Chapter 39 — Pericyclic Reactions and Woodward-Hoffmann Rules

"Pericyclic reactions are the most beautiful in organic chemistry. The Diels-Alder, the Cope and Claisen rearrangements, the electrocyclic ring closures — they all share a single property: a cyclic transition state with no charges or radicals. The Woodward-Hoffmann rules explain them all." — paraphrase from a physical organic chemistry text

"When orbital symmetry is conserved, the reaction is allowed. When it is not, the reaction is forbidden. A simple rule from quantum mechanics that has predicted thousands of reactions and earned a Nobel Prize."

This chapter covers pericyclic reactions: concerted reactions that proceed through a cyclic transition state without intermediates. They are governed by the Woodward-Hoffmann rules (1965), which use orbital symmetry to predict whether a reaction is allowed (proceeds easily under the given conditions) or forbidden (requires the opposite conditions, typically photochemical).

The three main classes: 1. Cycloadditions: two π systems combine to form a ring. The Diels-Alder (Ch 19) is the most famous. 2. Electrocyclic reactions: a conjugated π system closes to a ring, or a ring opens to a conjugated π system. 3. Sigmatropic rearrangements: a σ bond migrates within a π system.

By the end of this chapter you should be able to: - Identify a pericyclic reaction and classify it (cycloaddition, electrocyclic, sigmatropic). - Apply the Woodward-Hoffmann rules to predict whether a reaction is thermally or photochemically allowed. - Distinguish suprafacial vs. antarafacial bond formation. - Distinguish disrotatory vs. conrotatory ring-closing modes. - Predict the stereochemistry of pericyclic reactions. - Recognize the Cope and Claisen rearrangements; the Nazarov cyclization; and other named pericyclic reactions.

39.1 What is a pericyclic reaction?

A pericyclic reaction has these features: - Concerted: all bond making and bond breaking happens in a single elementary step. - Cyclic transition state: the bonds being made and broken form a closed loop. - No charges, radicals, or intermediates: the reaction goes from reactants directly to products via the cyclic TS. - Stereospecific: the geometry of the TS determines the stereochemistry of the product.

These features distinguish pericyclic reactions from: - Polar mechanisms (involving cations, anions, or charge-separated TSs). - Radical mechanisms (involving unpaired electrons). - Multi-step mechanisms (with discrete intermediates).

The orbital-symmetry insight

Robert B. Woodward and Roald Hoffmann (1965-1969) proposed that the conservation of orbital symmetry governs pericyclic reactions. The key idea: in the transition state, the orbitals of the reactant must connect smoothly (without symmetry "discontinuity") to the orbitals of the product.

For the Diels-Alder ([4+2] cycloaddition): - 4 electrons from the diene's HOMO. - 2 electrons from the dienophile's LUMO. - Total: 6 electrons (a Hückel-like aromatic TS).

For the [2+2] cycloaddition (two simple alkenes): - 2 electrons from one HOMO. - 2 electrons from the other LUMO. - Total: 4 electrons.

Under thermal conditions, the [4+2] is allowed (smooth orbital connection); the [2+2] is forbidden (orbital symmetry mismatch). Under photochemical conditions (one electron promoted to LUMO), the situation reverses.

The Woodward-Hoffmann rules capture this systematically.

39.2 Cycloadditions

A [m+n] cycloaddition combines an m-π-electron system with an n-π-electron system to form a ring with m+n atoms.

[4+2] Diels-Alder (the most famous)

Diels-Alder (Ch 19) is a [4+2] cycloaddition: a diene (4π) + a dienophile (2π) → 6-membered ring.

Stereochemistry features: - Suprafacial on both diene and dienophile (the two ends of each component bond to the same face). - Stereospecific: cis-dienophile gives cis-product; trans gives trans (Ch 19). - Thermal allowed (no light needed).

[2+2] Cycloaddition

Two alkenes combine to form a 4-membered ring (cyclobutane). Thermally forbidden (orbital symmetry mismatch). Photochemically allowed.

Why? The thermal [2+2] requires orbitals of the same symmetry to bond at both ends, but a HOMO + HOMO (or LUMO + LUMO) interaction is unfavorable. Under UV light, one electron is promoted; the resulting HOMO + LUMO* is now favorable.

Used in synthesis to make cyclobutanes from two alkenes under UV light.

Other cycloadditions

• [3+2] (1,3-dipolar cycloaddition): a 1,3-dipole (e.g., diazomethane, ozone) + dipolarophile (alkene) → 5-membered ring. Thermally allowed (6 electrons total: 4 from dipole + 2 from dipolarophile).
• [6+4]: 6π + 4π = 10 electrons. Allowed thermally (4n+2 = 10).

The general rule for cycloadditions

For a thermal cycloaddition with both components reacting suprafacially: - Allowed if total π electrons = 4n+2 (n = 0, 1, 2, ...): 6, 10, 14, ... - Forbidden if total π electrons = 4n (n = 1, 2, 3, ...): 4, 8, 12, ...

For photochemical: - The opposite: 4n is allowed; 4n+2 is forbidden.

Generalization (Hückel's rule analogy)

The thermal allowed cases are analogous to aromatic transition states (4n+2 electrons in a closed loop, like benzene). The forbidden cases are anti-aromatic (4n electrons).

39.3 Electrocyclic reactions

An electrocyclic reaction is the closure of a conjugated π system to a ring (or the reverse, ring-opening).

Cyclobutene ⇌ butadiene (4 electrons)

Cyclobutene (a 4-membered ring with one C=C) has 4 π electrons: the C=C + the two C-C bonds that will become C=C.

Wait, let me re-check. Cyclobutene's σ system + 1 C=C. The electrocyclic ring opening: the σ bond between two adjacent CH₂ groups breaks; the resulting biradical / π system is butadiene (1,3-butadiene with 4 π electrons).

So the ring opening converts a cyclobutene's σ-π system to butadiene's all-π system. The reverse converts butadiene to cyclobutene.

Disrotatory vs conrotatory

When two ends of a π system come together to form a new σ bond (or when a σ bond breaks to release a π system), the rotation can be: - Disrotatory: the two ends rotate in opposite directions. - Conrotatory: the two ends rotate in the same direction.

Selection rules

For thermal electrocyclic reactions: - 4n π electrons (e.g., 4 in butadiene → cyclobutene): conrotatory. - 4n+2 π electrons (e.g., 6 in 1,3,5-hexatriene → cyclohexadiene): disrotatory.

For photochemical (one electron promoted): - The opposite: 4n is disrotatory, 4n+2 is conrotatory.

Why does this matter? Stereochemistry

The rotation mode determines the stereochemistry of the product. Trans-substituents on the diene give a specific cis or trans relationship in the cyclobutene, depending on whether thermal (conrotatory) or photochemical (disrotatory) conditions are used.

For example: (E,E)-2,4-hexadiene + thermal closure (conrotatory) → trans-3,4-dimethylcyclobutene. The same diene + photochemical closure (disrotatory) → cis-3,4-dimethylcyclobutene.

This stereochemistry is one of the most striking confirmations of the Woodward-Hoffmann rules.

Hexatriene → cyclohexadiene

1,3,5-Hexatriene (6 π electrons) cyclizes thermally (disrotatory) to give cis-1,3-cyclohexadiene.

Photochemically (conrotatory) gives the trans product.

