Correspondence diagram for -cycloaddition C

Assume that some sym-op 5 present in G is missing in H, and that G can be generated as the direct or semidirect product of H and the two-element group E, 5. In the reaction under consideration, G is that can be generated as the direct product of either or with which comprises the identity 

Since the number of MOs in G must be the same as that in H, only one of the two linear combinations can represent ipi in the higher group. The choice of the proper sign is made on the basis of a few simple rules, that ensure continuity of the phases of the occupied orbitals along the reaction path, and guarantee that the result is independent of the particular sym-op used as anasymmetrizer  

If an atomic orbital that is included in any occupied MO is transformed in the higher group to itself, or to an AO that was symmetrically equivalent to it before anasymmetrization, it cannot be allowed to vanish in all of the anasymmetrized MOs. (A particularly useful corollary is that no MO can be allowed to disappear completely on anasymmetrization). 

When two AOs centered on initially non-equivalent atoms become equivalent upon anasymmetrization, any MO in which they appear, V (H), and its mirror image , S ipi(fl) are combined once with a positive and once with a negative sign. 

An AO that participates in a bonding-antibonding combination cannot be allowed to appear in one but disappear from the other on anasymmetrization. 

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