Woodward–Hoffmann rules template

Summary sheet: allowed modes for electrocyclic reactions (con/dis), cycloadditions and sigmatropic shifts (supra/antara), thermal and photochemical, with the Hückel HOMOs of butadiene and hexatriene that explain them.

What the template shows

• Which pericyclic reactions are allowed by heat (Δ) or by light (hν): count the electrons (4n or 4n + 2), then read off the mode
• Reaction Electrons Thermal (Δ) Photochemical (hν) Electrocyclic reactions 4n (4, 8 …) conrotatory disrotatory Electrocyclic reactions 4n + 2 (2, 6 …) disrotatory conrotatory Cycloadditions 4n + 2 ([4+2], [3+2]) supra–supra supra–antara Cycloadditions 4n ([2+2], [4+4]) supra–antara supra–supra Sigmatropic shifts 4n + 2 ([1,5]-H, [3,3]) supra–supra supra–antara Sigmatropic shifts 4n ([1,3]-H, [1,7]-H) supra–antara supra–supra
• Electrocyclic ring closure: the HOMO decides
• Δ (heat): HOMO ψ2
• termini out of phase → conrotatory
• hν (light): HOMO ψ3*
• termini in phase → disrotatory
• Δ (heat): HOMO ψ3
• hν (light): HOMO ψ4*
• * the photochemical HOMO is the ground-state LUMO, singly occupied after excitation. Blue and red lobes: the two phases of the p-orbital coefficients (Hückel).
• Worked examples: stereospecific ring closures
• 4π, heat: conrotatory → trans
• 6π, heat: disrotatory → cis
• General rule: a thermal pericyclic reaction is allowed when the number of (4q + 2)s and (4r)a components is odd; light reverses every entry.
• FMO shortcut for electrocyclisations: look at the terminal lobes of the HOMO. Same sign on the same face → disrotatory; opposite signs → conrotatory.
• Light promotes one electron, so the photochemical HOMO is one level higher (ψ3 for butadiene, ψ4 for hexatriene) and has the opposite terminal symmetry.
• Antarafacial components need a long or twisted π system: thermal [2+2] of alkenes is not seen, but ketenes ([π2s + π2a]) and [1,7]-H shifts work.

Drawn with 48 atoms, 7 arrows – every one editable in MolDraw.

Sources

• Clayden, Greeves & Warren, Organic Chemistry, 2nd ed., OUP 2012, ch. 34 Textbook
• Clayden, Greeves & Warren, Organic Chemistry, 2nd ed., OUP 2012, ch. 35 Textbook
• Fleming, Molecular Orbitals and Organic Chemical Reactions, Wiley 2010 Textbook