Woodward Hoffmann Rules
Table of Contents
The Woodward–Hoffmann rules are a set of principles in organic chemistry that help predict the outcomes of pericyclic reactions. These rules allow chemists to determine whether a reaction is allowed or forbidden under thermal or photochemical conditions, based on how electrons move during the process. The rules focus on the symmetry properties of molecular orbitals and the number of π electrons involved. This approach provides a reliable framework for predicting reaction outcomes without relying on trial and error: [1-4]
| Condition | Symmetry-Allowed When |
|---|---|
| Thermal Pericyclic Reaction | The sum of (4q + 2) suprafacial (s) and (4r) antarafacial (a) components is odd |
| Photochemical Pericyclic Reaction | The sum of (4q + 2) suprafacial (s) and (4r) antarafacial (a) components is even |
Where
- q and r are integers (0, 1, 2, …)
- Suprafacial: Orbital interactions occur on the same face of the molecule
- Antarafacial: Orbital interactions occur on opposite faces of the molecule
The rules were developed in the 1960s by Robert Burns Woodward, a Nobel Prize-winning synthetic chemist, and Roald Hoffmann, a theoretical chemist who later won the Nobel Prize in Chemistry in 1981. Their work revolutionized how chemists understand and predict the behavior of pericyclic reactions.
Let us explore how the Woodward–Hoffmann rules apply to different types of pericyclic reactions.
Applying the Woodward–Hoffmann Rules [1-4]
1. Electrocyclic Reactions
Electrocyclic reactions involve the interconversion between a linear conjugated system and a cyclic compound. A key question in these reactions is how the terminal ends of the molecule rotate during bond formation or breaking—whether they rotate in the same direction (conrotatory) or in opposite directions (disrotatory). According to the Woodward–Hoffmann rules:
- For systems with (4n) π electrons, thermal reactions proceed via conrotatory motion.
- For systems with (4n + 2) π electrons, thermal reactions proceed via disrotatory motion.
For example, the thermal ring closure of hexatriene (6 π electrons) to cyclohexadiene proceeds via a disrotatory pathway. In contrast, the thermal ring opening of cyclobutene (4 π electrons) to butadiene follows a conrotatory mechanism.
2. Cycloaddition Reactions
Cycloaddition reactions involve the formation of cyclic products by combining two or more unsaturated molecules. The Woodward–Hoffmann rules predict:
- [4+2] cycloadditions (like the Diels–Alder reaction) are allowed under thermal conditions because they involve (4n + 2) π electrons.
- [2+2] cycloadditions are forbidden thermally but allowed under photochemical conditions, where electronic configurations change in the excited state.
A classic example is the formation of cyclobutanes from alkenes using light instead of heat.
3. Sigmatropic Rearrangements
Sigmatropic rearrangements involve the shift of a σ-bonded atom or group across a π-system. Common examples include [1,5]-sigmatropic and [3,3]-sigmatropic rearrangements, such as the Cope and Claisen reactions.
According to the Woodward–Hoffmann rules:
- The [3,3]-sigmatropic rearrangement is thermally allowed because it involves a (4n + 2) π electron system.
- The [1,5]-sigmatropic rearrangement also typically proceeds thermally, following similar symmetry considerations.
By applying Woodward–Hoffmanns, it saves time in experimental design and highlights the power of molecular orbital theory in controlling chemical reactivity.
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