Question One
(Designed to make you think about symmetry & sub-groups of Oh )
Cubane, C8H8 , belongs to point group Oh . It is subjected to controlled fluorination (in which F atoms
replace H atoms) yielding all possible species C8H8-nFn. Determine the point groups to which each of these
belong.
[BIG HINT – you only need to go from n = 0 4, since C8H8-nFn. and C8HnF8-n will belong to the same point
group. ]
Question Two
(This and the next question are designed to test you understanding of molecular vibrations)
Consider the anionic species Ni(CN)5
3-
. Two forms are possible – trigonal bipyramidal (D3h ) and square
pyramidal (C4v ). Discover, by use of group theory, whether-or-not one may distinguish between these on
the basis of their IR/Raman spectra for their C-N stretches.
[HINT – The 5 C-N bonds transform exactly the same as the five Ni-C bonds.]
Question Three
Compounds containing the cubic-shaped cluster Cu8 can be synthesized.
Using group theory, determine the symmetry of the Cu-Cu bond stretches and indicate how many modes
are infra-red active and/or Raman active.
[Hint – follow how bonds move or do not move under the symmetry operations of the group]
Question Four
(Designed to get you thinking about bond stretches and expand your use of group theory to the π-orbitals of
aromatic organic molecules)
Consider benzene, C6H6 (D6h symmetry).
(1) Draw the six C-H bonds and determine the reducible representation that they define. Reduce this to its
irreducible representations and indicate which give rise to IR and/or Raman active vibrations.
(2) Use arrows to indicate the positive lobes of the out-of-plane π-orbitals. Determine the reducible
representation for these orbitals. Then break this down to determine the irreducible representations
spanned by these orbitals.
Question Five
(Designed to show you that complicated molecules can give simple answers;
Also designed to drive you crazy!)
Consider the species C60 (buckminsterfullerene), with icosahedral ( Ih ) symmetry.
How many infra-red active bands result from the C-C bond stretches.
Helpful illustration appears below.
[Hint #1. Do not start a full analysis of degrees of freedom. Just look at the C-C bonds.
Hint #2. You only need to consider which representation(s) can give rise to I-R active bands?]
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