"Cracking the Woodward-Hoffmann Rules for Sigmatropic Rearrangements"

 

"Cracking the Woodward-Hoffmann Rules for Sigmatropic Rearrangements"

Woodward-Hoffmann rules are a set of theoretical principles that describe the stereoselectivity and regioselectivity of pericyclic reactions, including sigmatropic rearrangements. Sigmatropic rearrangements are a type of pericyclic reaction where a σ bond is rearranged between two atoms in a molecule, resulting in a new σ bond and a rearranged molecular structure.

Understanding the Woodward-Hoffmann rules is crucial for predicting and rationalizing the outcomes of sigmatropic rearrangements, which have numerous applications in organic synthesis and natural product chemistry. In this article, we will discuss the Woodward-Hoffmann rules and their relevance to sigmatropic rearrangements.

The Woodward-Hoffmann rules were developed independently by Robert Burns Woodward and Roald Hoffmann in the 1960s. These rules are based on the principles of orbital symmetry and conservation of orbital symmetry during chemical reactions. According to the Woodward-Hoffmann rules, the stereochemistry and regiochemistry of pericyclic reactions are determined by the overlap of the orbitals involved in the reaction.

The Woodward-Hoffmann rules consist of four basic principles, which are as follows:

The Conservation of Orbital Symmetry:

This principle states that the symmetry of the orbitals involved in a pericyclic reaction must be conserved. This means that orbitals with the same symmetry will overlap and interact, while orbitals with different symmetry will not interact.

The Frontier Orbital Principle:

This principle states that the reaction will proceed through the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) involved in the reaction. The HOMO of the reactant becomes the LUMO of the product, and vice versa.

The Even-Electron Rule:

This principle states that pericyclic reactions involving an even number of electrons are allowed, while reactions involving an odd number of electrons are not forbidden.

The Correlation Diagram:

This principle is used to determine the stereochemistry and regiochemistry of the reaction by plotting the relative energies of the HOMO and LUMO orbitals involved in the reaction.

Keep in mind

• A thermal (ground state) sigmatropic rearrangement is symmetry allowed when total number of (4q + 2)s component and (4r)a component is odd.
• A sigmatropic change in the first excited state is symmetry allowed when total number of (4q + 2)s and (4r)a component is even.

Case # 1. Woodword-Hoffmann rules for (m, n) Sigmatropic rearrangements where migrating group is not hydrogen

1. Draw the mechanism for the reaction.
2. Choose the components. Only the bonds taking part in the reaction mechanism must be included.
3. Make a three-dimensional drawing of the way the components come together for the reaction, putting orbitals at the ends of the components.
4. Join up the components where new bonds are to be formed. Make sure you join orbitals that are going to form new bonds.
5. Label each component s or a. See below for the π and σ bond symmetries.

Whether π component is s or a

If both upper lobes and both lower lobes of the π component are involved in the reaction then the component will be s and it is label as π²s. If one upper lobe and other lower lobe of the π component are involved in the reaction then the component will be a and it is label as π²a.

Whether σ component is s or a

When sp³-hybrid orbital uses its large lobe for reaction then there will be retention or the small lobe then there will be inversion. 

When there is retention at both ends or inversion at both ends then σ component is σ²s. If there is retention at one end and inversion at other end then σ component is σ²a.

When applied to sigmatropic rearrangements, the Woodward-Hoffmann rules can be used to predict the stereochemistry and regiochemistry of the reaction. For example, in a [3,3] sigmatropic rearrangement, the Woodward-Hoffmann rules predict that the reaction will proceed through a concerted mechanism, with the HOMO of the reactant interacting with the LUMO of the product. The correlation diagram can be used to determine whether the reaction will result in a syn or anti stereoisomer, and whether the reaction will proceed through a suprafacial or antarafacial pathway.

Here are the clear examples of Suprafacial and Antarafacial rearrangements along with the hydrogen migratory group and carbon migratory group.

Conclusion:

 In conclusion, the Woodward-Hoffmann rules are a powerful tool for predicting and rationalizing the stereochemistry and regiochemistry of pericyclic reactions, including sigmatropic rearrangements. By understanding these principles, chemists can design more efficient and selective synthetic routes, and gain a deeper understanding of the fundamental principles that govern chemical reactivity.