Past exam of the chemistry B course of the University of Cambridge / 2021 / Paper 2

These are original worked solutions. The source paper occupies physical pages 131–137 of the released bundle, with questions on pages 132–137. ^[ref]

The biological design task is explicitly deferred at its printed location.

Each thiocyanate is a three-metal bridge, ${\mu }_3$-$\kappa N:\kappa S:\kappa S$: its nitrogen donates to one metal and its sulfur donates to two other metals. Thus the coordination ligand is ambidentate, but the structure uses both ends and shares the sulfur donor. Each metal receives two nitrogen and four sulfur donors, giving an approximately octahedral $\mathrm{M}{\mathrm{N}}_2{\mathrm{S}}_4$ coordination sphere. Six donor contacts per metal are consistent with two coordination ligands per metal because each coordination ligand contributes three contacts across the lattice. Sharing these contacts produces a coordination polymer within each layer; the interlayer Van der Waals force does not add coordination bonds. The index ${\mu }_3$ counts metal centres, whereas a hapticity label would count adjacent coordinated coordination ligand atoms and would not describe this connectivity correctly.^[ref]

Charge balance fixes each metal as ${\mathrm{M}}^{\mathrm{II}}$. In an octahedral crystal field the lower $t_{2g}$ set is $(d_{xy},d_{xz},d_{yz})$ and the upper $e_g$ set is $(d_{z^2},d_{x^2-y^2})$. The measured spin-only magnetic moments select the following occupations:The result follows from $S=n_{\mathrm{unpaired}}/2$ and $2\sqrt{S(S+1)}=\sqrt{n_{\mathrm{unpaired}}(n_{\mathrm{unpaired}}+2)}$. Manganese(II) and iron(II) are high-spin complexes: their octahedral splitting is too small to compensate the additional pairing cost of their low-spin alternatives. Copper(II) is $d^9$, with one unpaired electron regardless of which member of the upper pair is singly occupied. spin-orbit coupling and exchange interactions can produce deviations from the spin-only estimate in real measurements; no such correction is required to explain the supplied values.

At fixed $+2$ oxidation state, increasing effective nuclear charge across the first transition series generally contracts the ionic radius. The first expectation is therefore shorter average metal–nitrogen and metal–sulfur distances toward copper. This is a trend in comparable coordination environments, rather than a requirement that every individual contact shorten monotonically. The occupation of metal–coordination ligand antibonding orbitals, donor identity and lattice distortion all affect the observed distances.

The high-spin $d^5$ and $d^6$ ions both have two electrons in the strongly sigma-antibonding $e_g$ set, so adding the sixth electron to $t_{2g}$ does not itself introduce another sigma-antibonding electron. Copper(II), however, has $e_g^3$ occupation and is subject to the Jahn-Teller effect. A tetragonal Jahn-Teller distortion commonly gives four shorter and two longer contacts, so an elongated copper contact can oppose the overall size trend. Here the nitrogen and sulfur donors are already chemically inequivalent; the supplied schematic alone does not determine which trans pair becomes longest. One should compare actual M–N and M–S sets separately, rather than infer a unique axis or a numerical distance from the magnetic moments. The experimentally determined structures illustrate why the donor geometry and individual contacts matter.^[ref]

For A, linear nitrogen coordination with predominantly nitrile-like bonding is consistent with all three measurements:The short C–N and long C–S distances correspond approximately to a triple bond and a single bond. An approximately $sp$ nitrogen donor has its donor lone pair directed along the N–C axis, explaining the linear M–N–C angle.

For B, bent nitrogen coordination with increased ${}^{-}\mathrm{N}=\mathrm{C}=\mathrm{S}$ chemical resonance character accounts for the longer C–N and shorter C–S bonds. In this limiting description both internal bonds have substantial double-bond character and nitrogen is approximately $s{p}^2$. One nitrogen lone pair can bind a metal with an M–N–C angle near $120^{\circ }$; alternatively, donation of both nitrogen lone pairs can give a trigonal, nitrogen-bridging unit:The nitrogen-bridging drawing is a compatible proposed bonding mode, but the listed internal distances and one angle alone do not prove the number of attached metals. In particular, B cannot be identified simply as terminal sulfur coordination: the specified angle explicitly contains an M–N bond. resonance structures explain relative bond orders; they do not imply an isolated coordination ligand with permanently localized integer bonds.

