Bisectional bond

Symmetry elements used in the analysis must bisect bonds made or broken in the reaction. 

In non-simply connected transformations, it is not possible to construct the interaction diagram by the procedure of simple union of components at their ends. Processes of this type are nevertheless subject to analysis. Orbital correlation diagrams may still be constructed, using the symmetry or, if the symmetry does not offer sufficient guidance, as would be the case if no element bisects bonds being formed or broken, by tracing each individual orbital through the reaction in such a way as to preserve its nodal structure. 

Show that a correlation diagram for the v2s + n2s cycloaddition constructed by analysis with respect to either the C2 axis or the third mirror plane, neither of which bisect bonds made or broken, and by establishing correlations from the noncrossing rule leads to the incorrect conclusion that the reaction is allowed. How is the picture modified if correlation is established by preserving orbital nodal structure rather than by using the noncrossing rule ... 

Figure 11. Unit orthogonal base vectors a , a2, and a3 for local Cartesian coordinate system associated with chain interior atom / . Atoms / — 1,/ ,/ + 1 lie in ah a2 plane and a2 bisects bond angle 8. Also shown are bond vectors W1 and r 1.

Unlike Woodward and Hoffmann, Longuet-Higgins and Abrahamson do not specify that a symmetry element can be used only if it bisects bonds made or broken in the process. 

The orbital correlation diagram for the formation of cyclobutane from two ethylene molecules, using two perpendicular mirror planes as diagnostic symmetry elements, [1, p. 19] is too familiar to have to be reproduced. We recall that when the reactant molecules are set up in the coplanar [ 2s + 7r2s] orientation (Fig. 1.1b), other symmetry elements exist as well, including two rotational axes which also bisect bonds made or broken in the process [1, p. 31]. The use of these symmetry elements instead of the mirror planes is also more realistic, because cyclobutane is most stable in a puckered conformation [53], in which the rotational axes are retained but the mirror planes are not. 

The question posed in the preceding paragraphs as to the need for a reevaluation of the concept of allowedness , can be dismissed as a non-problem as long as it is taken as axiomatic that, for an orbital symmetry analysis to be of any use, the symmetry elements [retained along the pathway] must bisect bonds made or broken in the process . In contrast to the allowed conrotatory cyclization of butadiene to cyclobutene, in which the C2 axis bisects a newly formed cr bond, the only bond bisected by the axis in its conversion to bicyclobutane is the one between C2 and C3, which is essentially single in both the reactant and the product. 

---