Organic Chemistry · Orbitals and Organic Chemistry: Pericyclic Reactions
Sigmatropic Rearrangements
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A Sigmatropic rearrangement Pericyclic reaction in which a σ bond migrates while π bonds reorganize Full entry → is a pericyclic reaction in which a σ bond migrates to a new position in a molecule while the π bonds shift to compensate — all in one concerted step, with no intermediate and no atoms lost or gained. The name comes from the Greek sigma (σ) and tropos ("turn"): literally, the σ bond turns to a new location.
The simplest example is a hydrogen shift: in 1,3-pentadiene, a hydrogen moves from carbon 1 to carbon 5 while the double bonds reorganize, converting the 1,3-diene into a 1,4-diene. The product has the same formula — the reaction is an isomerization. What makes these reactions remarkable is that they occur without charged or radical intermediates: electrons reorganize in a single cyclic transition state, exactly like the electrocyclic reactions and cycloadditions of Topics 2–6. Whether a shift is allowed thermally or photochemically is governed by orbital symmetry — the Woodward–Hoffmann rules.
Why this matters
- They complete the pericyclic trilogy. Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are the three great pericyclic classes; understanding sigmatropic shifts ties the chapter together and is routinely tested.
- They explain surprising product structures. A simple diene heated gently rearranges into a different diene with the same formula — inexplicable by classical carbocation or radical mechanisms.
- They are central in biology and synthesis. The [3,3]-sigmatropic (Cope and Claisen) rearrangements build carbon–carbon bonds and set stereochemistry in natural-product synthesis; a biological [1,7]-hydrogen shift is a key step in the body's synthesis of vitamin D from sunlight.
- Orbital symmetry decides "allowed" vs "forbidden." Predicting whether a shift needs heat or light, and what stereochemistry results, is a classic exam problem that rewards a small set of counting rules.
The college version
Core Concepts
The [i,j] notation
Sigmatropic rearrangements are named by counting the atoms on each side of the migrating σ bond: the numbers in brackets give how many atoms lie in the chain on each side. A [1,5]-hydrogen shift H migrates along a five-atom chain, suprafacially Full entry → means the hydrogen (one atom) migrates along a chain of five atoms; a [3,3] shift (the Cope and Claisen rearrangements) means a σ bond between atoms 3 and 3' migrates. Both have six-electron, six-membered-ring-like transition states, and both are thermally allowed.
Hydrogen shifts: [1,3] versus [1,5]
The most-studied sigmatropic reactions are hydrogen migrations in conjugated dienes and trienes. In a [1,5]-hydrogen shift, a hydrogen moves from one end of a pentadienyl system to the other (from carbon 1 to carbon 5), with the two double bonds reorganizing. This shift is thermally allowed and occurs at moderate temperatures. In a [1,3]-hydrogen shift H migrates along a three-atom chain Full entry →, the hydrogen would migrate only three atoms along the chain. This shift is thermally forbidden by orbital symmetry — it requires light. So a 1,3-diene heated alone does not isomerize by a [1,3] shift; it needs photochemical activation or a different mechanism.
Why symmetry forbids the [1,3] shift
The migrating hydrogen's 1s orbital and the π system of the chain must overlap in the transition state. For a [1,3] shift, matching the phases of the orbitals requires the hydrogen to approach the π system from opposite faces at the two ends — an antarafacial process — which is geometrically impossible for a small, nearly linear chain. For a [1,5] shift, the phases match with the hydrogen staying on the same face (suprafacial), which is easy to achieve. In Woodward–Hoffmann terms: suprafacial [1,3] is forbidden; suprafacial [1,5] is allowed. Light promotes an electron to a higher orbital that changes the symmetry, making even the [1,3] shift allowed photochemically.
Carbon migrations and stereochemistry
When the migrating group is a carbon (not hydrogen), the reaction can proceed with either retention or inversion of configuration at the migrating carbon, depending on which face of the chain the group departs from and arrives at. For example, a [1,3]-alkyl shift that is suprafacial with inversion, or antarafacial with retention, is thermally allowed — the stereochemical outcome is a fingerprint of the mechanism. This is why textbooks draw the migrating group with a wedge or dash: the stereochemistry carries information.
The [3,3] shift: Cope and Claisen
The [3,3]-sigmatropic rearrangement of a 1,5-diene (the Cope rearrangement [3,3] shift of a 1,5-diene Full entry →) and of an allyl vinyl ether (the Claisen rearrangement [3,3] shift of an allyl vinyl ether to a carbonyl compound Full entry →) are the workhorses of this reaction class. Both proceed through a six-membered, chair-like transition state, are thermally allowed, and are covered in detail in Topic 8. The key point here is that a [3,3] shift is symmetry-allowed under heat because its transition state has six electrons — exactly the 4n + 2 count that the Woodward–Hoffmann rules favor.
Conformational control: the chair transition state
Because the [3,3] transition state is chair-like, the stereochemistry of the starting material is carried faithfully into the product. Substituents that can occupy equatorial positions in the transition state do so, which is why the Cope and Claisen rearrangements are prized for making single stereoisomers.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| [1,5]-H shift | [1,3]-H shift | [1,5] is thermally allowed (6 electrons); [1,3] is thermally forbidden (4 electrons) — a top exam trap |
| Sigmatropic rearrangement | Cycloaddition | Sigmatropic = one molecule, σ bond migrates, isomerization; cycloaddition = two molecules join to form a ring (Topic 5) |
| [3,3] shift (Cope) | [1,3] shift | [3,3] = six-electron, chair transition state, thermally allowed; [1,3] = four-electron, forbidden — the similar-looking numbers are easy to mix up |
| Isomerization | Fragmentation | Sigmatropic shifts change connectivity but keep the formula; they do not split the molecule or lose atoms |
| Retention | Inversion | Both describe configuration at the migrating carbon; the allowed combination depends on topology (suprafacial vs antarafacial) |
Eli explains
The same idea, in plain words
Explain it like I’m 10
A sigmatropic rearrangement is like a game of musical chairs for a molecule: one atom's "seat belt" (the σ bond) unbuckles and clicks onto a new seat at the other end of the molecule, while the double bonds shuffle one step over to keep everything connected. It all happens in one smooth motion — no one gets off the bus.
