# Lecture 22: Pericyclic Reactions Overview
## Organic Chemistry II
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## Learning Objectives
By the end of this lecture, students will be able to:
1. Define pericyclic reactions and identify their key features (concerted, cyclic transition state, no intermediates)
2. Classify the three major types of pericyclic reactions: electrocyclic, cycloaddition, and sigmatropic
3. Apply the Woodward-Hoffmann rules to predict whether a pericyclic reaction is thermally or photochemically allowed
4. Predict the stereochemical outcome of electrocyclic reactions (conrotatory vs. disrotatory)
5. Apply the rules for [4+2] and [2+2] cycloadditions (Diels-Alder and photocycloadditions)
6. Describe common sigmatropic rearrangements ([3,3] Cope and Claisen rearrangements)
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## Lecture Content
### I. What Are Pericyclic Reactions?
Pericyclic reactions are a distinctive class of concerted organic reactions that proceed through cyclic transition states without intermediates. No ionic or radical species are involved. Instead, bond breaking and bond formation occur simultaneously as electrons flow in a closed loop through the transition state. The feasibility and stereochemistry of these reactions are governed by orbital symmetry, as codified in the Woodward-Hoffmann rules, rather than by the nucleophile-electrophile interactions that dominate most other organic reactions.
Pericyclic reactions fall into three major categories. Electrocyclic reactions involve ring opening or ring closure of a single conjugated polyene. Cycloaddition reactions combine two unsaturated molecules to form a new ring. Sigmatropic rearrangements involve the migration of a sigma bond across a pi system. All three types are highly stereospecific: the stereochemical outcome is entirely determined by orbital symmetry and by whether the reaction is thermal or photochemical.
Frontier molecular orbital (FMO) theory provides the conceptual framework for understanding these reactions. The key interactions are between the HOMO of one component and the LUMO of the other, or, in the case of electrocyclic reactions, the symmetry properties of the HOMO alone.
### II. Molecular Orbital Review for Pericyclic Reactions
For a conjugated system of n p orbitals, there are n molecular orbitals. Energy increases with the number of nodes: psi-1 (zero nodes) is the lowest, and psi-n (n-1 nodes) is the highest. Electrons fill these orbitals from the bottom up.
The critical orbitals for pericyclic analysis are the HOMO and LUMO. Their symmetry, specifically the phase relationships at the terminal carbons, determines the reaction outcome. For ethylene (2 pi electrons), the HOMO is psi-1 (no nodes) and the LUMO is psi-2 (one node). For 1,3-butadiene (4 pi electrons), the HOMO is psi-2 (one node) and the LUMO is psi-3 (two nodes). For 1,3,5-hexatriene (6 pi electrons), the HOMO is psi-3 (two nodes) and the LUMO is psi-4 (three nodes).
Under photochemical conditions, absorption of light promotes an electron from the HOMO to the LUMO, making the former LUMO the new HOMO of the excited state. This changes the symmetry relationships at the terminal carbons and thereby reverses the stereochemical predictions.
### III. Electrocyclic Reactions
Electrocyclic reactions interconvert a conjugated polyene and a cyclic compound by forming (or breaking) a sigma bond between the terminal carbons. For example, 1,3-butadiene can close to cyclobutene (a 4-pi-electron system), and 1,3,5-hexatriene can close to 1,3-cyclohexadiene (a 6-pi-electron system). The reaction is concerted, meaning the terminal p orbitals must rotate to achieve the overlap needed for sigma bond formation.
The two possible modes of rotation are conrotatory (both terminal orbitals rotate in the same direction) and disrotatory (they rotate in opposite directions). The Woodward-Hoffmann rules dictate which mode operates. For systems with 4n pi electrons (such as butadiene, with 4 pi electrons), the thermal reaction is conrotatory and the photochemical reaction is disrotatory. For systems with 4n+2 pi electrons (such as hexatriene, with 6 pi electrons), the thermal reaction is disrotatory and the photochemical reaction is conrotatory.
The stereochemical consequences are absolute. For instance, conrotatory closure of a butadiene with trans,trans substituents at the termini produces a cyclobutene with trans substituents, while disrotatory closure of the same diene would give cis substituents. The mode of ring closure is not a matter of preference or selectivity; it is strictly determined by the number of pi electrons and the conditions.
A two-panel figure illustrating electrocyclic reactions. Panel A: The thermal electrocyclic ring closure of (E,Z)-2,4-hexadiene to form cis-3,4-dimethylcyclobutene via conrotatory rotation. The 4-pi-electron system is shown with terminal p orbitals rotating in the same direction (both clockwise or both counterclockwise). The HOMO (psi-2) of butadiene is drawn, showing that the terminal orbital lobes that must bond have the same phase on the same side only under conrotatory rotation. Panel B: The thermal electrocyclic ring closure of (E,Z,E)-2,4,6-octatriene to form cis-5,6-dimethyl-1,3-cyclohexadiene via disrotatory rotation. The 6-pi-electron HOMO (psi-3) is drawn, showing that the terminal lobes have the same phase for bonding under disrotatory rotation. A summary table at the bottom: 4n pi electrons -- thermal: conrotatory, photochemical: disrotatory; 4n+2 pi electrons -- thermal: disrotatory, photochemical: conrotatory. A caption reads: "The stereochemical outcome of electrocyclic reactions is determined by the number of pi electrons and the reaction conditions (thermal vs. photochemical)."
