Radical and Pericyclic Reactions
Anchor (Master): Carey and Sundberg, Advanced Organic Chemistry; Fleming, Pericyclic Reactions
Intuition [Beginner]
Most reactions you have studied proceed through ionic or polar mechanisms -- nucleophiles attack electrophiles, bonds break heterolytically, and charges move in pairs. Radical and pericyclic reactions break this pattern. Radicals are neutral species with a single unpaired electron. They react by moving single electrons rather than pairs. Pericyclic reactions are different again: they occur through a cyclic redistribution of bonding electrons in a single concerted step, with no intermediate at all.
Radical reactions are everywhere. Combustion is a radical chain reaction. The halogenation of alkanes proceeds through radicals. Polymerization of ethylene to make polyethylene is radical-initiated. Antioxidants work by intercepting radicals before they can damage biomolecules.
Pericyclic reactions are among the most elegant in all of organic chemistry. The Diels-Alder reaction builds six-membered rings in one step from a diene and a dienophile. Electrocyclic reactions open or close rings with precise stereochemical control. Sigmatropic rearrangements shift hydrogen atoms or groups across conjugated systems. What unites them all is the Woodward-Hoffmann rules, which predict which pericyclic reactions are allowed and which are forbidden, based purely on orbital symmetry.
Visual [Beginner]
Radical chain mechanism (chlorination of methane):
Initiation:
Cl-Cl --hv--> 2 Cl*
Propagation:
Cl* + CH4 --> HCl + *CH3
*CH3 + Cl2 --> CH3Cl + Cl*
(Cl* regenerated -- chain continues)
Termination:
Cl* + Cl* --> Cl2
*CH3 + Cl* --> CH3Cl
*CH3 + *CH3 --> CH3-CH3
Diels-Alder reaction (a [4+2] cycloaddition):
CH2 CH2
/ \ / \
CH2 CH2 + CH=CH2 --> CH CH--CH2-CH2
\ / \ /
CH2 CH
Frontier orbital picture:
Diene HOMO (4 pi electrons): Dienophile LUMO (2 pi electrons):
+ - + - - + (empty)
|_|_|_|_| |_|_|
Symmetry match: bonding interaction at both
new sigma bond-forming sites simultaneously.
This is a thermally allowed [4+2] cycloaddition
under the Woodward-Hoffmann rules.
Worked example [Beginner]
Problem: Predict the major monobromination product when propane is treated with Br2 under light. Explain the selectivity.
Solution:
The radical chain mechanism produces bromine radicals by homolysis of Br2. Propagation steps abstract a hydrogen from propane, generating a propyl radical, which then reacts with Br2 to form the alkyl bromide.
Propane has two types of hydrogen: primary (6H on the terminal carbons) and secondary (2H on the central carbon). The relevant bond dissociation energies and radical stabilities favor the secondary radical because it is more stable than the primary radical by hyperconjugation.
At 125 degrees C, the relative reactivity per hydrogen atom in bromination is approximately:
primary H : secondary H = 1 : 82
Expected product ratio:
1-bromopropane (primary): 6 x 1 = 6 2-bromopropane (secondary): 2 x 82 = 164
Fraction of 2-bromopropane = 164 / (6 + 164) = 0.965
2-bromopropane is the major product by a wide margin. Bromination is highly selective (unlike chlorination, which is much less selective because the chlorine radical is more reactive and less discriminating).
Check your understanding [Beginner]
Formal definition [Intermediate+]
Radical stability. Radical stability increases with substitution and delocalization:
methyl < primary < secondary < tertiary < allylic approximately equals benzylic
This order reflects hyperconjugation (for alkyl radicals) and resonance delocalization (for allylic and benzylic radicals). Bond dissociation energies (BDEs) quantify this: the C-H BDE for a tertiary carbon (~ 96 kcal/mol) is lower than for a primary carbon (~ 101 kcal/mol), meaning less energy is required to form the more stable radical.
Radical chain kinetics. For a chain reaction with initiation rate R_i, propagation rate constants k_p and k_p', and termination rate constant k_t, the steady-state rate of product formation is:
rate = k_p [R*] [substrate]
where [R*] is determined by the steady-state approximation:
d[R*]/dt = R_i - 2 k_t [R*]^2 = 0
giving [R*] = (R_i / 2 k_t)^(1/2). The chain length (propagations per initiation) is:
chain length = k_p [substrate] / (2 k_t R_i)^(1/2)
Pericyclic reaction classification. Pericyclic reactions are classified by the number of electrons involved and the topology of bond reorganization:
Cycloadditions [m+n]: Two components with m and n pi electrons combine to form a ring. The Diels-Alder reaction is a [4+2] cycloaddition. A [2+2] cycloaddition is thermally forbidden but photochemically allowed.