A distinct possibility is terminal sulfur coordination, $\mathrm{M}\leftarrow \mathrm{S}-\mathrm{C}\equiv \mathrm{N}$. Unlike the sulfur donor in the layer, this sulfur need bind only one metal. The limiting ${}^{-}\mathrm{S}-\mathrm{C}\equiv \mathrm{N}$ resonance structure suggests $r_{\mathrm{CN}}\approx 1.15\mathring{\mathrm{A}}$ and $r_{\mathrm{CS}}\approx 1.8\mathring{\mathrm{A}}$. These are single-/triple-bond-based estimates, not exact predictions for an unspecified metal complex. The M–S–C linkage should be bent, consistent with sulfur lone-pair donation.

Take the M–C–O direction as $z$. carbon monoxide binds through carbon because its occupied $5\sigma$ donor orbital has a substantial carbon-end lobe. End-on overlap with an empty metal orbital of sigma symmetry gives CO-to-metal sigma donation. At the same time, occupied metal $d_{xz}$ and $d_{yz}$ orbitals overlap sideways with the two corresponding empty CO $2{\pi }^{\ast }$ orbitals, giving metal-to-CO pi backbonding. Both channels strengthen the metal–carbon bond, while backbonding lowers the internal C–O bond order. The processes are synergic: sigma donation helps supply metal electron density for backbonding, while backbonding relieves electron accumulation at the metal.

The original orbital sketch shows one of the two perpendicular pi channels. It is the occupied metal orbital, rather than an empty metal orbital, that supplies electrons to CO antibonding orbitals.

The arene and three carbonyl ligands are neutral, so chromium is in oxidation state zero, with a $d^6$ metal count. The eta-six arene contributes six electrons and each CO contributes two:The methoxy group changes the electronic properties of the arene without changing this formal electron count. The complex is a piano-stool complex, with the coordinated arene as the seat and the three carbonyl ligands as the legs.

The methoxy substituent donates electron density into the coordinated arene by chemical resonance. This increases the electron density available at chromium for pi backbonding to CO, weakening C–O and lowering its stretching frequencies. The ester substituent withdraws electron density from the arene, reducing pi backbonding and raising the carbonyl stretching frequencies. For both observed bands, the methoxy-substituted compound has the lowest carbonyl frequency, the unsubstituted compound is intermediate, and the ester-substituted compound has the highest.

In the harmonic oscillator approximation,so the trend reflects an increasing effective C–O bond force constant rather than a change in the CO reduced mass. For example, comparison of the higher-frequency bands gives $k_{\mathrm{ester}}/k_{\mathrm{methoxy}}\approx (1992/1983{)}^2=1.0091$. This is only an approximate local-bond interpretation because the observed normal modes couple the three CO oscillators. In the idealized local $C_{3v}$ geometry they span $A_1+E$, giving two infrared-active frequencies. A substituted arene can lower the exact molecular symmetry and split the $E$ pair, even if that splitting is unresolved experimentally.

triphenylphosphine is a good sigma donor and a substantially poorer pi acceptor than CO. Replacing CO by this phosphine ligand increases electron density at chromium and reduces competition among carbonyl ligands for pi backbonding. Backbonding into each remaining CO therefore strengthens, their internal bond force constants fall, and both remaining carbonyl stretching frequencies are expected to shift downward relative to the parent tricarbonyl.

The two remaining carbonyl ligands have coupled approximately symmetric and antisymmetric stretches; both are generally infrared active in this geometry. One should not treat the spectral change as simply deleting one of the original two bands. The substituted complex still has $6+6+2(2)+2=18$ valence electrons. No numerical frequency shift follows from electron counting alone.

