Chemistry Reference
In-Depth Information
4.4 In dodecaborane,
B
12
H
2
−
12
, the twelve boron atoms occupy the vertices of an
icosahedral cage. Determine the irreducible representations of the set of their
tangential
π
-orbitals.
4.5 Consider a degenerate manifold, transforming as the irrep
Γ
i
. The appropriate
projector was applied to the basis to yield one component of the degeneracy
space. Which other projectors do you need to use to generate all the remaining
components?
4.6 Consider the expression for a totally symmetric projection operator and
demonstrate that it is indeed totally symmetric under any group element.
4.7 Construct the three
sp
2
hybrids in the
xy
plane.
4.8 The picture below shows the distortion of an equilateral triangle. Determine
the representation of this distortion.
4.9 Construct the character table for a cyclic group of order 5.
4.10 In a molecule with
D
6
h
symmetry, the choice of
C
2
and
C
2
directions is ar-
σ
d
reflection
planes are also fixed, as was indicated in Fig.
3.10
. Show that these spatial re-
lationships between the axes and the planes is in line with the character table
for
D
6
h
.
4.11 Consider a molecule with
D
3
h
symmetry and apply a distortion mode that
transforms according to the
a
2
bitrary, but, once the twofold directions are chosen, the
σ
v
and
ˆ
ˆ
irrep. A distortion along this coordinate breaks