### IV. Cycloaddition Reactions
In a cycloaddition, two unsaturated molecules combine to form a new ring through the formation of two new sigma bonds. Cycloadditions are classified by the number of pi electrons each component contributes.
The Diels-Alder reaction is a [4+2] cycloaddition in which a conjugated diene (4 pi electrons) reacts with a dienophile (2 pi electrons) to form a cyclohexene. The total number of pi electrons in the cyclic transition state is six (4n+2 with n=1), making the reaction thermally allowed with suprafacial-suprafacial geometry, meaning both components react on the same face. The diene must be in the s-cis conformation, and the reaction is stereospecific: cis substituents on the dienophile remain cis in the product, and the endo rule (secondary orbital interactions stabilize the endo transition state) governs the facial selectivity in bicyclic products. Normal electron demand Diels-Alder reactions are accelerated by electron-donating groups on the diene and electron-withdrawing groups on the dienophile, though inverse electron demand variants also exist.
The [2+2] cycloaddition combines two alkenes to form a cyclobutane. With only four pi electrons in the cyclic transition state (4n with n=1), the suprafacial-suprafacial process is thermally forbidden by the Woodward-Hoffmann rules. However, it is photochemically allowed because UV excitation changes the orbital symmetry. Photochemical [2+2] cycloadditions are valuable for synthesizing strained four-membered rings.
### V. Sigmatropic Rearrangements
In a sigmatropic rearrangement, a sigma bond migrates from one position to another across a pi system, with simultaneous reorganization of the pi bonds. These reactions are classified as [i,j] shifts based on the positions from which the sigma bond migrates.
The [1,5]-hydrogen shift involves migration of a hydrogen atom from one end of a pentadienyl system to the other. The transition state involves six electrons (4n+2), making this a thermally allowed suprafacial process that occurs readily at moderate temperatures and is extremely common in organic chemistry.
Among [3,3]-sigmatropic rearrangements, the Cope rearrangement converts a 1,5-diene into an isomeric 1,5-diene through a chair-like, six-membered transition state. The substituent preferences in this chair-like transition state determine product stereochemistry. The oxy-Cope variant, starting from a 3-hydroxy-1,5-diene, produces a delta,epsilon-unsaturated carbonyl compound after rearrangement and tautomerization.
The Claisen rearrangement is the oxygen analog of the Cope rearrangement. An allyl vinyl ether rearranges thermally through a chair-like transition state to give a gamma,delta-unsaturated carbonyl compound. In the aromatic Claisen rearrangement, an allyl aryl ether is converted to an ortho-allylphenol via a cyclohexadienone intermediate. Both the Cope and Claisen rearrangements are thermally allowed [3,3] shifts.
A two-panel figure on cycloaddition and sigmatropic reactions. Panel A: The Diels-Alder reaction between 1,3-butadiene and ethylene, showing the diene in s-cis conformation, the suprafacial approach of both components, the six-membered cyclic transition state with curved arrows showing simultaneous bond formation, and the cyclohexene product. Below, a specific example: cyclopentadiene + maleic anhydride, with the endo and exo products drawn and the endo product labeled as the kinetically favored product. Panel B: The Claisen rearrangement of allyl vinyl ether. The starting material is drawn showing the allyl group attached to oxygen, which is part of a vinyl ether. The chair-like six-membered transition state is drawn with the [3,3] bond shift indicated by curved arrows. The product is a gamma,delta-unsaturated aldehyde (pentenal derivative). Below, the aromatic Claisen rearrangement of allyl phenyl ether to ortho-allylphenol is shown. A caption reads: "Cycloadditions form new rings from pi systems, while sigmatropic rearrangements migrate sigma bonds across pi frameworks -- both proceed through highly ordered cyclic transition states."
### VI. Woodward-Hoffmann Rules: Summary
The Woodward-Hoffmann rules predict the feasibility of pericyclic reactions based on the total number of pi electrons in the cyclic transition state and whether the reaction is thermal or photochemical. Systems with 4n+2 electrons (2, 6, 10, etc.) are thermally allowed in the suprafacial mode and photochemically forbidden. Systems with 4n electrons (4, 8, etc.) are thermally forbidden (suprafacial) but photochemically allowed.
These rules apply uniformly across all three reaction types. For electrocyclic reactions, one counts the pi electrons in the polyene. For cycloadditions, one counts the total pi electrons from both components. For sigmatropic rearrangements, one counts the electrons involved in the migrating bond and the pi system.
The rules arise from the conservation of orbital symmetry: for a concerted reaction to proceed, the symmetry of the reactant HOMO must match the symmetry required for bonding in the product. Pericyclic reactions are among the most elegant and predictable in all of organic chemistry, precisely because stereochemistry and feasibility are determined entirely by orbital symmetry considerations.
### VII. Biological Relevance of Pericyclic Reactions
Pericyclic reactions are not limited to the laboratory. In vitamin D biosynthesis, UV light triggers a photochemical electrocyclic ring opening of 7-dehydrocholesterol (provitamin D3) to form previtamin D3. A subsequent thermal [1,7]-sigmatropic hydrogen shift then converts previtamin D3 to vitamin D3 (cholecalciferol). In the shikimate pathway for aromatic amino acid biosynthesis, the enzyme chorismate mutase catalyzes the Claisen rearrangement ([3,3] shift) of chorismate to prephenate. These examples demonstrate that pericyclic reactions are essential for biological function, not merely laboratory curiosities.
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