The Cope Rearrangement

What the Cope rearrangement does

Take a 1,5-diene — six carbons with a double bond at each end and a single bond in the middle. Heat it, and something almost magical happens: the molecule rewires itself. The central single bond snaps, a brand-new single bond forms across the other end, and both double bonds slide one position over. No acid, no base, no metal, no light. Just heat and the intrinsic symmetry of the electrons.

Number the carbons 1 through 6 along the chain. The starting diene has π bonds at C1=C2 and C5=C6 and the "central" σ bond at C3–C4. The Cope rearrangement:

1. Breaks the C3–C4 σ bond. This is the bond in the middle of the chain, allylic to both double bonds. It is the weakest, most polarizable σ bond because both ends can delocalize into an adjacent π system.
2. Forms a new C1–C6 σ bond. The two terminal carbons — which were sp², the ends of the two double bonds — swing toward each other and bond. The chain closes at one end as it opens at the other.
3. Migrates both π bonds inward. C1=C2 becomes C2=C3, and C5=C6 becomes C4=C5. Every atom keeps its place; only the electrons shuffle.

Because three σ/π bonds break and three form in one concerted, cyclic motion — a six-membered ring of six electrons in flight — the Cope is a textbook pericyclic reaction. It is a sigmatropic shift because a σ bond migrates from one framework position to another; the "[3,3]" counts three atoms on each side of the breaking bond to the atom where the new bond forms.

           1   2                      1   2
          C = C                        C — C
         /       \                    ‖       ‖
    6   C   3      (heat)         6   C   3
    C   |    \    ────────►       C   |    \
     \  C — C                      \\ C = C
      5      4                      5      4

   1,5-hexadiene  ───────►  1,5-hexadiene   (degenerate — same molecule!)

   bonds broken: σ C3–C4, π C1=C2, π C5=C6
   bonds formed: σ C1–C6, π C2=C3, π C4=C5

The stunning thing about the parent case is that the product is the same molecule as the starting material. 1,5-hexadiene turns into 1,5-hexadiene. Only an isotope label betrays that anything happened at all — which is exactly how it was proven.

The mechanism: a cyclic dance of six electrons

The Cope is concerted and (for the parent hydrocarbon) has no discrete intermediate. Draw three curved arrows chasing each other around a six-membered ring:

1. Arrow 1 pushes the C1=C2 π electrons out to form the new C1–C6 σ bond.
2. Arrow 2 pushes the C3–C4 σ electrons up to become the new C2=C3 π bond.
3. Arrow 3 pushes the C5=C6 π electrons over to become the new C4=C5 π bond.

Trace them and you find the three arrows form a closed loop — the electronic hallmark of a pericyclic reaction. There is no cation, no anion, no radical resting anywhere; the six electrons are delocalized over all six carbons at the transition state, which is why chemists call it an aromatic transition state. It has the same "6 electrons in a cyclic array" character as benzene, just fleeting.

The Woodward–Hoffmann rules classify this shift as suprafacial–suprafacial [3,3]. Count the electrons in the closed loop: 6, which equals 4n+2 for n=1. A (4n+2)-electron system reacting through a Hückel-topology (no sign inversion) transition state is thermally allowed. That is the deep reason the Cope runs cleanly on heating and does not run under photochemical conditions — the orbital-symmetry rules flip for the excited state.

Kinetically, the parent 1,5-hexadiene rearrangement is cleanly first-order with an activation enthalpy near 33.5 kcal/mol and a strongly negative entropy of activation (ΔS‡ ≈ −13 cal·mol⁻¹·K⁻¹). That negative ΔS‡ is the fingerprint of a highly ordered cyclic transition state: six atoms must line up in a ring before anything can happen, so the molecule loses rotational freedom on the way up the barrier.

Conditions, driving force, and how to speed it up

For an unactivated all-carbon 1,5-diene, the Cope is roughly thermoneutral — you break as much bonding as you make — so there is no thermodynamic engine, only equilibrium. You typically need 150–300 °C to push a meaningful population over the ~33.5 kcal/mol barrier in a reasonable time. Three levers change everything:

