Professor Dave here, I wanna tell you about crystal field theory.
As we just learned, coordination compounds have some very interesting geometries, and
many of these can’t be explained using the same models that we use for normal covalent
compounds, like VSEPR theory or valence bond theory, since the type of bonding involved
is more complex than mere overlapping of hybridized orbitals. Instead, we have to use another
model called crystal field theory, so let’s go through the finer points of this theory now.
Crystal field theory is based on the premise
that the metal ion and the ligands can be treated as point charges, and the spatial
arrangement of these point charges will affect the energies of the d orbitals for the central
metal atom. These are the orbitals that ligands donate electron density into, so these are
the chief concern for the model, and this model, although incomplete just like VSEPR
theory or valence bond theory, does wonderfully explain things like the colors, magnetic behavior,
and structures that can be observed with coordination compounds. The first thing we must understand
is that ligands all have excess electron density that they are donating to the metal ion, and
this electron density will repel existing electron density on the metal ion. Due to
this repulsion, the energy of certain d orbitals will be increased, and not in an equal manner.
To understand why, let’s look at this octahedral complex, a very common geometry for coordination
compounds. The central metal atom has valence electrons in these d orbitals, which when
unhybridized look like this. We must note that two of the d orbitals, the d (x squared
minus y squared) and the d z squared orbitals, have lobes that extend on the X, Y, and Z
axes, meaning that electron density is sitting on these axes, whereas the other three orbitals
have lobes that sit in between the axes. Looking at the octahedral complex, the bonds to the
ligands also sit on these axes, which means that in order for ligands to approach the
metal atom, their point charges must repel the electron density in these two orbitals.
For this reason, whereas for an isolated metal atom the d orbitals all have the same energy,
in an octahedral complex, these two orbitals we mentioned have a higher energy, as they
point in the direction of ligands, and we refer to them as the EG orbitals, while the
other three are the T2G orbitals, which point in between ligands. The difference in energy
between these two sets of orbitals is called the crystal field splitting energy. The magnitude
of this energy gap will depend on whether the orbitals involved are 3d, 4d, or 5d orbitals,
as well as the identity of the ligands themselves, with the impact following this trend here,
called the spectrochemical series. On the left we have weak field ligands, and on the
right, strong field ligands. Let’s put this into context. For an isolated
metal atom, once again, all the orbitals are of equal energy. If the metal is participating
in a complex with weak field ligands, the difference in energy is small, and not enough
to overcome the pairing energy, or the repulsion generated by doubling up electrons in an orbital.
In such a case, they will spread out evenly, putting unpaired electrons in the EG orbitals
before the T2G orbitals are completely full. These are called high-spin complexes. But
if in a complex with strong field ligands, the difference in energy is very great. In
such a case, the system will be at a lower energy by simply doubling up electrons in
the lower energy T2G orbitals. These are called low-spin complexes. Crystal field theory works
for geometries other than octahedral as well, like tetrahedral, which tend to be high-spin,
but the ligands orient themselves differently, so they interact with the orbitals differently,
and we get different energy diagrams. Specifically, with this geometry, ligands more closely approach
the d orbitals between the axes rather than the orbitals on the axes, so the higher energy
orbitals are precisely the opposite ones as in the case of octahedral geometry. Also,
the ligands don’t approach the orbitals as directly, so the energy splitting will
be of a lesser magnitude. We can do something similar for square planar geometry as well.
So to reiterate, the strength of the ligands surrounding the metal atom, along with other
factors like oxidation state and coordination number, will determine the magnitude of the
crystal field splitting energy, or the difference in energy between the T2G orbitals and the
EG orbitals. This in turn will determine the electron configuration, and thus other characteristics
of the complex, such as paramagnetism versus diamagnetism, and the corroboration of the
predicted magnetic behaviors of different coordination compounds is very strong evidence
in favor of crystal field theory. More evidence comes from examining the colors of visible
light emitted by certain compounds. We know that atoms absorb light of certain frequencies
depending on the element they belong to, which results in an electron going to an excited
state. And when an electron goes from an excited state to a lower state, it will emit a photon.
If that light is visible and hits our eyes, we see the object, and for coordination compounds,
the energy difference between the d orbitals results in the emission of photons in the
visible range. Even small changes in orbital energy can have a significant impact on the
color of the compound, as is seen here, with different transition metal ions exhibiting
totally different colors. And this is not just for different elements, we can look at
two different oxidation states for the same element, and they may have different colors.
So crystal field theory allows us to predict a variety of properties for coordination compounds,
making it a powerful model indeed.