16.27: Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for the symmetry-allowed thermal and photochemical reactions.

The theoretical basis for Woodward–Hoffmann rules rests on the principle of conservation of orbital symmetry. This approach suggests that reactions, where the symmetry characteristics of the reactants’ molecular orbitals correlate to the molecular orbitals of the products, proceed via a low energy transition state and become symmetry-allowed. However, a lack of correlation destabilizes the transition state and makes it a symmetry-forbidden process. The rules are expressed as follows:

• Thermal pericyclic reactions are symmetry-allowed when the sum of (4q + 2)_s and (4r)_a components is odd.
• Photochemical pericyclic reactions are symmetry-allowed when the sum of (4q + 2)_s and (4r)_a components is even.
  where q and r = 0, 1, 2, 3, …; s = suprafacial; a = antarafacial

Microscopic Reversibility

The principle of microscopic reversibility applies to systems at equilibrium. Since pericyclic reactions are equilibrium processes, it follows that the forward and reverse reactions will follow the same mechanism and proceed via the same transition state. So, the selection rules apply for both the forward and the reverse reactions.

For example, the electrocyclic ring-closure of octatriene under thermal conditions is a suprafacial, disrotatory process. The reverse ring-opening reaction will proceed in a similar manner.

Woodward–Hoffmann rules are a set of generalizations used to predict the stereochemistry of pericyclic reactions based on orbital symmetry.

The rule states that thermal pericyclic reactions are symmetry-allowed when the sum of (4q + 2)_s and (4r)_a components is odd and photochemically allowed when the sum is even.

Here, q and r are integers. (4q + 2)_s and (4r)_a designate the number of electrons in the suprafacial and antarafacial components.

Recall that suprafacial and antarafacial refer to the two distinct ways new bonds develop.

Let's apply this to the electrocyclization of octatriene.

First, identify the components. A triene is a _π6 component belonging to the (4q + 2) category.

Next, label the components as suprafacial or antarafacial. The ground state HOMO  has symmetric terminal lobes; bond formation occurs through a suprafacial, disrotatory pathway.

Finally, add the components. There is one (4q + 2)_s component and no (4r)_a components. The sum is one, and the reaction is thermally allowed.

Pericyclic reactions are reversible. The selection rules apply equally to the forward and reverse reactions as they proceed through the same transition state.