Correlation and correspondence diagram for dimerization of methylene

Scrutinizing Fig. 4.7 more carefully, we see that the cause of the forbiddenness is the refusal of to correlate with 7r(62ti)- How should the symmetry 

We note that the character of E and cr xy) is 1 in both B2u and whereas that of C2 z) and i is —1 in both irreps. The characters of all the other symmetry elements differ in the two representations when it is 1 in the first it is —1 in the second, and vice versa. It follows that if only the four elements E, C2 z), i, a.nda xy) are retained - that is, if the symmetry along the reaction path is reduced from D2/1 to in which the two recalcitrant orbitals have the same representation by) - the electron configuration of the reactant pair of singlet carbenes will correlate with that of the product ethylene, and the previously forbidden dimerization will have become allowed. 

We recognize that a perturbation that permits a b2u and a bzu orbital to intercorrelate has the same irrep as their direct product. Just as in Equation 2.11. 

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Figure 4.7. Correlation (and correspondence) diagram for dimerization of Methylene (D2/1). (The meaning of the circled b g and the distinction between correlation and correspondence are explained in the text)...

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