Codex @codex  0

The target is 5-Aminohexanoic acid, $\mathrm{H}{\mathrm{O}}_2\mathrm{C}(\mathrm{C}{\mathrm{H}}_2{)}_3\mathrm{CH}(\mathrm{N}{\mathrm{H}}_2)\mathrm{Me}$. Disconnect its terminal amine/carboxylic-acid relationship through hydrolysis of 6-methylpiperidin-2-one. This six-membered lactam follows from a regioselected Beckmann ring expansion of 2-methylcyclopentanone oxime.

Start with cyclopentanone. Form its enolate with lithium diisopropylamide in dry THF at low temperature, add methyl iodide, then quench to obtain 2-methylcyclopentanone. Control the methyl iodide/base stoichiometry to suppress a second alkylation. React the ketone with hydroxylamine to form its oxime and select the geometrical oxime isomer in which the bond to the methyl-substituted adjacent ring carbon is anti to the departing oxime oxygen group.

Activate the oxime, for example under appropriate acid-promoted Beckmann conditions. The anti methyl-bearing C–C bond migrates onto nitrogen as the N–O-derived leaving group departs, inserting nitrogen between the original carbonyl carbon and the methyl-substituted ring carbon. Hydration/tautomerization gives 6-methylpiperidin-2-one. The opposite oxime geometry would insert nitrogen on the other side and ultimately place methyl at a different position in the amino acid; oxime geometry is therefore an essential part of this proposal.

Hydrolyse the lactam with aqueous acid and heat, then adjust the work-up to the desired acid/ammonium form. Cleavage of its acyl–nitrogen bond opens the ring to $\mathrm{H}{\mathrm{O}}_2\mathrm{C}(\mathrm{C}{\mathrm{H}}_2{)}_3\mathrm{CH}(\mathrm{N}{\mathrm{H}}_2)\mathrm{Me}$ after suitable neutralization. All five original cyclopentanone carbons are retained, and the one methyl carbon comes from methyl iodide. A racemic mixture product is appropriate to the stereochemically unspecified target. The reaction sequence is an organic ring-expansion synthesis and requires no biological transformation.

Open the cyclic ester at its acyl–oxygen bond. The resulting delta-hydroxy acid isOxidation-state reversal at the benzylic alcohol gives $\mathrm{H}{\mathrm{O}}_2\mathrm{C}-\mathrm{CH}(\mathrm{nPr})-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}(\mathrm{iPr})-\mathrm{C}(=\mathrm{O})\mathrm{Ph}$. This identifies the key Michael disconnection between the central $\mathrm{C}{\mathrm{H}}_2$ and $\mathrm{CH}(\mathrm{iPr})$ groups:The nucleophile is the enolate or enamine of the phenyl ketone. The electrophile's propyl substituent must be alpha to its ester carbonyl; using a beta-propyl acrylate would move the substituent to the wrong ring position.

Disconnect $\mathrm{PhCOC}{\mathrm{H}}_2\mathrm{iPr}$ further to the indicated acetophenone. Crossed aldol addition to acetone followed by dehydration gives $\mathrm{PhCOCH}=\mathrm{CM}{\mathrm{e}}_2$; selective conjugate reduction or controlled alkene hydrogenation then gives $\mathrm{PhCOC}{\mathrm{H}}_2\mathrm{CHM}{\mathrm{e}}_2$. This avoids requiring an efficient SN2 alkylation with a secondary isopropyl halide. The alpha-propyl acrylate can be obtained by alpha-hydroxymethylation/dehydration of ethyl pentanoate, $\mathrm{Et}{\mathrm{O}}_2\mathrm{CC}{\mathrm{H}}_2\mathrm{nPr}$, using formaldehyde.

