Chemistry Reference
In-Depth Information
In the MO diagram, the ligand SALCs are drawn higher in energy than the metal
d-states, because donation of electron density from the ligands to the metal is expected.
The different symmetries for the ligand reference states have been separated out, but this
is really just to allow clear illustration; the SALCs should be thought of as practically
isoenergetic. All of the ligand SALCs match with metal-centred orbitals, and so there are
six bonding orbitals: 1
a
1g
,1
t
2u
and 1
e
g
. These are closer in energy to the metal d-orbitals,
signifying that the bond density will be polarized toward the metal, as we would expect
for a
σ
-donor interaction.
The next set of levels is the three nonbonding
t
2g
MOs derived from the metal d-orbitals
that have no symmetry match with the ligands. There are then six antibonding orbital
complements to the bonding set: 2
e
g
,2
a
1g
and 1
t
2u
.
As the ligand orbitals are initially filled, we can think of the six bonding states as tak-
ing up the ligand electrons. The metal d-electrons then enter the
t
2g
and possibly the
e
g
levels. This is, of course, an arbitrary choice, but gives a nice parallel to the ligand field
approach in Chapter 5, where the ligand electrons were only present via their 'field' at the
metal centre. The orbital filling shown in Figure 7.39 is representative of the d
8
complex
[Ni(H
2
O)
6
]
2
+
with the configuration (
t
2g
)
6
(
e
g
)
2
.Thetwo
e
g
electrons are drawn in separate
energy levels to minimize electron-electron repulsion.
On the MO diagram, the crystal field splitting parameter is indicated by the symbol
o
.
In the MO picture, this is interpreted as the separation between the nonbonding
t
2g
states
and the antibonding 2
e
g
levels.
7.7.2 The Jahn-Teller Effect
The MO diagram for
O
h
symmetry complexes has its highest filled MOs in degenerate
states for most transition metals. The Jahn-Teller effect is a change of geometry due to
an uneven filling of such degenerate states. For example, Cu
2
+
in the hexaaqua complex
[Cu(H
2
O)
6
]
2
+
has a d
9
configuration, one more than shown in Figure 7.39. This results in a
filling of all MOs up to the
e
g
states, with three electrons to be placed in these two MOs. In
O
h
symmetry there would be two choices: place two electrons in the
e
g
level derived from
the metal d
z
2
orbital and one in that from the d
x
2
−
y
2
or two in d
x
2
−
y
2
and only one in d
z
2
.
When such an imbalance is present, a shift of the complex geometry to a lower symmetry
can give a more stable system.
In this case, two
trans
-H
2
O ligands have longer Cu
O distances than the four equa-
torial ligands. So, the [Cu(H
2
O)
6
]
2
+
complex has
D
4h
symmetry, as shown in Figure 7.40,
and we will now show how this distortion is driven by MO energy by comparing the
O
h
and
D
4h
MO diagrams for d
9
...
systems.
D
4
h
Symmetry Complexes
The reducible representation and the application of the reduction formula for the
D
4h
com-
plex are set out in Table 7.14. This shows that the six
σ
-donor ligand orbitals give SALCs
with the following irreducible representations:
=
2
a
1g
+
b
1g
+
a
2u
+
e
u
(7.71)
