Woodward–Hoffmann rules

The Woodward–Hoffmann rules predict whether concerted pericyclic reactions are symmetry-allowed and what stereochemical outcomes they produce, using conservation of orbital symmetry.

Orbital symmetry: The symmetry properties of molecular orbitals under specified spatial operations. The rules track how orbital symmetry is conserved as bonds form and break.
Pericyclic reaction: A concerted reaction whose bonding changes occur through a cyclic arrangement of interacting orbitals. The rules apply to this family of concerted reactions rather than to reactions generally.
Robert Burns Woodward: An American organic chemist known for complex natural-product synthesis and contributions to theoretical organic chemistry. Woodward formulated the empirical reaction patterns that the rules systematized.
Electrocyclic ring opening: An electrocyclic reaction that opens a ring by breaking a sigma bond and forming a conjugated system. The rules predict whether terminal groups rotate conrotatorily or disrotatorily during opening.
Thermodynamic control: Reaction selectivity determined by the relative stability of products under reversible or equilibrating conditions. Symmetry allowance concerns pathway feasibility, not which product is most stable at equilibrium.
Electrocyclic reaction: A pericyclic reaction in which a conjugated system forms or breaks a sigma bond at its termini. Electrocyclic reactions provide the clearest cases of orbital-symmetry control over stereochemistry.
Molecular orbital: A wavefunction describing an electron in a molecule, distributed over one or more atoms. Orbital symmetry is defined from the shapes and phases of molecular orbitals.
Roald Hoffmann: A Polish-American theoretical chemist who developed influential methods for understanding molecular structure and reactivity. Hoffmann supplied orbital-symmetry analysis that helped establish the rules.
Diels–Alder reaction: A [4+2] cycloaddition between a conjugated diene and a dienophile that forms a six-membered ring. Its thermal allowedness and stereospecificity are classic applications of cycloaddition selection rules.
Kinetic control: Reaction selectivity determined by differences in activation barriers among competing pathways. The rules do not replace barrier comparisons when multiple symmetry-allowed pathways compete.

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