Q4(a). Photo-electrocyclisation of hexa-2,4-diene; Cope rearrangement

Introduction. Pericyclic reactions are concerted; their stereochemistry follows from the symmetry of the frontier orbital whose terminal lobes must overlap in phase. For an electrocyclic reaction the HOMO of the open-chain polyene decides: thermal reactions use the ground-state HOMO, photochemical ones the excited-state HOMO.

(i) (2E,4E)-Hexa-2,4-diene under light

The diene has four π electrons. In the ground state the HOMO is ψ₂; absorption of a photon promotes one electron into ψ₃, which becomes the HOMO of the excited state. In ψ₃ the lobes on C-2 and C-5 (the termini of the diene unit) have the same phase on the same face. To bring these lobes together for bonding, the two termini must turn in opposite senses: disrotatory motion (one clockwise, one anticlockwise).

In the (2E,4E) diene, in its s-cis conformation, both methyl groups point outward. In a disrotatory turn (one terminus clockwise, the other anticlockwise) both outward methyls rotate to the same face, so they end up cis on the new ring.

Figure: ψ₃, the excited-state HOMO (shaded = one phase): terminal lobes match on the same face, so closure is disrotatory.

Scheme: Photochemical 4π electrocyclic closure: E,E-diene → cis product.

The product is cis-3,4-dimethylcyclobut-1-ene, a meso compound. The thermal reaction would be conrotatory (ground-state HOMO ψ₂ has opposite phases at the termini), and in practice runs the other way: cis-3,4-dimethylcyclobutene opens on heating to the (2E,4Z) diene. So light and heat give complementary stereochemistry, as the Woodward–Hoffmann rules predict (4n electrons: thermal conrotatory, photochemical disrotatory).

(ii) Cope rearrangement of (3S,4S)-3,4-dimethylhexa-1,5-diene

The starting diene, as drawn, is one enantiomer of the chiral (dl, not meso) 3,4-dimethylhexa-1,5-diene. On heating it undergoes a [3,3]-sigmatropic (Cope) rearrangement: the C3–C4 bond breaks while a new C1–C6 bond forms, through a six-membered chair transition state.

• In the chair, each methyl may be equatorial or axial. For the dl isomer the two methyls are either both equatorial or both axial. The diequatorial chair is much lower in energy.
• An equatorial methyl on the breaking bond becomes trans (E) to the chain in the new double bond. So the diequatorial chair gives (2E,6E)-octa-2,6-diene; the diaxial chair gives the (2Z,6Z) isomer.

Scheme: The geometry of the new double bonds is fixed by the chair transition state.

Major product: (2E,6E)-octa-2,6-diene. The meso diastereomer would instead give (2E,6Z)-octa-2,6-diene almost exclusively (one methyl equatorial, one axial). These results (Doering and Roth) are the evidence for the chair transition state.

Conclusion. (i) Light closes (2E,4E)-hexa-2,4-diene disrotatorily, through ψ₃ as HOMO, to cis-3,4-dimethylcyclobutene. (ii) The dl 3,4-dimethylhexa-1,5-diene undergoes a Cope rearrangement through the diequatorial chair to (2E,6E)-octa-2,6-diene.

Application. The Cope and oxy-Cope rearrangements build medium rings and stereodefined alkenes in terpene synthesis; photochemical electrocyclic ring opening and closure is used in photochromic switches (dithienylethenes) for optical memory.