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# Symmetry and Group Theory

NPTEL via Swayam

### Overview

The objective of the course is to help recognize symmetry in molecules and understand its role in Chemistry. The course will explore the role of symmetry in (A) determining molecular properties (e.g. optical activity, dipole moment), (B) classifying and assigning nomenclature to molecules, molecular states and molecular motions and (C) bringing about simplifications in the application of quantum mechanics to molecules, and (D) determining spectroscopic selection rules based on molecular symmetry. Group theory applied to the study of molecular symmetry has far reaching consequences in chemistry and the course will provide an in-depth appreciation of this. INTENDED AUDIENCE :3rd year BS-MS students, 1st year M.Sc. students with Chemistry major, 1st year Chemistry Ph.D. studentsPREREQUISITES : General Physical Chemistry, Fundamentals of SpectroscopyINDUSTRIES SUPPORT :None

### Syllabus

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

### Taught by

Prof. Jeetender Chugh

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