By now we have become somewhat familiar with transition metal complexes, but before examining
the reactions they can participate in, we need to discuss a few more of their properties. First
let us recall some of the theories we know regarding chemical bonding and molecular geometry.
Way back at the beginning of general chemistry we learned about VSEPR theory,
and the repulsion between electron clouds that determines the geometries of simple molecules.
We also discussed crystal field theory, and the complications that arise when
looking at transition metal complexes which utilize d orbitals. We saw that the five
d orbitals in a given energy level are no longer degenerate when coordinating to ligands,
because some of these orbitals sit on axes which accommodate the metal-ligand bonds,
whereas some orbitals sit between these axes. So we introduced the concept of t2g orbitals, which
are the lower-energy dxy, dxz, and dyz orbitals, and the higher-energy eg orbitals, which are the
dx2-y2 and dz2 orbitals, and we called the energy between them the crystal field splitting energy.
Now we have to build on this understanding of bonding in transition metal complexes
by supplementing with another theory called ligand field theory, which can be thought of as somewhat
of an extension of crystal field theory. Ligand field theory is based on molecular
orbital theory, and it is a bit more successful in predicting certain properties of transition
metal complexes, such as certain data gathered from spectral analysis.
This model deals with the s, p, and d orbitals that are possessed by a metal for a given shell,
which gives a total of 9 valence orbitals for the metal. These are the orbitals that will
participate in bonding interactions with ligands. Let’s say we are looking at 4s, 4p, and 3d
orbitals, such as with the cobalt center in this complex with six ammonia ligands and a 3+ charge.
According to this model, we have six degenerate ligand orbitals that house the electrons involved
in the metal-ligand bonds, and when the 9 orbitals from the metal overlap with these 6 orbitals from
the ligands, 15 molecular orbitals will be produced. Six of these are bonding orbitals,
which are all of a lower energy than the original atomic orbitals, six are antibonding,
which are of a higher energy than the original atomic orbitals, and the remaining three are
nonbonding orbitals, which have the same energy as the 3d orbitals on the metal.
The molecular orbitals are populated precisely as we would expect, from lowest energy and moving
upwards, which in this case leaves us with all of the bonding orbitals full, as well as the
nonbonding, and the antibonding are all empty. This results in a very stable octahedral complex,
where metal-ligand bonding occurs due to the overlap of these atomic orbitals,
which accounts for covalent bonding. Ligand field theory also describes the manner in which these d
orbitals are affected differently by different sets of ligands, and can have their energies
raised or lowered depending on the strength of their interaction with the ligands.
There is much more that we could discuss regarding ligand field theory, but let’s return to crystal
field theory and discuss a particular ramification that will be of interest to us in learning about
transition metal complexes. The Jahn-Teller effect, also known as Jahn-Teller distortion,
is a phenomenon which describes the way that nonlinear molecules, and in particular
transition metal complexes, may distort their geometry in order to remove the degeneracy
of unequally occupied orbitals in order to lower the overall energy of the complex. In other words,
this is something that will happen when the d orbitals are not filled in a symmetrical manner.
Taking a typical octahedral complex, we recall that the d orbitals are split up into the
lower-energy t2g orbitals and the higher energy eg orbitals. If electrons are arranged in these
orbitals in a symmetrical manner, with one or both of these sets of orbitals either half full or
completely full, the Jahn-Teller effect will not be observed. In any other case, it will. So high
spin d4, low spin d7 or d9, these will be common situations that elicit the Jahn-Teller effect.
Let us now understand precisely what kind of distortion will occur. Take for example an
octahedral copper complex with a 2+ charge. This will have 9 electrons distributed around these d
orbitals, with the t2g orbitals completely full, while the eg orbitals will be one full
and the other half full. These eg orbitals are degenerate as shown, but the Jahn-Teller
effect predicts that the complex will distort in such a way that the degeneracy is eliminated,
which we call tetragonal distortion. When this happens, between the dx2-y2 and dz2 orbitals,
one will become higher energy than the other, and they will end up the same distance away from the
original orbital in energy, in either direction. The same goes for the other three orbitals,
where the dxy will no longer be the same energy as the dxz and dyz. One set will be higher-energy and
the other set will be lower-energy, compared with the original energies, and the distance to the dxy
will be twice the distance to the others, because of the 1 to 2 ratio. As a result of
this activity the complex will either stretch or compress along the z axis. If the asymmetry
is in the t2g orbitals, the effect is weak. If in the eg orbitals, the effect is strong.
Here are some examples so we can get a better understanding. First, a d4 high spin complex.
For these orbitals down here, there is no net energy change. But for the ones up here,
this lone electron will become lower in energy as it moves to the dx2-y2 orbital.
This stabilization produces a tetragonal compression, so the metal-ligand bonds along the
z axis will compress. If instead the dz2 orbital is the lower-energy orbital for a d4 high spin
complex, we will get the same stabilization but we will observe tetragonal elongation, where these
bonds will stretch instead of compress, due to the shape and orientation of the dz2 orbital. Compare
these to a d5 high spin complex, where now all the orbitals are half full, so when distributed
amongst the new orbitals there is actually no net energy change and therefore no distortion.
The Jahn-Teller effect will be something to keep in mind when considering the geometry and
properties of transition metal complexes. Now let’s move on to our next topic in the series.