This is the underlying chemistry of vitamin D photosynthesis in skin: 7-dehydrocholesterol absorbs UV light, undergoes a 6π photochemical electrocyclic ring opening to give pre-vitamin D3, which thermally rearranges to vitamin D3 (cholecalciferol).

The stereochemistry of vitamin D's active form is set by the photochemical conrotatory step.

39.4 Sigmatropic rearrangements

A sigmatropic rearrangement is a rearrangement where a σ bond migrates within a π system. Classified as [m,n] where m is the number of atoms in the σ bond's migrating end + 1, and n is the number on the other end + 1.

[1,5]-Hydrogen shift

A H atom migrates from one end of a 1,3-pentadiene to the other: $$CH_2=CH-CH=CH-CH_3 \to CH_3-CH=CH-CH=CH_2$$

• 6 electrons total (4 π + 2 σ in the C-H bond moving).
• Thermal allowed (suprafacial, 6 e⁻ = 4n+2).

Cope rearrangement [3,3]

1,5-Hexadiene rearranges to 1,5-hexadiene (the same starting material, but with the carbons shuffled — a "degenerate" rearrangement at 25 °C, but useful for chiral or labeled substrates): $$\text{1,5-hexadiene} \rightleftharpoons \text{1,5-hexadiene}$$

• 6 electrons total (3 σ + 3 π).
• Thermal allowed (suprafacial-suprafacial, 6 e⁻).
• Goes through a chair-like or boat-like TS.

The chair TS is preferred for non-substituted substrates. Substituted Cope rearrangements show high diastereoselectivity from the chair-like TS preference.

Claisen rearrangement [3,3]

An allyl vinyl ether rearranges to a γ,δ-unsaturated carbonyl: $$\text{R-O-CH}_2\text{-CH=CH}_2 \to \text{R-CH(=O)-CH}_2\text{-CH=CH}_2$$

(Wait, let me redo. Allyl vinyl ether is CH₂=CH-O-CH₂-CH=CH₂; thermal [3,3] gives 4-pentenal: CH₂=CH-CH₂-CH₂-CHO.)

• 6 electrons total (chair-like TS).
• Thermal allowed.
• Important in synthesis: used to install C-C bonds with stereocontrol.

The Claisen rearrangement is one of the most-used pericyclic reactions in synthesis. Variants: Ireland-Claisen (for ester enolates), Eschenmoser-Claisen, etc.

Other sigmatropic rearrangements

• [1,3]-shifts: 4 electrons; thermal antarafacial allowed (geometrically difficult); photochemical suprafacial allowed.
• [2,3]-Wittig rearrangement: ether α-anion + allyl group → homoallyl alcohol with C-C bond formed.

39.5 The Woodward-Hoffmann rules: the master selection

For all pericyclic reactions, the rule is: - A thermal pericyclic reaction is allowed if the total number of (4q + 2)s + (4r)a components is odd.

Where: - (4q + 2)s = component with 4q+2 electrons reacting suprafacially (s). - (4r)a = component with 4r electrons reacting antarafacially (a).

This is the generalized Woodward-Hoffmann rule. It encompasses cycloadditions, electrocyclics, and sigmatropics.

For photochemical, the rule reverses (allowed when total is even).

Aromatic transition state model

A simpler view: the TS of a thermally-allowed pericyclic reaction is aromatic (6, 10, 14, ... electrons in a closed loop). The TS of a forbidden reaction would be antiaromatic (4, 8, ... electrons).

This view applies to: - Cycloadditions (thermal allowed if 4n+2 electrons). - Electrocyclics (thermal allowed if 4n+2 electrons + disrotatory; or 4n electrons + conrotatory). - Sigmatropics (thermal allowed if 4n+2 electrons + suprafacial).

The view treats pericyclic reactions as the cyclic version of aromaticity.

39.6 Frontier molecular orbital (FMO) theory

Kenichi Fukui (Nobel 1981, with Hoffmann) developed frontier molecular orbital (FMO) theory as an alternative to Woodward-Hoffmann rules.

The idea: pericyclic reactions are governed by the HOMO-LUMO interaction between the two components.

For a Diels-Alder

• HOMO of diene + LUMO of dienophile.
• Or LUMO of diene + HOMO of dienophile.

Whichever interaction has the smaller HOMO-LUMO gap dominates. For "normal" Diels-Alder (electron-rich diene + electron-poor dienophile), the diene-HOMO + dienophile-LUMO interaction dominates.

For an electrocyclic reaction

The HOMO of the conjugated π system controls the rotation mode. The HOMO's symmetry (which depends on the number of nodes in the π system) determines whether disrotatory (in-phase orbitals) or conrotatory (anti-phase orbitals) is preferred.

FMO and HSAB

FMO theory connects to HSAB (hard-soft acid-base, Ch 29). Soft electrophiles have low LUMOs; soft nucleophiles have high HOMOs. The HOMO-LUMO interaction is the basis of soft-soft pairing in pericyclic reactions.

39.7 Important pericyclic reactions in synthesis

Diels-Alder (Ch 19)

The most-used pericyclic reaction. Forms 6-membered ring + 2 new C-C bonds + 2 new stereocenters in one step. Used everywhere in synthesis.

Claisen rearrangement

[3,3]-sigmatropic of allyl vinyl ether → γ,δ-unsaturated carbonyl. Used in many natural product syntheses.

Variants: - Ireland-Claisen: ester enolate version. - Eschenmoser-Claisen: amide-based. - Johnson-Claisen: orthoester version.

Cope rearrangement

[3,3] of 1,5-hexadienes. Used in natural product synthesis where suitable substrates can be prepared.

Nazarov cyclization

Electrocyclic closure of a divinyl ketone (a 4π system) → cyclopentenone. Goes through cation intermediate (via Lewis acid catalysis); 4π conrotatory closure.

Ene reaction

A C-H σ bond + a π bond (allylic H + alkene) → new C-C bond + new H-X bond. Concerted.

Carbonyl ene

Alkene + carbonyl (under Lewis acid catalysis) → β-hydroxyalkene. A variant of the ene reaction.

Cope-Claisen-Aza-Cope

Variants of [3,3] sigmatropic with N atoms instead of C or O.

[2+2] photocycloaddition

UV light + two alkenes → cyclobutane. Used for synthesizing strained rings. Industrial: vitamin A synthesis includes a photochemical step.

39.8 The Woodward-Hoffmann Nobel context

The Woodward-Hoffmann rules were first proposed in 1965. Robert B. Woodward and Roald Hoffmann (Cornell) published a series of papers in 1965-1969 establishing the rules.

The 1981 Nobel Prize in Chemistry was awarded to: - Kenichi Fukui (for FMO theory). - Roald Hoffmann (for the rules).

Woodward had passed away in 1979 (just before the prize), so was ineligible. Many believe Woodward would have shared had he lived.

The Woodward-Hoffmann rules transformed organic chemistry: they made what seemed like "magic" stereochemistry into predictable, understandable patterns. They are taught in every organic chemistry course since 1970.

39.9 Connection to total synthesis

Many great total syntheses include pericyclic key steps: - Diels-Alder in many natural product syntheses (taxol, ginkgolide, etc.). - Claisen rearrangement for stereocontrolled C-C bond formation. - Singlet oxygen [4+2] for endoperoxide installation (artemisinin, Ch 38). - Photochemical [2+2] for strained 4-membered rings.

