Sigmatropic Rearrangements

What the [i,j] notation means

Sigmatropic rearrangements are classified by an order [i,j] that counts how far each terminus of the breaking σ bond travels. To assign it, label the two atoms of the migrating σ bond as position 1 on each fragment, then count outward along each chain to the atoms that form the new bond. A [1,5]-hydrogen shift means the hydrogen stays bonded to atom 1 of its fragment (so i = 1) while the other bond terminus moves five atoms along the π system (j = 5).

The most important class is the [3,3] shift, where both ends of the new bond form three atoms away from the old one. The Cope rearrangement of 1,5-hexadiene is the prototype: the C3–C4 σ bond breaks while a new C1–C6 bond forms, and the two double bonds relocate. The molecule is degenerate—starting material and product are identical—which is why isotope labeling was needed to prove the reaction happens at all.

How it works: the cyclic transition state

The defining feature is that no ionic or radical intermediates form. Bond-breaking and bond-making occur simultaneously in a single cyclic array of interacting orbitals—the arrows all push in one continuous loop. For a [3,3] shift, six electrons (three bonds' worth) move through an aromatic-like six-membered transition state, which is why these reactions are sometimes called “no-mechanism” reactions.

• Cope: 1,5-hexadiene → 1,5-hexadiene (degenerate) via a chair-like TS; ΔH‡ is roughly 33–34 kcal/mol, so it typically needs 150–300 °C.
• Claisen: an allyl vinyl ether rearranges to a γ,δ-unsaturated carbonyl compound. The oxygen lowers the barrier, and the reaction is essentially irreversible because a strong C=O bond forms at the expense of a weaker C=C—a thermodynamic driving force worth roughly 15–20 kcal/mol.

The classic laboratory demonstration is the aromatic Claisen rearrangement: heating an allyl aryl ether gives an ortho-allyl phenol after re-aromatization, cleanly transferring the allyl group from oxygen to the ring carbon.

Orbital symmetry and the suprafacial/antarafacial rules

Whether a given shift is allowed thermally or only photochemically is decided by the Woodward–Hoffmann rules. The migrating group can move across the same face of the π system (suprafacial) or cross from one face to the other (antarafacial). For a thermal reaction, the transition state must be a Hückel-type aromatic array with (4n + 2) electrons in a suprafacial framework.

• A thermal [1,5]-H shift has 6 electrons and proceeds suprafacially—geometrically easy, so 1,3-cyclopentadienes scramble their hydrogens readily on warming.
• A thermal [1,3]-H shift has only 4 electrons; the allowed pathway would be antarafacial, forcing hydrogen to reach across both faces at once—geometrically impossible for a small H, so it does not occur thermally (it requires photochemical excitation instead).
• When carbon migrates in a thermal [1,3] shift, its p-orbital lobes let it react suprafacially with inversion of configuration—a subtle stereochemical signature Berson demonstrated with labeled bicyclic substrates.

Stereochemistry: chair transition states and chirality transfer

The synthetic power of [3,3] rearrangements comes from their predictable stereochemistry. Both Cope and Claisen prefer a chair-like transition state over a boat, and substituents adopt pseudo-equatorial positions. This means the geometry of the starting alkenes (E/Z) is faithfully translated into the relative configuration of the two new stereocenters—a phenomenon called chirality transfer or self-immolative asymmetric induction.

The Ireland–Claisen variant exploits this beautifully: an ester is deprotonated to a silyl ketene acetal, and the choice of enolization conditions (with or without HMPA) sets the geometry of the enolate, which in turn dictates whether the syn or anti diastereomer of the γ,δ-unsaturated acid is formed. A single point of stereocontrol at one carbon is relayed through the ordered chair TS to a distant new center—the reason chemists reach for these reactions to build quaternary and adjacent stereocenters.

Named variants and their driving forces

Chemists have engineered many Claisen and Cope variants that add a thermodynamic sink to make the reaction faster or irreversible:

• Oxy-Cope / anionic oxy-Cope: a hydroxyl at C3 becomes an alkoxide; the alkoxide accelerates the [3,3] shift by 10¹⁰–10¹⁷-fold (Evans, 1975) and the enol product tautomerizes to a stable carbonyl.
• Johnson–Claisen: an allylic alcohol reacts with an orthoester to make an unstable mixed acetal that undergoes Claisen, delivering a γ,δ-unsaturated ester.
• Aza-Claisen / Overman rearrangement: nitrogen replaces oxygen, letting the reaction install allylic amines and C–N bonds.
• Bellus–Claisen (ketene Claisen): a ketene traps an allyl vinyl system to give an amide or acid derivative.

In every case the concerted six-electron mechanism is the same; only the heteroatom and the terminating functional group change.

Why it matters: synthesis and biology

Sigmatropic rearrangements are workhorses of total synthesis because they build C–C bonds with high stereocontrol and 100% atom economy—nothing is lost, atoms only relocate. The Claisen has been used to construct steroids, terpenoids, and the ring systems of complex natural products where a stereocenter must be relayed across the molecule.

Nature runs the same chemistry. The enzyme chorismate mutase catalyzes a Claisen rearrangement of chorismate to prephenate in the shikimate pathway—a key step toward aromatic amino acids—accelerating the pericyclic process by roughly 10⁶-fold simply by pre-organizing the substrate into its reactive chair conformation. Industrially, [1,5]-hydrogen shifts govern the thermal isomerization of dienes and the “walk” rearrangements seen in cracking and polymer chemistry.

Thermal selection rules for common sigmatropic shifts (Woodward-Hoffmann)

Shift order	Migrating group	Thermally allowed pathway
[1,3]-H	Hydrogen	Antarafacial (geometrically forbidden) — needs photochemistry
[1,5]-H	Hydrogen	Suprafacial — allowed and facile
[1,3]-C	Carbon	Suprafacial with inversion at carbon
[1,5]-C	Carbon	Suprafacial with retention at carbon
[3,3]	Allyl (Cope/Claisen)	Suprafacial–suprafacial, chair TS — allowed