An example is the conversion of trans-cis-trans-2,4,6-octatriene to cis-dimethylcyclohexadiene (top of figure). The orbital mechanics of the reaction needs a disrotatory mode. The orbital symmetry of the octatriene's highest occupied molecular orbital (HOMO) requires for the end pi orbitals to move in opposite directions to form the correct symmetry found in the sigma bond.
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