Mastery of pericyclic reactions is essential for advanced synthesis design.

39.10 Diels-Alder reaction in detail

The Diels-Alder is the prototype pericyclic reaction. Let's analyze it in detail.

General reaction

$$\text{conjugated diene} + \text{dienophile} \to \text{cyclohexene}$$

A 4π diene + 2π dienophile in a [4+2] cycloaddition. 6 electrons total → thermally allowed (4n+2 = 6).

Mechanism

Concerted; no intermediate. The TS has: - All 6 atoms (4 from diene, 2 from dienophile) in a cyclic arrangement. - 6 electrons in motion: 2 from dienophile π, 2 from each end of diene. - The substituents' geometry is preserved (stereospecific syn addition).

Stereochemistry

• Stereospecific: cis dienophile gives cis product; trans dienophile gives trans.
• Endo selectivity: substituents on the dienophile prefer the endo position (under the ring) due to secondary orbital interactions.
• Cis-fused bicyclic in cyclic dienes (e.g., cyclopentadiene).

Electronic effects

• Normal Diels-Alder: electron-rich diene + electron-poor dienophile.
• Inverse electron demand Diels-Alder: electron-poor diene + electron-rich dienophile.

The HOMO-LUMO match (FMO theory) determines which is more favorable.

Hetero-Diels-Alder

• One or more atoms in the diene or dienophile is a heteroatom (N, O, S).
• Examples: aza-Diels-Alder, oxa-Diels-Alder.
• Used for heterocyclic synthesis (pyrans, pyridines).

Asymmetric Diels-Alder

Chiral catalysts (oxazaborolidines, chiral Lewis acids, Diels-Alder organocatalysts) give chiral products with high ee. Used in many drug syntheses.

Industrial application

Many natural products and pharmaceuticals use Diels-Alder as a key step. Examples: - Vitamin B12 (Woodward, 1972). - Reserpine (Woodward, 1956). - Taxol (multiple groups, 1990s). - Steroid syntheses. - Many alkaloids.

The Diels-Alder is among the most powerful synthetic reactions available.

39.11 Cope rearrangement in detail

The Cope rearrangement is a [3,3]-sigmatropic rearrangement of 1,5-hexadienes:

$$\text{1,5-hexadiene (CH}_2=\text{CH-CH}_2\text{-CH}_2\text{-CH=CH}_2\text{)} \rightleftharpoons \text{same product (degenerate)}$$

Degenerate: the product is identical to the starting material (in unsubstituted 1,5-hexadiene).

For substituted hexadienes, the rearrangement gives a different (often more stable) product. Stereospecific and predictable.

Examples

• 3,3-dimethyl-1,5-hexadiene → degenerate (same).
• 3-substituted derivatives: rearrange to give specific products.

Variants

• Aza-Cope: with a nitrogen in the chain.
• Oxy-Cope: with an oxygen; faster than parent.
• Anionic oxy-Cope: deprotonation to form alkoxide; rearrangement is much faster (10^17 acceleration!).

The anionic oxy-Cope is one of the most spectacular rate accelerations in organic chemistry.

39.12 Claisen rearrangement in detail

The Claisen rearrangement is a [3,3] of allyl vinyl ether → γ,δ-unsaturated carbonyl:

$$\text{CH}_2=\text{CH-O-CH}_2-\text{CH=CH-R} \to \text{R-CH=CH-CH}_2-\text{CH}_2-\text{CHO}$$

The OR group migrates; new C-C bond formed; new C=O formed.

Variants

Ireland-Claisen: - An ester enolate version. - Z-enolate gives one stereochemistry; E-enolate gives the other. - Stereoselective; widely used in natural product synthesis.

Eschenmoser-Claisen: - An amide-based version. - Used for vinylogous amide formation.

Johnson-Claisen: - An orthoester version. - Allyl alcohol + orthoester + cat. acid → unsaturated ester. - Mild conditions; good yields.

[2,3]-Wittig rearrangement (related): - Anionic version of Claisen. - α-allyloxy carbanion rearrangement.

Application

The Claisen rearrangement (and its variants) are used in many natural product syntheses for installing C-C bonds with controlled stereochemistry.

39.13 Electrocyclic reactions

Electrocyclic reactions interconvert a polyene and a cycloalkene with the same atom count:

Examples

6π electrocyclic (1,3,5-hexatriene → cyclohexadiene): - Thermally allowed in disrotatory mode. - Photochemically allowed in conrotatory mode.

4π electrocyclic (1,3-butadiene → cyclobutene): - Thermally allowed in conrotatory mode. - Photochemically allowed in disrotatory mode. - Reverse: cyclobutene → butadiene (thermally; conrotatory).

Vitamin D photosynthesis

A famous biological electrocyclic: 7-dehydrocholesterol (skin) + UV → previtamin D3 (a 6π conrotatory ring opening) → vitamin D3 (thermal isomerization).

This converts cholesterol-derived precursor to vitamin D in skin. The pericyclic chemistry of vitamin D is essential for human health.

Nazarov cyclization

A 4π electrocyclic of divinyl ketone: $$\text{R}_2\text{C=C-CR=CR}_2-\text{C=O} \to \text{cyclopentenone}$$

Goes through cation intermediate (Lewis acid catalysis); the cation undergoes conrotatory closure.

Used in synthesis of cyclopentenone natural products.

Stereospecificity

Electrocyclic reactions are stereospecific: - Conrotatory: substituents rotate in the same direction. - Disrotatory: substituents rotate in opposite directions.

The mode (con vs dis) is determined by orbital symmetry; the product stereochemistry is predictable.

39.14 Sigmatropic rearrangements

A σ bond migrates within a π system:

Notation

[i,j]-sigmatropic: the σ bond moves from position 1 of one π system to position i+1 of the same end and from position 1 of the other end to position j of the other end. Hard to describe verbally; the notation captures it.

Common examples

[3,3]: Cope, Claisen (most common). [2,3]: Wittig variants (anionic). [1,5]: Hydrogen shift in cyclopentadiene; rate-limiting step in fluxional NMR studies. [1,3]: Less common; usually photochemical.

Suprafacial vs antarafacial

The migration can be suprafacial (same face of the π system) or antarafacial (opposite faces).

• Suprafacial-suprafacial [3,3]: thermally allowed.
• Antarafacial component: usually photochemical.

Stereospecific

Sigmatropic rearrangements are stereospecific (predictable product geometry from substrate).

Aza-Cope and Aza-Claisen

Sigmatropic with nitrogen replacing carbon. Used for nitrogen heterocycle synthesis.

39.15 The Aromatic TS view

A useful conceptual framework: the TS of a thermally-allowed pericyclic reaction is aromatic (4n+2 electrons in a cyclic TS).

• Diels-Alder TS: 6 electrons in a 6-mem TS = aromatic.
• Cope TS: 6 electrons in a 6-mem TS = aromatic.
• Claisen TS: 6 electrons in a 6-mem TS = aromatic.
• Hexatriene → cyclohexadiene: 6 electrons in a 6-mem TS = aromatic (when disrotatory).

The TS aromaticity gives the reaction lower TS energy; thermally allowed.

For 4n electrons (4-mem TS, etc.): the TS would be antiaromatic; thermally forbidden.

This view, due to M.J.S. Dewar, complements the Woodward-Hoffmann rules. Both views give consistent predictions.

