(a) (i) Write the structure of the stereochemical product formed in the reaction of (2E, 4E)-hexa-2,4-diene under photochemical…

(a)(i) Photochemical reaction of (2E,4E)-hexa-2,4-diene (10 marks)

Irradiation of the diene causes a 4π-electron electrocyclic ring closure to a cyclobutene. The stereochemistry is decided by the symmetry of the frontier orbital that controls the closure, the HOMO.

In the ground state the four π electrons occupy ψ₁ and ψ₂, and the HOMO is ψ₂, whose terminal lobes at C1 and C4 have opposite phase. To form the σ bond, the termini must rotate so that lobes of the same phase overlap, which needs rotation in the same sense (conrotatory). This is the thermal path.

On photoexcitation an electron is promoted from ψ₂ to ψ₃, so the HOMO of the excited state is ψ₃. Its terminal lobes have the same phase, so bonding overlap needs the termini to turn in opposite senses (disrotatory).

Disrotatory closure of the (2E,4E) isomer, which has both methyl groups pointing outward, turns them both to the same face of the new ring. The product is therefore cis-3,4-dimethylcyclobut-1-ene, the meso compound (3R,4S). (The thermal conrotatory closure of the same diene would instead give the trans, racemic cyclobutene.)

(a)(ii) Thermal rearrangement of 3,4-dimethylhexa-1,5-diene (5 marks)

Heating a 1,5-diene brings about the Cope rearrangement, a [3,3]-sigmatropic shift. The C3-C4 σ bond breaks, a new bond forms between C1 and C6, and the double bonds move to C2=C3 and C4=C5, giving octa-2,6-diene.

The reaction goes through a chair-like six-membered transition state in which the bulkiest groups are equatorial. For the chiral (racemic, R*,R*) diastereomer, both methyl groups can be equatorial in the chair, which places them so that both new double bonds are E. The major product is therefore (2E,6E)-octa-2,6-diene. (The meso diastereomer would give (2E,6Z) instead.)

(b)(i) Photochemical rearrangement of isopropylidenecyclopentane (10 marks)

Irradiation causes a suprafacial [1,3]-hydrogen shift. The hydrogen moves from an allylic carbon to the other end of the C=C bond, and the double bond shifts. Two products are possible:

• H from a methyl group moves to the ring carbon, giving isopropenylcyclopentane (2-cyclopentylprop-1-ene, an exocyclic terminal alkene).
• H from a ring CH₂ next to the double bond moves to the CMe₂ carbon, giving the more substituted 1-isopropylcyclopent-1-ene.

FMO explanation. The [1,3] shift treats the system as an allyl fragment (C=C-C) plus a migrating hydrogen, with four electrons in total (two π electrons and the two σ-bond electrons), so it is a [σ2s + π2s] change. For the thermal reaction the HOMO of the allyl fragment is ψ₂, with a node at the central carbon and opposite phases at the termini. The H 1s orbital can overlap with both termini on the same face (suprafacial) only if they have the same phase, so it cannot bond to both, and the shift is thermally forbidden (it would need an antarafacial shift, geometrically impossible for H over a short three-carbon span). On photoexcitation an electron enters ψ₃, whose termini are in phase, so the suprafacial shift becomes allowed.

(b)(ii) Diels-Alder reaction of 1-methoxycyclopentadiene with methyl vinyl ketone (5 marks)

The reaction is a thermal [4+2] cycloaddition, which is suprafacial on both partners, and gives a bicyclo[2.2.1]hept-5-ene (norbornene).

Regiochemistry: the methoxy group on C1 of the diene makes C4 the largest HOMO coefficient (the terminus far from OMe) which bonds to the β-carbon (CH₂) of the dienophile (largest LUMO coefficient), so the acetyl-bearing carbon bonds to C1. This is the "ortho" product: the acetyl group ends up on the carbon adjacent to the bridgehead carrying OMe.

Stereochemistry: the endo orientation of the acetyl group (below the C5=C6 double bond, away from the CH₂ bridge) is favoured by secondary orbital overlap in the transition state.

Major product: racemic endo-2-acetyl-1-methoxybicyclo[2.2.1]hept-5-ene, 1-(1-methoxybicyclo[2.2.1]hept-5-en-2-yl)ethanone.

(c)(i) Bromination and Favorskii rearrangement of dicyclohexyl ketone (10 marks)

E: with one equivalent of Br₂ in acetic acid, the ketone brominates at an α-carbon through its enol, giving the α-bromo ketone (1-bromocyclohexyl)(cyclohexyl)ketone.

F: with KOH, this α-halo ketone, which has an enolisable hydrogen on the other α-carbon (the other cyclohexyl ring), undergoes the Favorskii rearrangement to give the carboxylic acid, [1,1′-bi(cyclohexane)]-1-carboxylic acid (1,1′-bicyclohexyl-1-carboxylic acid), isolated after acidification.

Mechanism:

• (1) KOH removes the α′-hydrogen (on the other cyclohexyl ring) to give an enolate.
• (2) The enolate carbon attacks the bromine-bearing carbon in an intramolecular SN2 displacement of Br⁻, closing a cyclopropanone (a spiro-fused, dispiro cyclopropanone).
• (3) OH⁻ adds to the strained cyclopropanone C=O to give a tetrahedral alkoxide.
• (4) The three-membered ring opens by cleavage of a C-C bond, giving the more stable carbanion (tertiary here, the same either way by symmetry); this is protonated by the solvent.
• (5) The carboxylate is protonated by acid to give F. Because the ring carbons join at a quaternary centre, the product has the two rings directly bonded at a carbon that also bears the CO₂H group.

(c)(ii) Reactivity of alkenes towards Br₂ in methanol (5 marks)

Order of increasing reactivity: CH₂=CH₂ (4) < trans-MeCH=CHMe (2) < Me₂C=CH₂ (1) < PhC(Me)=CH₂ (3).

The rate-determining step is the formation of the bromonium ion, which has substantial carbocation character at the more substituted carbon (the site attacked by MeO⁻/MeOH). Alkyl groups stabilise this positive charge by hyperconjugation and induction. Ethene gives only a primary-like, unstabilised ion and is the slowest. trans-2-Butene has two alkyl groups but the charge is secondary. Isobutene (Me₂C=CH₂) generates a tertiary centre and is much faster. α-Methylstyrene (3) generates a tertiary benzylic centre that is stabilised by resonance with the phenyl ring as well as by the methyl group, so it is the most reactive.

(c)(iii) Carboxylation of indole with n-BuLi and with n-BuMgBr (5 marks)

Indole is deprotonated at N-H by both organometallics to give an ambident indolyl anion, which can react at N or at C-3. The metal-nitrogen bond determines the site.

Reaction 1 (n-BuLi, then CO₂, then H⁺): the lithium-nitrogen bond is largely ionic, so the anion is essentially free at nitrogen, which reacts with CO₂ (the kinetic, hard site). The product is the N-carboxylate, indole-1-carboxylic acid (N-CO₂H), which on acidification is a labile carbamic acid that readily loses CO₂.

Reaction 2 (n-BuMgBr, then CO₂, then H⁺): the magnesium-nitrogen bond is much more covalent, which blocks nitrogen and leaves the enamine-like C-3 nucleophilic. CO₂ therefore reacts at C-3, and after acidification and rearomatisation the product is indole-3-carboxylic acid.