Introductory Group Theory and its Application to Molecular Structure

1 Symmetry.- 1-1. Introduction.- 1-2. Definition of Symmetry.- 1-3. Symmetry in Science.- 1-4. Symmetry in Structural Chemistry.- A. Point Symmetry Elements.- B. Point Groups.- C. Rules for Classification of Molecules into Point Groups.- D. The Character Table.- E. Space Symmetry.- Problems.- References.- 2 Derivation of Selection Rules.- 2-1. Selection Rules for Isolated Molecules.- A. The Td Point Group.- B. Linear Molecules.- C. Selection Rules for A3 to A8 Molecules.- D. Forbidden Vibrations for Several Point Groups.- 2-2. Selection Rules for Systems Involving Translations.- A. The Method of Bhagavantam and Venkatarayudu.- B. The Halford-Hornig Site Group Method.- C. Comparison of the BV and HH Methods.- D. Unambiguous Choice of Site Symmetry in the Bravais Unit Cell.- 2-3. Examples of the Halford-Hornig Site Group Method.- Problems.- References.- Recent Correlation Bibliography.- 3 Potential Force Fields.- 3-1. Introduction.- 3-2. Of What Value to Chemistry Is the Solution of Force Field Problems?.- 3-3. General Procedure in Determining Frequencies from Force Constants and Vice Versa.- References.- 4 The Normal Coordinate Treatment for Molecules with C2v, C3v, and Oh Symmetry.- 4-1. Procedure Necessary in the NCT Method.- 4-2. Normal Coordinate Treatment of H2O (C2v Symmetry).- 4-3. Normal Coordinate Treatment of NH3 (C3v Symmetry).- 4-4. Normal Coordinate Treatment of UF6 (Oh Symmetry).- 4-5. Some Results of NCT of Molecules.- 4-6. The Product Rule.- 4-7. The Sum Rule.- 4-8. Summary.- Problems.- References.- 5 Applications of Group Theory for the Determination of Molecular Structure.- 5-1. Introduction.- 5-2. Procedure Used in Determining the Structure of a Molecule.- 5-3. Examples Illustrating the Use of Group Theory in Determining Molecular Structure.- 5-4. Practice Problem.- Problems.- References.- Appendix 1.- Character Tables.- Appendix 2.- Description of Symbolism Used in the International Tables for X-Ray Crystallography.- Appendix 3.- Site Symmetries for the 230 Space Groups.- Appendix 4.- Correlation Tables.- Appendix 5.- Elementary Mathematics.- Appendix 6.- Appendix 7.- General Method of Obtaining Molecular Symmetry Coordinates.- Appendix 8.- Calculation of Thermodynamic Functions from Vibrational-Rotational Spectra.- Appendix 9.- Diagrams of Normal Vibrations for Common Point Groups.- Appendix 10.- Derivation of the Characters Necessary for Selection Rules.- Appendix 11.- Updated Bibliography.