• Relieve ring strain. Build the diene into a strained ring and the products are far more stable, so the barrier collapses. cis-1,2-Divinylcyclopropane rearranges to 1,4-cycloheptadiene below room temperature (barrier ≈ 20 kcal/mol) because the strained three-membered ring pops open. cis-1,2-Divinylcyclobutane gives 1,5-cyclooctadiene similarly.
• Add a thermodynamic sink (oxy-Cope). Put a hydroxyl at C3. After the [3,3] shift you get an enol, which tautomerizes irreversibly to a ketone or aldehyde. Now the reaction is downhill and can't run backward.
• Deprotonate that hydroxyl (anionic oxy-Cope). Convert the C3–OH to a C3–O⁻ alkoxide and the rate leaps by 10¹⁰ to 10¹⁷. The alkoxide lone pair raises the energy of the breaking C3–C4 σ bond (a "σ-donor" push), weakening it dramatically. David A. Evans reported this in 1975; using KH with 18-crown-6 to generate a "naked," un-ion-paired potassium alkoxide gives the largest accelerations, letting many oxy-Cope reactions run at 25–66 °C instead of 200 °C.

  anionic oxy-Cope:

     OK⁺                          O⁻K⁺              O
      |                            |               ‖
   HO–C3–C4  ──KH, 18-crown-6──►  [3,3]  ──────►  C   +   tautomerize
      (3-hydroxy-1,5-diene)        (fast!)        (enolate → ketone on workup)

     rate boost vs neutral oxy-Cope: 10¹⁰ – 10¹⁷ ×

Scope, selectivity, and stereochemistry

The Cope's synthetic value comes from its predictable, transferable stereochemistry. Because the transition state is a well-defined cyclohexane-like chair, you can forecast the geometry of the product double bonds and the configuration at new stereocenters from the geometry of the starting diene.

• Chair beats boat. The six carbons adopt a chair arrangement ~5.7 kcal/mol below the boat. Substituents on the chain go pseudo-equatorial to avoid 1,3-diaxial and gauche strain. Doering and Roth's landmark 1962 study of 3,4-dimethyl-1,5-hexadiene nailed this: the meso diene funnels almost exclusively to the (E,Z)-2,6-octadiene, and the (±) diene gives predominantly the (E,E) product — exactly what the chair predicts, and not what a boat would give.
• Suprafacial on both allyl fragments. Each allyl unit reacts on the same face throughout, so chirality is transferred, not scrambled. This lets the Cope relay stereochemical information across the molecule — useful for setting remote stereocenters.
• Substituents tune the rate. Radical-stabilizing groups (phenyl, vinyl, cyano) at C3/C4 lower the barrier by stabilizing the loosening central bond; the "aromatic vs. dissociative" character of the TS shifts toward more bond-breaking. Highly substituted cases can flirt with a diradical (cyclohexane-1,4-diyl) or bis-allyl continuum, but for most systems the concerted aromatic picture holds.

Cope vs Claisen vs other [3,3] shifts

	Cope rearrangement	Claisen rearrangement
Substrate	1,5-diene (all carbon)	Allyl vinyl ether (O at position 3)
Migrating framework	C–C–C / C–C–C	C–C–C / C–C–O
Sigmatropic order	[3,3]	[3,3]
Electrons in TS	6 (aromatic chair TS)	6 (aromatic chair TS)
Reversibility	Reversible (near thermoneutral for parent)	Irreversible — forms strong C=O
Driving force	Ring-strain relief or oxy-Cope sink needed	Enol ether → carbonyl (built in)
Typical temperature	150–300 °C (parent); RT for strained / anionic	150–200 °C (aliphatic); lower with catalysis
Product type	New 1,5-diene	γ,δ-unsaturated carbonyl
Discovered	Cope & Hardy, 1940	Ludwig Claisen, 1912
Named variants	Oxy-Cope, anionic oxy-Cope, aza-Cope	Ireland, Johnson, Eschenmoser, aza-Claisen

The one-line memory hook: the Claisen is a Cope with an oxygen at position 3. Everything else — the [3,3] count, the six-electron aromatic chair TS, the suprafacial–suprafacial geometry — is shared. Swapping a CH₂ for an O just installs a permanent thermodynamic ratchet (the carbonyl) that makes the Claisen run one way and stay there.

Worked example: an anionic oxy-Cope ring expansion

A classic Evans-style application builds a nine- or ten-membered ring in one step from a vinyl-addition product. Start by adding a vinyl Grignard (or vinyllithium) to a 2-vinyl cyclohexanone/cyclopentanone-type ketone to give a tertiary alcohol that is, crucially, a 3-hydroxy-1,5-diene:

  1) vinyl–MgBr onto a 2-vinylcycloalkanone
     → tertiary allylic/homoallylic alcohol (a 3-hydroxy-1,5-diene)

  2) KH (1.2 equiv), 18-crown-6, THF, 25–66 °C
     → deprotonate to the "naked" alkoxide
     → anionic oxy-Cope [3,3] shift (fast: barrier drops ~10–15 kcal/mol)
     → ring-expanded enolate