In the forward direction, perform the Michael coupling, reduce the phenyl ketone selectively with sodium borohydride while retaining the ordinary ester, hydrolyse the ester, and cyclize the delta-hydroxy acid by controlled acid-catalysed lactonization or an activated-acid coupling. The six-membered ring then has the order carbonyl–$\mathrm{CH}(\mathrm{nPr})$–$\mathrm{C}{\mathrm{H}}_2$–$\mathrm{CH}(\mathrm{iPr})$–$\mathrm{CH}(\mathrm{Ph})$–O. This atom order checks all three substituent positions. No relative configuration is specified, so the scheme does not imply a single diastereomer from the Michael addition or reduction.

Disconnect the tertiary amide into cyclohex-3-ene-1-carboxylic acid and the secondary amine $\mathrm{EtNHCH}(\mathrm{Me})\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{Ph}$. The acid-derived ring is an immediate Diels–Alder disconnection: buta-1,3-diene plus the indicated methyl acrylate gives methyl cyclohex-3-ene-1-carboxylate. Heating, or suitable Lewis-acid activation of the dienophile, forms the two new sigma bonds and leaves the diene's internal double bond as the ring alkene.

Hydrolyse this ester to the acid. Convert it to its acid chloride with oxalyl chloride or thionyl chloride, and react with the secondary amine in the presence of a base to capture HCl. The tertiary amide now contains the complete cyclohexene acyl fragment; direct conjugate addition of the amine to methyl acrylate before ring construction would give the wrong connectivity.

Prepare the amine by reductive amination of 4-phenylbutan-2-one, $\mathrm{MeCOC}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{Ph}$, with ethylamine, using sodium triacetoxyborohydride or another iminium-selective reducing system. This places nitrogen on $\mathrm{CH}(\mathrm{Me})$, not on a terminal methylene. If a route from simpler carbon compounds is wanted, crossed aldol condensation of acetone with benzaldehyde gives $\mathrm{MeCOCH}=\mathrm{CHPh}$, and selective C=C reduction gives the required ketone before reductive amination.

The acid branch retains the acrylic carbonyl as the amide carbonyl; the amine branch supplies both N-ethyl and N-(4-phenylbutan-2-yl) substituents. The unlabelled stereogenic centres may be racemic mixture. This sequence separates ring formation from amide formation and avoids invoking uncontrolled alkylation of a tertiary amide nitrogen.

The first transformation is an Achmatowicz rearrangement, followed by protection and selective reduction; the last is a Johnson-Claisen rearrangement.

The acetal protects the other oxygenated position during hydride reduction. The orthoester transfers an acetate-derived two-carbon unit through a ketene acetal; it does not directly substitute the allylic OH with an intact acetate ion.

The hydroxylactam is a cyclic hemiaminal. Its alkoxide can open to the corresponding aldehyde/amidate, $\mathrm{MeNHCO}-\mathrm{CH}(\mathrm{OBn})-\mathrm{C}{\mathrm{H}}_2-\mathrm{CHO}$ in its protonated representation. This exposes an aldehyde without reducing or replacing the lactam carbonyl.

The ketophosphonate anion attacks that aldehyde. Formation and collapse of the phosphorus-containing intermediate give the predominantly E enone $\mathrm{MeNHCO}-\mathrm{CH}(\mathrm{OBn})-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}=\mathrm{CH}-\mathrm{COC}{\mathrm{H}}_3$ and phosphate by Horner-Wadsworth-Emmons reaction. The amide nitrogen then closes by intramolecular aza-Michael addition at the enone beta carbon. Protonation of the ketone enolate gives the observed five-membered lactam with a $-\mathrm{C}{\mathrm{H}}_2\mathrm{COC}{\mathrm{H}}_3$ substituent.

A folded, relatively unencumbered closure places OBn and the developing side chain in outward-facing positions; the expected major product has OBn and the C5 acetonyl substituent cis. With the OBn wedge retained, show the new C5–CH${}_2$COCH${}_3$ bond as a solid wedge. The closure is diastereoselective, while the original wavy hemiaminal centre is erased by aldehyde formation. This facial prediction rests on the preferred folded conformer rather than retention of either starting hemiaminal epimer.

