Pericyclic Reactions and the Woodward–Hoffmann Rules — A Working Guide
A pericyclic reaction has no intermediate. Bonds break and form together, in one step, through a cyclic transition state in which the electrons move around a closed loop. There is no carbocation, no carbanion, no radical, and nothing to trap. Because everything happens at once, the geometry of the transition state controls the stereochemistry of the product completely — and that geometry is fixed by orbital symmetry, not by sterics. The Woodward–Hoffmann rules turn this into a set of selection rules you can apply in about thirty seconds. This guide gives you the rules, three equivalent ways of deriving them, and the stereochemical predictions that examiners actually test.
The four families you must recognise
| Class | What happens | Stereochemical vocabulary | Standard examples |
|---|---|---|---|
| Electrocyclic | A σ bond forms between the two ends of a conjugated π system (or the reverse) | conrotatory / disrotatory | Butadiene ⇌ cyclobutene; hexatriene ⇌ cyclohexadiene; Nazarov cyclisation |
| Cycloaddition | Two π systems join to form two new σ bonds and a ring | suprafacial / antarafacial on each component | Diels–Alder [4+2]; photochemical [2+2]; 1,3-dipolar [3+2]; ozonolysis |
| Sigmatropic | A σ bond migrates across a π system; the number of σ + π bonds does not change | suprafacial / antarafacial, plus retention/inversion at a migrating carbon | [1,5]-H shift; [3,3] Cope and Claisen; [2,3] Wittig |
| Cheletropic / group transfer | Both new bonds are made to (or broken from) one single atom; or a group is transferred with its bonding pair | linear / non-linear | SO2 extrusion from a sulfolene; carbene addition; the ene reaction; diimide reduction |
The core selection rules
Count the electrons taking part in the cyclic array — π electrons plus any σ electrons that are breaking. Then read the table. Every entry reverses when you switch from heat to light, because photoexcitation promotes one electron and changes the symmetry of the highest occupied orbital.
| Electrons in the cyclic array | Electrocyclic, thermal (Δ) | Electrocyclic, photochemical (hν) | Cycloaddition, thermal | Cycloaddition, photochemical |
|---|---|---|---|---|
| 4n (4, 8, …) | conrotatory | disrotatory | supra–antara | supra–supra |
| 4n + 2 (2, 6, 10, …) | disrotatory | conrotatory | supra–supra | supra–antara |
| Sigmatropic [1,j] hydrogen shift | Electrons | Thermal | Photochemical |
|---|---|---|---|
| [1,3] | 4 (4n) | antarafacial — geometrically impossible in an ordinary chain, so the shift does not occur | suprafacial, allowed |
| [1,5] | 6 (4n+2) | suprafacial, allowed and common | antarafacial |
| [1,7] | 8 (4n) | antarafacial — possible in a long, flexible chain | suprafacial |
| [3,3] (Cope, Claisen) | 6 (4n+2) | supra–supra, chair-like transition state | — |
Three ways to get the same answer
1. Frontier molecular orbital (FMO) analysis. Look only at the HOMO of the reacting system. For an electrocyclic closure, ask whether the two terminal lobes have matching phase for a face-to-face (disrotatory) closure or need one end to flip (conrotatory). Butadiene's HOMO (ψ2) has opposite phases at C1 and C4 on the same face, so the two ends must rotate the same way — conrotatory. Hexatriene's HOMO (ψ3) has matching phases at C1 and C6, so disrotatory. Fast, but it is a shortcut, not a proof.
2. Correlation diagrams. Identify a symmetry element preserved throughout the reaction (a mirror plane for disrotation, a C2 axis for conrotation), classify every reactant and product orbital as symmetric (S) or antisymmetric (A) with respect to it, and join them up. If every filled reactant orbital correlates with a filled product orbital, the pathway is allowed; if a filled orbital correlates with an empty one, there is a symmetry-imposed barrier and the pathway is forbidden. This is the rigorous version and the one worth drawing in a long-answer question.
