Chapter X. Octahedral Complexes

We definitely need to use d AOs now. The lessons that we will learn from the octahedron are vital. We will come back again and again to to this point. Because there are 5 d AOs and six ligand orbitals around it there are 11 MOs to be constructed. However, we will see that there is really a smaller subset, that I will call the "important valence region" that will need to be considered for any ML_n molecule. We also need to worry where all of these orbitals are with respect to each other. Plotted below are some ionization potentials for the 3d and 4s AOs along with some common ligand s ionization potentials.

A. The s Bonding in ML₆

We shall refer to L as any generic two electron s donating ligand. In other words, L has a filled orbital that can interact with the metal in a s sense. Some examples are:

This splitting pattern is appropriate for any of the molecules below.

This is a system that will be stable for 12 electrons as well as 18 depending upon wether the nonbonding t_2g set is filled or empty. But there is a bit more complication here. The energy difference between nonbonding t_2g and antibonding e_g is very sensitive to the s donor strength of L:

If e_g is destabilized by a large amount then the gap is large. The ligand should have a high-lying s MO which will overlap with the d AOs strongly. The M-L bonding is, therefore, primarily covalent.

On the other hand a weak s donor will be one where the atom in L connected to the metal is very electronegative. Therefore the s MO of L will lie at low energies -

Therefore the bonding is largely ionic. The M-L interaction is primarily electrostatic.

An important consequence is that the t_2g - e_g energy gap is not so large in this case and, since, it costs energy to pair electrons, high spin states are possible:

There are then two types of molecules in the transition metal field:

1. Coordination chemistry: Weak s donors around metal, frequently positively charged metals, small t_2g - e_g gap, 18 electron "rule" frequently violated.

2. Organometallic chemistry: Strong s donors around metal, frequently uncharged charged metals, large t_2g - e_g gap, 18 electron "rule" not violated.

B. p Effects

These can easily be added to the basic electronic structure from the s system by interaction with the t_2g set (these are the MOs in ML₆ which can interact in a p fashion). Let us look at two examples. First let's consider the change that is encountered when one of the generic ligands is replaced by CO. CO has a s donor MO just like L but it also posses p and p* orbitals -

Shown below is what occurs on going from ML₆ to ML₅(CO). The s splitting will essentially be the same. However, the t_2g interacts with p and p* on the CO ligand. The result is:

The t_2g set (2e) is the middle, nonbonding member of this three orbital pattern. It is constructed as follows:

Notice that a node develops on the carbon atom in 2e.

A reasonable, qualitative ordering of p-acceptor ability is given by:

And p-donors by:

Carbenes are a particularly interesting example of p bonding in organometallic complexes. An example of a so-called Fisher complex is shown below.

There are really two types of carbene complexes which have different chemical behavior. The origin of their difference can be traced to the relative height of the p AO on carbon relative to the t_2g set at the metal (see the first plot in this Chapter):

Now suppose there were two carbenes at the metal positioned trans to one another. Which would be the most favored conformation from that shown below?

An interaction diagram for each case can be constructed and compared.

The two MOs are stabilized more than one-half of the situation on the left side. Therefore, the D_2d geometry is more stable. This is a general result and is called "the busy orbital problem".

C. Distortions at the Octahedron

There are times when the octahedral structure is not the most stable one. This most frequently occurs when the ML₆ complex has less than an 18 electron count. We shall look at two examples. First consider what happens when two trans L goups are bent towards each other

The lowest level, f₁, is stabilized even though overlap between metal p and the two L s-donor functions decreases. This is because f₁ mixes d character into itself. Notice also that the f₂ MO stays nonbonding. It becomes hybridized away from the ligands. So the resultant picture is:

The behavior of f₁ and f₂ is one that we will see a number of times in the context of other metal complexes.

Now suppose we have WMe₆. This is a real molecule. We will go into electron counting in the next Chapter. For now take it that this molecule is d⁰, i.e. it has no d electrons in t_2g. So returning to the interaction diagram for ML₆, this will have 12 electrons - six electron pairs. The VSEPR method tells us that the octahedral geometry is going to be the most stable one. This is not even close to being the case. Below is a Walsh diagram from converting an octahedron to a trigonal prism.

Two members of the t_1u set have the same symmetry as two from t_2g at the trigonal prism. So t_2g mixes and stabilizes the former two MOs. What this means is that metal d character mixes into the M-L bonds which before only had metal p character. In a valence bond sense the six M-L bonds at the octahedron have sp³d² hybridization. At the trigonal prism these become sp³d^2+x hybrids which will form stronger M-L s bonds because of the increase of d character. The third member of t_2g can mix with the third member of t_1u if the molecule distorts to C_3v. This in fact really happens. The x-ray structure of WMe₆ and MoMe₆ have been determined. A side and top view of WMe₆ is shown below. The result is very unusual and certainly not at all from what one would think from a steric sense.