Rudimentary correspondence diagram for cyclization of butadiene

At this level of analysis, it is sufEcient to include in Fig. 5.1 the doubly-occupied MOs that appear in Fig. 19 of Reference [1] xi. nd X2 of butadiene and a and 7T of cyclobutene. The latter molecule has C2v symmetry, so the former is put into the same symmetry point group by adopting the s-cis conformation, on the reasonable assumption that the attainment of conformational equilibrium is a much faster process than cyclization. Xi and tt have the same irrep (6i), so they remain in correlation whether C y symmetry is retained or not. However, in order to deliver a pair of electrons from X2(fl2) to the reaction has 

Only two sym-ops, E and 6 2(2 ), have the character 1 in A2] therefore, the reaction will become allowed if the pathway is desymmetrized to C2, the kernel of A2, in which A and A2 both map onto the same irrep (A). The conrotatory pathway, along which the two sym-ops that comprise C are the only ones retained, is therefore selected. 

In analogy with Equation 4.1, the pathway must be displaced away from C y along a symmetry coordinate of the same irrep as the direct product of the irreps of the two orbitals between which the correspondence has to be induced  

The reaction coordinate along the allowed pathway must therefore include, in addition to totally symmetric displacements, such as decreasing the C1C4 distance and shortening the C2C3 bond, at least one 02 symmetry coordinate Conrotation of the methylene groups evidently fulfills this requirement. 

Any 02 displacement desymmetrizes the pathway to so the two ways of reading the Character Table are completely equivalent their common conclusion is symbolized in Fig. 5.1, as in Fig. 4.7, by a two-headed arrow - here labeled U2- It indicates that the reaction, which is forbidden in C yj is made allowed by an induced correspondence between the non-correlating orbitals of the reactant (02) and product (ai) that is produced when the pathway is desymmetrized to C2 by a conrotation (02). 

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Figure 5.1. Rudimentary correspondence diagram for cyclization of Butadiene. (The orbitals are labeled as in Fig. 19 of ref. [1] their irreps in are given in parenthesis)...

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