Photoinduced CO loss gives a 16-electron fragment. In the ester-substituted complex the pendant ester carbonyl oxygen can reach chromium and capture that vacant site. A suitable structure is $\mathrm{Cr}({\eta }^6\text{-}{\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{O}}_2\mathrm{Me})(\mathrm{CO}{)}_2(\kappa O\text{-ester})$, retaining the coordinated arene and adding intramolecular coordination of its ester oxygen. The added oxygen lone-pair donation restores an 18-electron count. The gaseous by-product is carbon monoxide.

heptane is a poor donor, but intramolecular ligand trapping avoids needing a donor solvent. Benzene has no pendant donor. Although the methoxy group has oxygen lone pairs, its directly attached oxygen does not have the same reach and favourable geometry as the projecting ester carbonyl oxygen; possession of a lone pair alone is insufficient. For these two substrates, acetonitrile can trap the unsaturated fragment through nitrogen to give $\mathrm{Cr}({\eta }^6\text{-arene})(\mathrm{CO}{)}_2(\mathrm{NCMe})$. Without a suitable trap, CO recombination can reverse the initial photochemical dissociation.

Let $z$ be normal to the Cp ring through its centre. The five carbon $p_z$ orbitals form symmetry-adapted linear combinations with angular patterns $m=0$, $|m|=1$, and $|m|=2$. The all-in-phase $a_1$ combination has sigma symmetry about this axis and can interact with $d_{z^2}$. The $e_1$ pair matches $(d_{xz},d_{yz})$ by pi symmetry, while the $e_2$ pair matches $(d_{xy},d_{x^2-y^2})$ by delta symmetry. Rotating within either degenerate pair changes the drawing but not the physical interaction.

For the usual eta-five geometry, the metal $d$ interactions are ranked qualitatively pi > delta > sigma. The $d_{xz},d_{yz}$ lobes overlap effectively with the occupied ring combinations. The delta interaction is weaker and involves the higher, initially unoccupied Cp combinations; the $d_{z^2}$ interaction with the ring is particularly weak because its axial and equatorial parts contribute little net overlap in this geometry. Thus the statement that a sigma bond is always stronger than a pi bond cannot be transferred indiscriminately to this delocalized ring–metal overlap problem. metal $s$ and $p_z$ orbitals also have the symmetry of the $a_1$ coordination ligand combination and contribute to overall bonding, so weak $d_{z^2}$ overlap does not mean the entire sigma-symmetry channel is absent.

In ionic electron counting, Cp is ${\mathrm{C}}_5{\mathrm{H}}_5^{-}$ with six pi electrons in its three occupied ring combinations, hence a six-electron donor. The same coordination ligand is assigned five electrons in neutral counting.

In a metallocene, several orbitals with substantial metal $d$ character are nonbonding molecular orbitals or only weakly bonding or antibonding with respect to the strong Cp–metal framework. Adding or removing a small number of electrons from them can therefore change oxidation state or spin without destroying the principal ring–metal bonds. This allows stable compounds on either side of the 18-electron count: for example, the usual neutral counts for chromocene, ferrocene, cobaltocene and nickelocene are respectively 16, 18, 19 and 20. The 18-electron rule remains a useful reference, but occupation of a weakly antibonding orbital is much less disruptive than occupation of a strongly antibonding orbital. Redox stability also depends on geometry, substituents and reaction conditions, so this is a bonding explanation of the observed flexibility rather than a guarantee of equal stability for all counts.

Use neutral electron counting consistently: each terminal Cp supplies five electrons, while the eight pi electrons of neutral pentalene must be allocated across the shared fused framework rather than counted twice as two independent Cp coordination ligands. One set of 18-electron-consistent proposals is:

The original schematic shows the donor regions and the required iron–iron bond; dashed metal-to-region lines denote delocalized coordination rather than localized carbon–metal single bonds.

