Past exam of the chemistry B course of the University of Cambridge / 2022 / Paper 2 / B7

Four chloride ligands give Ti(IV), $d^0$. Ionic electron counting givestetrahedral molecular geometry separates the four donors without placing them at $90^{\circ }$. A $d^0$ centre has no occupied d orbitals providing a square-planar stabilization; the 18-electron rule is not a requirement for this early-metal compound.

Six neutral ammonia donors leave Cu(II), $d^9$, soThe donor skeleton has octahedral molecular geometry with a pronounced tetragonal Jahn–Teller distortion, normally four shorter equatorial and two longer axial Cu–N distances. The $t_{2g}^6{e}_g^3$ occupation is orbitally degenerate in the ideal octahedral limit. An electron count above 18 is not a contradiction: ammonia is primarily a sigma donor and the occupied metal-derived antibonding levels make this a weak-field coordination complex rather than a low-valent carbonyl closed shell.

Neutral CO ligands require formal Cr($-\mathrm{II}$), hence $d^8$. With five two-electron carbonyl ligands,A trigonal-bipyramidal molecular geometry is expected, analogous in electron count to $\mathrm{Fe}(\mathrm{CO}{)}_5$. Strong pi-acceptor ligands stabilize a low oxidation state through backbonding, and this five-coordinate structure accommodates the closed-shell 18-electron configuration. The negative oxidation state is a formal assignment; it does not mean that a free chromium dianion is trapped inside the molecule.

With oxide charge $-2$ and four thiocyanates each $-1$, $x-2-4=-2$ gives V(IV), $d^1$. Counting the terminal oxo as $X_2$ and each thiocyanate as X givesThe expected structure is square-pyramidal molecular geometry, with the short V=O unit at the apex and the four thiocyanate donors in the basal plane. The remaining d electron can occupy an approximately basal $d_{xy}$ orbital that avoids the strongest donor directions and the oxo pi-antibonding orbitals. This is a high-oxidation-state oxovanadium complex; reaching 18 electrons is not its governing stability criterion. The displayed $\mathrm{SCN}$ composition alone does not establish N versus S linkage, and that choice does not change this count. The stated 13-electron result consistently uses a four-electron $\mathrm{M}=\mathrm{O}$ convention; counting extra oxide pi-donor interactions as additional ligand electrons requires a different convention throughout.

In ionic counting, two ${\eta }^5$ cyclopentadienyl anions donate $12$ electrons. Therefore ferrocene, cobaltocene and nickelocene contain 18, 19 and 20 valence electrons, respectively: Fe(II) is $d^6$, Co(II) $d^7$ and Ni(II) $d^8$. ferrocene fills the bonding and approximately nonbonding levels while leaving the next metal–ring antibonding pair empty. cobaltocene and nickelocene add one and two electrons to that antibonding set.

Increasing antibonding occupation lowers the net metal–ring bond order. It therefore explains the simultaneous increase in M–C distance and decrease in dissociation enthalpy from Fe to Co to Ni. The trend does not follow the shrinking size of the isolated metal ions; the orbital occupation is decisive here. The specified enthalpy separates the entire sandwich into a gaseous metal dication and two gaseous ring anions. It measures that complete ionic dissociation process, not ten independent localized M–C bond energies, so dividing it by ten is not a justified bond-energy determination.

Oxidizing cobaltocene removes its antibonding nineteenth electron and gives the particularly favourable 18-electron cobaltocenium cation. iodine can accept the electrons, giving cobaltocenium iodide at the simple stoichiometryEach cobalt changes from Co(II), $d^7$, to Co(III), $d^6$; each iodine atom changes from 0 to $-1$. Excess iodine can change the isolated counterion to a polyiodide such as ${\mathrm{I}}_3^{-}$. In contrast, oxidation of 18-electron ferrocene would remove an electron from its occupied closed-shell manifold to form 17-electron ferrocenium. iodine is insufficient to drive that reaction under the conditions implicit here. ferrocene can still be oxidized by suitable stronger oxidants; an electron count is a useful rationale for the comparative redox behaviour, not a universal proof of a numerical electrode potential.

The anionic nitrogen donor replaces iodide to giveHere Cp denotes ${\eta }^5$ cyclopentadienyl and $\kappa N$ specifies attachment through the ring nitrogen of the pyrrolyl anion, ${\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}^{-}$. Fe(II), $d^6$, receives six electrons from Cp, four from the two CO ligands and two from an N-bound pyrrolyl ligand: $6+6+4+2=18$.

Two coupled CO stretching modes, approximately symmetric and antisymmetric combinations, account for the two strong carbonyl-region absorptions. The bent two-CO arrangement of this piano-stool complex permits both combinations to be infrared active. They are not evidence for two different chemical products.

Heating expels two CO molecules and changes the binding of the pyrrolyl ligand from ${\eta }^1$ to ${\eta }^5$, giving the sandwich azaferrocene,The four electrons lost with CO are replaced by the four additional electrons donated on changing the hapticity of the pyrrolyl ligand. Thus $B$ is also Fe(II), $d^6$, and 18-electron: $6+6+6=18$. Each complex has one time-averaged Cp proton environment, two pairs of protons from the pyrrolyl ligand, one adjacent to N and one farther from N. Hence three proton environments, with integrals $5:2:2$, fit both structures. For proton nuclear magnetic resonance, three signals means three chemical shift environments; the individual resonances can still show coupling.