page_title: Woodward–Hoffmann rules
section_title: Electrocyclic reactions
hierarchical_section_title: Woodward–Hoffmann rules / Correlation diagrams / Electrocyclic reactions
caption_attribution_description: English: First excited state of 1,3-butadiene
context_page_description: The Woodward–Hoffmann rules, devised by Robert Burns Woodward and Roald Hoffmann, are a set of rules used to rationalize or predict certain aspects of the stereochemistry and activation energy of pericyclic reactions, an important class of reactions in organic chemistry. The rules are best understood in terms of the concept of the conservation of orbital symmetry using orbital correlation diagrams, for which an elementary description is given in Section 10.4 of a student level text book. The Woodward–Hoffmann rules are a consequence of the changes in electronic structure that occur during a pericyclic reaction and are predicated on the phasing of the interacting molecular orbitals. They are applicable to all classes of pericyclic reactions, including electrocyclizations, cycloadditions, sigmatropic reactions, group transfer reactions, ene reactions, cheletropic reactions, and dyotropic reactions. Due to their elegance, simplicity, and generality, the Woodward–Hoffmann rules are credited with first exemplifying the power of molecular orbital theory to experimental chemists.
context_section_description: Considering the electrocyclic ring closure of the substituted 1,3-butadiene, the reaction can proceed through either a conrotatory or a disrotatory reaction mechanism.  As shown to the left, in the conrotatory transition state there is a C₂ axis of symmetry and in the disrotatory transition state there is a σ mirror plane of symmetry.  In order to correlate orbitals of the starting material and product, one must determine whether the molecular orbitals are symmetric or antisymmetric with respect to these symmetry elements. The π-system molecular orbitals of butadiene are shown to the right along with the symmetry element with which they are symmetric.  They are antisymmetric with respect to the other.  For example, Ψ₂ of 1,3-butadiene is symmetric with respect to 180ᵒ rotation about the C₂ axis, and antisymmetric with respect to reflection in the mirror plane.
  Ψ₁ and Ψ₃ are symmetric with respect to the mirror plane as the sign of the p-orbital lobes is preserved under the symmetry transformation.  Similarly, Ψ₁ and Ψ₃ are antisymmetric with respect to the C₂ axis as the rotation inverts the sign of the p-orbital lobes uniformly.  Conversely Ψ₂ and Ψ₄ are symmetric with respect to the C₂ axis and antisymmetric with respect to the σ mirror plane.
  The same analysis can be carried out for the molecular orbitals of cyclobutene.  The result of both symmetry operations on each of the MOs is shown to the left. As the σ and σ* orbitals lie entirely in the plane containing C₂ perpendicular to σ, they are uniformly symmetric and antisymmetric (respectively) to both symmetry elements.  On the other hand, π is symmetric with respect to reflection and antisymmetric with respect to rotation, while π* is antisymmetric with respect to reflection and symmetric with respect to rotation.
  Correlation lines are drawn to connect molecular orbitals in the starting material and the product that have the same symmetry with respect to the conserved symmetry element.  In the case of the conrotatory 4 electron electrocyclic ring closure of 1,3-butadiene, the lowest molecular orbital Ψ₁ is asymmetric (A) with respect to the C₂ axis.  So this molecular orbital is correlated with the π orbital of cyclobutene, the lowest energy orbital that is also (A) with respect to the C₂ axis.  Similarly, Ψ₂, which is symmetric (S) with respect to the C₂ axis, is correlated with σ of cyclobutene.  The final two correlations are between the antisymmetric (A) molecular orbitals Ψ₃ and σ*, and the symmetric (S) molecular orbitals Ψ₄ and π*.
  Similarly, there exists a correlation diagram for a disrotatory mechanism.  In this mechanism, the symmetry element that persists throughout the entire mechanism is the σ mirror plane of reflection.  Here the lowest energy MO Ψ₁ of 1,3-butadiene is symmetric with respect to the reflection plane, and as such correlates with the symmetric σ MO of cyclobutene.  Similarly the higher energy pair of symmetric molecular orbitals Ψ₃ and π correlate.  As for the asymmetric molecular orbitals, the lower energy pair Ψ₂ and π* form a correlation pair, as do Ψ₄ and σ*.
  Evaluating the two mechanisms, the conrotatory mechanism is predicted to have a lower barrier because it transforms the electrons from ground-state orbitals of the reactants (Ψ₁ and Ψ₂) into ground-state orbitals of the product (σ and π).  Conversely, the disrotatory mechanism forces the conversion of the Ψ₁ orbital into the σ orbital, and the Ψ₂ orbital into the π* orbital.  Thus the two electrons in the ground-state Ψ₂ orbital are transferred to an excited antibonding orbital, creating a doubly excited electronic state of the cyclobutene.  This would lead to a significantly higher transition state barrier to reaction.
  However, as reactions do not take place between disjointed molecular orbitals, but electronic states, the final analysis involves state correlation diagrams.  A state correlation diagram correlates the overall symmetry of electronic states in the starting material and product.  The ground state of 1,3-butadiene, as shown above, has 2 electrons in Ψ₁ and 2 electron
caption: First excited state (ES-1) of butadiene.
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