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Introductory Group Theory and Its Application to Molecular Structure

This volume is a consequence of a series of seminars presented by the authors at the Infrared Spectroscopy Institute, Canisius College, Buffalo, New York, over the last nine years. Many participants on an intermediate level lacked a sufficient background in mathematics and quantum mechan­ ics, and i...

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Bibliographic Details
Main Authors: Ferraro, John R., Ziomek, Joseph S. (Author)
Format: eBook
Language:English
Published: New York, NY Springer US 1969, 1969
Edition:1st ed. 1969
Subjects:
Science, Humanities And Social Sciences, Multidisciplinary
Group Theory
Group Theory And Generalizations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 7-11. References
  • 8 Applications of Group Theory
  • 8-1. Introduction
  • 8-2. Procedure Used in Determing the Structure of a Molecule
  • 8-3. Examples Illustrating the Use of Group Theory in Determining Molecular Structure
  • 8-4. Practice Problem
  • 8-5. Selection of Rules for A3 to A8 Molecules
  • 8-6. Forbidden Vibrations for Several Point Groups
  • 8-7. Problems
  • 8-8. References
  • Appendices
  • 1. Conversion Table for Wavelength and Wave Number Units
  • 3. Diagrams of Normal Vibrations for Common Point Groups
  • 4. Calculation of Thermodynamic Functions for Vibrational—Rotational Spectra
  • 6. General Method of Obtaining Molecular Symmetry Coordinates
  • 7. Conversion Chart for Various Forms of Energy and Velocities
  • 1 Symmetry in General
  • 1-1. Introduction
  • 1-2. Definition of Symmetry
  • 1-3. Symmetry in Our Culture
  • 1-4. Symmetry in Nature
  • 1-5. Symmetry in Science
  • 1-6. References
  • 2 Symmetry in Chemistry
  • 2-1. Introduction
  • 2-2. Symmetry Elements
  • 2-3. Point Groups
  • 2-4. Rules for Classification of Molecules into Point Groups
  • 2-5. Problems
  • 2-6. References
  • 2-7. Bibliography
  • 3 Elementary Mathematics
  • 3-1. Definition of a Group
  • 3-2. Finite and Infinite Groups
  • 3-3. Subgroups
  • 3-4. Classes
  • 3-5. Definition of a Matrix
  • 3-6. Multiplication of Matrices
  • 3-7. Transpose of a Matrix
  • 3-8. Representation of Groups
  • 3-9. Problems
  • 3-10. References
  • 4 The Character Table
  • 4-1. Introduction
  • 4-2. Types of Representations
  • 4-3. Character Tables for the More Common Point Groups
  • 4-4. Problem
  • 5 Derivation of Selection Rules
  • 5-1. Derivation of Selection Rules for Nonlinear Molecules of the Most Common Point Groups
  • 5-2. The Td Point Group
  • 5-3. The D4h Point Group
  • 5-4. The Oh Point Group
  • 5-5. The D3h Point Group
  • 5-6. The C3v Point Group
  • 5-7. The C2v Point Group
  • 5-8. Derivation of Selection Rules for Linear Molecules
  • 5-9. Problem
  • 5-10. References
  • 6 Potential Force Fields
  • 6-1. The General Quadratic Potential Function
  • 6-2. The Central Force Field
  • 6-3. The Valence Force Field
  • 6-4. The Generalized Valence Force Field
  • 6-5. The Urey—Bradley Function
  • 6-6. References
  • 7 The Normal Coordinate Treatment for Molecules with C2v, C3v, Td, and Oh Symmetry
  • 7-1. Procedure Necessary in the NCT Method
  • 7-2. Normal Coordinate Treatment of H2O (C2v Symmetry)
  • 7-3. Normal Coordinate Treatment of NH3(C3v Symmetry)
  • 7-4. Normal Coordinate Treatment of CH4(Td Symmetry)
  • 7-5. Normal Coordinate Treatment of UF6(Oh Symmetry)
  • 7-6. Some Results of NCT of Molecules
  • 7-7. The Product Rule
  • 7-8. The Sum Rule
  • 7-9. Summary
  • 7-10. Problems

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