Q1(e). Electrocyclic closure of (2E,4E)-hexa-2,4-diene: FMO

Reading of the question: the diene is printed s-cis with both double bonds E, i.e. (2E,4E)-hexa-2,4-diene; each side gives a 3,4-dimethylcyclobutene.

Introduction. Ring closure of a 1,3-diene to a cyclobutene is a 4π electrocyclic reaction. In the FMO method the stereochemistry is decided by the symmetry of the HOMO at the two termini (C-2 and C-5 here): the termini rotate so that lobes of the same phase overlap to form the new σ bond.

Figure: Terminal lobes of the HOMO: shaded and open lobes have opposite phase.

1. Thermal (Δ). Ground-state HOMO of butadiene is ψ₂: the terminal lobes on the same face have opposite phase. Bonding overlap needs both termini to turn the same way: conrotatory. In the (E,E) diene both methyls point outward; one turns up and one down, so they end on opposite faces: trans-3,4-dimethylcyclobutene.
2. Photochemical (hν). One electron is promoted, the HOMO is ψ₃; its terminal lobes on the same face have the same phase. Closure is disrotatory: one methyl turns up, the other also up relative to the ring plane, giving cis-3,4-dimethylcyclobutene.
3. Both are reversible as printed. Thermally the equilibrium lies on the diene side (ring strain), so trans-3,4-dimethylcyclobutene opens conrotatorily back to (E,E)-hexadiene; photochemically the cyclobutene accumulates because it does not absorb at the wavelength used.

Scheme: Products drawn with the methyl groups on wedge and hash bonds.

Conclusion. hν: disrotatory closure gives cis-3,4-dimethylcyclobut-1-ene; Δ: conrotatory closure gives trans-3,4-dimethylcyclobut-1-ene. The outcome follows from the HOMO symmetry (ψ₃ excited, ψ₂ ground state).

Application. The same con/dis rule fixes the ring-junction stereochemistry in the photochemical ring-opening of provitamin D (7-dehydrocholesterol) and in the Nazarov cyclisation.