Chemistry Reference
In-Depth Information
fully (and four-coordination is achieved), with increasing separation of the two types of
orbitals in each originally degenerate set.
One classic example of bond elongation is the behaviour of d
9
Cu(II) octahedral com-
plexes, which typically display elongation of M L bond lengths along one axis direction.
This is predicted by the
Jahn-Teller
theory. Without resorting to detail of this theory (inap-
propriate at this level), it predicts that, where the ground state is degenerate, it is only if the
complete orbital set is empty, half-filled or filled with electrons that the complex is stable
with respect to distortion that will relieve the degeneracy through splitting the low-lying
orbital set into separate orbitals. Otherwise, distortion from regular octahedral geometry,
easily achieved through usually axial elongation (or more rarely compression) occurs to
relieve orbital degeneracy. The effect is only strong where the
e
g
level carries electrons,
since these have the capacity to split much more strongly than the essentially nonbonding
t
2g
set. Strong Jahn-Teller distortions arise where the two
e
g
orbitals are differentiated by
electron occupancy, that is when there are one or three electrons present in the
e
g
level.
This is routinely observed for d
9
,low-spind
7
and high-spin d
4
systems, with particularly
strong evidence coming from structural studies of d
9
Cu(II) complexes.
The extreme case of elongation, complete removal of two ligands along one axis, leads
to the four-coordination square-planar shape. The d
x
2
−
y
2
orbital is then high in energy
compared with the other four (Figure 3.15), which favours the d
8
configuration since all
electrons fill the four low-energy levels, leaving the high energy one empty, providing an
energetically favourable arrangement. The experimental observation of a large number of
square planar d
8
complexes is consistent with this model. The energy gain also increases
with increasing ligand field strength; since this occurs for the heavier (4d and 5d) transition
elements, the observation in those rows of four-coordinate square planar as a more common
geometry is also consistent with the model.
What the above shows is that
the bonding model is responsive to molecular shape
, which
is one of its key attributes. In principle, it can be manipulated to yield an energy level
arrangement for any shape. For the best known of the four-coordination shapes, tetrahedral,
the ligand arrangement is distinguished by none of the point charges lying along the
x
,
y
,
z
,
axes that we employed for the octahedral case. The tetrahedron can be visualized as based
on a cube, with pairs on point charges on opposite corners of a cube. Thus the tetrahedral
ligand field is closely related to the rare cubic ligand field. This cube has the metal atom at
its centre and the axes passing through the centres of each face. From this cubic framework
at least, it becomes clear that the orbitals lying along the axes (d
x
2
-y
2
and d
z
2
) will interact
least with the point charges, the opposite to the behaviour in an octahedral field (Figure
3.16). Conversely, the d
xy
,d
yz
and d
xz
orbitals that lie between axes are angled out more
towards the corners of the cube and will thus interact most.
This interaction hierarchy is the reverse of the situation in the octahedral field, and,
as a consequence, the orbital energy sets are also reversed in both the cubic and related
tetrahedral fields (Figure 3.17). For the tetrahedral field they also change point group names
slightly (now simply
e
and
t
2
, associated with the change in overall symmetry).
Geometric arguments relating to relative distances between point charges and orbital
lobes allow calculation of the relative strength of the splitting in the tetrahedral case
(called, now,
o
when identical ligands (as point charges) are placed identical distances from the metal
centre in each case (Figure 3.18). For the related cubic field, where there are twice as
many point charges present, the splitting energy is twice the tetrahedral value, or
t
) compared with the octahedral case (
o
), which shows that
t
=
4/9
cubic
=
8/9
o
.
