(a) (i) Acetone shows a weak absorption at 280 nm and a strong absorption at 190 nm in the UV spectrum. Account for the…

(a)(i)

Acetone shows two bands because two different electronic transitions of the carbonyl group fall in this region.

• 280 nm, weak (ε about 15 L mol⁻¹ cm⁻¹): n → π∗. A non-bonding (lone-pair) electron on oxygen is promoted into the π∗ orbital of C=O. The n–π∗ gap is the smallest in the molecule, so the band lies at the longest wavelength. The n orbital lies in the molecular plane and π∗ is perpendicular to it, so overlap is poor and the transition is symmetry-forbidden, hence the low intensity.
• 190 nm, strong (ε of the order of 10³): π → π∗. An electron of the C=O π bond is promoted into π∗. The bonding π level lies well below the non-bonding level, so more energy (a shorter wavelength) is needed, but the two orbitals overlap well and the transition is allowed, hence the high intensity. (The n → σ∗ transition of acetone lies at still shorter wavelength, near 166 nm.)

Thus the weak long-wavelength band is the forbidden, low-energy n → π∗ transition and the strong short-wavelength band is the allowed, higher-energy π → π∗ transition.

(a)(ii)

Woodward–Fieser rules for α,β-unsaturated ketones (ethanol): base value for an acyclic or six-membered-ring ketone 215 nm, five-membered-ring ketone 202 nm; α-alkyl/ring residue +10, β +12, γ and higher +18; each exocyclic C=C +5; extended conjugation (each extra C=C) +30; homoannular diene component +39.

A — (E)-3-methylpent-3-en-2-one, CH₃–CH=C(CH₃)–CO–CH₃

Base (acyclic enone): 215; α-alkyl (CH₃ on C-3): +10; β-alkyl (CH₃ on C-4): +12; λmax = 237 nm

B — 2-cyclohexylidenecyclohexan-1-one

Base (six-membered ring ketone): 215; α ring residue (C-3 of cyclohexanone): +10; β ring residues (two, of the cyclohexylidene ring): +24; C=C exocyclic to both rings (2 × 5): +10; λmax = 259 nm

C — 1-acetylcyclopentene

The C=O is acyclic (a methyl ketone); only the C=C is in the ring, so the base is 215 nm, not the cyclopentenone value.

Base: 215; α ring residue (C-5): +10; β ring residue (C-3): +12; λmax = 237 nm

D — 4-methyl-4,4a,5,6-tetrahydronaphthalen-2(3H)-one (a heteroannular dienone: O=C2–C1=C8a–C8=C7)

Base (six-membered ring ketone): 215; Extended conjugation (second C=C): +30; β ring residue (C-4a on C-8a): +12; δ ring residue (C-6 on C-7): +18; Exocyclic C=C (C-1=C-8a, exocyclic to the left ring): +5; λmax = 280 nm

(b)(i)

A Diels–Alder reaction needs the diene in the s-cis conformation, so that C-1 and C-4 can bond to the two dienophile carbons at the same time.

Order of increasing reactivity: A (1) < B (2) < C (3) < D (4).

1. A (least reactive) — the bicyclic hexahydronaphthalene diene has its two C=C bonds on opposite sides of the ring-fusion bond. It is locked s-trans; rotation to s-cis is impossible, so it does not undergo Diels–Alder reaction.
2. B — buta-1,3-diene drawn in the s-trans conformation (the more stable conformer, which predominates at room temperature). It must first rotate to s-cis, which costs energy.
3. C — the same buta-1,3-diene drawn in the s-cis conformation, the conformer that reacts directly (B and C interconvert rapidly).
4. D (most reactive) — cyclohexa-1,3-diene is locked s-cis by the ring. No conformational energy is needed, so it reacts most readily.

(b)(ii)

The diene is 2-methoxybuta-1,3-diene (an electron-rich diene) and the dienophile is acrylonitrile (electron-poor).

• Step 1 (heat): Diels–Alder. The +M OMe group at C-2 puts the largest HOMO coefficient on C-1; the largest LUMO coefficient of acrylonitrile is on its CH₂. Joining these gives the "para" (1,4) adduct, 4-methoxycyclohex-3-ene-1-carbonitrile.
• Step 2 (H⁺, H₂O): the product contains an enol ether, which is protonated at C-3 and hydrolysed to a ketone. The nitrile survives dilute aqueous acid.

Product: 4-oxocyclohexane-1-carbonitrile (4-cyanocyclohexanone). C-1 is not a stereocentre.

(c)(i)

The substrate is a cis-1,2-divinylcyclopropane: one vinyl group carries the n-butyl group at its end (an (E)-hex-1-enyl group), and the two ring hydrogens are cis. The system C=C–C(ring)–C(ring)–C=C is a 1,5-diene whose central σ bond is a strained cyclopropane bond.

Category: a [3,3]-sigmatropic (Cope) rearrangement, the divinylcyclopropane rearrangement. A σ bond flanked by two allyl units migrates from position 1,1′ to 3,3′: the cyclopropane C1–C2 bond breaks, a new σ bond forms between the two vinyl termini, and the π bonds move into the old C1–C=C and C2–C=C positions. The cis geometry allows a boat-like transition state, and relief of cyclopropane ring strain explains the mild conditions (80 °C).

Product: 6-butylcyclohepta-1,4-diene (seven-membered ring; Bu on the carbon formed from the vinyl terminus).

Thermal feasibility (FMO). Treat the transition state as two allyl radicals. Each has ψ₂ as its singly occupied frontier orbital, with a node at the central carbon and opposite phases on the two termini. In the suprafacial–suprafacial geometry the lobes are in phase both at the bond that breaks (C1…C1′) and at the bond that forms (C3…C3′). The reaction is therefore thermally allowed ([π2s + σ2s + π2s]).

(c)(ii)

Woodward–Hoffmann rules for thermal electrocyclic reactions: 4n π electrons → conrotatory; (4n + 2) π electrons → disrotatory. The stereochemistry follows from the geometry of the terminal double bonds of the polyene.

(1) Mode of ring closure

• (A) Cycloocta-1,3-diene → bicyclo[4.2.0]oct-7-ene. This is a 4π (n = 1) diene → cyclobutene closure, so under heat it is conrotatory (HOMO ψ₂ has opposite phases at the termini).
• (B) Cyclonona-1,3,5-triene → bicyclo[4.3.0]nona-2,4-diene. This is a 6π (4n + 2) triene → cyclohexadiene closure, so under heat it is disrotatory (HOMO ψ₃ has the same phase at the termini).

(2) Relative configuration of the indicated hydrogens

• (A) trans. As drawn, both ring double bonds are cis (Z). The ring carbons attached to the termini (C-8 and C-5) therefore both occupy "inside" positions, and the hydrogens both occupy "outside" positions. Conrotation turns the two termini in the same sense, so like groups end up on opposite faces: the ring-fusion hydrogens are trans.
• (B) trans. The printed triene has the C-5=C-6 double bond drawn E, with the other two Z (a Z,Z,E-cyclononatriene). One ring-attached carbon at a terminus is therefore "inside" and the other "outside", so the hydrogens are likewise one inside and one outside. Disrotation turns the termini in opposite senses and puts such a pair on opposite faces. The ring-fusion hydrogens are trans, giving trans-bicyclo[4.3.0]nona-2,4-diene.