CH 224	Group Theory	3-0-0-6
Syllabus: Definitions and Theorems of Group Theory: Properties of Group and examples, Subgroups, Classes. Molecular Symmetry and the Symmetry Groups: Symmetry elements and Operations: symmetry planes and reflections, the inversion Center, Proper Axes and proper rotation, and Improper axes and improper rotations. Products of symmetry Operations. Equivalent symmetry elements and equivalent Atoms. General relations among symmetry elements and Operations. Symmetry Elements and Optical Isomerism. The symmetry point groups. Symmetries with multiple High- Order Axes. Classes of symmetry Operations. A systematic Procedure for symmetry Classification of molecules. Representations of Groups: Comments on Matrices and Vectors. Representation of groups. The "Great Orthogonality Theorem" and its consequences. Character Tables. Representation for Cyclic Groups. Group Theory and Quantum Mechanics: Wave function as bases for irreducible representations. The Direct Product. Detection of non-zero integrals. Symmetry Adapted Linear Combinations: Derivation of Projection Operators. Use of Projection Operators to construct SALCs. Molecular Orbital Theory and its Application in Organic Chemistry: General Remarks. Symmetry factoring of secular equations. Carbocyclic system. More general cases of LCAO-MO bonding. Naphthalene. Electronic excitations of Naphthalene:selection rules and configuration interaction. Three center Bonding. Symmetry based selection rules for cyclization reactions. Molecular Orbital Theory for Inorganic and Organometallic Compounds: Transformation Properties of Atomic Orbitals. Molecular orbitals for bonding in ABn molecules: The Tetrahedral AB4 cases. Molecular orbitals for bonding in ABn molecules. Text Book 1. F. A. Cotton, Chemical Applications of Group Theory, 3rd Ed, John Wiley & Sons, 1990. Reference: 1. Molecular Symmetry and Group Theory: "A Programmed Introduction to Chemical Applications" by Alan Vincent; 2nd Edition, Wiley.