Q7(b). Electrocyclic reactions: hexatriene, pentadiene, and ethene

Reading of the question: (ii) as printed is penta-1,2-diene, an allene with cumulated (not conjugated) double bonds, which cannot undergo an electrocyclic ring closure; it is read as penta-1,3-diene, CH₃-CH=CH-CH=CH₂. (iii) involves two molecules and is a cycloaddition, answered by the same orbital rules.

Introduction. An electrocyclic reaction closes a conjugated polyene into a ring by forming a σ bond between its termini (or the reverse). The mode of rotation of the terminal p orbitals is fixed by the symmetry of the HOMO: thermal 4n π systems close conrotatory, (4n+2) systems disrotatory; light reverses both.

Figure: Sketch: terminal p lobes of hexatriene; shaded = one phase. Bonding overlap needs like phases to meet.

(i) Hexa-1,3,5-triene

Scheme: The central C=C must be Z for the termini to meet.

1. A six-electron system: the thermal HOMO ψ₃ has like phases on the same face at C-1 and C-6, reached by disrotatory motion; the closure is thermally allowed (also allowed photochemically, conrotatory).
2. Product: cyclohexa-1,3-diene. With the unsubstituted triene both modes give the same compound; with terminal substituents the modes give cis or trans-5,6-disubstituted dienes (e.g. (2E,4Z,6E)-octatriene → cis-5,6-dimethylcyclohexa-1,3-diene on heating).

(ii) Penta-1,3-diene (reading of the misprint)

Scheme: Photochemical ring closure of a diene; the thermal reaction runs the other way.

1. A four-electron system. On irradiation the HOMO is ψ₃, and the closure is disrotatory: penta-1,3-diene gives 3-methylcyclobutene.
2. Thermally the closure would be conrotatory, but the strained cyclobutene is less stable than the open diene, so on heating the equilibrium lies on the diene side: cyclobutenes open conrotatorily to dienes (e.g. cis-3,4-dimethylcyclobutene → (2E,4Z)-hexa-2,4-diene).
3. As printed, CH₃CH₂CH=C=CH₂ is an allene: its two π bonds are perpendicular, not conjugated, so no electrocyclic product can form.

(iii) Two molecules of ethene

Scheme: Photochemical [2+2] cycloaddition.

1. Two ethene molecules bond through both ends at once: a [π2ₛ+π2ₛ] cycloaddition (an intermolecular reaction, not electrocyclic). Thermally the HOMO (π) of one and LUMO (π*) of the other have opposite phases at one end: forbidden. Photochemically the excited molecule uses π* as its HOMO, which matches the LUMO of the other: allowed.
2. Product: cyclobutane, C₄H₈.

Conclusion. (i) cyclohexa-1,3-diene (thermal, disrotatory 6π). (ii) Read as penta-1,3-diene: 3-methylcyclobutene (photochemical, disrotatory 4π); the printed allene cannot cyclise. (iii) cyclobutane by photochemical [π2ₛ+π2ₛ] cycloaddition.

Application. Electrocyclic ring opening of 7-dehydrocholesterol by sunlight (conrotatory, 6π) gives previtamin D₃ in the skin; photochemical [2+2] additions build cyclobutane rings, as in thymine dimers formed in DNA by UV light.