Chemistry Reference
In-Depth Information
C
2
C
2
F
F
b
1
b
1
F
F
H
1
H
1
b
3
b
3
b
2
b
2
H
3
H
2
H
2
H
3
b
4
b
4
H
4
H
4
1
1
φ
1
(
A
1
)
=
φ
2
(
A
1
)
=
2
(
b
1
+
b
2
+
b
3
+
b
4
)
2
(
b
1
+
b
2
-
b
3
-
b
4
)
C
2
C
2
F
F
b
1
b
1
F
F
H
1
H
1
b
3
b
3
b
2
b
2
H
3
H
3
H
2
H
2
b
4
b
4
H
4
H
4
1
1
φ
1
(
B
2
) =
φ
2
(
B
2
)
=
2
(
b
1
-
b
2
+
b
3
-
b
4
)
2
(
b
1
-
b
2
-
b
3
+
b
4
)
Figure 6.22
The four C H stretching modes obtained for 1,2-difluorobenzene. Note that
the Z-direction is along the principal axis and y is in the molecular plane.
the functions shown in Figure 6.22. This will not be the case when the atom masses or
chemical bond strengths for atoms in different subsets are not the same, as the relative
atom displacements will also depend on these factors. This means that renormalization is
not possible on the basis of symmetry alone. However, the phase patterns that give us the
relative motion of the atoms can still be obtained.
As a simple example we return once again to the stretching modes of H
2
O. In
Figure 6.18 we defined a simple basis set of vectors so that each of the H atoms had a
basis vector pointing down their respective O H bond. This choice of basis vectors leads
to the H atom motions for the stretching modes with the normalized SALCs:
1
√
2
φ
(
A
1
)
=
(
b
1
+
b
2
)
(6.56)
1
√
2
φ
(
B
2
)
=
(
b
1
−
b
2
)
The symmetry operations of the
C
2v
point group link the two H atoms, but the O atom
is clearly always distinct; for a complete picture we need to add in the O atom motion.
Each of the SALCs constructed for the H atoms has been given a symmetry label, and
so in each case the O atom must move in a way that conforms to the symmetry of the H
atom movement. In Section 5.2 it was shown that the O atom can only move along the
direction defined by principal axis in an
A
1
mode and only in the in-plane
Y
-direction in a
