Organic Chemistry · Orbitals and Organic Chemistry: Pericyclic Reactions
A Summary of Rules for Pericyclic Reactions
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This topic collects the selection rules developed across Topics 1–8 into one decision table. A Pericyclic reaction Concerted reaction with a single cyclic transition state Full entry → is a concerted reaction in which bonds form and break in a single cyclic transition state. There are exactly three families — electrocyclic (ring closing/opening), cycloadditions (two molecules join to make a ring), and sigmatropic rearrangements (a σ bond migrates) — and one master rule governs all of them: the Woodward–Hoffmann rules Selection rules relating electron count and condition to allowedness Full entry →, which tie thermal or photochemical "allowedness" to the number of electrons moving in the cyclic array and to the topology (suprafacial vs antarafacial) of the interaction.
The practical payoff is prediction. Given a proposed pericyclic reaction, you count the electrons in the cyclic transition state, decide whether the reaction is thermal or photochemical, and read off whether it is allowed. If it is allowed, the reaction proceeds easily with characteristic stereochemistry; if forbidden, it requires a different condition (light instead of heat) or a different mechanism altogether. "Forbidden" never means "impossible" — it means symmetry-disfavored under those conditions.
Why this matters
- One framework, three reactions. Memorizing three separate lists of rules is wasteful; the electron-counting framework replaces them with one consistent logic that exam questions reward.
- Predicting conditions. The rules tell you whether to apply heat or light — a question that comes up constantly in synthesis planning and in exams.
- Stereochemical prediction. Allowed pericyclic reactions are Stereospecific Reactant geometry fully determines product geometry Full entry →: the stereochemistry of the starting material is carried through the transition state into the product. The rules let you predict which stereoisomer forms.
- Interpreting "forbidden." Understanding that forbidden = high symmetry-imposed barrier (not impossible) prevents the classic mistake of assuming such reactions never occur.
The college version
Core Concepts
The master rule: count the electrons, set the condition
Every pericyclic reaction has a cyclic array of electrons in its transition state. Count the total number of electrons moving in that array (the π electrons of double bonds plus the electrons of the σ bond being formed or broken):
- 4n + 2 electrons (6, 10, 14, ...) → the reaction is thermally allowed (proceeds on heating) by the suprafacial path.
- 4n electrons (4, 8, 12, ...) → the reaction is thermally forbidden; it becomes photochemically allowed when light promotes an electron to change the symmetry of the highest occupied molecular orbital.
This single statement is the heart of the Woodward–Hoffmann rules and reproduces every individual rule in the chapter.
Electrocyclic reactions (Topics 2–4)
A conjugated polyene cyclizes by rotating its termini to form a new σ bond (or a ring opens by the reverse). The rule: with 4n + 2 π electrons the thermal ring closure is conrotatory (both ends rotate the same way); with 4n π electrons the thermal closure is disrotatory (ends rotate in opposite directions). Under photochemical conditions the preferences flip: 4n becomes conrotatory, 4n + 2 becomes disrotatory. The rotation mode decides the stereochemistry of the new ring stereocenters.
Cycloadditions (Topics 5–6)
Two unsaturated molecules join end-to-end, consuming two π bonds and forming two σ bonds. The rule: a [4 + 2] cycloaddition (the Diels–Alder reaction) has six electrons, is thermally allowed, and is suprafacial on both components. A [2 + 2] cycloaddition has four electrons, is thermally forbidden, and requires photochemical activation. The suprafacial–suprafacial [2+2] path is the one that forms thymine dimers in UV-damaged DNA.
Sigmatropic rearrangements (Topics 7–8)
A σ bond migrates along a π system. The rule: [1,5]-hydrogen shifts and [3,3] shifts (six electrons) are thermally allowed suprafacially; [1,3]-hydrogen shifts (four electrons) are thermally forbidden and photochemically allowed. Carbon migrations carry the extra stereochemical constraint (retention vs inversion) discussed in Topic 7.
Suprafacial vs antarafacial: the topology modifier
For each component, the new bonds can form on the same face (suprafacial) or opposite faces (antarafacial) of the π system. The thermal rules above assume the suprafacial path, which is the only geometrically feasible one for small molecules. Where antarafacial participation is possible (large rings, flexible systems), a thermally "forbidden" reaction can sometimes proceed by an antarafacial route — the rules are a ranking of paths, not a ban on reactions.
The decision procedure (how to solve any problem)
- Identify the reaction family (ring close/open? two molecules joining? bond migrating?).
- Count the electrons in the cyclic transition state.
- Note the condition (thermal or photochemical).
- Apply the 4n + 2 / 4n rule to predict allowed/forbidden and the stereochemical mode (conrotatory/disrotatory, suprafacial/antarafacial).
- Check the result against the starting geometry to name the product stereoisomer.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| 4n + 2 allowed | 4n allowed | 4n + 2 (6, 10 electrons) → thermal; 4n (4, 8) → photochemical. The most common exam error is applying the rule backwards. |
| Conrotatory | Disrotatory | Same-direction rotation vs opposite-direction rotation of ring termini; the mode decides product stereochemistry and depends on electron count and condition. |
| [4 + 2] cycloaddition | [2 + 2] cycloaddition | [4 + 2] (Diels–Alder) has 6 electrons, thermally allowed; [2 + 2] has 4, photochemically allowed. |
| Thermal allowedness | Reaction feasibility | "Forbidden" means a high symmetry-imposed barrier under thermal suprafacial conditions — light or an antarafacial path can still achieve the reaction. |
| Stereospecific | Stereoselective | Pericyclic reactions are stereospecific (geometry fully determined); stereoselective reactions merely favor one product. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Pericyclic reactions are like a dance where everyone holds hands in a circle and moves in one smooth step. Whether the dance is allowed depends on how many dancers there are: with 6 dancers it works with music (heat); with 4 dancers it only works with a strobe light (light). Count the dancers, know the music, and you can predict the whole dance.