39.16 More detailed orbital analysis

For orbital symmetry analysis of a pericyclic reaction:

Step 1: identify the orbitals involved

For Diels-Alder: - Diene HOMO: ψ₂ of butadiene (2 electrons). - Dienophile LUMO: π* of ethylene (0 electrons).

Step 2: check symmetry

For [4+2] cycloaddition: - Diene HOMO has nodes (in/out of plane character). - Dienophile LUMO has nodes. - Suprafacial approach: in-phase orbitals overlap on the same face → bonding.

If in-phase overlap is possible on the same face: thermally allowed.

Step 3: check the alternative

If the suprafacial doesn't work, try antarafacial (one face of one component, other face of the other).

For [4+2]: suprafacial-suprafacial works (Möbius-like; 6 electrons; aromatic TS). For [2+2]: suprafacial-suprafacial would require antibonding overlap → forbidden thermally.

This orbital analysis gives the same conclusion as Woodward-Hoffmann rules.

For sigmatropic

[3,3] suprafacial-suprafacial: 6 electrons in cyclic TS; aromatic; allowed. [1,3] suprafacial: 4 electrons; antiaromatic; forbidden. Suprafacial-antarafacial is allowed but geometrically difficult.

39.17 The Woodward-Hoffmann rules: a closer look

The full statement: - A pericyclic reaction is thermally allowed when the total number of (4q+2) suprafacial + (4r) antarafacial components is odd. - For photochemical, the rule reverses.

For specific cases: - Diels-Alder: [4+2] suprafacial-suprafacial = 1 (4q+2) suprafacial + 0 (4r) antarafacial = 1 (odd) → thermally allowed. - [2+2] cycloaddition: suprafacial-suprafacial = 0 (4q+2) suprafacial + 0 (4r) antarafacial = 0 (even) → thermally forbidden; photochemically allowed (rule reversed). - Cope [3,3] suprafacial-suprafacial: 6 electrons; same as [4+2]; allowed thermally.

The rule encompasses cycloadditions, electrocyclic, sigmatropic.

Application

When you encounter a new pericyclic reaction: 1. Identify the components (number of electrons in each). 2. Apply the Woodward-Hoffmann rule. 3. Predict whether thermal or photochemical conditions are needed. 4. Check the experimental literature.

Most pericyclic reactions can be predicted this way.

39.18 Photochemistry and pericyclic reactions

Photochemistry adds an extra electron-volt of energy to the substrate by absorption of UV light. This: - Promotes an electron from HOMO to LUMO. - Changes the orbital symmetry. - Reverses the Woodward-Hoffmann rules.

Photochemical [2+2]

Two alkenes + UV → cyclobutane. Allowed photochemically.

Used in: - Vitamin A synthesis (Hoffmann-La Roche). - Some natural product syntheses. - Material chemistry (cross-linking polymers).

Photochemical 4π electrocyclic

Cyclobutene → 1,3-butadiene + UV: disrotatory mode. Allowed photochemically.

Vitamin D photosynthesis

7-dehydrocholesterol + UV → previtamin D3 (6π conrotatory ring opening; allowed photochemically).

This is the photobiological reaction that produces vitamin D in skin.

Modern photochemistry

Visible-light photoredox catalysis (Ch 40) has revolutionized photochemistry. Visible light is used (not UV) with a photocatalyst (Ru, Ir bipyridyl complexes) to generate radicals.

This is different from classical pericyclic photochemistry but builds on related ideas.

39.19 Computational analysis of pericyclic reactions

DFT calculations of pericyclic TSs: - The Diels-Alder TS has been mapped extensively; the TS energy is ~25-30 kcal/mol. - The Claisen rearrangement TS is similar. - Electrocyclic and sigmatropic TSs likewise.

The aromatic TS character is verified computationally: - Negative NICS values at the TS center (aromatic). - Bond order analysis shows partial bonding. - Orbital plots show closed loop of bonding electrons.

These computational confirmations validate the Woodward-Hoffmann/aromatic TS framework.

39.20 Pericyclic reactions in biology

Several biological reactions are pericyclic:

Vitamin D biosynthesis (electrocyclic)

7-dehydrocholesterol in skin + UV (290 nm; UV-B sunlight) → previtamin D3 → vitamin D3.

The first step is a 6π conrotatory electrocyclic ring opening (photochemically allowed). The cyclohexadiene of the steroid B ring opens to give an extended hexatriene.

The next step is a thermal [1,7]-sigmatropic hydrogen shift to give vitamin D3 (cholecalciferol).

Vitamin D3 is then hydroxylated in the liver and kidney to give the active form (calcitriol). This is the only known biological reaction triggered by sunlight.

Squalene cyclization

Squalene 2,3-epoxide + squalene-hopene cyclase enzyme → lanosterol (steroid precursor).

The mechanism involves a series of cation-stabilized cyclizations, but the geometry and stereochemistry are pericyclic-like (concerted or stepwise via cations).

This is the first committed step of cholesterol biosynthesis.

Lanosterol → cholesterol

A series of enzymatic reactions, including some that are pericyclic in nature (rearrangements, cleavages).

Light-driven biological reactions

Beyond vitamin D: - Visual cycle (rhodopsin): a photochemical isomerization of 11-cis-retinal to all-trans. - Photosynthesis: photochemistry of chlorophyll initiates electron transport.

These photochemical reactions are mechanistically related to pericyclic chemistry.

Pericyclic reactions and enzyme evolution

Enzymes that catalyze pericyclic reactions are rare (most enzymes use ionic or radical mechanisms). But some enzymes (like Diels-Alderase enzymes) do catalyze [4+2] cycloadditions in nature. Their catalytic mechanism is debated; possibly they stabilize the cyclic TS or act as templates.

39.21 Asymmetric pericyclic reactions

Most pericyclic reactions are inherently selective (stereospecific). Adding chirality:

Asymmetric Diels-Alder

• Chiral Lewis acid catalysts (Bronsted, Trost, Yamamoto, Corey).
• Chiral auxiliaries on the dienophile.
• Chiral dienes.
• Chiral aza-Diels-Alder: with iminium-Lewis acid complexes.

Asymmetric Claisen rearrangement

• Chiral allyl groups in the substrate (substrate control).
• Chiral catalysts for variants (e.g., Ireland-Claisen with chiral enolates).

Asymmetric Nazarov

• Chiral Lewis acids (Trost, Frontier, Tius).
• Gives chiral cyclopentenones.

Asymmetric ene reaction

• Chiral Lewis acid catalysis.
• Used for some natural product syntheses.

Modern advances

The 2010s+ saw rapid development of asymmetric pericyclic methods. Each new chiral catalyst opens new opportunities.

39.22 Examples in pharmaceutical synthesis

Vitamin B12 (Eschenmoser-Woodward)

The synthesis of vitamin B12 includes several pericyclic steps: - Intramolecular Diels-Alder for ring formation. - Sigmatropic rearrangements.

Reserpine (Woodward, 1956)

A key step uses a Diels-Alder cycloaddition for ring formation.

Many cyclopentanoids

Made by Nazarov cyclization or photochemical [2+2].

Many natural product macrocycles

Made by Claisen rearrangement for stereocontrolled C-C bond formation.

Modern drugs

Many modern drugs include rings made by pericyclic reactions: - Some statins (cyclic intermediates from Diels-Alder). - Some kinase inhibitors (heterocyclic Diels-Alder). - Many antibiotic syntheses.

