7.3 Sigmatropic rearrangements

Types of Sigmatropic Rearrangements

A sigmatropic rearrangement is the migration of a σ bond across a conjugated π system in a concerted, pericyclic process. The notation [i,j] tells you which atoms the σ bond connects before and after the shift. These reactions are powerful because they reorganize carbon skeletons with high stereoselectivity and no intermediates.

[1,3] Sigmatropic Rearrangements

A [1,3] shift moves a σ bond across a 3-atom framework (one atom stays put, the bond migrates to the atom three positions away). For carbon, a thermal suprafacial [1,3] shift is symmetry-forbidden because it involves 4 electrons (one σ bond + one π bond) and would require inversion at the migrating carbon, which is geometrically impossible for most substrates.

• Hydrogen [1,3] shifts are thermally forbidden suprafacially (the H has no back lobe to allow antarafacial migration)
• Observed in heteroatom systems (O, N) where the barrier is lower
• Can become allowed under photochemical conditions

[1,5] Sigmatropic Rearrangements

The [1,5] shift is the most commonly encountered sigmatropic hydrogen migration. It involves 6 electrons (one σ bond + two π bonds), making it thermally allowed as a suprafacial process by the Woodward-Hoffmann rules.

• Proceeds through a 6-membered cyclic transition state, which keeps the activation energy manageable
• The classic example is the rapid [1,5]-H shift in cyclopentadiene, which scrambles the hydrogens at room temperature
• Important in terpene biosynthesis and vitamin D chemistry

[1,7] Sigmatropic Rearrangements

A [1,7] shift migrates a σ bond across a 7-atom system, involving 8 electrons (4n, where n = 2). Thermally, this shift is allowed antarafacially, which requires the π system to be long and flexible enough for the migrating group to reach the opposite face.

• Observed in extended polyene systems like heptatriene derivatives
• Less common than [1,5] shifts because the antarafacial geometry is demanding
• Can compete with electrocyclic ring closures in the same substrates

[3,3] Sigmatropic Rearrangements

These are among the most synthetically useful pericyclic reactions. Both ends of the breaking σ bond migrate, so two σ bonds break and two new ones form simultaneously. The reaction involves 6 electrons and proceeds through a 6-membered cyclic transition state.

• Includes the Cope rearrangement (1,5-dienes) and Claisen rearrangement (allyl vinyl ethers)
• Highly stereospecific because the chair-like transition state locks substituent geometry
• Widely used for constructing C–C bonds with predictable stereochemistry

Mechanism of Sigmatropic Rearrangements

All sigmatropic rearrangements share a concerted mechanism: bonds break and form in a single step with no intermediates. The key to predicting whether a given shift is allowed lies in orbital symmetry.

Concerted Electron Movement

Because these reactions are concerted, electrons flow in a cyclic loop through the transition state. There's no carbocation, carbanion, or radical intermediate at any point.

• You can draw curved arrows in a closed loop to track electron flow
• The lack of intermediates means lower activation energies compared to stepwise alternatives
• This concerted nature is directly responsible for the high stereoselectivity

Suprafacial vs. Antarafacial Shifts

These terms describe which face(s) of the π system the migrating group interacts with.

• Suprafacial: the bond breaks and reforms on the same face of the π system. Think of it as the migrating group sliding along one side. This is geometrically easy.
• Antarafacial: the bond breaks on one face and reforms on the opposite face. The migrating group must reach across the π system, which requires a long, flexible chain.

Whether a shift must be suprafacial or antarafacial to be symmetry-allowed depends on the electron count:

Orbital Symmetry Considerations

To determine if a sigmatropic shift is allowed, examine the HOMO of the π component. The migrating group must overlap constructively with both terminal lobes of the HOMO.

• For a [1,5]-H shift (6 electrons): the HOMO of the pentadienyl system ($\psi_3$) has the same phase at both ends on the same face → suprafacial shift is thermally allowed
• For a [1,3]-H shift (4 electrons): the HOMO ($\psi_2$) has opposite phases at the two ends on the same face → suprafacial shift is thermally forbidden
• Correlation diagrams plot how reactant orbitals connect to product orbitals; smooth correlations mean allowed, orbital crossings mean forbidden

Woodward-Hoffmann Rules

These rules, developed by Woodward and Hoffmann in the 1960s, provide a systematic way to predict whether a pericyclic reaction is thermally or photochemically allowed based on the total number of electrons involved.

