Molecular Symmetry and Group Theory

Workshop 1 — Symmetry elements and operations


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  • Exercise 3

      Let's now consider Sn where n is odd. For the BF3 molecule, for instance, we might think that S3 ≡ C3, but this only appears to be the case because the molecule is planar. In fact, S3 and C3 are not equivalent and need to be specified separately.
    Click for larger image
      In the eclipsed conformation, ethane has an S3 axis. Using the images in the table below, click on the H atom in the product which should be coloured red for each operation performed about the S3 axis in C2H6.

    Operations Clickable Image Corresponding Answer
    S3
    S32
    S33

    Note that the S3 operation is equivalent to neither C3 nor σ.

    Using the S3 operations, we must rotate the ethane molecule through a total of 720 before it ends up where it started.

    Using the images in the table below, click on the H atom in the product which should be coloured red for each further operation performed about the S3 axis in C2H6.

    Operations Clickable Image Corresponding Answer
    S34
    S35
    S36

    Fill in the table below for those S3 operations you think have equivalent symmetry operations generated by other symmetry elements of ethane. Hence, check all the independent symmetry operations we should assign to S3.
    (Note — There maybe more than one equivalent symmetry operation for a given S3 operation, if so enter the operations in alphabetical order separated by a comma i.e. a,b )

    Symmetry
    Operations
    S3
    S32
    S33
    S34
    S35
    S36
    Equivalent Symmetry
    Element (if any)
    Independent Symmetry
    Operation?

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