In a series of publications starting in 1965, the American chemists Robert Woodward and Roald Hoffmann suggested a theory to predict the products obtained in certain concerted reactions. Their contributions became known as Woodward-Hoffmann rules which are applied especially to pericyclic reactions which include the reorganization of electron pairs within a chain of atomic orbitals. Here, the symmetry of the involved orbitals is of fundamental importance. An adiabatic path within the correlation diagram depicts the proceeding reaction. This path connects the orbital energies of reactants and products.
For instance, we present the cyclization of the reactant (1) cis-butadiene with four π-electrons towards the product (2) cyclobutene with two π- and two σ-electrons.
There are the cases of a conrotatory and a disrotatory mechanism. The first mechanism is characterized by terminal groups (CH2-groups in the case of butadiene) rotating in the same, the latter by rotation in different directions.
During the cyclization of a molecule which initially has one axis of rotation C2 and two mirror planes, it is possible that the number of symmetry elements is reduced.
The series of pictures on the right shows the intramolecular movements for a cyclization of butadiene as an example and the consequences with respect to symmetry
The intermediate states of this procedure are depicted in the Figure below. As well, the manner in which orbitals are involved is presented.
The paths for electronic transitions, the symmetry relations (A for antisymmetric, S for symmetric) between orbitals of the initial molecule and the cyclic product are illustrated in the next scheme.
The orbital correlation diagram below focusses on questions of electronic energy states for both mechanisms. In principle, orbitals of the butadiene molecule (in the middle) can rearrange via a conrotatory (left) or disrotatory (right) mechanism, thereby forming cyclobutene.
This correlation diagram suggests that the intermediate state for a conrotatory mechanism is of lower energy. Therefore, for reaction conditions with only small amounts of available energy, i.e. reactions where the activation energy is drawn from the reactants' thermal energy, we would expect a conrotatory mechanism. Thus, with these conditions and stereochemistry as point of view, the relation between reactants and products is well defined.
In contrast, the mechanism of a cyclization introduced by photonic energy involves an excited state with an electronic configuration