Symmetry and Group Theory

By Prof. Jeetender Chugh   |   IISER Pune
Learners enrolled: 137
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.

3rd year BS-MS students, 1st year M.Sc. students with Chemistry major, 1st year Chemistry Ph.D. students
PREREQUISITES : General Physical Chemistry, Fundamentals of Spectroscopy
Course Status : Upcoming
Course Type : Core
Duration : 12 weeks
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Exam Date : 23 Apr 2022 IST
Category :
  • Chemistry
Credit Points : 3
Level : Postgraduate

Course layout

Week 1: Introduction to the course; Symmetry and Parity Operator; Symmetry Elements and Operations
Week 2: Symmetry Elements and Operations; Coordinate System; Product of symmetry operations
Week 3: Symmetry Point Groups; Schönflies Notations of the Point Groups; Point Group Determination; Applications of Symmetry - Prediction of Dipole Moment and Optical Activity
Week 4: Definition of Group, Sub-group, Class; Group Multiplication Tables; Matrix Representation of the Symmetry Operations in Point Groups
Week 5: Reducible, Equivalent, and Irreducible Representations; The Great Orthogonality Theorem and its Corollaries
Week 6: 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
Week 7: Representations of a Cyclic Group; Application of Group Theory to Quantum Mechanics; Degenerate Eigen Functions; Direct Product of Irreducible Representations
Week 8: Applications of Direct Product, Symmetry Adapted Linear Combinations
Week 9:  Projection Operator and its application to Symmetry Adapted Linear Combinations (SALCs); Symmetry and Chemical Bonding; Valence Bond Theory
Week 10: Localized and Delocalized Molecular Orbital Theory; Ascent and Descent in Symmetry
Week 11: Crystal Field Theory; Jahn Teller Distortion; Introduction to Spectroscopy; Rotational Spectroscopy
Week 12: Vibrational Spectroscopy; Raman Spectroscopy; Atomic Motions; Symmetry of Normal Modes; Visualizing Molecular Vibrations; Spectral Transition Probabilities

Books and references

• Chemical Applications of Group theory: F. A. Cotton (Wiley Interscience)
• Molecular symmetry & group theory: R. L. Carter (John Wiley & Sons)
• Symmetry and Spectroscopy: D. C. Harris and M. D. Bertolucci (Dover)
• Group Theory and Quantum Mechanics: Michael Tinkham (Dover)

Instructor bio

Prof. Jeetender Chugh

I have obtained my M.Sc. in Organic Chemistry from the University of Delhi in 2002; and my Ph.D. in Molecular Biophysics (under the supervision of Prof. R V Hosur) from the Tata Institute of Fundamental Research, Mumbai in 2008 while working in NMR Spectroscopy. I joined IISER Pune as an Assistant Professor in the Department of Chemistry and Biology in 2013 after finishing a postdoctoral fellowship at the University of Michigan, USA (mentor: Prof. Hashim M Al-Hashimi). During my tenure at the University of Michigan, I taught a course on Physical Chemistry Experiments. After joining IISER Pune, I have been teaching several theory and lab courses. I have also been teaching Introduction to NMR spectroscopy in Structural Biology at multiple departments of Savitribai Phule Pune University since 2014. I have been teaching the proposed course (Symmetry and Group Theory) at IISER Pune since Aug 2017. In this course, I will be using whiteboard to teach, with my voice over and video inset to explain. This is specifically important in this course as students need to see how to draw various symmetry elements and carry out respective operations, which is not so clear in pre-drawn power-point based teaching. Also, all the derivations will be done on the whiteboard and not by showing pre-written equations in power-point. I believe this style of teaching will be really beneficial for the students.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 23 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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