Courses » Chemical Applications of Symmetry And Group Theory

Chemical Applications of Symmetry And Group Theory


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
CORE/ELECTIVE: PG level elective

UG/PG: Senior UG students also can take this course

PREREQUISITES: Basic knowledge of quantum mechanics would be helpful.



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


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


•    “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.
  • The exam is optional for a fee.
  • Date and Time of Exams: April 28 (Saturday) and April 29 (Sunday) : Morning session 9am to 12 noon;
  • Exam for this course will be available in one session on both 28 and 29 April.
  • 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.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 6 out of 8 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. 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.