Chemistry Reference
In-Depth Information
turns out that the d
z
2
orbital is in reality a linear combination of two orbital functions, d
z
2
-y
2
and d
z
2
-x
2
that are shaped just like the separate d
x
2
-y
2
orbital, but oriented differently. It is
then less surprising that the composite we see as the d
z
2
orbital is energetically identical
to the d
x
2
-y
2
orbital. But if you're now wondering why these orbital functions need to be
combined in the first place - well, that's a story you simply won't find here.
The outcome of the introduction of a defined spatial arrangement of point charges, here
an octahedral field, is that the degeneracy of the five d orbitals is removed, and the orbitals
arrange themselves in new sets of differing energy. The d orbitals pointing directly towards
the ligands (d
x
2
-y
2
and d
z
2
), and thus along what are the M
L bonds, can be considered
to be involved in a traditional
bond; they sometimes are referred to as d
orbitals. The
three remaining and more stable orbitals (d
xy
,d
yz
and d
xz
) point away from the M
L bond
direction, but may possibly be capable of involving themselves in
-type bonding, and as a
consequence are sometimes called d
orbitals. However, this view is mixing conventional
covalent bonding thinking with a purely ionic model, and thus is problematical, and we
shall largely avoid it.
The formation of doubly and triply degenerate sets of orbitals is a characteristic of the
octahedral field. Because it is the spatial location of the set of point charges that is significant
in generating this outcome, it will hardly come as a surprise to find that
every different shape
arrangement of point charges will lead to a different characteristic outcome
- but more on
that later. At present, focusing on the octahedral field, the outcome shown in Figure 3.9
applies. The lower energy set of three orbitals (d
xy
,d
yz
and d
xz
) is called the
diagonal
set
(or, applying mathematical group theory, which we shall not develop here, also called
t
2g
where
t
stands for triplet degeneracy), and the higher energy set of two orbitals (d
x
2
-y
2
and
d
z
2
) is called the
axial
set (or from group theory,
e
g
, a doublet level), the names relating to
where the orbitals point versus imposed axes. The energy difference between these levels
is, compared with the differences between atomic orbital levels generally, relatively small,
in line with the influence of the ligand set being a relatively modest one. This energy
difference is called the crystal field splitting, represented by a parameter termed
o
(where
the subscript 'o' is an abbreviation for 'octahedral'). An energy balance between the two
sets of orbitals is struck, so that the three lower levels are
−
0.4
o
lower and the upper
two levels
o
higher than the spherical field position set as the zero reference point.
The language of chemistry contains several dialects, and you will find some texts refer to
the energy gap
+
0.6
o
as 10D
q
(with the diagonal and axial sets lowered 4D
q
or raised 6D
q
respectively); don't be confused, as the same conceptual model is being applied. Using the
o
symbolism is more appropriate, since it carries some additional information that defines
the type of field operating in the subscript.
One key question that begs an answer at this stage is simply what factors govern the
size of
o
? Answering this should give us the satisfaction of being able to predict certain
spectroscopic properties. Obviously, since we are involving both metal and ligand in our
complex, we can anticipate that both have a role to play. If we fix the metal's identity,
then we can focus on the ligands, and their particular properties that influence
o
.For
octahedral complexes of most first-row transition metal ions at least, the presence of colour
suggests that somehow part of the visible (white) light spectrum is being removed. This
can be envisaged if the energy gap between the diagonal (
t
2g
) and axial (
e
g
) levels equates
with the visible region, leading to absorption of a selected part of the visible light that
occurs to cause the complex to undergo electron promotion from the lower to the higher
energy level. Simply by monitoring the change in colour as ligands are changed, we can
determine the energy gap
o
applying for any ligand set. The stronger the crystal field,
