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Group theory for chemists: Fundamental theory and applications

K C Molloy, University of Bath, UK

An excellent introduction to group theory with many illustrations to aid understanding. Most appropriate as a course resource for undergraduates. Recommended for Lower-division graduates through graduate students.
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This undergraduate text deals with basics of group theory and its application to the analysis of vibrational spectra, molecular orbital description of bonding, ligand field theory and other themes within inorganic chemistry. Concise and student- friendly, the book adopts a diagrammatic rather than a rigorous mathematic approach, providing support for lecture courses in chemical group theory offering students opportunities to test their understanding. Problem solving is stressed with numerous self-assessment questions and problem exercises, along with tutorial hints and solutions to selected problems.

Part 1 covers the essentials of symmetry and group theory, including symmetry elements and operations, point groups and representations. Part 2 focuses on the application of group theory to vibrational spectroscop building step-wise to show how group theory guides the analysis of vibrational spectra. A brief overview of infrared and Raman spectroscopy techniques is followed by a complete worked example to reiterate key points from earlier sections.

Part 3 describes the application of group theory to a molecular orbital approach to chemical bonding. After laying a foundation of the basic rules for forming molecular orbitals using H, and H as examples, the book addresses more complex problems by comparing angular and linear structures for water and planar and pyramidal structures for ammonia. A description of the application of group theory to the bonding in octahedral main group and transitional metal complexes then follows, including an analysis of the I influencing crystal field splitting energies. The book concludes with a description of the bonding in ferrocene, bringing together all the ideas presented in earlier sections.

ISBN 1 904275 16 8
ISBN-13: 978 1 904275 16 9
November 2004
156 pages  234 x 156mm  paperback  
£25.00 / US$40.00 / €30.00

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About the author

Kieran C Molloy, University of Bath, UK

Contents

PART 1 SYMMETRY AND GROUPS
PART 2 APPLICATION OF GROUP THEORY TO VIBRATIONAL SPECTROSCOPY
PART 3 APPLICATION OF GROUP THEORY TO STRUCTURE AND BONDING

PART 1 SYMMETRY AND GROUPS

Symmetry
 - Symmetry
 - Point Groups
 - Chirality and Polarity
 - Summary
 - Problems

Groups and representations
 - Groups
 - Transformation Matrices
 - Representations of Groups
 - Character Tables
 - Symmetry Labels
 - Summary
 - Problems

PART 2 APPLICATION OF GROUP THEORY TO VIBRATIONAL SPECTROSCOPY

Reducible representations
 - Reducible Representations
 - The Reduction Formula
 - The Vibrational Spectrum of SO
 - Chi Per Unshifted Atom
 - Summary
 - Problems

Techniques of vibrational spectroscopy
 - General Considerations
 - infrared Spectroscopy
 - Raman Spectroscopy
 - Rule of Mutual Exclusion
 - Summary
 - Problems

The vibrational spectrum of Xe(O)F4
 - Stretching and bending Modes
 - The Vibrational Spectrum of Xe(O)F
 - Group Frequencies
 - Problems

PART 3 APPLICATION OF GROUP THEORY TO STRUCTURE AND BONDING

Fundamentals of molecular orbital theory
 - Bonding in H2
 - Bonding in Linear H2
 - Limitations in a Qualitative Approach
 - Summary
 - Problems

H2O: Linear or angular?
 - Symmetry Adapted Linear Combinations
 - Central Atom Orbital Symmetries
 - A Molecular Orbital Diagram for H2O
 - A C2V / Dh, Correlation Diagram
 - Summary
 - Problems

NH3: Planar or pyramidal?
 - Linear or Triangular H3?
 - A Molecular Orbital Diagram for BH3
 - Other Cyclic Arrays
 - Summary
 - Problems

Octahedral complexes
 - SALCS for Octahedral Complexes
 - d-Orbital Symmetry Labels
 - Octahedral P-B lock Complexes
 - Octahedral ‘Transition Metal Complexes
 - Bonding and the Spectrocheniical Series
 - Summary
 - Problems

Ferrocene
 - Central Atom Orbital Symmetries
 - SALCs for Cyclopentadienyl Anion
 - Molecular Orbitals for Ferrocene
 - Problems

Appendices and index