Chemistry Reference
In-Depth Information
Table 5.25
The characters derived for the d-orbital functions for the central atom in a
D
∞h
complex.
E
∞
S
∞
D
∞h
...
σ
v
(
XZ
)
i
...
C
2
(
X
)
xy
1c s(2
)
...
−
1
1
cos(2
)
...
−
1
xz
1c s(
)
...
1
1
cos(
)
...
−
1
yz
1c s(
)
...
−
1
1
cos(
)
...
1
x
2
−
y
2
1c s(2
)
...
1
1
cos(2
)
...
1
z
2
11
...
1
1
1
...
1
(
xy
,
x
2
−
y
2
) 2 c s(2
)
...
0
2
2 cos(2
)
...
0
(
xz
,
yz
) 2 c s(
)
...
0
2
2 cos(
)
...
0
(
z
2
)
11
...
1
1
1
...
1
X
C
2
Z
C
Au
N
C
CN
∞
Y
Σ
g
+
, z
2
Z
C
∞
Au
N
C
C
N
Π
g
, xz, yz
Y
Δ
g
, xy, x
2
-y
2
Z
C
Au
C
C
N
N
∞
Y
Figure 5.27
The ligand-field-derived energy diagram for the central metal atom d-orbital
system of a D
∞h
complex.
5.10
Summary
In this chapter we have covered the use of representations in symmetry analysis. The
general approach to problems in symmetry can be written out as follows.
1. Decide on the point group of the molecule using the symmetry operations the atoms
obey.
2. Decide on a basis for the analysis, using a suitable set of atom displacement vectors
for vibrational modes or sets of atomic orbital (AO) functions for the description of
