Why can't we use orbital correlation diagrams for sigmatropic rearrangements?

Question

In Ian Fleming's Molecular Orbitals and Organic Chemical Reactions book, he describes the use of correlation diagrams as a method for predicting whether pericyclic reactions will be allowed/forbidden on a symmetry argument (he calls this a basis for the Woodward–Hoffmann rules).

Correlation diagrams have given us a convincing sense of where the barriers come from for those reactions that we have been calling forbidden.

Whilst there are given examples of cycloadditions and electrocyclic reactions there are no examples of sigmatropic rearrangements, and on the internet a few sources say the diagram is not appropriate for these sigmatropic rearrangements.

I am curious why a correlation diagram does not work for sigmatropic rearrangements, since the the Woodward–Hoffmann rules are able predict which are allowed and forbidden.

Answer 1

The reason that comes up again and again is the one below, taken from Orbital Interaction Theory of Organic Chemistry.

Orbital correlation diagrams are useful for cycloadditions and electrocyclic reactions but not for sigmatropic rearrangements since no element of symmetry is preserved.

Source: Orbital Interaction Theory of Organic Chemistry. Arvi Rauk.

In order to (easily) draw a correlation diagram you need to find some symmetry element that is preserved throughout the reaction. A correlation diagram is shown below for an electrocyclic ring closing reaction, note how the C₂ axis is preserved during the process, allowing the various correlations to be made.

Source: Dr Wallace's web notes on pericyclic reactions

Since you mention Fleming's book, I'll quote him on this matter:

Step 3. Identify any symmetry elements maintained throughout the course of the reaction.

Source: Molecular Orbitals and Organic Chemical Reactions: Reference ed. Ian Fleming.

Essentially, you have to be able to look at the orbitals directly involved in the reaction (i.e. we don't care about random groups hanging off the side that play no role).

In a sigmatropic rearrangement there is rarely (possibly never but I'm sure there are exceptions to the rule) a preserved symmetry element, which makes it impossible to draw a correlation diagram.

There are, of course other approaches, each of which have advantages and limitations depending on the reaction in question:

• Just apply the Woodward–Hoffmann rules
• Use frontier orbital theory to look at the HOMO–LUMO interactions
• Use a Zimmerman approach and look if the transition state is aromatic, or anti-aromatic.