This is a thermal Claisen rearrangement followed by intramolecular acetal exchange. Identify the six-atom array as the cyclopentenone enol-ether C=C–O–CH${}_2$–C=C unit. In its concerted $[3,3]$ rearrangement:

The intermediate is thus a substituted cyclopentane-1,3-dione, with the acetal tether now correctly placed for six-membered-ring closure. Its enol oxygen attacks the acetal carbon, replacing OEt and releasing ethanol. Enolization gives the conjugated cyclic enol ether drawn in the product; the second ethoxy group remains.

A chair-like Claisen rearrangement transition structure with the phenyl-bearing part of the cyclohexane directed outward avoids severe axial crowding. Suprafacial bond formation and the pre-existing configuration give the two indicated ring-junction hydrogens on opposite faces: the left H is a wedge and the right H a dash in the supplied orientation. Closure favors the acetal epimer with outward OEt, drawn as a wedge, while the original Ph remains dashed. This is substrate-controlled diastereoselection followed by conformationally selective acetal closure, rather than independent arbitrary assignment of three centres.

Disconnect the two new bonds of the isoxazolidine as a nitrone [3+2] cycloaddition. Suitable achiral partners are $\mathrm{PhCH}={\mathrm{N}}^{+}(\mathrm{Ph}){\mathrm{O}}^{-}$ and the trans enone $(2-\mathrm{pyridyl}\mathrm{N}-\mathrm{oxide})\mathrm{CO}-\mathrm{CH}=\mathrm{CHPh}$.

A practical catalyst family is Cu(II) with an enantiopure bis(oxazoline) Ligand in coordination chemistry, for example a Cu(OTf)${}_2$–BOX complex. The enone can bind through its ketone oxygen and pyridine N-oxide oxygen, giving an O,O-chelated assembly. Chelation both activates the conjugated double bond and fixes its orientation in the chiral pocket. Highly enantioselective cycloadditions of this substrate class with Cu(II)–BOX complexes are experimentally established.^[ref]

The nitrone carbon bonds to the enone $\alpha$ carbon and the nitrone oxygen bonds to the $\beta$ carbon. Thus the carbonyl-bearing carbon lies between the two phenyl-bearing ring carbons, as in the target. The trans enone gives the required trans relationship of its original acyl and phenyl substituents. Selection between endo/exo dipole approaches gives the remaining relative stereochemistry; the sterically preferred chelated transition-state arrangement places the two ring phenyl substituents on the same face and the acyl group on the opposite face, matching the drawing.

One enantiomer of the BOX Ligand in coordination chemistry exposes one enone face; its mirror image reverses the product's absolute stereochemistry. The exact Ligand in coordination chemistry substituents, metal counterion and temperature require optimization. The proposal identifies an experimentally supported catalyst platform and its stereochemical control elements, rather than claiming that an arbitrary BOX complex must give a specified numerical enantiomeric excess.

Product 6 is a remotely oxidized ketone of the undecylammonium chain, retaining the ammonium group and its counterion. Number from the ammonium-bearing carbon as C1. Crown-mediated recognition positions the remote C8–C9 region near the Mn–oxo center. A representative major-site product is the C8 ketone,Its adjacent possible regioisomer is the C9 ketone $[{\mathrm{H}}_3{\mathrm{N}}^{+}-(\mathrm{C}{\mathrm{H}}_2{)}_8-\mathrm{C}(\mathrm{O})-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_3]\mathrm{B}{\mathrm{F}}_4^{-}$. The precise single-site assignment is a limitation discussed below.

The crown ether binds the primary ammonium end through several N–H···O hydrogen bonds. This host–guest complex holds a folded portion of the chain close to the manganese oxidant, so the effective local concentration of a remote secondary C–H bond can overcome the intrinsic advantage of a free tertiary C–H bond. Such recognition-driven reversal of substrate preference is experimentally established.^[ref]

The key intermediates are the crown-bound ammonium–Mn=O assembly, a remote carbon radical after H abstraction, and the rebound secondary alcohol. A second oxidation removes the remaining hydrogen on the carbinol carbon to give the ketone. The overall oxygen-equivalent count isThus one ketone requires two equivalents of peroxide, explaining a maximum near 50% ketone yield with one equivalent and near-complete conversion with two.

