Pericyclic Reactions & the Woodward–Hoffmann Rules
The reactions with no intermediate: bonds break and form together, in one concerted step, as electrons flow round a closed loop of overlapping orbitals. Because there is no cation, anion or radical to stabilise, what decides whether a pericyclic reaction happens — and with what stereochemistry — is orbital symmetry, codified by the Woodward–Hoffmann rules. Three ways to reach the same verdict run through this Part: frontier molecular orbitals (FMO) (does the HOMO of one component overlap in-phase with the LUMO of the other?), orbital-symmetry correlation diagrams, and the aromatic-transition-state / Möbius–Hückel electron count. Two layers on every reaction: a hand-held beginner path (plain “what it does”, orbital-picture mechanism, graded worked examples, trap boxes) and a research-grade advanced/reference path (FMO analysis with orbital-symmetry diagrams, the full 4n / 4n+2 · thermal/photochemical · supra/antarafacial selection tables, stereospecificity, regio/endo selectivity, catalytic and asymmetric variants, research-level problems). Cycloadditions: Diels–Alder [4+2] (regio & endo rules, s-cis diene, hetero-DA, retro-DA, Danishefsky diene), 1,3-dipolar / Huisgen (azides, nitrile oxides, ozonolysis, CuAAC click), [2+2] photochemical & Paterno–Büchi, cheletropic. Electrocyclic: con-/disrotatory ring closure/opening, thermal vs photochemical, Nazarov. Sigmatropic: [1,5] & [1,7] H-shifts (supra/antara), with [3,3] Claisen/Cope cross-referenced to Part 5. Group transfer: the Alder-ene and Conia-ene reactions. — closing with a Woodward–Hoffmann master selection-rules table and an “allowed or forbidden?” decision guide.
The 13 sections in Part 7
- 1Three tools that all give the same answer Free below
- 2The Diels–Alder reaction (the [4+2] cycloaddition)
- 3Diels–Alder variants: hetero-DA, retro-DA and the Danishefsky diene
- 41,3-Dipolar (Huisgen) cycloaddition — and ‘click’ chemistry
- 5The [2+2] cycloaddition (photochemical) and Paterno–Büchi
- 6Cheletropic reactions (both bonds to one atom)
- 7The con/dis rules — count electrons, check heat or light
- 8[1,5]- and [1,7]-hydrogen shifts
- 9The Alder-ene reaction
- 10Woodward–Hoffmann master selection-rules table
- 11The general rule and how to apply it
- 12Quick ‘heat or light?’ lookup
- 13Mixed research-level problems
Three tools that all give the same answer
Free extractSection S.0 of Part 7, reproduced in full from the book — figures and all. No sign-in, no paywall on this section.
You can predict any pericyclic reaction three ways — frontier orbitals, correlation diagrams, or the aromatic-TS electron count. They always agree; learn one well and check with another.
In one line: to decide if a pericyclic reaction is allowed, you may (1) use frontier molecular orbitals (FMO) — ask whether the HOMO of one component overlaps in phase with the LUMO of the other; (2) build an orbital-symmetry correlation diagram and check that filled reactant orbitals connect to filled product orbitals of the same symmetry; or (3) count electrons in the aromatic transition state (Hückel/Möbius). All three are consequences of one idea: orbital symmetry is conserved in a concerted reaction.
Tool 1 — Frontier Molecular Orbitals (FMO)
The HOMO (highest occupied MO) is where the electrons that will form new bonds live; the LUMO (lowest unoccupied MO) is where they go. A bond can form only where two orbital lobes of the same phase (same shading) overlap. Pair the HOMO of the electron-rich partner with the LUMO of the electron-poor partner, line up the atoms that must bond, and check the phases at both new-bond positions. If both match, the reaction is allowed.
Tool 2 — Suprafacial / antarafacial bookkeeping
Each component in the cyclic TS reacts through one face (suprafacial, symbol s) or through both faces (antarafacial, symbol a). Suprafacial is geometrically easy; antarafacial needs the π-ribbon to twist and is only feasible for long chains or a migrating σ-bond. The Woodward–Hoffmann rule is then a statement about the number of (4q+2)s and (4r)a components.
Tool 3 — Aromatic transition state (Hückel / Möbius)
Treat the cyclic array of interacting orbitals in the TS like a ring of overlapping p-orbitals and count phase inversions. An even number of inversions = Hückel topology (aromatic, hence allowed, for 4n+2 electrons); an odd number = Möbius topology (aromatic/allowed for 4n electrons). Thermal reactions prefer the aromatic TS; photochemical reactions prefer the anti-aromatic count.
⚠ Common mistakes & exam traps
- Concerted ≠ two-step. A pericyclic reaction has no intermediate; do not draw a carbocation. If you can trap an intermediate, it is not pericyclic (it may be a stepwise look-alike).
