Chemistry Reference
In-Depth Information
z
y
x
Figure 3.16
A view representing the interaction of the d
z
2
and d
x
2
-y
2
orbitals with a cubic field (black circles) and
an octahedral field (grey circles). The orientation of the d-orbital lobes directly towards the octahedral
set contrasts with the orientation for the cubic set.
The derivation of a model that manipulates the d-orbital set is incomplete without
consideration of placement of d electrons into the orbitals. Because the model we have
developed is ionic in character, one of the advantages is that we do not have to worry about
any additional electrons coming from attached groups. The only electrons of concern are
the initial d electrons themselves, which will vary from zero (a trivial case) to a maximum of
ten (all that the five d orbitals can accommodate) depending on the metal and its oxidation
state. At first, we can apply simple rules for filling atomic energy levels - fill in order of
increasing energy - and apply Hund's rule (for degenerate levels, electrons add to each
orbital separately maintaining parallel spins before pairing up commences). The outcome
is the set of electron arrangements shown for the octahedral case in Figure 3.19. What this
model provides is support for complexation, since in most cases the energy of the assembly
in the presence of the octahedral field is lower than the zero field situation. To clarify this,
consider the simple d
1
case. Here, an electron resides only in a
t
2g
orbital, which is more
stable by
−
0.4
o
than the spherical field zero-point. The energy of this stabilization is
z
E
d
xy
d
xz
d
yz
y
+0.4
∆
t
∆
t
x
-0.6
∆
t
d
z
2
d
x
2
-y
2
tetrahedral field
Figure 3.17
The d-orbital splitting diagram for a tetrahedral field.