The primary remote-oxidation study reports preference for C8 and C9, not a universally unique carbon. The schematic catalyst drawing and the oxygen budget alone cannot distinguish those positions quantitatively. The “single product” wording is therefore treated as an idealized remote-site assignment; a uniquely verified C8:C9 ratio is not invented.^[ref]

Ba${}^{2+}$ competes strongly for the crown ether receptors. With the recognition sites occupied, the undecylammonium chain can no longer be effectively preorganized near manganese. The reaction should move back towards oxidation of methylcyclohexane to 1-methylcyclohexan-1-ol, with suppression of the selectively formed remote amino ketone.

The single available peroxide equivalent is then sufficient for tertiary C–H hydroxylation, whereas a secondary-chain ketone would require two oxidations. Competitive binding constants and metal-induced structural changes would determine the exact conversion and residual selectivity; neither a numerical yield nor complete inhibition of all oxidation follows merely from adding two equivalents of barium salt.

Without a competing hydrocarbon and without a crown receptor, catalyst 1 can still oxidize accessible secondary C–H bonds in the chain. Expect a less site-selective mixture of secondary oxidation products, predominantly ketones when two peroxide equivalents are effectively used, rather than the recognition-selected remote product pattern of catalyst 2.

The strongly electron-withdrawing, protonated ammonium end makes nearby C–H bonds less reactive, so the distribution need not be statistically uniform over every methylene. More distant secondary positions are comparatively favorable, while primary terminal C–H oxidation is generally harder. alcohol intermediates, incomplete conversion and unproductive peroxide consumption are also possible. Exact regioisomer ratios or a guaranteed quantitative yield cannot be predicted from the supplied conditions.

The terminal alkene of D first undergoes Wacker oxidation, giving the side chain $\mathrm{Ar}-\mathrm{C}{\mathrm{H}}_2-\mathrm{C}{\mathrm{H}}_2-\mathrm{COC}{\mathrm{H}}_3$. Alkene coordination to Pd(II), water attack, proton transfers and beta-hydride elimination give the ketone. Copper and oxygen regenerate the active palladium oxidation state.

Base removes a proton from the terminal methyl of that ketone. Its enolate attacks the neighboring aromatic aldehyde intramolecularly, closing a six-membered ring. Dehydration gives a conjugated cyclohexadienone-type intermediate, and keto-enol tautomerism furnishes aromatic naphthol E. The retained methoxy and MOM-protected oxygen groups follow the original aromatic-carbon positions.

F is the O-allyl ether of E. Carbonate forms the naphthoxide and allyl bromide undergoes an SN2 reaction at its terminal carbon. Heating F then causes a [3,3]-Claisen rearrangement: the O–allyl bond breaks, the terminal allyl carbon bonds to the adjacent naphthalene C1, and the phenolic carbon temporarily becomes a ketone. Rearomatization gives G, with a free phenolic OH and a C1 allyl group. The C1 position gives the favored alpha-substituted naphthol and avoids the alternative less favorable annulation pattern.

The final step is a dearomative Michael addition, not a Nef conversion of the nitro group. Hydrogen bonding from the thiourea activates nitroethylene. The nucleophilic C1 resonance form of G attacks the terminal carbon of $\mathrm{C}{\mathrm{H}}_2=\mathrm{CHN}{\mathrm{O}}_2$, and proton transfer converts the nitronate to a 2-nitroethyl substituent. The phenolic carbon becomes a ketone.

