Symmetry and Group Theory

COURSE LAYOUT

Week1:Introduction to the course; Symmetry and Parity Operator; Symmetry Elements and Operations
Week2:Symmetry Elements and Operations; Coordinate System; Product of symmetry operations
Week3:Symmetry Point Groups; Schönflies Notations of the Point Groups; Point Group Determination; Applications of Symmetry - Prediction of Dipole Moment and Optical Activity
Week4:Definition of Group, Sub-group, Class; Group Multiplication Tables; Matrix Representation of the Symmetry Operations in Point Groups
Week5:Reducible, Equivalent, and Irreducible Representations; The Great Orthogonality Theorem and its Corollaries
Week6:Irreducible Representations using The Great Orthogonality Theorem; Construction of Character Tables and Meaning of all the terms in the Character Table; Mulliken Symbols for Irreducible Representations
Week7:Representations of a Cyclic Group; Application of Group Theory to Quantum Mechanics; Degenerate Eigen Functions; Direct Product of Irreducible Representations
Week8:Applications of Direct Product, Symmetry Adapted Linear Combinations
Week9:Projection Operator and its application to Symmetry Adapted Linear Combinations (SALCs); Symmetry and Chemical Bonding; Valence Bond Theory
Week10:Localized and Delocalized Molecular Orbital Theory; Ascent and Descent in Symmetry
Week11:Crystal Field Theory; Jahn Teller Distortion; Introduction to Spectroscopy; Rotational Spectroscopy
Week12:Vibrational Spectroscopy; Raman Spectroscopy; Atomic Motions; Symmetry of Normal Modes; Visualizing Molecular Vibrations; Spectral Transition Probabilities