Chemistry Reference
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to the composite nature of the molecule being considered, with several fragments
bound to one central atom.
4.10 Problems
4.1 A Schlegel diagram of a polyhedron is a projection into a plane figure. The fig-
ure below shows the Schlegel diagram for a dodecahedron. As was explained
in the preceding chapter (see Fig.
3.8
(a)), a dodecahedron contains five cubes,
e.g., the cube based on the nodes
. Symmetry elements of
I
h
permute these cubes. Construct the set of the five cubes and determine the
irreps of this set. Can you obtain this result by induction?
1
,
3
,
9
,
10
,a,c,i,j
4.2 Consider the set of eight tangential
π
-orbitals on a tetrahedron. Derive the
irreducible representations in the
T
d
point group. How would you label the
canonical symmetry of the combinations that are shown in the figure below?
4.3 Consider the set of perpendicular
p
z
-orbitals in the polyaromatic planar
molecule coronene shown below. This set gives rise to a symmetry of molec-
ular orbitals of
a
1
u
and
b
1
g
. Can you draw both these orbitals? (Use the stan-
dard orientation of the central benzene frame, as shown in Fig.
3.10
)