Electrocyclic reactions: A single conjugated system opens to or closes from a ring. The stereochemical outcome depends on whether the reaction is thermal or photochemical and on the number of pi electrons. For a thermal reaction with 4n pi electrons, ring closure is conrotatory; for 4n+2 pi electrons, it is disrotatory.
Sigmatropic rearrangements [m,n]: A sigma bond migrates across a conjugated system. The [3,3]-sigmatropic rearrangements (Cope and Claisen) are the most synthetically important.
Woodward-Hoffmann rules. A pericyclic reaction is thermally allowed if the total number of (4q+2) suprafacial components plus (4r) antarafacial components is odd. In practice:
- Thermal [4+2] cycloaddition (Diels-Alder): allowed (suprafacial on both components)
- Thermal [2+2] cycloaddition: forbidden (suprafacial-suprafacial); allowed if one component reacts antarafacially (geometrically difficult for small systems)
- Photochemical [2+2]: allowed (one component is excited, inverting the selection rule)
Frontier molecular orbital (FMO) analysis. The Woodward-Hoffmann rules can be understood through orbital symmetry conservation. In a Diels-Alder reaction, the HOMO of the diene and the LUMO of the dienophile have matching symmetry at both reacting termini, allowing constructive overlap and bond formation. For a thermal [2+2] reaction between two ethylenes, the HOMO-LUMO interactions have one bonding and one antibonding overlap, making the reaction symmetry-forbidden.
Key results [Intermediate+]
Hammond's postulate applied to radical selectivity. Hydrogen abstraction by a reactive radical (Cl*) has an early transition state resembling the reactants, so stability differences in the product radical barely affect the barrier. This is why chlorination is unselective. Bromination has a late transition state (Br* is less reactive), so radical stability strongly affects the barrier, giving high selectivity. This is a direct application of the Hammond postulate and the reactivity-selectivity principle.
Endo rule for Diels-Alder reactions. When the dienophile bears electron-withdrawing substituents, the endo transition state is favored over the exo. In the endo TS, secondary (non-bond-forming) orbital interactions between the diene and the dienophile substituents stabilize the TS. The endo product is the kinetic product; the exo is typically more thermodynamically stable. This is the Alder endo rule.
Cope rearrangement. The [3,3]-sigmatropic rearrangement of 1,5-dienes proceeds through a chair-like or boat-like transition state. The chair TS is favored by 5--6 kcal/mol. For 3,3-dimethyl-1,5-hexadiene, the rearrangement is degenerate (the product is identical to the reactant) and proceeds with Delta G double dagger approximately 33 kcal/mol, making it observable at 200--300 degrees C. Substituent effects can dramatically lower the barrier: oxy-Cope rearrangements (with an OH at C-3) proceed at much lower temperatures, especially when the OH is deprotonated (anionic oxy-Cope, rate acceleration of 10^17).
Electrocyclic ring opening of cyclobutenes. Cyclobutene opens to 1,3-butadiene in a conrotatory fashion under thermal conditions (4 pi electrons) and a disrotatory fashion under photochemical conditions. The stereochemical outcome is predicted by the Woodward-Hoffmann rules and confirmed experimentally: trans-3,4-dimethylcyclobutene gives (E,Z)-2,4-hexadiene thermally, not the (E,E) isomer.
Advanced treatment [Master]
Orbital correlation diagrams. The Woodward-Hoffmann rules were originally derived using orbital correlation diagrams. For a pericyclic reaction, the molecular orbitals of the reactants are correlated with those of the products, respecting the symmetry elements preserved through the reaction. If all occupied orbitals of the reactants correlate with occupied orbitals of the products, the reaction is symmetry-allowed. If an occupied orbital correlates with an unoccupied orbital (or vice versa), there is a symmetry-imposed barrier, and the reaction is thermally forbidden.
Aromatic transition state theory (Dewar-Zimmerman). An alternative formulation classifies the pericyclic transition state as aromatic or antiaromatic. A pericyclic TS with (4n+2) electrons in a Huckel topology (all suprafacial) or 4n electrons in a Mobius topology (one antarafacial component) is aromatic and stabilized. The reverse combination is antiaromatic and destabilized. This framework unifies cycloadditions, electrocyclic reactions, and sigmatropic rearrangements under a single principle.
Regioselectivity and stereoselectivity in Diels-Alder reactions. For unsymmetrical dienes and dienophiles, two regioisomeric products are possible ("ortho" and "meta" substitution patterns). FMO theory predicts the favored regioisomer: the larger coefficient on the diene HOMO pairs with the larger coefficient on the dienophile LUMO. Electron-donating groups on the diene raise its HOMO energy; electron-withdrawing groups on the dienophile lower its LUMO energy, accelerating normal-electron-demand Diels-Alder reactions. Inverse-electron-demand Diels-Alder reactions (electron-poor diene, electron-rich dienophile) proceed via diene LUMO-dienophile HOMO interaction.