Worked example
Example 1: Classifying a shift and predicting the condition
Problem. 1,3-Pentadiene is treated with heat alone. A product with the same formula is observed. Identify the reaction type, the shift designation, and why heat works.
Step 1 — Identify the reaction. The formula is unchanged, so this is an isomerization, not an addition or elimination. The hydrogen has moved from carbon 1 to carbon 5.
Step 2 — Count the shift. One atom (H) migrates along a five-atom chain: a [1,5]-hydrogen shift.
Step 3 — Apply the selection rule. A [1,5] shift has six electrons in its transition state (4n + 2 with n = 1), so it is thermally allowed suprafacially. Heat suffices.
Answer. A [1,5]-sigmatropic hydrogen shift; thermally allowed; the product is the isomeric 1,4-pentadiene.
Example 2: Why the [1,3] shift needs light
Problem. Predict whether heating a 1,3-diene can cause a [1,3]-hydrogen shift, and state what condition would make it occur.
Step 1 — Count electrons in the transition state. A [1,3] shift involves the two π bonds of the chain plus the migrating H's orbital — four electrons in the cyclic array (4n with n = 1).
Step 2 — Apply the rule. Four-electron pericyclic processes are thermally forbidden; the suprafacial [1,3] path is disallowed in the ground state.
Step 3 — The fix. Photoexcitation moves an electron into a higher orbital, changing the symmetry of the highest occupied orbital so that the suprafacial path becomes allowed.
Answer. No — heating alone will not promote the [1,3] shift; photochemical excitation is required.
Example 3: Reading stereochemistry from a carbon shift
Problem. A chiral migrating group undergoes a thermal [1,3]-alkyl shift with suprafacial topology. Should the migrating carbon retain or invert configuration?
Step 1 — Recall the rule. For carbon migrations, a thermally allowed [1,3] shift is suprafacial with inversion (or antarafacial with retention).
Step 2 — Apply. The problem specifies suprafacial topology, so the allowed partner is inversion.
Answer. The migrating carbon inverts configuration. If the product shows retention instead, the mechanism must be different (e.g., radical) — a classic diagnostic.
Key takeaways
- Sigmatropic rearrangement = σ bond migrates, π bonds shift, one concerted step, no intermediates, isomerization (same molecular formula).
- Notation [i,j] counts atoms on each side of the migrating bond: [1,3], [1,5], [1,7], [3,3], etc.
- Thermally allowed: suprafacial [1,5]-H shift (six electrons) and [3,3] shifts (six electrons, chair transition state).
- Thermally forbidden / photochemically allowed: suprafacial [1,3]-H shift (four electrons).
- Hydrogen migrates suprafacially (same face) in allowed thermal shifts; an antarafacial component is needed for the forbidden cases and is geometrically hard for small systems.
- Carbon migrations may occur with retention or inversion of configuration — the stereochemical outcome is mechanistically informative.
- The Cope ([3,3] of a 1,5-diene) and Claisen ([3,3] of an allyl vinyl ether) rearrangements are the synthetically important examples (Topic 8).
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
What is the defining feature of a sigmatropic rearrangement? What is conserved in the reaction?
Show answer
A σ bond migrates to a new position while π bonds reorganize, in one concerted step with no intermediate; the molecular formula is conserved (an isomerization).
Write the [i,j] designation for a hydrogen shift along a five-atom chain and state whether it is thermally allowed.
Show answer
[1,5]-hydrogen shift; yes, thermally allowed (six-electron, suprafacial).
Why is the suprafacial [1,3]-hydrogen shift forbidden by heat but allowed by light?
Show answer
The suprafacial [1,3] path has four electrons in its transition state (4n count), which orbital symmetry forbids in the ground state; photoexcitation changes the frontier-orbital symmetry and makes it allowed.
Name the two famous [3,3] rearrangements and the functional group each starts from.
Show answer
The Cope rearrangement (1,5-diene) and the Claisen rearrangement (allyl vinyl ether).
In a thermal [1,3]-alkyl shift with suprafacial topology, does the migrating carbon retain or invert configuration?
Show answer
Inversion (suprafacial-with-inversion is the thermally allowed combination; retention would require antarafacial topology).
What shape is the [3,3] transition state, and why does that matter for stereochemistry?
Show answer
A chair-like six-membered transition state; it constrains substituents to favorable equatorial positions and carries starting-material stereochemistry into the product.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Sigmatropic rearrangement
- Pericyclic reaction in which a σ bond migrates while π bonds reorganize
- [1,5]-hydrogen shift
- H migrates along a five-atom chain, suprafacially
- [1,3]-hydrogen shift
- H migrates along a three-atom chain
- Suprafacial / antarafacial
- New bonds form on the same face / opposite faces of the π system
- Cope rearrangement
- [3,3] shift of a 1,5-diene
- Claisen rearrangement
- [3,3] shift of an allyl vinyl ether to a carbonyl compound
Sources & references
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