The pericyclic toolkit is at the heart of complex molecule synthesis.

39.23 The Diels-Alder reaction zoom-in

Diene requirements

A diene must be in the s-cis conformation for Diels-Alder. The two C=C bonds must be on the same side of the central single bond:

• s-cis: 1,3-butadiene with C1-C2-C3-C4 dihedral angle ~ 0°.
• s-trans: dihedral angle ~ 180° (more stable but unreactive in DA).

The s-cis is required for the cyclic TS geometry.

Cyclic dienes

Cyclic dienes (e.g., cyclopentadiene, cyclohexadiene) are locked in s-cis. They are the most reactive dienes: - Cyclopentadiene reacts fast even at room temperature. - Furan, anthracene reactive too.

Acyclic dienes

Acyclic dienes (e.g., 1,3-butadiene, isoprene) are mostly in s-trans equilibrium; only a small fraction is s-cis, slowing the DA.

Substituted dienes

Substituents on the diene affect: - Reactivity (electron-donating substituents accelerate normal DA). - Regiochemistry (with substituted dienophiles, two possible regioisomers). - Stereochemistry (substituents end up in specific positions).

Diene examples

• 1,3-butadiene: parent.
• Isoprene (2-methyl-1,3-butadiene): more reactive than butadiene.
• 2,3-dimethyl-1,3-butadiene: most reactive simple diene.
• Cyclopentadiene: very reactive.
• Furan: a hetero-diene; can do DA but slower.

Dienophile requirements

Dienophiles must be electron-poor for "normal" DA: - α,β-unsaturated carbonyls: enals, enones, esters, amides. - Maleic anhydride, maleimide: very electron-poor; classic dienophiles. - Quinones: also good dienophiles. - Cyclopropene, benzyne: highly strained, very reactive.

Endo selectivity

The endo product is preferred when the dienophile has a substituent (R-C=O, ester, etc.). Why? - Secondary orbital interactions between the dienophile substituent and the diene's π system stabilize the endo TS. - The endo product has the substituent close to the C=C of the new cyclohexene; this is sterically less hindered than exo in the early TS.

The endo:exo ratio depends on substrate and conditions; often endo > 90%.

Asymmetric DA

Chiral catalysts (Lewis acids with chiral ligands) make the dienophile face-selective. Used in many natural product syntheses for enantioselective DA.

39.24 Hetero-Diels-Alder reactions

When the diene or dienophile contains heteroatoms (N, O, S), we get a hetero-Diels-Alder.

Aza-Diels-Alder

• An imine (C=N) as the dienophile.
• Or 1-aza-1,3-butadiene as the diene.
• Gives nitrogen-containing 6-membered rings (pyridines, etc.).

Oxa-Diels-Alder

• A carbonyl (C=O) as the dienophile.
• Or oxygen-containing dienes.
• Gives pyrans (6-mem O-containing rings).

Inverse electron demand DA

• Electron-poor diene + electron-rich dienophile.
• E.g., a tetrazine (very electron-poor diene; 4 N's).
• Used in some natural product syntheses.

Bioconjugation by hetero-DA

Some bioconjugation reactions use hetero-DA: - Tetrazine-norbornene click (bioorthogonal). - Used for in-cell labeling of biomolecules.

These extensions show DA's broad scope.

39.25 More about the FMO theory

Frontier Molecular Orbital (FMO) theory was developed by Kenichi Fukui in the 1960s. The core ideas:

HOMO and LUMO

The HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) are the most important orbitals for reactivity: - HOMO is the most easily donated electron pair (nucleophile-like). - LUMO is the most easily accepted (electrophile-like).

Pericyclic reactions

The pericyclic reaction's reactivity is governed by the HOMO-LUMO interaction between the two components: - Smaller HOMO-LUMO gap = stronger interaction = faster reaction. - The orbitals must have matching symmetry for productive overlap.

For Diels-Alder

The relevant orbitals: - Diene HOMO (ψ₂ of butadiene, 2 electrons in this orbital). - Dienophile LUMO (π* of ethylene, 0 electrons).

For these to have productive overlap, they must have matching node patterns at the 1- and 4-positions (where the new bonds form).

For [4+2] suprafacial: in-phase overlap is possible. Reaction allowed. For [2+2] suprafacial: in-phase overlap is not possible. Reaction not allowed thermally.

Substituent effects

Electron-donating substituents on the diene raise its HOMO. Electron-withdrawing substituents on the dienophile lower its LUMO. Both effects bring HOMO and LUMO closer; faster reaction.

This explains why "normal" DA prefers electron-rich diene + electron-poor dienophile.

FMO and Markovnikov-like regiochemistry

For an asymmetrically substituted DA, the regiochemistry is predictable from FMO: - Match the largest coefficient on diene with the largest coefficient on dienophile. - Gives the "ortho" or "para" product of DA (similar to ortho/para in EAS).

The "rule of like-with-like" emerges from FMO analysis.

FMO won the Nobel

Fukui's 1981 Nobel Prize was for FMO theory. It complements Woodward-Hoffmann rules and is conceptually simpler (just HOMO-LUMO interaction).

39.26 The aromatic TS theory in detail

The aromatic TS view, due to M.J.S. Dewar (1969), provides an alternative perspective:

Aromatic vs antiaromatic TSs

• Aromatic TS: 4n+2 electrons in a closed loop; very stable.
• Antiaromatic TS: 4n electrons in a closed loop; very unstable.
• Nonaromatic TS: not a closed loop; intermediate stability.

For pericyclic reactions: - The TS has electrons in a closed loop (cyclic geometry). - Counting electrons in the loop gives 4n+2 (allowed) or 4n (forbidden).

Diels-Alder

6 electrons in cyclic TS (4 from diene HOMO + 2 from dienophile LUMO transitioning). 4n+2 = 6 → aromatic TS → thermally allowed.

[2+2] cycloaddition

4 electrons in cyclic TS. 4n = 4 → antiaromatic TS → thermally forbidden.

Photochemical reversal

Under UV, an electron is promoted from HOMO to LUMO. The "occupied" set has different orbital count. The aromaticity criterion shifts; previously forbidden becomes allowed.

This reversal explains why [2+2] photochemistry works but thermal [2+2] doesn't.

Möbius topology

For some 6-electron sigmatropic reactions: the TS has a Möbius-like topology (one face twist). This changes the aromaticity criterion: 4n electrons in Möbius = aromatic.

This is a niche topic but explains some unusual sigmatropic geometries.

Computational aromatic indicator

NICS (Nucleus-Independent Chemical Shift) at the center of the cyclic TS can be calculated. Negative NICS = aromatic; positive = antiaromatic.

Pericyclic TSs typically have NICS ≈ -10 to -30 ppm (clearly aromatic).

39.27 Common mistakes

Common Mistake 39.1 — Forgetting that pericyclic reactions are concerted. There's no intermediate; one TS connects reactants to products. This means the stereochemistry of substrates is preserved in products.

Common Mistake 39.2 — Misapplying Woodward-Hoffmann. The rule is for the conditions (thermal vs photochemical) under which the reaction is allowed. It doesn't tell you whether the reaction will run; just whether the orbital symmetry is right.

Common Mistake 39.3 — Confusing electrocyclic with cycloaddition. Electrocyclic = one π system → ring (no intermolecular partner). Cycloaddition = two π systems combining (intermolecular).