Radical clocks. The rates of known radical rearrangements serve as internal clocks to measure the lifetime of radical intermediates. For example, the ring opening of the cyclopropylmethyl radical proceeds at k = 1.3 x 10^8 s^-1 at 25 degrees C. If a reaction produces this radical and it is trapped by a hydrogen atom donor faster than it rearranges, the radical lifetime is less than 10^-8 s. Radical clocks have been used to determine whether enzymatic C-H hydroxylation (by cytochrome P450) proceeds through a radical "oxygen rebound" mechanism or a concerted insertion. The observation of ring-opened products from cyclopropyl-containing substrates supports the radical pathway.
Persistent and stable radicals. Most radicals are transient, but steric protection or extensive delocalization can produce persistent (long-lived) or even stable radicals. TEMPO (2,2,6,6-tetramethylpiperidin-1-oxyl) is a stable nitroxyl radical used as a radical trap, a mediator in nitroxide-mediated polymerization (NMP), and a catalyst for selective alcohol oxidation (TEMPO oxidation). Galvinoxyl, verdazyl, and triphenylmethyl radicals are other examples. The stability of triphenylmethyl radical, discovered by Gomberg in 1900, established the existence of carbon-centered radicals.
Connections [Master]
Radical and pericyclic reactions intersect with many areas of chemistry:
Synthesis: The Diels-Alder reaction is one of the most powerful C-C bond-forming reactions in synthesis, used extensively in natural product total synthesis (e.g., Woodward's synthesis of reserpine, Corey's prostaglandin syntheses). The Claisen rearrangement reliably installs quaternary stereocenters. Radical reactions enable C-C bond formation under mild, neutral conditions that tolerate many functional groups.
Polymer chemistry: Radical polymerization accounts for the majority of commercial polymer production (polyethylene, poly(vinyl chloride), polystyrene). Controlled radical polymerization techniques (ATRP, RAFT, NMP) provide molecular weight control and narrow dispersities by maintaining a persistent radical that reversibly deactivates growing chains.
Biochemistry: Radical enzymes (ribonucleotide reductase, pyruvate formate-lyase, galactose oxidase) catalyze difficult transformations using transient organic radicals as cofactors. The adenosylcobalamin (vitamin B12) cofactor generates a 5'-deoxyadenosyl radical that initiates radical rearrangements. DNA damage by hydroxyl radicals (from ionizing radiation) produces strand breaks and base modifications.
Atmospheric chemistry: The hydroxyl radical (HO*) is the primary oxidant in the troposphere, initiating the degradation of most volatile organic compounds. Chlorine radicals from CFC photolysis catalyze ozone destruction in the stratosphere through the Chapman cycle and its radical chain extensions.
Materials science: Pericyclic reactions are used in photoresist chemistry for semiconductor lithography. Thermal [4+2] cycloadditions are exploited in self-healing polymers (embedded diene/dienophile pairs that react when cracks form). Click chemistry, though not strictly pericyclic, shares the conceptual simplicity of concerted, high-yielding bond formation.
Theoretical chemistry: The Woodward-Hoffmann rules were a triumph of molecular orbital theory and one of the first examples where theoretical analysis predicted a broad class of experimental outcomes. The 1981 Nobel Prize to Fukui and Hoffmann recognized this achievement. Modern computational chemistry can now predict pericyclic reaction barriers and selectivities with quantitative accuracy using DFT and coupled cluster methods.
Bibliography [Master]
Carey, F. A. and Sundberg, R. J. Advanced Organic Chemistry, 5th ed. Springer, 2007. Part A, Chapters 11--12 cover pericyclic reactions and radical chemistry in depth.
Fleming, I. Pericyclic Reactions. Oxford University Press, 1999. A concise, beautifully written monograph focused entirely on pericyclic reactions with clear FMO analysis throughout.
Clayden, J., Greeves, N., and Warren, S. Organic Chemistry, 2nd ed. Oxford University Press, 2012. Chapters 35--36 provide an excellent intermediate-level treatment of pericyclic and radical reactions with numerous synthetic examples.
Houk, K. N., Gonzalez, J., and Li, Y. "Pericyclic Reaction Transition States: Passions and Punctilios, 1935--1995." Accounts of Chemical Research 28 (1995): 81--90. A historical and conceptual review of computational studies on pericyclic TS geometries.
Curran, D. P. "Radical Cyclization and Organic Synthesis." In Comprehensive Organic Synthesis, Vol. 4, Pergamon, 1991. The definitive review of radical cyclization methodology in synthesis.