Example 2 Square-Planar Cyclobutadiene D

In D4/1, / 3 and (j)2 are degenerate like x and y they belong to the doubly degenerate irrep Eg. The four space functions that can be formed from them have therefore to be assigned to irreps included in the direct product Eg Eg, which is evaluated in Table 9.1. 

These are evidently the four one-dimensional irreps that are symmetric with respect to E, C2, i and one of the four space functions is assigned to each of them. 

As in rectangular CBD, the three space functions that are symmetric to electron interchange are assigned to the singlet and that changes its 

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