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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:Predicting whether a given molecule will be chiral, or polar; Examining chemical bonding and visualizing molecular orbitals; Predicting whether a molecule may absorb light of a given polarisation, and which spectroscopic transitions may be excited if it does; Investigating the vibrational motions of the molecule, etc.INTENDED AUDIENCE :Senior UG and PG studentsPREREQUISITES :Basic knowledge of quantum mechanics would be helpful.INDUSTRY SUPPORT :NIL
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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
