This simple, bare-bones Web page serves to provide links to the material used in Chemistry 163, Chemical Applications of Group Theory.

1. the syllabus for the course

2. homework assignments not found in the text
   • Problem Set I.
     Problem 1 on this set deals with the symmetry elements of puckered cyclobutane. To facilitate the visualization of the molecule in three dimensions, a 3D structural file in .pdb format is available.
   Cotton has an excellent set of problems at the end of Chapter 3 that address the identication of point groups defined by the symmetry operations of molecules. The exact structures of two of the species in Set D, Some Less Obvious Molecules are not spelled out.
   • Structure (6) in Set D. The species is the core of a larger molecule whose full structure is found in the Cambridge Crystallographic Database as structure OMPZID. The four nitrogens in the structure form a planar square. Consider the 4 phosphorus atoms going around the ring in a clockwise manner. The first two, e.g. P1 and P2, are symmetrically oriented above the ring defined by the 4 nitrogen atoms and the next two, e.g. P3 and P4 are oriented below the ring. P1, P3, and the 4 N's define a chair conformation as do P2, P4, and the 4 N's.
   • Structure (7) in Set D. This is a cyclic polyene with the molecular formula (CH=CHCH₂CH₂)₃. Many conformations are possible for this species. Most of these belong to the point group C1. However, one can fiddle with the dihedral angles in the ring and end up with a highly symmetric crown-like structure in which axial hydrogens on the carbons alternately point up and down. This symmetric structure, likely the global minimum, was created using Spartan and the Merck Molecular force field and is provided here in the pdb format.

3. graded exercises
   • Graded Exercise 1 which deals with the use of group theory in MO calculations
   • Graded Exercise 2 which deals with grou theory and crystallography

4. a selective, annotated bibliography
   • F. A. Cotton, Chemical Applications of Group Theory, 3rd. ed., Wiley, 1990.
     This is the required textbook for the course. It is a well written introduction to group theory. It covers crystallography, molecular bonding, and molecular spectroscopy but not angular momentum theory. The book gives consierabler attention to electronic spectroscopy of transition-metal complexes.
   • M. Tinkham, Group Theory and Quantum Mechanics, McGraw-Hill, New York, 1964.
     This book is written for physicists and is a good companion to Cotton. It does provide an introduction to the full rotation group and angular momentum.
   • E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations, MCGraw-Hill, New York, 1955.
     This book is the classic treatment of vibrations of molecules and the quantitative treatment of normal modes. The monograph makes extensive use of group theory.
   • E. P. Wigner, Group TRheory, Academic Press, New York, 1959.
     This edition, a translation by J. J. Griffin from the original in German, is the classic treatment of the full rotation group. The material in the monograph must be mastered by any chemical physicist who makes extensive use of angular momentum.
   • T. Hahn, ed. International Tables for Crystallography, 3rd. ed., D. Reidel, Dordrect.
     Crystallography makes extensive use of group theory. This indispensible reference work that has a student edition contains comprehensive information on all crystallographic space groups.

5. useful Web sites in group theory
   The search for useful information on the WWW can be compared with mining for gold. One sifts through tons of gravel and ends up with a few grains of gold that are hardly worth the effort. Occasionally one finds a nugget. Here are group theory Web sites that are worthy to be compared with gold nugget.
   • Character Tables for Chemically Important Point Groups
     Here is a WWW version of the character tables in Cotton's book. Professor Gelassus has contributed additional features. For example, if you provide a reducible representation, his software will determine the irreducible representations.
   • Wallpaper Groups
     Professor Joyce at Clark University has developed a colorful yet very instructive Web page that uses wallpaper patterns as a vehicle to cover the symmetry of each two-dimensional lattice.
   • A Timeline of Symmetry in Physics, Chemistry, and Mathematics
     Goeran Lindblad's Web site presents the history of the study of symmetry. The site has a link to a useful site on Platonic solids.
   • Mineralogy
     This is the Web page for the mineralogy course at ther University of Bristol. Chapters 4, 5, and 6 of the page are relevant to our study of crystallography.
   • Exercises in Point Group Theory
     Arie Aizman has developed a number of Applets that you might find useful in the visualization of symmetry operations on molecules.
   • Crystal Lattice Structures, Index by Space Groups
     The crystallography group at the Naval Research Laborlatory has assembled a collection of structures of ionic compoiunds that are organized according to space groups and point groups. The Web site also has links to other useful Web sites.
   • Space Group Diagrams and Tables
     Professor Cockcroft at Birnbeck College provides a table of all 230 space groups organized according to crystal systems. The full diagram is provided for a small number of space groups, e.g. numbers 14, 19, 62, 133, 178, and 205.
   • Bilbao Crystallographic Center
     This Web site provides the Wyckoff positions for every one of the 230 space groups.
   • Generation of standard and alternate settings of the 230 space groups
     This Web site hosted by the Canadian National Research Council provides a comprehensive list of the 230 space groups with all alternate notations.
   • MolData
     Finally, do not overlook the Inorganic and Physical Chemistry sections of MolData. These contain links to sources of data and the process of determining a structure from X-ray data. Symmetry plays a role in this process.

index.htm, last revised 3 April 2002