Woodward-Hoffmann Rules and Topology

The continuing progress of the theory of pericyclic reactions made it, however, still more apparent that irrespective of its nondisputable conceptual contribution, neither is the technique of the correlation diagrams able to explain all types of reactions [29,30]. The example of the situation where this technique encounters with certain difficulties are, e.g., the valence isomerizations. These difficulties are due to specific form of the correlation diagrams where both the HOMO and the LUMO are frequently of the same symmetry so that it is not possible to decide on the basis of symmetry only, which of the possible alternative correlations are in a given case correct. 

The situations of this type are not, fortunately, very frequent for thermal reactions (e.g. the benzene to benzvalene or cyclooktatetraene to cubane transformations), but in photochemistry are quite common. For the analysis of these reactions the concept of the so-called natural correlation diagrams was introduced [31]. The construction of these diagrams is not, however, so straightforward as the construction of the 

---