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.