30.8 Some Examples of Sigmatropic Rearrangements

Sigmatropic Rearrangements

Sigmatropic rearrangements in cyclic systems

A [1,5] sigmatropic rearrangement involves the migration of a sigma bond across a $\pi$ system through a concerted, cyclic transition state. The "1,5" notation means the bond migrates from atom 1 to atom 5, counting along the conjugated framework.

These shifts proceed through a six-membered cyclic transition state, which provides optimal orbital overlap between the migrating group and the $\pi$ system.

• In cyclopentadiene, a [1,5] hydrogen shift moves a hydrogen from one carbon to another, effectively interconverting the positions of the two double bonds. This process is rapid at room temperature, with a half-life of only a few minutes at 25°C.
• In 1,3-pentadiene systems, a [1,5] hydrogen shift between terminal carbons produces a conjugated diene, gaining stability from extended $\pi$ conjugation.

These rearrangements are thermally allowed under the Woodward-Hoffmann rules. The thermal [1,5] shift involves $(4q+2)$ electrons in the cyclic transition state (here, 6 electrons with $q = 1$), making the suprafacial-suprafacial pathway symmetry-allowed. That suprafacial pathway means the migrating group stays on the same face of the $\pi$ system throughout, which conserves stereochemistry.

Orbital symmetry is what ultimately dictates which pathways are allowed or forbidden. A [1,3] suprafacial hydrogen shift, by contrast, is thermally forbidden because it would involve 4 electrons $(4q)$ in the transition state.

Mechanism of Claisen rearrangement

The Claisen rearrangement is a [3,3] sigmatropic rearrangement in which an allyl group migrates from oxygen to carbon. It converts allyl vinyl ethers (or allyl aryl ethers) into $\gamma,\delta$-unsaturated carbonyl compounds.

The reaction proceeds through a highly ordered, chair-like six-membered transition state that minimizes steric strain and maximizes orbital overlap. This geometry is what makes the Claisen rearrangement so reliably stereospecific: substituent stereochemistry in the starting material translates predictably into the product.

Step-by-step mechanism:

1. Heating the allyl vinyl ether (typically ~200°C) provides enough energy to reach the cyclic transition state.
2. In a single concerted step, the C–O bond breaks while a new C–C bond forms through the six-membered transition state.
3. The allyl group migrates to the $\alpha$-carbon, and the oxygen becomes part of a newly formed carbonyl group.
4. The product is a $\gamma,\delta$-unsaturated aldehyde or ketone.

Because every bond-breaking and bond-forming event happens simultaneously, stereochemical information from the starting material is preserved in the product. Electron-donating substituents on an aromatic ring (in the aryl Claisen variant) can lower the required temperature by stabilizing the transition state.

The Claisen rearrangement is widely used in synthesis to build carbon skeletons with controlled stereochemistry.

Cope vs. oxy-Cope rearrangements

Both the Cope and oxy-Cope are [3,3] sigmatropic rearrangements, but they differ in substrate, conditions, and products.

The Cope rearrangement converts one 1,5-diene into an isomeric 1,5-diene. It proceeds through a six-membered chair-like transition state and typically requires high temperatures (200–300°C). The reaction is reversible, so the equilibrium favors whichever diene isomer is more thermodynamically stable.

The oxy-Cope rearrangement starts from a 1,5-dien-3-ol. After the [3,3] shift, the initial product is an enol, which tautomerizes to give a $\delta,\varepsilon$-unsaturated carbonyl compound. This tautomerization step is what drives the equilibrium forward, making the oxy-Cope effectively irreversible.

Both reactions are valuable in synthesis. The Cope rearrangement appears in routes to natural products and pharmaceuticals, while the oxy-Cope is a powerful way to generate unsaturated carbonyl intermediates with ring-expanded or otherwise hard-to-access frameworks.

Molecular orbital considerations in sigmatropic rearrangements

Orbital symmetry is the foundation for understanding why certain sigmatropic shifts are allowed and others are not. The Woodward-Hoffmann rules predict allowedness based on the number of electrons in the cyclic transition state and whether the pathway is suprafacial or antarafacial.

For a thermally allowed sigmatropic shift, the HOMO of the migrating group must have the correct symmetry to overlap constructively with the terminus of the $\pi$ system. In a [1,5] hydrogen shift, the relevant HOMO ($\psi_2$ of the pentadienyl system) has lobes of the same phase at C-1 and C-5 on the same face, permitting a suprafacial shift. In a [1,3] shift, the HOMO symmetry requires an antarafacial pathway, which is geometrically impossible for hydrogen, so the thermal [1,3]-H shift is forbidden.

For [3,3] shifts like the Cope and Claisen, both fragments contribute 2 electrons each to the six-electron cyclic transition state. The suprafacial-suprafacial pathway is thermally allowed, consistent with the $(4q+2)$ electron count ($q = 1$). This is why these reactions proceed with predictable stereochemistry through chair-like transition states.

Thermal activation provides the energy to reach these transition states, but it's the orbital symmetry match that determines whether the reaction can happen at all.