(a) Draw the structures of various iron-sulphur proteins and their corresponding redox states. (10 marks) (b) How would you…

The three parts are explained by connecting cluster structure, dynamic NMR exchange, and photon stoichiometry.

Iron-sulphur proteins. The structures are drawn as discrete Fe–S cores. The [2Fe–2S] cluster is a rhombus of two Fe and two S²⁻ bridging atoms, each Fe also bound to cysteine thiolates; its couple is [2Fe–2S]²⁺/⁺, formally Fe³⁺/Fe³⁺ in the oxidized state and Fe³⁺/Fe²⁺ when reduced. The [4Fe–4S] cluster is a cubane of four Fe and four S²⁻; the [4Fe–4S]²⁺/⁺ couple is Fe³⁺₂Fe²⁺₂/Fe³⁺₁Fe²⁺₃. HiPIPs contain this cubane but with a higher potential. The [3Fe–4S] cluster is a distorted cubane missing one Fe; the [3Fe–4S]⁴⁺/³⁺ couple is Fe³⁺₃/Fe³⁺₂Fe²⁺. The redox electron is delocalized over Fe–S–Fe bridges, which is why mixed-valence descriptions are used. Ferredoxins and HiPIPs therefore represent different redox families because cluster geometry and mixed-valence state control potential.

Fluxional organometallics. Variable-temperature ¹H NMR accounts for bonding by showing how exchange rates change: at low T, inequivalent protons or methyl groups give separate resonances; at high T, coalescence to one averaged resonance proves rapid site exchange. The coalescence temperature is diagnostic: below it exchange is slow; above it the NMR sees a time-averaged environment.

(i) (C₅H₅)₄Ti is best formulated as (η⁵-C₅H₅)₂(η¹-C₅H₅)₂Ti. Ti(IV) is d⁰ and the complex is a 16-electron species: two η⁵ Cp⁻ rings donate 6 e each, and two η¹ Cp⁻ rings donate 2 e each. The 16-electron d⁰ framework is fluxional because η¹ rings rotate and change hapticity while η⁵ rings can become η¹; this ring-whizzing/hapticity interchange makes all four Cp rings equivalent. Hence room-temperature ¹H NMR gives a single Cp signal, and low-temperature spectra separate the ring environments.

(ii) C₃(CH₃)₄Fe(CO)₄ is the η²-tetramethylallene complex of Fe(CO)₄, not a trimethylenemethane complex. Fe(0) is d⁸; four CO ligands and one η² C=C bond of the allene give an 18-electron complex. In the static η²-allene complex the allene ligand is unsymmetrical: methyl groups on the coordinated terminal carbon and those on the other terminal carbon are not all equivalent. Fluxionality arises from rotation/interchange of the allene ligand, including re-coordination through the other C=C or rotation about the Fe–C bond, which interchanges the methyl sites. Low-temperature ¹H NMR shows separate methyl resonances; on heating they coalesce to one signal as allene-site exchange becomes rapid, so all methyl groups become equivalent in the fast-exchange limit. Carbonyl Berry pseudorotation is not the accepted mechanism.

Photochemical quantum yield. Uranyl sulphate is the photosensitizer in the classic uranyl-oxalate actinometer: UO₂²⁺ absorbs 2500 Å light, is excited, and transfers energy/electron to oxalate, producing CO, CO₂ and water; the measured loss of oxalic acid therefore reports photons absorbed by the sensitizer. The calculation assumes all 80 J are absorbed by the uranyl chromophore and that one photon corresponds to one quantum event. The solution volume is 10 ml = 0.010 L. Initial oxalic acid = 0.05 × 0.010 = 5.0 × 10⁻⁴ mol. Final concentration = 0.04 M, so final moles = 0.04 × 0.010 = 4.0 × 10⁻⁴ mol. Decomposed oxalic acid = 1.0 × 10⁻⁴ mol. The wavelength is 2500 Å = 2.5 × 10⁻⁷ m. Energy per photon = hc/λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(2.5 × 10⁻⁷) = 7.95 × 10⁻¹⁹ J. Moles of photons absorbed = 80/(7.95 × 10⁻¹⁹ × 6.022 × 10²³) = 1.67 × 10⁻⁴ mol. Quantum yield Φ = moles of oxalic acid decomposed per mole of photons absorbed = 1.0 × 10⁻⁴/1.67 × 10⁻⁴ = 0.60. The sub-unity value indicates that not every absorbed uranyl excited state leads to oxalic acid decomposition; some energy is dissipated or follows other pathways.