Q1(e). Thermal electrocyclisation of (2E,4Z,6E)-octa-2,4,6-triene

Introduction. The substrate is (2E,4Z,6E)-octa-2,4,6-triene. On heating, a conjugated triene closes to a cyclohexa-1,3-diene: a 6π electrocyclic reaction, which is pericyclic, concerted and stereospecific.

Scheme: Both methyl groups turn the same way (both outward), so they end up on the same face of the ring.

Figure: End lobes of ψ₃ (shaded = same phase) lie on the same face; they meet only if C2 and C7 rotate in opposite senses.

1. Type. Thermal 6π electrocyclic ring closure; a new σ bond forms between C2 and C7, and the three C=C become two.
2. Woodward–Hoffmann rule. In the ground state the HOMO of a hexatriene is ψ₃, whose end lobes have the same phase on the same face. They overlap only if the termini rotate in opposite senses: thermal 4n+2 electrocyclisation is disrotatory (4n+2 electrons, Hückel array, aromatic transition state).
3. Stereochemistry. In the (E,Z,E) triene the 4Z bond allows the s-cis,s-cis helical shape; both terminal methyls point outward. Disrotation turns both outward groups the same way, so they end up cis.
4. Product. cis-5,6-dimethylcyclohexa-1,3-diene (meso, the only product). The (2E,4Z,6Z) isomer would give the trans diene; photochemical (conrotatory) closure of the (E,Z,E) triene would also give trans.

Conclusion. The reaction is a thermal, concerted 6π electrocyclic ring closure that is disrotatory (allowed for 6 electrons under heat). (2E,4Z,6E)-Octa-2,4,6-triene gives cis-5,6-dimethylcyclohexa-1,3-diene stereospecifically.

Application. In skin, sunlight opens ring B of 7-dehydrocholesterol by a photochemical (conrotatory) 6π electrocyclic ring opening to previtamin D₃; a thermal [1,7]-hydrogen shift then gives vitamin D₃.