(a) (i) Calculate the number of metal-metal bond in Cp₂Fe₂(CO)₄. (ii) Determine the structural type of the metal atom cluster…

(a) Metal–metal bond and Bi₅³⁺ cluster

In Cp₂Fe₂(CO)₄, each CpFe(CO)₂ fragment can be counted as a 17-electron unit: Fe contributes 8 valence electrons, η⁵-Cp contributes 5 in the neutral covalent count, and two CO ligands contribute 4, giving 17. Equivalently, in the dimer the average Fe oxidation state is +1, so each Fe is d⁷; d⁷ + 6 from Cp⁻ + 4 from two CO = 17. Two such fragments would have 34 electrons; one Fe–Fe bond supplies one electron to each metal and brings both to the 18-electron configuration. Therefore the dimer contains one metal–metal bond, and no additional Fe–Fe bond is required.

For Bi₅³⁺, n = 5 vertices. The total valence electron count is 5 × 5 − 3 = 22; after allowing for one exo lone pair at each Bi, the skeletal electron count is 12 electrons, i.e. 6 pairs. This equals n + 1, the closo requirement of Wade–Mingos rules. The cluster is therefore a closo deltahedron, specifically trigonal bipyramidal.

(b) Lanthanide colour and spectra

Lanthanide ions are generally pale because their 4f orbitals lie inside the 5s²5p⁶ shell and are strongly shielded from the ligand field. The crystal-field splitting of the 4f levels is therefore small, and 4f–4f transitions are parity-forbidden; they gain intensity only weakly through vibronic coupling or slight 5d/5p mixing. The resulting molar absorptivities are low, so solutions are often pale. Because the 4f–4f transitions are weak, only ions with several low-energy f-f bands or charge-transfer bands appear strongly coloured; most are pale. The spectra are line-like because the 4f electrons are weakly coupled to the lattice and to the ligand field; the transitions are essentially intraconfigurational 4f–4f transitions between fine-structure levels, so the band positions depend only weakly on the coordination environment and appear as sharp lines rather than broad d-d bands.

(c) Neutral mixed sandwich compounds

The rings drawn with inscribed circles are aromatic 6π donors in the ionic count: Cp⁻ (C₅H₅⁻), the cyclobutadienyl dianion C₄H₄²⁻ and neutral benzene C₆H₆. Each donates 6 electrons, so a d⁶ metal centre between two such rings reaches 6 + 6 + 6 = 18 electrons. A neutral compound also needs the metal charge to cancel the ring charges.

• Pair (I), Cp⁻ + C₄H₄²⁻ (total −3): the metal must be formally +3 and d⁶. Cobalt fits. The Co(0) atom gives CpCo(η⁴-C₄H₄). In the ionic count this is Co(III), d⁶, with 6 + 6 + 6 = 18 e. In the neutral count it is Co 9 + Cp 5 + C₄H₄ 4 = 18 e. Fe(III) is d⁵ and would give only 17 e, while Fe(II) would give the anion [CpFe(C₄H₄)]⁻.
• Pair (II), Cp⁻ + C₆H₆ (total −1): the metal must be +1 and d⁶. Mn(I) fits, giving neutral CpMn(η⁶-C₆H₆) with d⁶ + 6 + 6 = 18 e. Fe(II), also d⁶, gives the cation [CpFe(C₆H₆)]⁺, so it forms a neutral mixed sandwich with neither pair.

Hence the d⁶ centres that form neutral mixed sandwiches are cobalt, as Co(III) with Cp⁻/C₄H₄²⁻ (pair I), and Mn(I) with Cp⁻/C₆H₆ (pair II). Fe(II) and Fe(III) do not.

(d) Separating XeF₆ and diborane products

XeF₆ can be separated from XeF₂ and XeF₄ by selective adduct formation with NaF. XeF₆ reacts to give the ionic, non-volatile heptafluoroxenate(VI): XeF₆ + NaF → NaXeF₇ (Na₂XeF₈ can also form). XeF₂ and XeF₄ are less reactive toward NaF under these conditions and remain covalent and volatile; the ionic adduct is retained, while the covalent fluorides can be removed by sublimation or fractional sublimation because their volatilities differ. Heating NaXeF₇ regenerates XeF₆: NaXeF₇ → XeF₆ + NaF. Thus the separation uses differential reactivity with NaF followed by thermal recovery.

Diborane contains two B–H–B bridges, which are three-centre two-electron bonds. Lewis bases attack boron and convert these bridges into ordinary B–H and B–N bonds. With trimethylamine, steric bulk favours symmetrical cleavage of the bridges, giving two neutral adducts: B₂H₆ + 2 Me₃N → 2 Me₃N·BH₃. Each boron receives one bridging hydride and coordinates to one Me₃N, completing a four-coordinate neutral borane. With ammonia, the smaller and strongly donating NH₃ allows unsymmetrical ionic cleavage: B₂H₆ + 2 NH₃ → [H₂B(NH₃)₂]⁺[BH₄]⁻. One boron becomes tetrahydridoborate, the other a tetracoordinate ammoniated boron cation. The difference is electronic and steric: NH₃ can approach and stabilise the ionic pair, whereas bulky Me₃N favours the neutral 1:1 adduct.

(e) Colour of aqueous FeCl₃

High-spin d⁵ Fe(III) has a half-filled 3d shell; its d-d transitions are both spin-forbidden and Laporte-forbidden, so an aqua complex such as [Fe(H₂O)₆]³⁺ is only pale violet. In aqueous FeCl₃, the bright yellow colour is dominated by ligand-to-metal charge transfer (LMCT), in which an electron is promoted from a filled ligand orbital, mainly Cl⁻ 3p or hydroxo/aqua oxygen p, to an Fe acceptor orbital of 3d character. These CT transitions are electric-dipole allowed and much more intense than d-d bands. Chloride raises the donor orbital energy relative to water, lowering the LMCT energy into the visible and giving yellow/orange absorption; the yellow colour corresponds to absorption in the violet-blue region. Hydrolysis also contributes: [Fe(H₂O)₆]³⁺ forms [Fe(H₂O)₅OH]²⁺ and, on further hydrolysis, oligomeric or colloidal ferric hydroxide, FeO(OH), whose surface and ligand environments produce additional yellow-brown CT absorption. Hence the observed colour is not the intrinsic pale d-d colour of high-spin d⁵ Fe(III), but a charge-transfer and hydrolysis effect.