Molecular Orbitals in Diels-Alder and Other Cycloaddition Reactions
Practice
There are several ways the following triene can react with maleonitrile. Show the relevant HOMO and LUMO interactions to explain why the [6+2] cycloaddition is thermally forbidden but photochemically allowed.
Determine whether a [4+2] cycloaddition is thermally allowed, and draw the possible product of that reaction:

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Draw a curved-arrow mechanism to explain the following reaction and address all the relevant stereochemistry:

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Draw a curved-arrow mechanism for the following reaction:

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Explain why only one of the following reactions occurs under thermal conditions:

Both reactions are retro-Diels-Alder reactions, which are reverse cycloadditions. The important thing to remember is that the rules for regular cycloadditions, and pericyclic reactions in general, often apply to the reverse reactions as well.
If we look at these reactions retrosynthetically, we can treat them as 6-electron (4n + 2) reactions. Under thermal conditions, these reactions favor a suprafacial mechanism. Therefore, the reverse reactions should follow the same rules and proceed through a suprafacial transition state.
The cis isomer fits this requirement perfectly because the HOMO of the diene and the LUMO of the dienophile interact constructively:

However, the retro-Diels-Alder reaction of the trans isomer would require an antarafacial transition state to place the methyl group and hydrogen in a trans orientation. This pathway is symmetry-forbidden because the HOMO of the diene and the LUMO of the dienophile interact destructively. In addition, an antarafacial arrangement is geometrically difficult to achieve in a 4+2 cycloaddition:

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