Chemistry Reference
In-Depth Information
ones. In the case of neutral ligands, such as water and ammonia, dipolar charge separations are considered. The
central point in this theory is the effect of the symmetry of the arrangement of ligands on the energy of the
d orbitals of a central metal atom. Imagine a cube with a metal ion occupying its centre and a Cartesian system
of xyz-axes going through it. There are five d orbitals for the metal ion: two aligned along the principle axes
hence referred to as d
z
2
and d
x
2
2
and three distributed between the axes and hence referred to as d
xy
,d
xz
,d
yz
.
In the absence of any ligand, the d orbitals are all of equal energy. We describe such orbitals as degenerate.
Imagine now negatively charged ligands approaching the cube along the xyz-axes. For an octahedral compound
that means six ligands moving toward the centres of the faces of the cube. The ligands have a negative field
around them which will be at a maximum along the direction of the approach, that is, the xyz-axes. For s and p
electrons, this is of little consequence but for any d electrons this is of great importance. Not only will such
electrons be repelled, but those in the orbits along one of the Cartesian axes will experience a greater repulsion
than those in an orbit between the axes, since such electrons will be pointing toward where the ligand negative
field is at its maximum value. Such unevenness in the repulsion will lift the degeneracy of the orbitals and will
create preferences for occupation along the orbitals of the lowest energy: the electrons will occupy the orbitals
in between the xyz-axes, i.e., the d
xy
, d
yz
,andd
xz
y
2
,
which lie along the direction of approach of the ligands. In other words, the field associated with the ligands
splits the previously homogenous spherical field of the central ion into two groups of different energy level: the
e
g
group of the d
z
2
and d
x
2
rather than the orbitals along the axes, i.e., d
z
2
and d
x
2
y
2
orbitals of relatively high energy and the t
2g
group of the d
xy
,d
xz
,d
yz
orbitals of
relatively low energy. The notation/symbol used for each subset of orbitals indicates its symmetry: e is used for
doubly degenerate orbitals,
y
t
for triply degenerate ones. The energy splitting is shown schematically in
Δ
tet
=
4/9 Δ
oct
d
x
2
-y
2
d
x
2
d
x
2
-y
2
e
g
b
1g
d
xy
d
yx
d
xx
t
2
Δ
oct
Δ
oct
Δ
tet
e
d
x
2
-y
2
d
x
2
t
2g
b
2g
d
xy
d
xy
d
yx
d
xx
d
yx
d
xx
e
g
a
1g
d
x
2
tetrahedral field
free-ion
octahedral field
square-planar field
FIGURE 2.7
Crystal field d orbital splitting diagrams for common geometries.
The above treatment considers the ligands in an octahedral geometry (i.e., with the ligands placed at the centre
of the faces of the cube). The square planar case is simply an extension of the octahedral where two ligands are
removed from the z-axis. The repulsion of electrons in the d
z
2
and d
x
2
2
orbitals will not be the same and the result
y
is a square planar shape.
Consider now the cube and the ligands fitting into a tetrahedral geometry (i.e., the ligands are placed at four
corners of the cube). The energy of the d orbitals which point towards the edges should now be raised in energy
higher than those which point towards the faces. The tetrahedral ligand field splitting is exactly the opposite to that
of the octahedral field.
