Chemical Applications Of Symmetry And Group Theory

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