Thermal Reactions

Thermal sigmatropic shifts occur from the ground-state electronic configuration. The selection rule for a suprafacial shift on all components:

• Allowed when the total electron count is $4n + 2$ (n = 0, 1, 2, ...)
• [1,5] shifts: 6 electrons → $4(1) + 2 = 6$ → thermally allowed (suprafacial)
• [3,3] shifts: 6 electrons → thermally allowed (suprafacial on both components)
• [1,3] shifts: 4 electrons → $4(1) = 4$ → thermally forbidden suprafacially

Photochemical Reactions

Photochemical conditions promote an electron to an excited state, effectively reversing the selection rules.

• Allowed when the total electron count is $4n$
• [1,3] shifts become photochemically allowed
• [1,5] shifts become photochemically forbidden
• Altered orbital symmetry in the excited state can open antarafacial pathways that are geometrically inaccessible thermally

Correlation Diagrams

These diagrams track how the symmetry labels of molecular orbitals in the reactant map onto those in the product.

1. Assign symmetry labels (symmetric/antisymmetric) to each MO of reactant and product with respect to a conserved symmetry element
2. Connect orbitals of the same symmetry, matching from lowest to highest energy
3. If bonding orbitals in the reactant connect smoothly to bonding orbitals in the product, the reaction is allowed
4. If a bonding orbital must correlate to an antibonding orbital, the reaction is forbidden (high activation barrier)

Cope Rearrangement

The Cope rearrangement is the [3,3] sigmatropic shift of a 1,5-diene. It's a reversible, all-carbon reaction that reaches thermodynamic equilibrium, favoring whichever diene is more substituted or less strained.

Mechanism and Stereochemistry

The reaction proceeds through a chair-like six-membered transition state (a boat-like TS is also possible but higher in energy).

• Substituents prefer pseudo-equatorial positions in the chair TS, just like in cyclohexane conformational analysis
• Both σ bond-breaking and σ bond-forming occur suprafacially
• The E/Z geometry of the starting diene directly determines the stereochemistry of the product

Synthetic Applications

• Rearranges carbon skeletons without requiring reactive intermediates or harsh reagents
• Generates new C–C bonds with defined stereochemistry
• Can form cyclohexene rings from acyclic 1,5-dienes (when tethered appropriately)
• Used in total syntheses of terpenes and steroids

Oxy-Cope Rearrangement

When a 1,5-dien-3-ol undergoes Cope rearrangement, the initial product is an enol that tautomerizes irreversibly to a carbonyl compound. This makes the reaction irreversible, unlike the standard Cope.

• The anionic oxy-Cope (deprotonation of the alcohol with KH or NaH before rearrangement) accelerates the reaction by a factor of $10^{10}$ to $10^{17}$
• Particularly useful for constructing medium-sized rings (8- to 10-membered) that are otherwise difficult to access
• The driving force is the formation of the stable C=O bond

Claisen Rearrangement

The Claisen rearrangement is the [3,3] sigmatropic shift of an allyl vinyl ether to produce a $\gamma,\delta$-unsaturated carbonyl compound. Because a C–O bond breaks and a C–C bond forms, this reaction is essentially irreversible and thermodynamically favorable.

Aliphatic Claisen Rearrangement

This is the classic version: an allyl vinyl ether rearranges through a chair-like transition state.

• Typically requires temperatures of 150–200°C
• The chair TS means you can predict E/Z and relative stereochemistry of the product from the geometry of the starting ether
• Useful for forming quaternary carbon centers, which are otherwise challenging to build

Aromatic Claisen Rearrangement

When the vinyl ether component is part of an aromatic ring (allyl aryl ether), the initial [3,3] shift produces a cyclohexadienone that quickly tautomerizes to an ortho-allylphenol.

• If the ortho position is blocked, a second [3,3] shift (Cope-type) moves the allyl group to the para position
• Historically used in the synthesis of natural phenols like eugenol
• Lewis acid catalysts (e.g., $\text{BCl}_3$, $\text{AlCl}_3$) can lower the required temperature significantly

Ireland-Claisen Rearrangement

This variant converts an allylic ester into a silyl ketene acetal using a base and a silyl chloride (e.g., LDA then $\text{TMSCl}$), which then undergoes [3,3] rearrangement at much lower temperatures.

1. Deprotonate the ester with LDA to form an enolate
2. Trap the enolate with $\text{TMSCl}$ to give the silyl ketene acetal
3. The [3,3] shift occurs, often at room temperature or mild heating
4. Hydrolysis gives a $\gamma,\delta$-unsaturated carboxylic acid

• The geometry of the enolate (E vs. Z, controlled by enolization conditions) determines product stereochemistry
• Widely used in complex molecule synthesis because of its mild conditions and stereochemical control

Other Important Rearrangements

Benzidine Rearrangement

This is a [5,5] sigmatropic rearrangement of hydrazobenzene (N,N'-diarylhydrazines) under acidic conditions to give 4,4'-diaminobiphenyls (benzidines).

