Chemistry Reference
In-Depth Information
Table 7.13
The
reducible
representation
for
the six
-donor orbitals shown in Figure 7.38,
within the rotational subgroup O.
OE
8
C
3
σ
3
C
2
(
=
C
4
2
)
C
4
6
C
2
6
0
2
2
0
For the central metal atom we can read the irreducible representations for the s-, p- and
d-orbitals directly from the functional forms quoted in the right-hand columns of the
O
character table:
M(
n
d
xy
),M(
n
d
yz
) and M(
n
d
xz
):
t
2
M(
n
d
z
2
) and
M
(
n
d
x
2
−
y
2
):
e
M( (
n
+
1) p
x
),M((
n
+
1) p
y
) and M( (
n
+
1) p
z
):
t
1
M( (
n
+
1) s):
a
1
,
(7.69)
Rotational subgroup symbols are always linked to the longer list of irreducible represen-
tations in the parent group. So, in this case, reading from the
O
h
character table we find
M(
n
d
xy
),M(
n
d
yz
) and M(
n
d
xz
):
t
2g
M(
n
d
z
2
) and M(
n
d
x
2
−
y
2
):
e
g
M( (
n
+
1) p
x
),M((
n
+
1) p
y
) and M( (
n
+
1) p
z
):
t
1u
M( (
n
+
1) s):
a
1g
.
(7.70)
The 'g' and 'u' labels can be understood from the effect of the inversion operation
i
on the
AOs; d-orbitals are
gerade
and p-orbitals
ungerade
.
For the ligand orbitals, we can deduce the phase pattern of the SALCs for each of the
irreducible representations identified in Equation (7.68) through thinking about the bond-
ing/antibonding orbitals that will be formed with the metal centre. These are shown to the
right of the ligand reference levels in the MO diagram of Figure 7.39.
2
t
2u
2
a
1g
2
e
g
4p,
t
2u
e
g
4s,
a
1g
Δ
o
t
2u
a
1g
1
t
2g
t
2g
e
g
3d
1
e
g
1
t
2u
1
a
1g
Figure 7.39
The MO diagram for an O
h
symmetry complex with
σ
-donor orbitals.