Common Mistake 39.4 — Forgetting the s-cis requirement for diene in DA. If the diene is locked in s-trans (e.g., via steric blocking), the DA is much slower or doesn't occur.

Common Mistake 39.5 — Predicting the wrong rotation mode (con vs dis) for electrocyclic. Use the Woodward-Hoffmann rule: for 4n electrons, thermal conrotatory; for 4n+2 thermal disrotatory.

Common Mistake 39.6 — Forgetting that endo selectivity applies to DA with substituted dienophiles. The endo product has the substituent under the new ring (sterically less hindered).

39.28 Singlet oxygen reactions

Singlet oxygen (¹O₂) is an electronically excited form of O₂ (no unpaired electrons; reactive). It can undergo pericyclic reactions:

[4+2] with diene

Singlet oxygen + 1,3-cyclohexadiene → cyclic peroxide (an endoperoxide).

This is a hetero-Diels-Alder; ¹O₂ acts as the dienophile.

Industrial use: synthesis of artemisinin (antimalarial). The endoperoxide is the active functional group; installed via singlet oxygen DA.

Ene reaction with alkene

Singlet oxygen + alkene with allylic H → allylic hydroperoxide.

Useful in some natural product syntheses.

Generation of singlet oxygen

• Photosensitization with rose bengal or methylene blue dyes + visible light + O₂.
• Chemical: H₂O₂ + NaOCl.
• Industrial: photoreactor with sensitizer.

Singlet oxygen chemistry is a niche but important branch of photochemistry.

Vitamin D synthesis (industrial)

Industrial vitamin D synthesis includes a photochemical [4+2] step. Originally cumbersome; modern processes have improved efficiency.

39.29 More on Cope and Claisen variants

Anionic oxy-Cope

The deprotonated form of an oxy-Cope substrate (an alkoxide):

$$\text{HO-CH}_2\text{-CH=CH-CH}_2\text{-CH=CH}_2 \xrightarrow{\text{base}} \text{O}^-\text{-CH}_2\text{-CH=CH-CH}_2\text{-CH=CH}_2 \to \text{rearranged product}$$

The deprotonation accelerates the [3,3] sigmatropic by ~10¹⁷-fold over the neutral oxy-Cope. One of the largest rate accelerations in organic chemistry.

The product: a δ,ε-unsaturated aldehyde (or carbonyl).

Used in many natural product syntheses for stereocontrolled C-C bond formation.

Aza-Cope and Aza-Claisen

The Aza-Cope substitutes an N for one of the alkene C's. Aza-Claisen substitutes an N for the O of allyl vinyl ether.

These give nitrogen heterocycles in concerted, stereospecific reactions. Useful in alkaloid synthesis.

Iridium-catalyzed Cope

Modern Ir catalysts can catalyze sluggish Cope rearrangements. Applies to natural product synthesis.

39.30 The cyclopentadienyl chemistry

Cyclopentadienyl (Cp) chemistry is rich because Cp is a stable cyclic 6π aromatic anion.

Cp anion (Cp⁻)

Deprotonation of cyclopentadiene gives Cp⁻. The anion has 6 π electrons; aromatic; stable.

Ferrocene and metallocenes

Cp⁻ binds tightly to transition metals: - Ferrocene (Cp₂Fe): Fe sandwiched between two Cp rings. - Cobaltocene, nickelocene, etc. - Many metallocenes used as catalysts (Cp₂ZrCl₂ in metallocene polymerization).

Pericyclic chemistry of Cp

Cyclopentadiene + dienophile = standard DA; cyclopentadiene is very reactive.

The cyclopentadienyl-MO chemistry is the foundation of metallocene chemistry, which is central to modern catalysis.

39.31 1,3-dipolar cycloadditions

A close relative of Diels-Alder: 1,3-dipolar cycloadditions.

What's a 1,3-dipole?

A 1,3-dipole is a 4-electron, 3-atom species with a positive end, a negative end, and two adjacent atoms. Examples: - Ozone (O₃). - Diazomethane (CH₂N₂). - Azide (R-N₃, where R-N=N-N⁻). - Nitrone (R₂C=N(O)R). - Carbonyl ylide.

[3+2] cycloaddition

A 1,3-dipole + a dipolarophile (alkene or alkyne) → 5-membered ring.

The mechanism: concerted; pericyclic; 6 electrons (4 from dipole, 2 from dipolarophile); allowed thermally.

CuAAC click chemistry

The CuAAC (Cu-catalyzed azide-alkyne cycloaddition) is the most famous 1,3-dipolar cycloaddition: - Azide + terminal alkyne + Cu(I) → 1,4-substituted 1,2,3-triazole. - Sharpless 2022 Nobel Prize.

The mechanism is debated (purely pericyclic vs Cu-bonded intermediate), but it's a [3+2] cycloaddition between azide (1,3-dipole) and alkyne (dipolarophile).

Other examples

• Ozonolysis: O₃ + alkene → ozonide (a 5-membered ring with O-O bonds).
• Nitrone + alkene → isoxazolidine (5-membered O-N-C-C-C ring).
• Nitrile oxide + alkene → isoxazoline (5-mem O-N-C-C-N ring).

These provide diverse routes to 5-membered rings; common in natural product synthesis.

39.32 The history of pericyclic chemistry

1930s: Diels-Alder discovery

Otto Diels and Kurt Alder (Kiel, 1928) reported the cycloaddition that bears their name. They won the 1950 Nobel Prize in Chemistry.

1950s-1960s: empirical observations

Many pericyclic reactions were known and used in synthesis, but the mechanism was unclear. Why did some reactions work thermally and others photochemically? Why did some give specific stereochemistry?

1965-1969: Woodward-Hoffmann rules

Robert Woodward (Harvard) and Roald Hoffmann (Cornell) published a series of papers establishing the orbital symmetry rules. The rules: - Made pericyclic chemistry predictable. - Connected to MO theory. - Won the 1981 Nobel Prize for Hoffmann (Woodward had passed away).

1971: FMO theory

Kenichi Fukui (Kyoto) developed FMO theory (HOMO-LUMO interactions) as an alternative to Woodward-Hoffmann. Won the 1981 Nobel Prize jointly with Hoffmann.

1969: Aromatic TS theory

M.J.S. Dewar proposed that pericyclic TSs can be aromatic or antiaromatic, providing a third equivalent perspective.

1980s+: extensions and asymmetric versions

The pericyclic toolkit was expanded with: - Asymmetric variants (chiral catalysts). - New reactions (Nazarov, ene, etc.). - Heterocyclic versions. - Bioorganic applications. - Computational confirmation via DFT.

2022: click chemistry Nobel

Sharpless (his second Chemistry Nobel; first was 2001 for asymmetric oxidation), Bertozzi, and Meldal won the 2022 Nobel for click chemistry. The flagship CuAAC is a 1,3-dipolar cycloaddition (related to pericyclic chemistry).

The history shows pericyclic chemistry's central place in modern synthesis.

39.33 Pericyclic reactions in industry

Despite their elegance, pericyclic reactions are limited in industrial scale because: - Many are slow (need heat). - Some require photochemistry (specialized equipment). - Selectivity issues with substrate scope.

But several are used industrially:

Polymer industry

• Diels-Alder cross-linking of polymers.
• Bisphenol-A epoxy polymers (DA-related ring formation).
• Some fragrance synthesis (Diels-Alder of acyclic dienes).

