Chemistry Reference
In-Depth Information
This sort of analysis provides a powerful use of spectroscopy to aid in the identification
of molecular structure through the application of symmetry. If we had made a sample
of difluorobenzene and believed it to be a pure isomer of either the 1,4- or 1,2-form,
vibrational spectroscopy would provide one way to distinguish which isomer we had made.
Problem 6.7:
Figure 6.13 shows the experimental spectra of two isomers of 1,2-
dichloroethene. The set of basis arrows shown in Figure 6.16 is one possible choice
of the three arrows per atom for a complete basis. This choice has the advantage that
each atom has one basis arrow perpendicular to the molecular plane and one aligned
with a bond.
Figure 6.16
One choice for a complete basis set for either isomer of 1,2-dichloroethene.
The
symbol is used to imply an arrow coming out of the page.
1. Show that the irreducible representations for the 12 vibrational modes are:
C
2h
:
=
5
A
g
+
B
g
+
2
A
u
+
4
B
u
(6.21)
C
2v
:
=
5
A
1
+
2
A
2
+
B
1
+
4
B
2
(6.22)
(remember to align
Z
-direction with the principal axis, with
Y
in the molecular plane
for
C
2v
).
How many IR and Raman bands would you expect to see in the spectra of each
isomer of 1,2-dichloroethene? Is your prediction higher or lower than seen in the
experimental spectra?
2. For
cis
-1,2-dichloroethene, some bands are too weak to be detected in the experi-
mental spectra. However, all active modes in the frequency range of the spectrometer
can be seen for
trans
-1,2-dichloroethene (Figure 6.13a). The modes that are off
scale in Figure 6.13 have the atom displacements shown in Figure 6.17. Assign
irreducible representations to each of these modes and hence decide on their IR or
Raman activity. Using this information, confirm the number of modes predicted in
part (1) is correct.
6.4 Symmetry-Adapted Linear Combinations
The preceding sections have shown how to use symmetry analysis on a basis of vec-
tors to determine the irreducible representations for molecular vibrations. In building
the reducible representation the basis vectors are treated as individual objects to which
characters are assigned. This makes the total character for the basis easy to calculate by
summing the results for each of the basis vectors in isolation.
