Woodward-Hoffmann rules
/ WOOD-werd HOFF-man /
For a long time, pericyclic reactions were baffling: some happened readily with heat, some only with light, and the stereochemistry seemed mysteriously precise. The Woodward-Hoffmann rules cracked the mystery. They state that pericyclic reactions are governed by the symmetry of the molecular orbitals involved — a reaction is 'allowed' (fast, clean, stereospecific) only when the orbitals can overlap with matching symmetry as the bonds reorganize, and 'forbidden' (won't go that way) when the symmetry clashes.
The intuitive version is the frontier-orbital picture. Look at the highest occupied molecular orbital (the HOMO) of one partner and the lowest unoccupied (the LUMO) of the other, or the relevant frontier orbital of a reacting system. If the lobes that need to come together happen to have the same sign (the same phase) where the new bonds form, they overlap constructively and the reaction is allowed; if they have opposite signs, overlap is destructive and that pathway is forbidden. Crucially, light changes the answer: absorbing a photon promotes an electron to a different orbital with different symmetry, so a reaction forbidden under heat can become allowed under light, and vice versa. The whole pattern boils down to simple counting rules tied to the number of electrons and whether the conditions are thermal or photochemical.
These rules are one of the great triumphs of theoretical organic chemistry. They explain, in advance and without exception, why a four-pi-electron electrocyclic ring closure is conrotatory under heat but disrotatory under light, why the Diels-Alder (a six-electron process) sails along thermally, and the stereochemistry of countless sigmatropic shifts. Robert Woodward and Roald Hoffmann developed them in the 1960s, and Hoffmann shared the 1981 Nobel Prize for the underlying theory (Woodward had died by then; Nobel Prizes are not awarded posthumously). They turned pericyclic reactivity from a collection of curiosities into a predictable, unified subject.
The rules predict, with no exceptions, that a thermal Diels-Alder ([4+2], six electrons) is allowed and runs smoothly on heating, whereas the analogous thermal [2+2] cycloaddition of two simple alkenes (four electrons) is forbidden — which is exactly why [2+2] reactions instead need light.
Orbital symmetry, not just energy, decides which pericyclic reactions go and under heat versus light.
'Forbidden' does not mean the molecules cannot react at all — it means they cannot react by that concerted pericyclic pathway; a forbidden reaction may still occur slowly by a different, stepwise mechanism (through a radical or ion), which is not pericyclic and is not stereospecific.