These proposals explain the requested electron counts and distance ordering. electron counting alone does not establish the unique ground-state structure: orbital calculations on related pentalene complexes also identify stable formally electron-deficient arrangements. In particular, the formal requirement of a metal–metal bond in the proposed 18-electron iron model should not be converted into a claim that every known iron pentalene complex adopts that model.^[ref]

One equivalent of butyllithium removes one proton per hydrocarbon, giving the hydropentalenyl monoanion ${\mathrm{C}}_8{\mathrm{H}}_7^{-}$. It does not give the doubly deprotonated pentalenide. salt metathesis with half an equivalent of iron(II) chloride therefore gives the sandwich complexEach coordination ligand binds through its aromatic five-membered portion and retains an uncoordinated double bond in the fused ring. The orientation of this unsymmetrical fused appendage makes the two coordinated coordination ligand faces distinguishable. Pairing matching and opposite planar configurations gives a racemic form, $(R_p,R_p)/(S_p,S_p)$, and a meso form, $(R_p,S_p)$. This describes the two stereoisomeric classes, rather than assigning the two easily interconverting rotations of ordinary ferrocene as separate configurational isomers. The molecular structure and double-bond disorder of bis(hydropentalenyl)iron have been examined crystallographically.^[ref]

Cleavage of the disulfide supplies one methylthiolate per cobalt. A monomer $\mathrm{CpCo}(\mathrm{SMe})$ would have only $7+6+2=15$ electrons by ionic counting. Dimerization with two bridging thiolates supplies a second sulfur interaction at each cobalt, and a direct Co–Co bond completes each count. Thus a suitable structure is $[\mathrm{CpCo}(\mu \text{-}\mathrm{SMe}){]}_2$ with a Co–Co single bond, containing an $\mathrm{C}{\mathrm{o}}_2{\mathrm{S}}_2$ diamond:Each cobalt is formally $+2$: Cp and methylthiolate each carry one negative charge. The stoichiometry isThe molecular formula ${\mathrm{C}}_{12}{\mathrm{H}}_{16}\mathrm{C}{\mathrm{o}}_2{\mathrm{S}}_2$ reduces to the required empirical formula. The sulfur–sulfur bond has been cleaved, both sulfur atoms now bridge the metals, and the loss of two CO molecules per cobalt is balanced. Formally cobalt(I) is oxidized to cobalt(II), while the disulfide is reduced to thiolate.

For the two-atom inorganic backbone unit, $Z_{\mathrm{Si}}+Z_{\mathrm{O}}=14+8=22$ and $Z_{\mathrm{P}}+Z_{\mathrm{N}}=15+7=22$. Their valence-electron sums also agree: $4+6=5+5=10$. Since each unit bears the same two organic groups, ${\mathrm{R}}_2\mathrm{SiO}$ and ${\mathrm{R}}_2\mathrm{PN}$ are isoelectronic species. This electron-count relationship does not require identical bond localization, bond angles or chemical reactivity.

In a boroxine, each boron has three sigma bonds and is approximately trigonal planar, with an $s{p}^2$ description for its sigma framework and an available perpendicular $2p$ orbital. oxygen can be described approximately as $s{p}^2$: two in-plane hybrids form B–O sigma bonds, one contains an in-plane lone pair, and a perpendicular $2p$ lone pair overlaps with neighbouring boron $2p$ orbitals. These three oxygen donor pairs supply a six-electron pi system around the alternating ring. The combination of good same-shell overlap and a low-strain six-membered ring favours planarity and partial B–O multiple-bond character. The bonds remain polar; a six-electron diagram alone does not establish benzene-like aromatic stabilization quantitatively.

