The Generalised Woodward-Hoffmann Rule

We have now seen a large number of rules, expressed differently for each kind of pericyclic reaction. Learning them would seem to impose a considerable burden, but Woodward and Hoffmann saved us from this effort by rewriting them in one all-encompassing rule that applies to all thermal pericyclic reactions 20 

A ground-state pericyclic change is symmetry allowed when the total number of (Aq I 2), and (4r)a components is odd. 

This admirably concise statement is compelling, but we must now see what it means, and learn how to apply it to each of the classes of pericyclic reaction. 

The diene has four electrons, a number that can be expressed in the form (4r), with r = 1. Since the new bonds are forming on the diene in a suprafacial manner, both lines coming to the lower surface, the diene is a (4r)s component. The dienophile has two electrons, a number that can be expressed in the form (4q + 2), with q 0. Since the new bonds are forming on the dienophile in a suprafacial manner, both lines coming to the upper surface, the dienophile is a (Aq + 2)s component. Thus, the Diels-Alder reaction has one (4q + 2)s component and no (4r)a components. We ignore (4q + 2)a and (4r)s components, when there are any. The total number of (Aq + 2)s and (4r)a components is therefore 1, and, since this is an odd number, the reaction is symmetry-allowed. The Diels-Alder reaction is, as we have been calling it all along, a [4 + 2] cycloaddition. Since it takes place suprafacially on both components, it is more informatively described as a [4S+2S] cycloaddition, 

It is easy enough to see how to extend the labelling of cycloaddition reactions to those involving larger conjugated systems. As just one example, the cycloaddition of heptafulvalene to tetracyanoethylene has overlap developing on opposite sides of the 14-electron component, which is therefore a (4q + 2)a 

1 Cycloadditions. Let us begin with the bare bones of the Diels-Alder reaction in Fig. 6.6. The components of a cycloaddition are obvious enough—we have been using the word already to refer to the core electronic systems undergoing change. For a Diels-Alder reaction the components are the n orbitals of the 

In order to describe the ring opening of the aziridine 6.80, we need to define what suprafacial and antarafacial mean when applied to a p orbital. This is shown in Fig. 6.11, and applied there to the conrotatory aziridine opening. When both lines are drawn into the same lobe it is suprafacial, and when there is one line dawn into the top lobe and one into the bottom, it is antarafacial. Since this is neither a n nor a a orbital, it is given the Greek letter to. The same designations apply whether the orbital is filled (on the left) or unfilled (on the right), and whether it is a p orbital or any of the sp hybrids. 

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