• The mechanism involves double protonation followed by concerted N–N bond cleavage and C–C bond formation
• Historically important in dye manufacturing
• Unsymmetrical substrates can give mixtures of regioisomers

Sommelet-Hauser Rearrangement

A [2,3] sigmatropic rearrangement of benzylic ammonium ylides that places a new substituent ortho to the original benzylic position.

• Generated by treating quaternary benzylammonium salts with strong base (e.g., $\text{NaNH}_2$)
• Competes with the Stevens rearrangement ([1,2] shift), which gives a different product
• The Sommelet-Hauser pathway is generally favored at higher temperatures (kinetic vs. thermodynamic control)

Wittig Rearrangement

The [2,3]-Wittig rearrangement converts ethers into homoallylic alcohols via treatment with a strong base (typically an organolithium).

• The base generates a carbanion adjacent to oxygen, which undergoes a concerted [2,3] shift
• Produces alcohols with good stereocontrol
• The [1,2]-Wittig rearrangement (a competing pathway) is a stepwise radical process and gives different products

Stereochemistry in Sigmatropic Reactions

The concerted nature of sigmatropic rearrangements makes them inherently stereospecific. A single stereoisomer of starting material gives a single stereoisomer of product, provided you know the transition state geometry.

Retention vs. Inversion

At the migrating group, the stereochemical outcome depends on whether the shift is suprafacial or antarafacial at that center.

• Suprafacial migration at carbon → retention of configuration at the migrating group
• Antarafacial migration at carbon → inversion of configuration
• In [3,3] rearrangements (Cope, Claisen), both components undergo suprafacial shifts → overall retention

Chirality Transfer

Because these reactions are concerted, stereogenic centers in the starting material can be faithfully transferred to new positions in the product.

• A chiral allyl vinyl ether undergoing Claisen rearrangement produces a product whose new stereocenter has predictable absolute configuration
• This makes sigmatropic rearrangements valuable in asymmetric synthesis
• Chiral auxiliaries or catalysts can further enhance enantioselectivity

Stereospecificity

Stereospecificity means that each stereoisomer of starting material gives a different, specific stereoisomer of product. This is distinct from stereoselectivity (where one stereoisomer is simply preferred).

• The chair-like transition state of [3,3] shifts is the structural basis for this stereospecificity
• To predict the product: draw the starting material in the chair TS, place substituents equatorial where possible, and read off the product geometry
• This predictability is what makes these reactions so valuable for constructing molecules with multiple stereocenters

Synthetic Applications

Natural Product Synthesis

Sigmatropic rearrangements frequently appear as key steps in total synthesis because they build complexity quickly and with stereochemical precision.

• The Cope rearrangement has been used in syntheses of germacrane sesquiterpenes
• Claisen and Ireland-Claisen rearrangements feature prominently in prostaglandin and polyketide synthesis
• The oxy-Cope rearrangement was a key step in Paquette's synthesis of dodecahedrane precursors

Pharmaceutical Applications

Drug synthesis benefits from the stereocontrol these reactions provide.

• The Ireland-Claisen rearrangement is used in process chemistry to set stereocenters in anti-inflammatory and antiviral agents
• [3,3] shifts can construct the $\gamma,\delta$-unsaturated carbonyl motifs found in many bioactive molecules
• The mild conditions of modern variants (Ireland-Claisen, anionic oxy-Cope) make them compatible with sensitive functional groups

Materials Science

While less central than in pharmaceutical synthesis, sigmatropic rearrangements find use in materials chemistry.

• Cope rearrangements in fluxional molecules (e.g., bullvalene) create dynamic molecular systems
• Claisen-type rearrangements have been used to construct monomers for specialty polymers
• Photochromic materials sometimes exploit sigmatropic shifts for reversible structural changes

Computational Studies

Modern computational chemistry provides detailed pictures of sigmatropic transition states that complement experimental observations.

Transition State Modeling

Density functional theory (DFT) calculations can locate transition state geometries and predict activation barriers for sigmatropic shifts. These calculations confirm the chair-like preference in [3,3] shifts and quantify how substituents affect barrier heights.

Energy Profile Analysis

Mapping the potential energy surface reveals activation energies, reaction thermodynamics, and whether competing pathways (e.g., [1,5] shift vs. electrocyclic closure) are kinetically accessible. This is especially useful for systems where multiple pericyclic reactions compete.

Reaction Rate Predictions

Transition state theory, combined with computed barriers, allows estimation of reaction rates at different temperatures. This helps optimize conditions in synthesis and explains why some rearrangements (like the anionic oxy-Cope) are dramatically accelerated by seemingly small structural changes.