In a siloxane, each silicon instead has four sigma bonds, two to oxygen and two to its organic groups, giving an approximately tetrahedral $s{p}^3$ sigma framework. oxygen has two sigma bonds and two lone pairs, so an approximately $s{p}^3$ localized description is a useful starting point, although actual Si–O–Si angles and lone-pair hybrids vary considerably. There is no comparable ring of vacant silicon $2p$ orbitals. A description based on strong oxygen-$2p$ to silicon-$3d$ pi bonds is also misleading: those orbitals have poor energy and radial matching. Strongly polar Si–O sigma bonding, supplemented by negative hyperconjugation from oxygen lone pairs into appropriate Si–R antibonding orbitals, gives a better account. The ring can therefore pucker rather than requiring continuous planar pi overlap. This follows the broader conclusion that strong main-group bonds and apparently expanded valence do not imply dominant valence $d$-orbital participation.^[ref]

boron is sufficiently small for effective oxygen-$2p$/boron-$2p$ overlap, and three-coordinate planar boron benefits from the pi donation just described. A six-membered boroxine ring provides this overlap without severe angle strain. The larger aluminium centre has poorer oxygen-$2p$/aluminium-$3p$ matching and remains strongly Lewis acidic. It can lower its electron deficiency by accepting additional oxygen coordination, making a three-dimensional aluminoxane cage favourable. Four-coordinate aluminium does not require a boroxine-like planar pi system.

An appropriate hexamer model is an alternating Al/O hexagonal prism, with six aluminium and six oxygen vertices. Colour the twelve-vertex prism alternately Al and O: each aluminium then has three oxygen neighbours and an outward organic substituent, making it four-coordinate, while each oxygen bridges three aluminium centres. The graph has 18 Al–O edges, hence six Al centres with three Al–O bonds each. Different polyhedral connectivities and sizes can meet similar local coordination requirements, so the hexamer is a proposal rather than a claim that the empirical repeat unit fixes a unique cage.

Ring cleavage of 1,3,5-Trioxane regenerates formaldehyde, whose strong carbon–oxygen pi bond stabilizes the monomer; in water much of it is further stabilized as its hydrate. acetal hydrolysis, particularly under acid catalysis, provides a route between the cyclic trimer and these monomeric forms.

The corresponding formal depolymerization of a siloxane would create ${\mathrm{R}}_2\mathrm{Si}=\mathrm{O}$ silanone units. Such ordinary small-substituent silanones have much less favourable pi bonding and are very reactive toward forming new Si–O–Si linkages. The connected siloxane is consequently preferred over a persistent aqueous solution of silanone monomers. This explains the intended contrast, but aqueous stability is conditional: acid or base can catalyse siloxane cleavage to silanols, and those silanols can condense again. Neither neutral-water inertness of every siloxane nor instantaneous neutral-water dissociation of every trioxane should be inferred.

First count the organic groups and then the unsatisfied oxygen valences. A is the fully condensed T8 silsesquioxane cage, $\mathrm{C}{\mathrm{y}}_8\mathrm{S}{\mathrm{i}}_8{\mathrm{O}}_{12}$, with silicon at the eight vertices of a cube and bridging oxygen on its twelve edges. Each silicon has one cyclohexyl group and three siloxane bridges. Its eight cyclohexyl groups supply exactly ${\mathrm{C}}_{48}{\mathrm{H}}_{88}$.

B is a fully condensed T10 silsesquioxane cage, $\mathrm{C}{\mathrm{y}}_{10}\mathrm{S}{\mathrm{i}}_{10}{\mathrm{O}}_{15}$, for which a pentagonal-prismatic silicon skeleton with an oxygen on every edge is a standard compatible structure. Its ten groups give ${\mathrm{C}}_{60}{\mathrm{H}}_{110}$. The formula establishes full condensation but does not, without more structural data, rule out every other possible ten-vertex cage connectivity.

C is a corner-deficient T7 trisilanol cage, $\mathrm{C}{\mathrm{y}}_7\mathrm{S}{\mathrm{i}}_7{\mathrm{O}}_9(\mathrm{OH}{)}_3$. Seven cyclohexyl groups account for ${\mathrm{C}}_{42}{\mathrm{H}}_{77}$, leaving three hydrogen atoms as Si–OH groups. Remove one silicon corner of the T8 cube and replace the three severed connections by terminal hydroxyl groups. Nine oxygen atoms remain as bridges and three become terminal silanol oxygen atoms, giving precisely twelve oxygen atoms. There are three silicon sites bearing OH, three further equivalent fully condensed sites, and one opposite fully condensed site, consistent with three silicon environments in a 3:3:1 site-count ratio. The less negative resonance is naturally associated with the three silanol-bearing sites; the remaining two resonances belong to the two fully condensed classes. Peak heights alone are not quantitative integrations.