Worked example
Example 1: Classifying and predicting an electrocyclic reaction
Problem. 1,3,5-Hexatriene (six π electrons) is heated. Predict whether the ring closure is conrotatory or disrotatory, and name the ring product.
Step 1 — Count electrons. The triene has six π electrons (4n + 2 with n = 1).
Step 2 — Apply the rule. Thermal, 4n + 2 → disrotatory closure.
Step 3 — Name the product. 1,3,5-Hexatriene closes to 1,3-cyclohexadiene; the disrotatory mode determines the relative configuration of the two new stereocenters (both hydrogens cis in the standard drawing).
Answer. Disrotatory thermal ring closure giving 1,3-cyclohexadiene with the stereochemistry set by the rotation mode.
Example 2: Choosing the condition for a cycloaddition
Problem. Two molecules of ethylene are to be converted to cyclobutane. Should the chemist plan for heat or light?
Step 1 — Count electrons. Each ethylene contributes two π electrons: total = 4 (a [2 + 2] cycloaddition).
Step 2 — Apply the rule. Four electrons (4n, n = 1) → thermally forbidden.
Step 3 — Choose the condition. Photochemical activation makes the [2 + 2] reaction allowed.
Answer. Light, not heat. Heating ethylene gives no cyclobutane by this path; UV excitation is required (the same chemistry that forms thymine dimers in DNA).
Example 3: Selecting the allowed sigmatropic path
Problem. A 1,3-pentadiene is proposed to undergo a [1,3]-hydrogen shift on heating. Is this allowed, and if not, what condition would work?
Step 1 — Count electrons. A [1,3] shift involves the two π bonds plus the migrating hydrogen's orbital: four electrons in the cyclic array.
Step 2 — Apply the rule. Four electrons → thermally forbidden for the suprafacial path.
Step 3 — State the alternative. Photoexcitation changes the frontier-orbital symmetry and allows the shift.
Answer. Not allowed thermally; the [1,3] shift requires photochemical conditions. (Compare: the [1,5]-H shift, with six electrons, proceeds on heating.)
Key takeaways
- Three families, one rule: electrocyclic, cycloaddition, sigmatropic — all governed by the electron count in the cyclic transition state.
- 4n + 2 electrons → thermally allowed (suprafacial path); 4n electrons → photochemically allowed.
- Electrocyclic thermal closures: 4n + 2 → conrotatory; 4n → disrotatory; photochemical conditions flip both.
- Cycloadditions: [4 + 2] (six electrons, Diels–Alder) thermally allowed; [2 + 2] (four electrons) photochemically allowed.
- Sigmatropic: [1,5]-H and [3,3] shifts thermally allowed; [1,3]-H shifts photochemically allowed.
- "Forbidden" = symmetry-imposed barrier under those conditions, not impossible; other topologies (antarafacial) or conditions (light) can allow the reaction.
- Allowed pericyclic reactions are stereospecific — reactant geometry maps to product geometry through the cyclic transition state.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
State the master Woodward–Hoffmann rule in one sentence.
Show answer
A pericyclic reaction is thermally allowed when the cyclic transition state has 4n + 2 electrons (suprafacial path) and photochemically allowed when it has 4n electrons.
A thermal electrocyclic closure of a 4π system: conrotatory or disrotatory?
Show answer
Disrotatory (4n electrons → disrotatory on heating; the preference flips under light).
Why is the Diels–Alder reaction thermally allowed while the [2 + 2] cycloaddition is not?
Show answer
The Diels–Alder [4 + 2] reaction has six electrons (4n + 2, thermally allowed); the [2 + 2] reaction has four electrons (4n, thermally forbidden, photochemically allowed).
A [1,5]-hydrogen shift is thermally allowed; what electron count makes this true?
Show answer
Six electrons (4n + 2 with n = 1).
What does "forbidden" mean in the Woodward–Hoffmann sense?
Show answer
The reaction is symmetry-disfavored under those conditions — it faces a high barrier in the ground state but is not impossible; light or a different topology can allow it.
Name the three families of pericyclic reactions and one example reaction of each.
Show answer
Electrocyclic (e.g., hexatriene → cyclohexadiene), cycloaddition (e.g., Diels–Alder), and sigmatropic (e.g., Cope rearrangement of a 1,5-diene).
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Pericyclic reaction
- Concerted reaction with a single cyclic transition state
- Woodward–Hoffmann rules
- Selection rules relating electron count and condition to allowedness
- 4n + 2 rule
- Electron count that makes a pericyclic reaction thermally allowed
- Conrotatory / disrotatory
- Termini rotate same direction / opposite directions on ring closure
- Suprafacial / antarafacial
- Bonds form on same face / opposite faces of a π system
- Stereospecific
- Reactant geometry fully determines product geometry
Sources & references
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