Introductory Group Theory and Its Application to Molecular Structure

ISBN-13: 9781468487978 / Angielski / Miękka / 2012 / 292 str.

John Ferraro

Opis

The success of the first edition of this book has encouraged us to revise and update it. In the second edition we have attempted to further clarify por- tions of the text in reference to point symmetry, keeping certain sections and removing others. The ever-expanding interest in solids necessitates some discussion on space symmetry. In this edition we have expanded the discus- sion on point symmetry to include space symmetry. The selection rules in- clude space group selection rules (for k = 0). Numerous examples are pro- vided to acquaint the reader with the procedure necessary to accomplish this. Recent examples from the literature are given to illustrate the use of group theory in the interpretation of molecular spectra and in the determination of molecular structure. The text is intended for scientists and students with only a limited theoretical background in spectroscopy. For this reason we have presented detailed procedures for carrying out the selection rules and normal coor- dinate treatment of molecules. We have chosen to exclude discussion on symmetry aspects of molecular orbital theory and ligand field theory. It has been our approach to highlight vibrational data only, primarily to keep the size and cost of the book to a reasonable limit.

Spis treści

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.