The source figure appears to label the spectrum ${}^{27}\mathrm{Si}$. The chemically appropriate routine experiment here is silicon-29 NMR, using the spin-one-half isotope ${}^{29}\mathrm{Si}$; the figure label is treated as an apparent isotope-label typographical error, not as evidence for another cage.

Each trisilanol cage loses its three hydroxyl protons and supplies a facial tridentate silanolate ligand of charge $3-$. Two such coordination ligands replace all six chlorides of tungsten(VI), givingwith approximately octahedral $\mathrm{W}{\mathrm{O}}_6$ coordination. tungsten remains $+6$, is $d^0$, and is bound to six oxygen donors, three from each cage. The six liberated protons combine with the six chlorides to give six HCl; no W=O bond or tungsten reduction is needed. The molecular formula is ${\mathrm{C}}_{84}{\mathrm{H}}_{154}\mathrm{S}{\mathrm{i}}_{14}{\mathrm{O}}_{24}\mathrm{W}$. This bis(cage) tungsten structure was directly prepared and characterized in the primary literature.^[ref]

Treat the reacting carbon skeletons as an activated glycosyl donor and a 3-substituted indole. The new linkage is an anomeric-carbon–indole-C2 carbon–carbon bond, not a bond to indole nitrogen. A plausible purely chemical pathway is a dissociative electrophilic aromatic substitution:

The drawn donor and product have opposite anomeric faces: the anomeric leaving group is on the same face as the hydroxymethyl substituent, while the new carbon substituent is on the opposite face. Thus the target has net inversion at the anomeric carbon. A tight ion pair with the departing group shielding its original face can rationalize opposite-face capture in this proposed pathway. A freely solvated planar oxocarbenium ion would not by itself guarantee exclusive inversion; competing faces, hydrolysis and other products remain possible without an experimentally specified chemical promoter. This is a plausible non-enzymatic mechanism, not a claim that the uncatalysed reaction is rapid or clean in neutral water.

For the three elementary transformations just proposed, a qualitative free-energy profile has three transition states and two intermediates. The sugar substituents and indole C3 substituent stay unchanged, so the structural shorthand below suppresses them while retaining the reacting atoms.

The first transition state has a partially broken anomeric C1–O(leaving group) bond and developing oxocarbenium character, $[{\mathrm{O}}_{\mathrm{ring}}-{\mathrm{C}}_1^{\delta +}\cdots {\mathrm{O}}_{\mathrm{LG}}{]}^{‡}$. Its following minimum is the glycosyloxocarbenium ion plus counterion. The second transition state has a forming C1–C2 bond, $[{\mathrm{O}}_{\mathrm{ring}}-{\mathrm{C}}_1\cdots {\mathrm{C}}_2(\mathrm{H}{)}_{\mathrm{ind}}{]}^{‡}$, and developing positive charge in the indole. Its following minimum is the covalently joined arenium ion with an intact C2–H bond. The third transition state has simultaneous C2–H cleavage, B–H formation and restoration of the indole pi bond, $[\mathrm{B}\cdots \mathrm{H}\cdots {\mathrm{C}}_2-{\mathrm{C}}_3{]}^{‡}$. It leads to the aromatic C-linked product and protonated base.

The vertical separations are illustrative because no activation free energies or equilibrium constants are supplied. In particular, the highest barrier cannot be identified experimentally from this drawing alone. protonation of the leaving group is treated as an initial rapid equilibrium in the chosen mechanism; explicitly resolving it would add the corresponding proton-transfer state and intermediate.

TODO — user-deferred biology. The requested enzyme design, including all sites A–K, peptide recognition and residue-mediated catalysis at the specified pH, is deferred under the instruction to skip biological mechanism and design questions. No residue assignments are proposed.