Specialty chemicals

• Some pheromone syntheses use Claisen rearrangement.
• Some natural-product analogues use pericyclic key steps.
• Cosmetics: Diels-Alder for some specialty dyes.

Pharmaceutical synthesis

Many drug syntheses include pericyclic steps: - Diels-Alder for cyclic intermediate formation. - Claisen for stereocontrolled C-C bond formation. - 1,3-dipolar cycloaddition for heterocycle synthesis.

The chemistry isn't always large-scale, but it's strategically important.

39.34 Worked problems

Problem A: predict the Diels-Alder product

1,3-butadiene + maleic anhydride →

The cyclic TS forms 6-mem ring; new C-C bonds at C1-C2 of butadiene + C-C of maleic anhydride.

Product: cis-1,2,3,6-tetrahydrophthalic anhydride (a 6-mem ring fused with the anhydride 5-mem ring).

Problem B: predict the Cope product

1,5-hexadiene + heat → ?

Degenerate rearrangement; same product.

3-methyl-1,5-hexadiene + heat → ?

The methyl ends up at the new C2 position. Product: 1-methyl-1,5-hexadiene.

Problem C: Claisen rearrangement

Allyl vinyl ether + heat → ?

[3,3] sigmatropic; vinyl O migrates, allyl C migrates.

Product: 4-pentenal (γ,δ-unsaturated aldehyde).

Problem D: electrocyclic ring opening

cis-3,4-dimethylcyclobutene + heat → ?

4π electrocyclic; thermal conrotatory.

cis-3,4-dimethyl: substituents both on top face of ring. Conrotatory: both substituents rotate to the same direction (both go to up, OR both go to down).

If both methyls rotate up: gives (Z,Z)-2,4-hexadiene. If both methyls rotate down: gives (E,E)-2,4-hexadiene.

The two products are equivalent (same compound; same diastereomer).

Product: a single diastereomer (combination of conrotation outcomes).

Problem E: photochemical electrocyclic

Same substrate, photochemically:

4π photochemically allowed in disrotatory mode.

cis-3,4-dimethyl: methyls on same face. Disrotatory: rotate in opposite directions; one goes up, one goes down.

Product: (E,Z)-2,4-hexadiene (single diastereomer).

This contrasts with the thermal product. The two stereoisomers from thermal vs photo are diagnostic.

These problems illustrate the predictive power of Woodward-Hoffmann rules.

39.35 Connections to other chapters

• Chapter 5: thermodynamics (TS energies; activation barriers).
• Chapter 7: stereochemistry (cis/trans; E/Z; chirality).
• Chapter 8: stereochemistry of reactions (stereospecific, stereoselective).
• Chapter 19: conjugated dienes and Diels-Alder (Ch 19 covers DA in more detail; Ch 39 puts it in the WH framework).
• Chapter 20: aromaticity (Hückel rule; aromatic TS view).
• Chapter 27: enol/enolate chemistry (some Claisen variants).
• Chapter 36: oxidation/reduction (singlet oxygen reactions).
• Chapter 37: organometallic catalysis (some Cope and Diels-Alder catalysts).
• Chapter 38: total synthesis (uses pericyclic key steps).
• Chapter 40: photoredox chemistry (visible light variants).

The chemistry of Chapter 39 is woven throughout the textbook.

39.36 Modern frontiers

Dynamic kinetic asymmetric Diels-Alder

A diene rapidly equilibrating between cis and trans isomers; chiral catalyst preferentially reacts with the cis (or trans). Gives single chiral product despite equilibrating starting material.

Bioorthogonal click chemistry

CuAAC and SPAAC (Sharpless and Bertozzi 2022 Nobel) used for in-cell labeling and bioconjugation.

Photoredox Diels-Alder

Visible-light photocatalysts activate substrates for difficult Diels-Alder.

Asymmetric pericyclic catalysis

Modern chiral Lewis acids and organocatalysts make pericyclic reactions enantioselective.

Pericyclic reactions in carbon nanostructures

Graphene-related materials made via pericyclic chemistry (DA polymerization, etc.).

The chemistry continues to evolve.

39.37 The aromatic TS theorem revisited

Dewar's aromatic TS theory states: - Thermal pericyclic reactions are allowed if the TS is aromatic (4n+2 electrons in the cyclic TS). - They are forbidden if the TS would be antiaromatic (4n electrons). - Photochemical reactions reverse this (because adding a photon promotes an electron, changing the count).

This theorem is general and unifies cycloaddition, electrocyclic, and sigmatropic reactions.

Examples

• Diels-Alder: 6 electrons (2π + 4π) in cyclic TS = 4n+2 = aromatic = thermally allowed.
• [2+2] cycloaddition: 4 electrons in cyclic TS = 4n = antiaromatic = thermally forbidden; photochemically allowed.
• Cope: 6 electrons in [3,3] cyclic TS = aromatic = allowed.
• Vitamin D photo-opening: 6 electrons in TS, but conrotation is required (Möbius topology); aromatic for Möbius if 4n electrons. Photochemically allowed.

Möbius vs Hückel topology

• Hückel topology: planar cyclic TS; aromatic with 4n+2 electrons.
• Möbius topology: twisted cyclic TS (with one face flip); aromatic with 4n electrons.

This distinction explains why some reactions need conrotation (Möbius geometry) and others disrotation (Hückel geometry) for thermal allowedness.

39.38 The Pauson-Khand reaction

A pericyclic-related reaction: Pauson-Khand is a [2+2+1] cycloaddition of an alkene + alkyne + CO + Co catalyst → cyclopentenone:

$$\text{alkyne} + \text{alkene} + CO + \text{Co}_2(CO)_8 \to \text{cyclopentenone}$$

The cobalt-bonded alkyne reacts with an alkene + CO; gives a 5-mem ring with a ketone. Often intramolecular for natural product synthesis.

This isn't strictly pericyclic (Co is involved), but the geometry resembles a pericyclic [3+2+1] cycloaddition.

Used in many natural product syntheses for cyclopentenone-containing rings.

39.39 The take-home message

Pericyclic reactions (Diels-Alder, Cope, Claisen, electrocyclic, sigmatropic) are concerted, stereospecific reactions through a cyclic TS.

The Woodward-Hoffmann rules predict whether a reaction is thermally or photochemically allowed: - Aromatic TS = allowed. - Antiaromatic TS = forbidden.

Or equivalently: - (4n+2) electrons in a Hückel-topology TS = allowed. - (4n) electrons in a Möbius-topology TS = allowed. - Photochemistry reverses the rule.

The FMO theory provides an alternative view: HOMO-LUMO interaction governs reactivity.

The 1981 Nobel Prize was for these unifying ideas. Pericyclic chemistry has been central to organic synthesis since.

Master the rules; predict the chemistry. The Diels-Alder, Claisen, and Cope rearrangements are workhorse reactions in natural product synthesis.

39.40 The chemistry of [4+2] vs [2+2]

Why does [4+2] work thermally but [2+2] doesn't?

[4+2] cycloaddition

• 4π electrons (from diene's HOMO) + 2π electrons (from dienophile's LUMO) = 6 in the cyclic TS.
• Both components in suprafacial geometry.
• Cyclic TS has aromatic character (6 electrons, Hückel).
• Thermally allowed.

