(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 compound. The d⁶ centres in the list are Mn(I) and Fe(II). Mn(I) is d⁶ because Mn is group 7 and the +1 oxidation state leaves 6 d electrons; Fe(II) is d⁶ because Fe is group 8 and the +2 oxidation state leaves 6 d electrons. For the Cp/benzene pair, charge neutrality fixes the metal oxidation state: Cp⁻ is anionic and benzene is neutral, so the metal must be +1. Mn(I) therefore gives the neutral mixed sandwich [CpMn(C₆H₆)], and its electron count is d⁶ + 6 from η⁵-Cp + 6 from η⁶-benzene = 18. Fe(II) is also d⁶, but with Cp⁻ and a neutral arene it gives [CpFe(C₆H₆)]⁺, not a neutral compound; Fe(II) gives a neutral sandwich only with two Cp⁻ ligands, as in ferrocene. Co(0) is d⁹ and Fe(III) is d⁵, so they are not the required d⁶ centres; with Cp⁻ and benzene, Co(0) would be anionic and 21-electron, while Fe(III) would be dicationic and 17-electron. For the four-membered ligand in pair (I), if it is the neutral η⁴-cyclobutadiene ligand, charge neutrality again points to Mn(I), although the count is 16 electrons; the unambiguous 18-electron neutral mixed sandwich from the figure is the Cp/benzene manganese(I) compound.

(d) Noble-gas fluoride separation and diborane adducts. 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. 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 heterolytic 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 spin-allowed but 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/4d 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.

In each case, the observed structural or spectral property is controlled by a specific electronic cause: 18-electron completion, Wade–Mingos skeletal electron count, 4f shielding, charge neutrality, selective fluoride adduct formation, and allowed ligand-to-metal charge transfer.