Chemical Applications Of Symmetry And Group Theory

By Prof. Manabendra Chandra   |   IIT Kanpur
Learners enrolled: 737
The aim of this course is to provide a systematic treatment of symmetry in chemical systems within the mathematical framework known as group theory. Once we have classified the symmetry of a molecule, group theory provides a powerful set of tools that provide us with considerable insight into many of its chemical and physical properties. Some applications of group theory that will be covered in this course include: 
  1. Predicting whether a given molecule will be chiral, or polar;
  2. Examining chemical bonding and visualizing molecular orbitals;
  3. Predicting whether a molecule may absorb light of a given polarisation, and which spectroscopic transitions may be excited if it does;
  4. Investigating the vibrational motions of the molecule, etc.

 Senior UG and PG students 
PREREQUISITES :Basic knowledge of quantum mechanics would be helpful.
Course Status : Completed
Course Type : Elective
Duration : 8 weeks
Category :
  • Chemistry
Credit Points : 2
Level : Undergraduate/Postgraduate
Start Date : 24 Jan 2022
End Date : 18 Mar 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 27 Mar 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1  : Introduction; Mathematical definition of a group, Symmetry operations and symmetry elements
Week 2  : Symmetry classification of molecules – point groups, symmetry and physical properties:  Polarity, Chirality etc.;
Week 3  : Combining symmetry operations: ‘group multiplication’ Review of Matrices, Matrix representations of
groups with examples

Week 4 : Properties of matrix representations:  Similarity transforms, Characters of representations, Irreducible
representations (IR) and symmetry species, character tables

Week 5  : Reduction of representations:  The Great Orthogonality Theorem; Using the GOT to determine the irreducible
representations spanned by a basis

Week 6  : Symmetry adapted linear combinations, bonding in polyatomics, constructing molecular orbitals from SALCs,
calculating and solving the orbital energies and expansion coefficients

Week 7  : Molecular vibrations :  determining the number of vibrational normal modes, determining the symmetries of molecular
motions, Molecular vibrations using internal coordinates

Week 8 : Spectroscopy –Group theory and molecular electronic states, electronic transitions in molecules, vibrational transitions in
molecules, Raman scattering. Summary of the course

Books and references

•    “Chemical Applications of Group Theory” by F. A. Cotton; Third Edition, Wiley.
•    “Molecular Symmetry and Group Theory: A Programmed Introduction to Chemical Applications” by Alan Vincent; 2nd Edition, Wiley.
•    “Symmetry and Spectroscopy” by D. C. Harris and M. D. Bertolucci; Dover publications.

Instructor bio

Prof. Manabendra Chandra

IIT Kanpur
Dr. Manabendra Chandra is an assistant professor in the Department of Chemistry at IIT Kanpur. His area of specialization is experimental physical chemistry.

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: 27 March 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 6 assignments out of the total 8 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 Kanpur .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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