[2+2] cycloaddition

• 2π + 2π = 4 in the cyclic TS.
• For both suprafacial: the resulting cyclic TS would be antiaromatic (4 electrons, Hückel).
• Thermally forbidden.

For [2+2] to be thermally allowed, one component must be antarafacial. But this requires twisting (geometrically difficult; high TS energy).

For photochemical [2+2]: the rules reverse. UV-excited alkene has different orbital occupation; suprafacial [2+2] becomes allowed (would have been antiaromatic in the ground state, but photoexcitation changes this).

This is why [2+2] is photochemical (not thermal) for most substrates. Common in natural product synthesis (especially with vinyl-aromatic compounds).

Asymmetric [2+2]

Some asymmetric photo-[2+2] use chiral catalysts in addition to UV light.

Industrial [2+2]

Limited industrial use; usually for specialty chemicals.

39.41 Pericyclic reactions in green chemistry

Pericyclic reactions have several green chemistry advantages: - Atom-economical: all atoms in the substrates end up in the product. - No protecting groups typically needed. - No catalysts sometimes needed (concerted thermal). - Mild conditions often (just heat or light).

These features make pericyclic reactions attractive for sustainable synthesis.

Examples

• Diels-Alder of biomass-derived dienes + dienophiles.
• Asymmetric DA with chiral organocatalysts (no metal).
• Photo-[2+2] using visible light + photoredox.

Modern developments

The combination of pericyclic chemistry with biocatalysis (Diels-Alderase enzymes) is an active research area. Engineered enzymes that catalyze [4+2] cycloadditions show promise for asymmetric synthesis.

39.42 The Schreiber and Sharpless connection

K.B. Sharpless's first Nobel (2001) was for asymmetric oxidation; his second Nobel (2022) was for click chemistry (CuAAC, a 1,3-dipolar cycloaddition).

Stuart Schreiber's work on diversity-oriented synthesis uses Diels-Alder for combinatorial libraries.

These prominent organic chemists exemplify the centrality of pericyclic chemistry in modern organic synthesis.

39.43 More about Diels-Alder regiochemistry

For substituted Diels-Alder reactions, the regiochemistry is predictable by FMO:

"Ortho" rule

For a 1-substituted diene + 1-substituted dienophile: - Like-with-like: the diene substituent ends up ortho to the dienophile substituent in the product cyclohexene. - This corresponds to the largest-coefficient atoms of the HOMO and LUMO matching.

"Para" rule

For a 2-substituted diene + 1-substituted dienophile: - The substituents end up para in the product cyclohexene. - Same rule (matching largest coefficients).

Examples

• Isoprene (2-methyl-1,3-butadiene) + methyl acrylate → 4-methylcyclohex-3-ene-1-carboxylate (para isomer dominant; not 5-methyl).

These rules let you predict the regiochemistry of asymmetric Diels-Alder.

39.44 The Hetero-DA in pharmaceutical synthesis

Hetero-Diels-Alder reactions (with heteroatoms in diene or dienophile) are widely used in drug synthesis:

Heteroaromatic synthesis

Pyridine, pyrimidine, isoquinoline, etc., can be made by hetero-DA.

Drug examples

• Paroxetine (antidepressant, Paxil): contains a piperidine ring built by hetero-DA.
• Modafinil (wakefulness drug): synthesis includes hetero-DA.
• Many other heterocyclic drugs.

The hetero-DA's stereospecificity makes it ideal for stereoselective drug synthesis.

39.45 Final overview

Pericyclic reactions are concerted, stereospecific transformations through cyclic TSs. The Woodward-Hoffmann rules and FMO theory unify them.

Three main classes: - Cycloadditions: two π systems → ring (Diels-Alder is the prototype). - Electrocyclic: one π system → ring (or ring → π system). - Sigmatropic: σ bond migration (Cope, Claisen).

Key features: - Concerted (no intermediate). - Stereospecific (substrate stereochemistry determines product stereochemistry). - Predictable from orbital symmetry (Woodward-Hoffmann). - Often thermally allowed for 4n+2 electrons; photochemically allowed for 4n.

Used widely in synthesis (Diels-Alder, Cope, Claisen are workhorses) and in biology (vitamin D, squalene cyclization).

The 1981 Nobel Prize was for Fukui and Hoffmann for their theories. Many subsequent Nobels (Sharpless 2001 + 2022) extend related chemistry.

Master pericyclic chemistry; predict stereochemistry; design syntheses.

Chapter 40 closes the textbook with green chemistry, flow chemistry, and the future of synthesis.

39.46 The closing thought

The mechanism-first thesis applies beautifully to pericyclic chemistry. Once you understand: - Cyclic TS geometry. - Orbital symmetry. - HOMO-LUMO interactions. - The Woodward-Hoffmann rule.

You can predict any pericyclic reaction's outcome. The chemistry is highly systematic; the rules are mathematically precise; the predictions are reliable.

This is one of the most beautifully systematic chapters in organic chemistry.

39.47 Final summary

Pericyclic reactions are concerted reactions through cyclic TSs. The Woodward-Hoffmann rules and FMO theory unify the prediction. The 1981 Nobel Prize recognized this work; many subsequent Nobel Prizes (2001, 2022) extend related chemistry.

These reactions are essential in modern synthesis: Diels-Alder for ring formation, Cope/Claisen for rearrangements, electrocyclic for ring closure, sigmatropic for σ bond migration. All stereospecific; all predictable.

Master the rules; design the chemistry. Pericyclic reactions are some of the most powerful tools in synthetic organic chemistry.

39.48 Summary

1. Pericyclic reactions are concerted reactions through a cyclic TS, with no intermediates or charges.
2. Three classes: cycloadditions, electrocyclic reactions, sigmatropic rearrangements.
3. Woodward-Hoffmann rules: orbital symmetry governs whether thermal or photochemical conditions are allowed.
4. Cycloadditions: - Thermal allowed: total electrons = 4n+2 (e.g., Diels-Alder [4+2] = 6 electrons). - Photochemical allowed: total electrons = 4n (e.g., [2+2] = 4 electrons).
5. Electrocyclic reactions: - 4n electrons: thermal conrotatory, photo disrotatory. - 4n+2 electrons: thermal disrotatory, photo conrotatory.
6. Sigmatropic rearrangements: a σ bond migrates within a π system. [3,3]: 6 electrons, thermal suprafacial-suprafacial.
7. Cope rearrangement [3,3] of 1,5-hexadiene; degenerate but stereoselective.
8. Claisen rearrangement [3,3] of allyl vinyl ether → γ,δ-unsaturated carbonyl. Key synthesis tool.
9. Nazarov cyclization: electrocyclic of divinyl ketone → cyclopentenone.
10. Aromatic TS view: thermal allowed pericyclic reactions have 4n+2 electrons in the cyclic TS (Hückel-like aromaticity).
11. FMO theory (Fukui): HOMO-LUMO interaction governs pericyclic reactivity.
12. Vitamin D photosynthesis is a 6π electrocyclic ring opening (photochemical conrotatory).
13. 1981 Nobel Prize: Fukui and Hoffmann (Woodward had passed). Recognized pericyclic chemistry.
14. Many total syntheses use pericyclic key steps: Diels-Alder, Claisen, Cope, photochemical [2+2].

Chapter 40 closes the textbook with green chemistry, flow chemistry, and the future of synthesis.