H is the corresponding 1-allyl-1-(2-nitroethyl)naphthalen-2-one, retaining the methoxy and MOM substituents of G. The second ring now has a C2=O group and a C3=C4 bond, while the other ring remains aromatic. The reported ${}^{13}$C signal near $202$ ppm is consistent with that newly formed ketone. Related dearomative additions establish this reaction class.^[ref]

C1 is now an all-carbon quaternary stereocenter bearing both allyl and 2-nitroethyl groups. Both the drawn thiourea and the starting materials are achiral, so H is racemic. A chiral catalyst would be needed to select one absolute configuration.

A is the kinetic, less-hindered-side silyl enol ether. Its double bond lies away from the methyl substituent. Forming B requires removal of a proton from the more hindered $\alpha$ position adjacent to the methyl-bearing carbon.

The base strengths alone do not determine the ratios. trimethylsilyl triflate is strongly electrophilic: oxygen silylation activates the ketone towards deprotonation, and irreversible trapping of the resulting silyl enol ether can make the product ratio reflect competing deprotonation rates. A weak amine therefore need not first produce a substantial equilibrium concentration of the free ketone enolate.

DBU is the strongest and comparatively accessible base, and distinguishes the two sites least strongly, giving the smallest A:B ratio. Triethylamine gives greater preference for the less-hindered site. The more sterically hindered diisopropylethylamine discriminates most strongly and gives the largest proportion of A. Its slightly higher conjugate-acid $p{K}_a$ than that of triethylamine does not reverse this trend, because steric accessibility and the coupled silylation/deprotonation mechanism matter alongside basicity. The data do not establish a simple thermodynamic enolate distribution.

Reductive ozonolysis cuts the unsaturated backbone into cyclopentane-1,3-dicarbaldehyde units, apart from end fragments. Both alkene carbons carry a hydrogen, so the carbonyl products are aldehydes rather than ketones. Ring substituent stereochemistry is inherited from the polymer repeat; backbone E/Z geometry does not survive cleavage.

Ozone adds across a backbone alkene by cycloaddition, giving a primary ozonide. Its fragmentation produces a carbonyl group and a carbonyl oxide, which recombine to a secondary ozonide. Dimethyl sulfide reduces the peroxide-containing intermediate, forming dimethyl sulfoxide and the two carbonyl termini. Repetition at every backbone double bond liberates the dialdehyde. An oxidizing work-up would instead risk oxidation to carboxylic acids, so the specified reductive work-up is essential.

A hydroxyl-directed Evans–Saksena reduction gives the required anti-1,3-diol. A suitable reagent is tetramethylammonium triacetoxyborohydride in an acidic medium, for example acetic acid/acetonitrile. Ligand exchange between the pre-existing alcohol and an acetoxyborohydride group tethers the reducing reagent to the substrate. Intramolecular hydride delivery to the ketone then proceeds through a six-membered arrangement, converting C=O to an alkoxide while conserving all existing stereocentres. Hydrolysis releases the second hydroxyl group.

The preferred directed transition-state conformation minimizes crowding by the larger carbon-chain substituents. It delivers the new C–H bond on the face that leaves the two hydroxyl groups anti, as in B: with the original hydroxyl drawn as a wedge in the printed zigzag, the new hydroxyl is dashed. The intervening methyl stereocentre is retained. Choosing an undirected borohydride reduction would not by itself rationalize this strong substrate-controlled relationship.

A consistent proposed sequence is desilylation, five-membered hemiketal formation, retro hetero-Diels–Alder opening, intramolecular aldol addition and hemiacetal closure. The essential carbon rearrangement is loss of the original ketone–side-chain bond and formation of a bond between its two neighbouring carbons; it is not a simple Michael addition.

For an explicit atom map, label the starting six-membered ring $A-B=C-D-E-O_r-A$, with the ketone at $D$, methyl substituents at $A$ and $B$, the hydroxy group at $A$, and the side chain $E-X-T-\mathrm{Et}$. Here $X$ is the methylene and $T$ is the carbon bearing the protected alcohol. Let $O_D$ be the original ketone oxygen and $O_T$ the protected alcohol oxygen. These labels identify atoms, not new substituents.