  3) aqueous workup (H₃O⁺)
     → tautomerize the enol/enolate to the ketone
     → ring-expanded cyclic ketone, isolated in one pot

• Why it works. The alkoxide at C3 pumps electron density into the breaking C3–C4 bond, so the [3,3] runs at room temperature instead of ~200 °C. The final tautomerization to a ketone makes the whole sequence irreversible.
• What you get. A ring four carbons larger than you started with (a 2-vinylcyclohexanone-derived 1,2-divinylcyclohexanol gives a ten-membered cyclodecenone), with a new carbonyl set at a defined position — a route to medium rings that are otherwise painful to close by classical macrocyclization.
• Practical notes. Rigorously dry THF, exclude O₂ and CO₂ (the alkoxide is basic and air-sensitive), and add 18-crown-6 to sequester K⁺ so the alkoxide is "naked" and maximally reactive.

Named variants and real applications

• Oxy-Cope / anionic oxy-Cope (Berson 1964; Evans 1975). The workhorse for ring expansion and stereocontrolled synthesis of γ,δ-unsaturated ketones. Used to assemble medium-ring and bridged skeletons in terpene and steroid synthesis.
• Aza-Cope / Mannich (Overman). Replace a carbon with nitrogen to get a 2-aza-[3,3] shift; coupling it to an intramolecular Mannich reaction (the cationic aza-Cope–Mannich) builds acylpyrrolidines and is a cornerstone of Overman's alkaloid syntheses (e.g., strychnine).
• Divinylcyclopropane rearrangement. cis-Divinylcyclopropanes ring-expand to cycloheptadienes below room temperature — a fast, strain-driven Cope used to make seven-membered carbocycles found in guaiane and pseudoguaiane terpenoids.
• Cope elimination (do not confuse). A completely different Cope reaction — a syn-periplanar E_i elimination of an amine oxide to give an alkene plus a hydroxylamine. Same chemist, different reaction; the [3,3] sigmatropic rearrangement is the one on this page.
• Mechanistic touchstone. The degenerate 1,5-hexadiene Cope is one of the most studied reactions in physical organic chemistry — a benchmark for computational methods (its aromatic-vs-diradical transition state has been dissected by high-level ab initio and DFT for decades) and a proving ground for the very idea of the aromatic transition state.

Limitations and side reactions

• No driving force for the parent case. An unactivated 1,5-diene sits at equilibrium. Without ring strain or an oxy-Cope sink, you get a mixture, not a clean conversion — the reaction just interconverts isomers.
• High temperatures invite decomposition. Pushing a sluggish thermal Cope at 250–300 °C can trigger competing retro-ene reactions, radical fragmentation, polymerization of the diene, or unwanted [1,5]-H shifts. The anionic oxy-Cope exists largely to avoid these temperatures.
• Geometry can forbid the chair. If a substituent forces the transition state to be boat-like (e.g., in constrained rings), rates drop and stereochemical predictions must switch to the boat model.
• Diradical leakage. Heavily radical-stabilized substrates (e.g., 2,5-diphenyl or 3,4-diphenyl dienes) can drift toward a stepwise cyclohexane-1,4-diyl diradical, eroding the clean concerted stereospecificity.
• Air-sensitivity in the anionic version. The oxy-Cope alkoxide is a strong base; moisture, O₂, or CO₂ quench it. Reactions must be run under inert atmosphere with dry solvent.

Historical discovery

Arthur C. Cope and Elizabeth M. Hardy reported the rearrangement in 1940 (J. Am. Chem. Soc. 62, 441), studying substituted 1,5-dienes such as ethyl (1-methylpropenyl)allylcyanoacetate that rearranged cleanly on heating. Cope, then at Bryn Mawr and later a towering figure at MIT, gave the reaction its name; the same Arthur Cope is honored today by the ACS Arthur C. Cope Award.

The mechanism took two more decades to settle. In 1962, William von Eggers Doering and Wolfgang Roth used the meso and (±) diastereomers of 3,4-dimethyl-1,5-hexadiene to prove the chair-preferred, suprafacial–suprafacial pathway — a masterpiece of stereochemical logic. Doering's isotope-labeling of the degenerate 1,5-hexadiene case confirmed the [3,3] connectivity even when the two ends are identical. Then R. B. Woodward and Roald Hoffmann (1965–1969) folded the Cope into their general orbital-symmetry framework, classifying it as a thermally allowed [σ2s + π2s + π2s]-type six-electron process (one breaking σ bond plus the two migrating π bonds, all suprafacial). The anionic oxy-Cope acceleration was discovered by David A. Evans and Alan Golob in 1975. Together these results made the Cope one of the founding case studies of modern pericyclic theory.