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Molecular Symmetry and Group Theory
(6 lectures & workshops)

Dr P A Anderson (Haworth 506)

This course aims to provide you with sufficient understanding of symmetry and group theory to allow their application to problems in bonding and spectroscopy.

The course consists of 6 lectures, each followed by an online workshop, which is designed to complement and amplify lecture material, and provide practice in using the methods of group theory. Together your lecture notes and workshop exercises should provide a complete guide to all you need to use group theory. The workshops are designed for self-tuition and each one should take 1-2 hours to complete. Attendance at all lectures and completion of all workshops is essential.


  1. Symmetry elements and operations — The symmetry elements Cn, E, σ, i, Sn, and the symmetry operations associated with these elements. Combinations of operations.
  2. Point groups — Classification of molecules into point groups. Group ‘multiplication’ tables; mathematical groups.
  3. Character tables — The ‘character’ of an operation. Irreducible and reducible representations. The reduction of reducible representations through the reduction formula.
  4. Matrices and degenerate representations — Matrices representing operations; the character of a matrix. Degenerate orbitals.
  5. Chemical bonding — Hybrid orbitals. Molecular orbital treatment of simple molecules and transition metal complexes.
  6. Molecular vibrations — IR and Raman active vibrations.

Textbooks — The course follows closely the approach used in textbooks such as Molecular Symmetry and Group Theory, Vincent (Wiley, 1st & 2nd eds.), and Beginning Group Theory for Chemistry, Walton (OUP). Useful chapters on this subject are also to be found in general textbooks e.g. Inorganic Chemistry, Shriver & Atkins (OUP, 3rd ed.), Concepts and Models of Inorganic Chemistry, Douglas, McDaniel & Alexander (Wiley, 3rd ed.), and Physical Chemistry, Atkins (OUP, 6th ed.)