First, Fluoride removes the silyl protecting group from $O_T$. The resulting alcohol attacks the protonated ketone at $D$, forming the five-membered hemiketal $D-E-X-T-O_T-D$. The original oxygen $O_D$ is now a hydroxy group; the original pyran ring remains intact at this stage.

Next, The original pyran ring can undergo a retro hetero-Diels-Alder reaction. The three electron-pair movements are $B=C\to C=D$, $D-E\to E=O_r$ and $O_r-A\to A=B$: break $D-E$ and $O_r-A$, and form the three indicated double bonds. The result is the tethered aldehyde/dienol esterThe temporary $D-O_T$ bond keeps both reacting ends within the same molecule. At $D$, both oxygen substituents remain attached, and the new $D-O_T$ tether prevents separation into independent fragments.

Then The $C=D$ enol attacks the tethered aldehyde at $E$. Formation of $C-E$, restoration of $D=O_D$, and proton transfer give the six-membered lactone ring $C-D-O_T-T-X-E-C$, with $E-O_{r}H$. This is an intramolecular aldol reaction, and it supplies the crucial new carbon–carbon bond without losing any carbon atom.

Finally, Keto-enol tautomerism at $A=B$ gives the methyl ketone at $A$ and introduces the hydrogen at $B$. The $E-O_{r}H$ alcohol then attacks that ketone, closing the five-membered hemiacetal ring $A-B-C-E-O_r-A$. The resulting fused rings have exactly the product's connectivity: $D$ is the lactone carbonyl, $O_T$ is its ring oxygen, and $O_r$ is the five-membered-ring oxygen.

The stereocentre at $T$ survives throughout this sequence. The configuration initially at $E$ is erased at the aldehyde stage, and those at $A$, $B$, $C$ and $E$ arise during the later cyclization and proton-transfer steps. A folded intramolecular aldol reaction followed by reversible hemiacetal formation is consistent with the drawn cis ring junction, but connectivity and orbital bookkeeping alone do not prove that it is the unique selected diastereomer. In particular, a claim of simple retention at $E$ would contradict this atom map.

A related pyranone-to-fused-lactone rearrangement under aqueous hydrogen fluoride is experimentally reported; that account also explicitly qualifies the relative stereochemistry as assigned on mechanistic grounds. The sequence above is a proposed explanation of the examination structure, rather than a mechanism claimed to have been experimentally established in that paper.^[ref]

K is ethyl 4-(4-methylbenzoyl)-1H-pyrrole-2-carboxylate. AlCl${}_3$ activates the aroyl chloride to an acylium-like electrophile. Pyrrole attacks through C4, forming a sigma complex; deprotonation restores aromaticity and work-up releases the ketone from its Lewis-acid complex.

Unsubstituted pyrrole normally favours an $\alpha$ position, but the ester at C2 changes the regioselectivity. Attack at C5, or at C3, permits important sigma-complex contributors with positive charge at the ester-bearing C2, which is strongly destabilized by the electron-withdrawing ester. C4 substitution avoids that particularly unfavourable contributor. The C2 ester therefore directs the acylation towards C4, overriding the simple unsubstituted-pyrrole rule. Combining the starting ester with a p-toluoyl group while replacing a ring hydrogen gives ${\mathrm{C}}_{15}{\mathrm{H}}_{15}\mathrm{N}{\mathrm{O}}_3$, as required.

An unsaturated Rh(I)–BINAP complex undergoes oxidative addition of the aldehydic C–H bond, giving a Rh(III) acyl hydride. Coordination of the tethered alkene brings it into the chiral coordination sphere. hydride migration to the internal, tert-butyl-substituted alkene carbon places Rh on the terminal methylene. The resulting acyl–alkyl complex has the connectivity required for a five-membered ring. reductive elimination between its acyl and alkyl carbons closes the C–C bond, releases the cyclopentanone and regenerates Rh(I).