3. The generalised Woodward–Hoffmann rule. The fastest reliable method, and the one to use under exam time pressure:
(For a photochemical reaction the requirement becomes an even count. Subscript s = suprafacial, a = antarafacial.)
Break the transition state into components. Each component is a set of contiguous orbitals with a number of electrons; label it by the electron count and by whether the new bonds are made to the same face (suprafacial) or opposite faces (antarafacial). Then count only those components that are either a (4q+2)-electron component used suprafacially, or a 4r-electron component used antarafacially.
4. The Dewar–Zimmerman test is a useful cross-check. Count the phase inversions around the cyclic array of interacting orbitals. An even number (including zero) gives a Hückel transition state, which is aromatic — and therefore favourable — with 4n+2 electrons. An odd number gives a Möbius transition state, aromatic with 4n electrons. Conrotation introduces one phase inversion; disrotation introduces none.
Worked example 1 — the Diels–Alder reaction by the generalised rule.
The transition state is written [π4s + π2s].
• π2s: 2 = 4(0) + 2, and it is suprafacial → this is a
(4q+2)s component. Count 1.
• π4s: 4 = 4(1), so it is a (4r) component — but it is suprafacial, not
antarafacial. Count 0.
Total = 1, which is odd → thermally allowed. This is why a diene and a
dienophile simply react on heating, with both new bonds formed on the same face of each
partner, so cis substituents on the dienophile stay cis in the adduct.
Worked example 2 — why [2+2] needs light.
Face-to-face dimerisation of two alkenes is [π2s + π2s].
Both components are (4q+2)s → count 2, which is even → thermally
forbidden.
Under photochemical conditions the requirement flips to even, so the same
supra–supra geometry becomes allowed. That is exactly what is observed:
alkenes do not dimerise to cyclobutanes on heating, but they do so cleanly on irradiation.
The thermal alternative [π2s + π2a] gives a count
of 1 (odd, allowed) — but it demands that one alkene be attacked from opposite faces at its
two ends, which is geometrically impossible for an ordinary alkene. Allowed is not
the same as feasible, and saying so earns marks.
Stereochemistry — the part that is actually examined
Selection rules are only interesting because they predict which diastereomer forms. Work through these carefully; the pattern repeats in every exam.
Worked example 3 — 4π electrocyclic closure.
(2E,4E)-hexa-2,4-diene has 4 π electrons, so thermal closure is
conrotatory. In conrotation both termini turn the same way, so one methyl
group rises above the forming ring while the other drops below it.
Product: trans-3,4-dimethylcyclobutene.
Under irradiation the same diene closes disrotatorily — the two ends turn in
opposite senses, both methyls end up on the same face —
giving cis-3,4-dimethylcyclobutene.
Run it in reverse and the logic still holds: heating trans-3,4-dimethylcyclobutene
opens conrotatorily back to (2E,4E)-hexa-2,4-diene, while
cis-3,4-dimethylcyclobutene opens to the (2E,4Z) isomer. Cyclobutene ring
opening needs real heat (well above 100 °C) because a strained four-membered ring must break,
but the stereochemical outcome is decided by symmetry alone.
Worked example 4 — 6π electrocyclic closure.
(2E,4Z,6E)-octa-2,4,6-triene has 6 π electrons = 4n+2, so thermal closure is
disrotatory, and the two methyl groups finish on the same face:
Product: cis-5,6-dimethylcyclohexa-1,3-diene.
Change one double-bond geometry to (2E,4Z,6Z) and the same disrotatory closure now
delivers the trans product. Irradiating the (2E,4Z,6E)
triene switches the mode to conrotatory and also gives the trans product.
The lesson: the rotation mode comes from the electron count and the
conditions; the product comes from combining that mode with the starting geometry.
Two steps, never one.
Worked example 5 — why [1,5] shifts happen and [1,3] shifts do not.
