Chapter XV The Isolobal Analogy

In previous chapters we have shown that there are electronic relationships between various ML_n fragments with specific d electron counts. In the Chapter we are going to formalize these relationships and more importantly make a connection between the ML_n fragments from the inorganic world to the AH_n fragments in the organic/main group world. This is called the isolobal analogy. Two fragments or molecules are said to be isolobal if their frontier orbitals are:

1. the same in number

2. possess the same symmetries

3. have the same occupation by electrons

4. are similar in radial extent.

We symbolize this relationship by:

If two fragments are isolobal then they should have very similar bonding capabilities. If molecules are isolobal then they should have similar electronic structures. The uses of the isolobal analogy are then:

1. provide a short-cut to understand the electronic structure

2. unusual ways to classify molecules

3. provide a mechanism to predict new, hopefully stable, molecules

4. offer clues about reactivity and reaction mechanisms.

The isolobal analogy is very simple and, therefore, quite crude. The frontier orbitals we are talking about are small in number. The radial extent, therefore, the overlap and stabilization of the bonding levels will be different among isolobal fragments. Thus, there will be instances where it will fail.

The generation of isolobal fragments starts with saturated (molecules where all bonding and nonbonding MOs are filled and the antibonding MOs are empty) molecules of any sort:

A. Isolobal Fragments

The number of starting points is nearly infinite! One can also go up or down in the Periodic Table:

Furthermore, the number of electrons in the frontier orbitals can be adjusted to form other relationships:

Let's start with the CH₂ example and show the use of the isolobal analogy in terms of reactions and new molecules.

All of the compounds above are molecules. They should have singlet and triplet states and have similar reactivity -

Here are some olefin complexes:

Normally we would not draw cyclopropane as an olefin complex. But the bonding is the same as in the other molecules.

B. Caveats

There are two areas of concern that may, at first seem con

fusing. First consider the ways of forming a Ni(CO)₃ fragment:

So is Ni(CO)₃ isolobal to CH₂, CH₃+, or CH-? The answer is that it is isolobal to all three!

Secondly it is important to realize that there can be relaxations of the geometry. This is particularly true for bridging and terminal CO groups:

C. Illustrations of the Isolobal Analogy

1. CH₂ analogs revisited

Reactivity or kinetic instability does not necessarily mean that the molecules is thermodynamically unstable. The d AOs are more diffuse than the 2p AOs; their overlap is much weaker.

2. CH₃ analogs

Lets first take a problem that we have seen before.

For the series below as molecules, the geometries do not show analogous behavior:

But this does form the basis for an interesting series:

3. CH Fragments

Obviously ring strain in the tetrahedrane complex is larger than that for Co₄(CO)₁₂. For the CH fragment the p AOs form an angle of 180°, whereas in Co(CO)₃ the angle between the lobes is close to 90°.

Here are a couple of examples:

D. Reaction Mechaisms

This is a set of examples from the organic world - sigmatropic rearrangements which in this case is called circumambulation. For the organometallic processes it is called ring whizzing: