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.
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
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