Chemistry Reference
In-Depth Information
C
4
,
C
2
s
5
B
C
2
″
s
2
C
2
″
A
s
3
C
2
′
A
s
1
s
4
C
2
′
B
s
6
Figure 7.40
The basis of
-donor orbitals for a six-coordinate complex after a distortion to
D
4h
symmetry. The axial ligands represented by s
5
and s
6
are further from the metal centre than
the equatorial ligands. Also shown are the axes used in the projection operator calculations:
the principal C
4
, collinear C
2
and the four horizontal C
2
axes.
σ
Table 7.14
The reducible representation and application of the reduction formula for the six
σ
-donor orbitals in D
4h
, [Cu(H
2
O)
6
]
2+
.
D
4h
2
C
2
2
C
2
E
2
C
4
C
2
i
2
S
4
σ
h
2
σ
ν
2
σ
d
h
=
16
6
2
2
2
0
0
0
4
4
2
C
h
−1
C
g
c
χ
i
(
C
)
χ
(
C
)
A
1g
6
4
2
4
4
8
4
32
2
A
2g
6
4
2
−
4
4
−
8
−
4
0
0
B
1g
6
−
4
2
4
4
8
−
4 6
1
B
2g
6
−
4
2
−
4
4
−
8
4
0
0
E
g
12
0
−
4
0
−
8
0
0
0
0
A
1u
6
4
2
4
−
4
−
8
−
4
0
0
A
2u
6
4
2
−
4
−
4
8
4
16
1
B
1u
6
−
4
2
4
−
4
−
8
4
0
0
B
2u
6
−
4
2
−
4
−
4
8
−
4
0
0
E
u
12
0
−
4
0
8
0
0
16
1
The projection operator method for the
a
1g
representation will give functions having
the same phase at symmetry-related positions, because it has character 1 for all classes.
In the
D
4h
basis shown in Figure 7.40 there are actually two separate groups of
-donor
orbitals. The operations in the group do not swap the axial with the equatorial ligands,
so the orbitals
s
1
to
s
4
form one symmetry-related set and the axial orbitals,
s
5
and
s
6
,are
another. Accordingly, the two
a
1g
SALCs are the combinations of the two sets in phase and
out of phase with one another, i.e.
σ
a
1g
=
s
1
+
s
2
+
s
3
+
s
4
+
s
5
+
s
6
and
a
1g
=
s
1
+
s
2
+
s
3
+
s
4
−
s
5
−
s
6
(7.72)
For the
b
1g
representation we can use the projection operator method along with the
D
4
rotational subgroup of
D
4h
as laid out in Table 7.15. The rotational subgroup does not
contain the inversion centre, and so the
gerade
(g) and
ungerade
(u) labels do not appear.