- Only HOMO(one)–LUMO(other) interactions are net stabilising — always pair occupied with unoccupied. LUMO–LUMO (empty–empty) genuinely does nothing; HOMO–HOMO (filled–filled) is a four-electron closed-shell interaction that is net repulsive, which is why two very electron-rich partners react sluggishly.
- Light flips the rule. Whatever is thermally allowed is photochemically forbidden and vice versa, because excitation moves an electron up and changes the HOMO.
- Count electrons, not atoms. [4+2] means 4π + 2π electrons; the numbers in brackets are electron counts of each component.
- Stereospecific, not merely stereoselective. The geometry of the starting material maps to a definite product geometry — that is the fingerprint of orbital-symmetry control.
The general Woodward–Hoffmann rule, the master 4n / 4n+2 · thermal/photo · supra/antara selection tables for all three reaction types, and the correlation-diagram logic.
The general Woodward–Hoffmann rule (1969) unifies every pericyclic process into one sentence. Count the bonding components in the cyclic TS; classify each as suprafacial (s) or antarafacial (a) and by its electron count as a (4q+2) or (4r) component. Then:
Master table A — Cycloadditions
| Total π electrons | Thermal (Δ) — allowed mode | Photochemical (hν) — allowed mode | Example |
|---|---|---|---|
| 4n+2 (e.g. 6, [4+2]) | supra–supra (π4s + π2s) | supra–antara (forbidden s/s) | Diels–Alder (thermal) |
| 4n (e.g. 4, [2+2]) | supra–antara (geometrically hard) | supra–supra (π2s + π2s) | [2+2] (photochemical) |
| 4n+2 (e.g. 6, [4+2] 1,3-dipolar) | supra–supra | supra–antara | Huisgen 1,3-dipolar |
| 4n (e.g. 8, [6+2] / [4+4]) | supra–antara | supra–supra | higher-order cycloadditions |
Master table B — Electrocyclic reactions (m π electrons in the open form)
| π electrons in open chain | Thermal (Δ) | Photochemical (hν) | Example |
|---|---|---|---|
| 4n (e.g. 4: butadiene↔cyclobutene) | conrotatory | disrotatory | butadiene / cyclobutene |
| 4n+2 (e.g. 6: hexatriene↔cyclohexadiene; also 10) | disrotatory | conrotatory | hexatriene / cyclohexadiene |
| 4n (e.g. 8) | conrotatory | disrotatory | octatetraene systems |
| 4n+2 (2: allyl cation, cationic 2π) | disrotatory | conrotatory | cyclopropyl cation ↔ allyl cation |
| 4n (4: pentadienyl cation, cationic 4π) | conrotatory | disrotatory | Nazarov cyclisation |
Master table C — Sigmatropic [1,j] and [i,j] shifts
| Migration / electrons | Thermal (Δ) allowed geometry | Photochemical (hν) | Example |
|---|---|---|---|
| [1,3] H (4 e⁻) | antarafacial (H) — geometrically forbidden | suprafacial | rare thermally for H |
| [1,5] H (6 e⁻) | suprafacial (easy) | antarafacial | cyclopentadiene H-scramble |
| [1,7] H (8 e⁻) | antarafacial (helical, e.g. vitamin D) | suprafacial | previtamin D₃ → vitamin D₃ |
| [1,3] C (4 e⁻) | suprafacial with inversion at C | supra, retention | alkyl shifts |
| [3,3] (6 e⁻) | supra–supra, chair TS | — | Cope / Claisen (Part 5) |
Why correlation diagrams give the same verdict
The deepest justification is the orbital-symmetry correlation diagram: classify every reactant and product MO by its behaviour under the symmetry element preserved along the reaction path (a mirror plane for disrotatory / suprafacial modes, a C₂ axis for conrotatory / antarafacial modes), then connect reactant and product orbitals of the same symmetry without crossing. If every filled reactant orbital correlates with a filled product orbital, the ground state maps smoothly to the ground state and the thermal reaction is allowed. If a filled reactant orbital correlates with an empty, high-energy product orbital, there is a symmetry-imposed barrier — the thermal reaction is forbidden but the corresponding photochemical reaction (starting from the excited state) is allowed. The FMO and aromatic-TS tools are shortcuts to this same conclusion.
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Further reading.
- The orbital-symmetry rules were formulated by R. B. Woodward and Roald Hoffmann (1965–1969); Hoffmann and Fukui shared the 1981 Nobel Prize in Chemistry for theories of chemical reactivity (Woodward had died in 1979). Kenichi Fukui developed frontier-orbital theory. Standard textbook content.
Read the rest of Part 7
The remaining 12 sections of this part — The Diels–Alder reaction (the [4+2] cycloaddition), Diels–Alder variants: hetero-DA, retro-DA and the Danishefsky diene, 1,3-Dipolar (Huisgen) cycloaddition — and ‘click’ chemistry, The… — and all nine parts of Named Reactions are part of ChemVidya Full Access, along with the other books, 55 Study Notes and 6,000+ practice questions.
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