)F4
      3. 5.3 GROUP FREQUENCIES
      4. PROBLEMS
  9. Part III: Application of Group Theory to Structure and Bonding
    1. Chapter 6: Fundamentals of Molecular Orbital Theory
      1. 6.1 BONDING IN H2
      2. 6.2 BONDING IN LINEAR H3
      3. 6.3 LIMITATIONS IN A QUALITATIVE APPROACH
      4. 6.4 SUMMARY
      5. PROBLEMS
    2. Chapter 7: H2O – Linear or Angular ?
      1. 7.1 SYMMETRY-ADAPTED LINEAR COMBINATIONS
      2. 7.2 CENTRAL ATOM ORBITAL SYMMETRIES
      3. 7.3 A MOLECULAR ORBITAL DIAGRAM FOR H2O
      4. 7.4 A C2v/D∞h MO CORRELATION DIAGRAM
      5. 7.5 SUMMARY
      6. PROBLEMS
    3. Chapter 8: NH3 – Planar or Pyramidal ?
      1. 8.1 LINEAR OR TRIANGULAR H3 ?
      2. 8.2 A MOLECULAR ORBITAL DIAGRAM FOR BH3
      3. 8.3 OTHER CYCLIC ARRAYS
      4. 8.4 SUMMARY
      5. PROBLEMS
    4. Chapter 9: Octahedral Complexes
      1. 9.1 SALCS FOR OCTAHEDRAL COMPLEXES
      2. 9.2 d-ORBITAL SYMMETRY LABELS
      3. 9.3 OCTAHEDRAL P-BLOCK COMPLEXES
      4. 9.4 OCTAHEDRAL TRANSITION METAL COMPLEXES
      5. 9.5 π-BONDING AND THE SPECTROCHEMICAL SERIES
      6. 9.6 SUMMARY
      7. PROBLEMS
    5. Chapter 10: Ferrocene
      1. 10.1 CENTRAL ATOM ORBITAL SYMMETRIES
      2. 10.2 SALCS FOR CYCLOPENTADIENYL ANION
      3. 10.3 MOLECULAR ORBITALS FOR FERROCENE
      4. PROBLEMS
  10. Part IV: Application of Group Theory to Electronic Spectroscopy
    1. Chapter 11: Symmetry and Selection Rules
      1. 11.1 SYMMETRY OF ELECTRONIC STATES
      2. 11.2 SELECTION RULES
      3. 11.3 THE IMPORTANCE OF SPIN
      4. 11.4 DEGENERATE SYSTEMS
      5. 11.5 EPILOGUE – SELECTION RULES FOR VIBRATIONAL SPECTROSCOPY
      6. 11.6 SUMMARY
      7. PROBLEMS
    2. Chapter 12: Terms and Configurations
      1. 12.1 TERM SYMBOLS
      2. 12.2 THE EFFECT OF A LIGAND FIELD – ORBITALS
      3. 12.3 SYMMETRY LABELS FOR dn CONFIGURATIONS – AN OPENING
      4. Table 12.5 Direct product table for octahedral symmetry
      5. 12.4 WEAK LIGAND FIELDS, TERMS AND CORRELATION DIAGRAMS
      6. 12.5 SYMMETRY LABELS FOR dn CONFIGURATIONS – CONCLUSION
      7. 12.6 SUMMARY
      8. PROBLEMS
    3. Chapter 13: d-d Spectra
      1. 13.1 THE BEER-LAMBERT LAW
      2. 13.2 SELECTION RULES AND VIBRONIC COUPLING
      3. 13.3 THE SPIN SELECTION RULE
      4. 13.4 d-d SPECTRA – HIGH-SPIN OCTAHEDRAL COMPLEXES
      5. 13.5 d-d SPECTRA – TETRAHEDRAL COMPLEXES
      6. 13.6 d-d SPECTRA – LOW-SPIN COMPLEXES
      7. 13.7 DESCENDING SYMMETRY
      8. 13.8 SUMMARY
      9. PROBLEMS
  11. Appendices
    1. Appendix 1: Projection Operators
    2. APPENDIX 2: Microstates and Term Symbols
    3. Appendix 3: Answers to SAQs
    4. APPENDIX 4: Answers to Problems
    5. Appendix 5: Selected Character Tables
  12. Index