Woodward-Hoffmann rules alkene dimerization

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of alkenes to cyclobutanes (15-63) gives very poor results in most cases, except when photochemically induced. Woodward and Hoffmann, and Fukui have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, for example, mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three... 

Alkenes may undergo uncatalyzed dimerization which, according to the Woodward-Hoffmann rules, is nonconcerted. The salient feature is that the major products are often contrathermodynamic, e.g.,... 

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