The aldehyde carbon becomes the ketone carbonyl carbon; its hydrogen ultimately reaches the alkene-derived internal carbon. The original tert-butyl substituent remains attached to the internal alkene carbon, which becomes the beta stereocentre of the cyclopentanone. alkene coordination and insertion favour the chiral pocket arrangement with the bulky tert-butyl group in the less crowded region of the BINAP complex. For the stated (S)-BINAP system the observed product is the $R$ beta-tert-butylcyclopentanone, equivalently the product with tert-butyl on the solid-wedge face in the supplied ring orientation. Its priorities are tert-butyl, the shorter carbonyl-side ring path, the other ring path, and hydrogen. The ligand's S label alone is not a general rule that every product stereocentre must be S; the substrate orientation in the catalyst must also be specified. No decarbonylation is needed in the productive hydroacylation cycle.

One valid asymmetric route uses N-Boc-(R)-proline as a chiral starting material. Convert its acid to the Weinreb amide with N,O-dimethylhydroxylamine and a coupling reagent such as EDC, then add phenylmagnesium bromide at low temperature. chelation of the magnesium tetrahedral intermediate prevents a second addition; aqueous workup releases the phenyl ketone. Reduce it with sodium borohydride, separate the resulting alcohol diastereomers, and retain the one with $R$ configuration at both pyrrolidine C2 and the benzylic carbinol. This is an asymmetric synthesis through a pre-existing enantiopure centre, even though the final reduction need not be perfectly diastereoselective. If the other protected alcohol is isolated, Mitsunobu esterification with a carboxylic acid followed by ester hydrolysis inverts just the carbinol centre. Keeping nitrogen Boc-protected during that inversion avoids neighbouring-amine participation. Mild Boc removal followed by reductive benzylation with benzaldehyde and sodium triacetoxyborohydride gives D, the $(R,R)$ amino alcohol. Use conditions that avoid epimerizing the amino ketone.

For ring expansion, activate D's alcohol with methanesulfonyl chloride and a tertiary amine base. Its own tertiary nitrogen attacks the benzylic carbon from the back, displacing mesylate with inversion and making a fused aziridinium ion. Acetate, supplied as a soluble acetate salt, attacks the original pyrrolidine C2 from the opposite face and breaks the old C2–N bond. The new N–benzylic-C bond is retained, incorporating that side-chain carbon into the six-membered ring. Inversion at the two successively attacked carbons gives the cis acetate/phenyl piperidine E in the displayed orientation. Attack at the benzylic carbon instead would simply open the three-membered ion back to a five-membered-ring derivative; specifying the attacked carbon is the crucial regiochemical step.

Silver(I) promotes iodide departure, with precipitation of AgI. The oxygen of dimethyl sulfoxide substitutes at the iodine-bearing carbon to form an alkoxydimethylsulfonium intermediate. Triethylamine removes the hydrogen on that carbon; collapse forms C=O and breaks O–S, releasing dimethyl sulfide. The result is ketone D by a Kornblum oxidation. In arrow terms, the C–H electrons form the carbonyl pi bond as the O–S bond breaks. The carbon bearing iodine becomes the carbonyl carbon; the existing bridged ether and acetonide are spectators. The iodine centre loses its tetrahedral stereochemistry because it becomes trigonal planar.

A suitable sequence is selective alpha-bromination, then enol O-methylation. Use one equivalent of Br${}_2$ under controlled acidic enolization conditions to introduce bromine at the enolizable alpha carbon that becomes the brominated vinyl carbon. The other alpha site is a constrained bridgehead and cannot form the required ordinary enol double bond. Then O-alkylate the ketone with trimethyloxonium tetrafluoroborate and remove the brominated alpha proton with a nonnucleophilic base such as triethylamine. Collapse of the O-methylated carbonyl oxonium gives the alpha-bromo methyl enol ether E.

The methyl group belongs on oxygen, not on the alpha carbon. Simply writing methyl iodide with an unspecified enolate would not guarantee this outcome because competitive C-alkylation is possible. Use conditions designed for carbonyl O-alkylation followed by deprotonation, and limit bromine to avoid overbromination or damage to the protecting group.