Author | Ferraro, John R. author |
---|---|
Title | Introductory Group Theory [electronic resource] : and Its Application to Molecular Structure / by John R. Ferraro, Joseph S. Ziomek |
Imprint | Boston, MA : Springer US : Imprint: Springer, 1969 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-4821-8 |
Descript | XIII, 240 p. online resource |
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 UreyโBradley 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 -- 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 VibrationalโRotational Spectra -- 6. General Method of Obtaining Molecular Symmetry Coordinates -- 7. Conversion Chart for Various Forms of Energy and Velocities