Week 2 review – character tables and representations

We built on our discussion of symmetry and introduction to character tables by ‘generating’ the character table for the C2v point group using the set of coordinate vectors (and the idea of ‘orthogonality’), and defined both irreducible and reducible representations. From there, we discussed groups and defined several terms and symbols associated with chemically relevant character tables. We ended the week by considering transform matrices associated with symmetry operations, their use in generating reducible representations, and the reduction of reducible representations.

C2v_CT

Some things to think about / consider:

  • symmetry with respect to (wrt) an operation is denoted by a 1, while -1 represents anti-symmetry wrt an operation
  • irreducible vs. reducible representations
  • the properties of groups
  • definitions associated with character tables: order, classes, orthogonality…
  • the meaning of symbols commonly encountered with character tables (A, E, T, u, g….)
  • the transform matrix
  • reducing reducible representations

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