A [1,5]-H shift uses 6 electrons (4 π + the 2 in the migrating C–H σ bond) = 4n+2, so the
thermal pathway is suprafacial — the hydrogen slides across one face of the
system through a comfortable six-membered, envelope-like transition state. In cyclopentadiene
such shifts scramble the ring positions readily at or a little above room temperature, with no
catalyst and no intermediate.
By the generalised rule: [σ2s + π4s] → the
σ2s counts, the π4s does not → total 1, odd, allowed.
A [1,3]-H shift uses only 4 electrons = 4n, so the thermal pathway would have to be
antarafacial: the hydrogen would need to leave one face and arrive on the
other, two carbons away. Nothing in a normal chain is flexible enough. By the generalised
rule the suprafacial version [σ2s + π2s] gives a
count of 2 — even, forbidden. This is why thermal 1,3-hydrogen migrations are
absent from organic chemistry while 1,5-shifts are everywhere.
A real sequence that uses two of the rules
The formation of vitamin D3 in skin is the standard illustration, and it is worth knowing because it chains two different pericyclic steps:
- Photochemical 6π electrocyclic ring opening of 7-dehydrocholesterol. Six electrons under light → conrotatory → previtamin D3.
- Thermal antarafacial [1,7]-H sigmatropic shift converting previtamin D3 into vitamin D3. Eight electrons = 4n, so thermal must be antarafacial — and here the open, flexible triene chain genuinely can deliver the hydrogen to the opposite face, which is why this otherwise awkward mode works.
Notice that the second step is thermal and happens slowly at body temperature, while the first needs a photon. The selection rules explain both facts without any additional assumption.
Mistakes that cost marks
- Applying the rules to a stepwise reaction. Woodward–Hoffmann governs concerted processes only. A Lewis-acid-catalysed "[2+2]" that goes through a zwitterion is not forbidden — it is simply not pericyclic. Say so explicitly rather than calling the observation a violation.
- Counting only π electrons in a sigmatropic shift. The migrating σ bond contributes two electrons. Forget them and [1,5] looks like a 4-electron process, and every subsequent answer is wrong.
- Reporting the rotation mode as if it were the product. "Conrotatory" is not an answer. Combine the mode with the starting geometry and name the diastereomer.
- Forgetting the photochemical reversal. Every thermal entry flips under light, and the generalised rule flips from odd to even.
- Treating "allowed" as "will happen". Allowed means no symmetry-imposed barrier. Ring strain, geometric impossibility ([2s+2a]) and simple thermodynamics can still stop the reaction cold.
- Calling the Diels–Alder endo preference a symmetry rule. Both endo and exo approaches are supra–supra and both are symmetry-allowed. The endo preference is a kinetic selectivity, usually explained by secondary orbital interactions and sterics, and it can be reversed by heating to equilibrium.
- Mixing up conrotatory with cis. Conrotatory and disrotatory describe the motion; cis and trans describe the product. There is no fixed pairing between them — it depends on the substituent geometry you started from.
- Using the wrong symmetry element in a correlation diagram. Disrotatory motion preserves a mirror plane; conrotatory motion preserves a C2 axis. Choose the wrong one and the correlations come out meaningless.
Where this appears in the exam
| Exam | Typical demand |
|---|---|
| CSIR-NET Chemical Sciences | Predict the stereochemistry of an electrocyclic closure or opening; identify allowed vs forbidden from a drawn transition state; recognise a [3,3] shift and draw its chair-like transition state |
| GATE Chemistry | Electron counting; conrotatory/disrotatory assignment under Δ and hν; the generalised component rule; FMO phase arguments |
| IIT-JAM / CUET-PG | Recognising the reaction class from the arrow-pushing; Diels–Alder regiochemistry and endo selectivity; retro-Diels–Alder |
| MSc coursework | Full correlation diagrams; Dewar–Zimmerman Hückel/Möbius analysis; sigmatropic shifts with retention or inversion at a migrating carbon |
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