Woodward-Hoffmann rule

The Woodward–Hoffmann rules, devised by Robert Burns Woodward and Roald Hoffmann, are a set of rules in organic chemistry predicting the barrier heights of pericyclic reactions based upon conservation of orbital symmetry. The Woodward–Hoffmann rules can be applied to understand electrocyclic reactions, cycloadditions (including cheletropic reactions), sigmatropic reactions, and group transfer reactions. Reactions are classified as forbidden if there is an additional symmetry imposed energetic barrier arising from correlation of the ground state electronic configuration of the starting material with an excited state in the product. A reaction is classified as allowed if no such additional barrier exists. Thus, these terms do not imply whether a reaction in question will actually take place. Rather, with all other energetic factors being equal, an additional electronic factor exists to impede the symmetry forbidden reaction. Symmetry forbidden reactions can still take place via a pericyclic pathway if other factors (e.g. strain release) favor the reaction.

The Woodward–Hoffmann rules were first formulated to explain the striking stereospecificity of electrocyclic reactions under thermal and control. Thermolysis of the substituted cyclobutene trans-1,2,3,4-tetramethylcyclobutene (1) gave only one geometric isomer, the (E,E)-3,4-dimethyl-2,4-hexadiene (2) as shown below; the (Z,Z) and the (E,Z) geometric isomers were not detected in the product. Similarly, thermolysis of cis-1,2,3,4-tetramethylcyclobutene (3) gave only the (E,Z) geometric isomer (4).

Eventually, it was recognized that all thermally allowed pericyclic reactions obey one set of generalized selection rules, depending on the electron count and topology of the orbital interactions. The key concept involved is the faciality of the orbital interactions during the bond forming/breaking event. A set of contiguous atoms and their associated orbitals that react as one unit in a pericyclic reaction is known as a component, and each component is said to be antarafacial or suprafacial depending on whether the orbital lobes that interact during the reaction are on the opposite or same side of the nodal plane, respectively. Given these general definitions, the Woodward–Hoffmann rules can be stated succinctly as a single sentence:

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