Molecular Symmetry and Group Theory

Workshop 1 — Symmetry elements and operations

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    • Exercise 9

      The molecule opposite possesses the symmetry elements: E, C2, σ(xz) and σ(yz).

    By noting the movement of the dark-coloured H atom, it can be seen that the operation C2 followed by σ(xz) is equivalent to the operation σ(yz).

    This may be represented by the following equation:

    σ(xz)C2 = σ(yz)

    where (by convention) the notation σ(xz)C2 means ‘C2 followed by σ(xz)’.

    Complete the following ‘multiplication table’ for this molecule.

      First Operation
    Second Operation
      E C2 σ(xz) σ(yz)
    E C2
    C2
    σ(xz) σ(yz) E
    σ(yz)

    Note: The result of any two operations is also a symmetry operation of the molecule. This is a requirement for the operations to form a mathematical group.

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