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Addition of an enolate or enol to an aldehyde or ketone, giving a beta-hydroxy carbonyl compound. Subsequent dehydration is a distinct step and gives an aldol condensation.

Addition of a nitroalkane-derived nitronate to an aldehyde or ketone gives a beta-nitro alcohol after protonation. Subsequent dehydration is possible under some conditions but is a separate step.

The new bridge is made by an intramolecular Michael addition. On the cyclohexanone side, the methyl-bearing fused alpha carbon is quaternary and cannot be deprotonated there. triethylamine can instead generate a small equilibrium population of the enolate at the other, methylene alpha carbon. Its carbon attacks the beta carbon of the enone in the seven-membered ring. The enone pi electrons move towards its carbonyl and then onto oxygen, creating the new bridge and a second enolate.

protonation of that enolate at the former methyl-substituted enone alpha carbon restores the left-hand ketone. The initial enone C=C has therefore become a saturated C–C bond while one new transannular C–C bond forms. Both ketones are retained, and the initial two-ring framework becomes a three-ring framework without changing the total index of hydrogen deficiency. The methyl originally at the fused quaternary centre does not migrate; the other methyl ends up on a protonated, formerly unsaturated carbon. A strong-base concentration large enough for quantitative enolate generation is unnecessary for a favourable intramolecular trapping reaction, and neither an aldol dehydration nor a methyl shift is needed.

triethylamine removes an alpha proton from nitromethane to generate a nitronate population. Its carbon attacks the cyclic ketone carbonyl of E, forming a new C–CH2NO2 bond while the C=O pi pair moves onto oxygen. protonation by triethylammonium or another proton donor gives the tertiary alcohol F and regenerates base. This is a Henry reaction, also called a nitroaldol reaction: the former ketone carbon now bears both OH and CH2NO2.

The nitro group remains attached to its original nitromethane carbon; attack through oxygen would give a different connectivity. The methyl acetal and the original alcohol substituents need not be cleaved or displaced. This addition produces the isolated connectivity without requiring dehydration to a nitroalkene. The stated complex mixture is compatible with competing additions or stereoisomers, but the scheme supplies no basis for claiming F is the unique or kinetically dominant product. Only its formation is being explained.

Let $\mathrm{Ar}=p-\mathrm{MeO}{\mathrm{C}}_6{\mathrm{H}}_4$. One standard route is:where the last two carbons are joined through oxygen to form the epoxide shown in the product drawing.

Use rigorously dry conditions for Grignard formation/addition; quench only after the aldehyde addition. Dehydration gives the styrene, and peracid oxidation transfers oxygen across its double bond. The methoxy substituent is compatible with this sequence. No asymmetric reagent is specified, so the target epoxide is racemic.

Open the lactone formally at its acyl–oxygen bond, then replace the resulting secondary alcohol by its ketone precursor. With $R=\mathrm{CH}(\mathrm{Me})\mathrm{CH}(\mathrm{Me}{)}_2$, the useful sequence of retrosynthetic intermediates isDisconnect the last compound as a Michael addition product of the methyl-side enolate of $\mathrm{RCOC}{\mathrm{H}}_3$ and ethyl methacrylate:The substituted carbon of the methacrylate becomes the methyl-bearing carbon alpha to the lactone carbonyl. The ketone carbon becomes the oxygen-bearing ring carbon. This checks the six-membered ring connectivity.

The required branched methyl ketone itself comes from butan-2-one by ethyl-side aldol addition to acetone, followed by dehydration and selective hydrogenation:Choose and isolate the aldol regioisomer shown. For the subsequent Michael step, use a bulky base at low temperature to favour its less hindered methyl-side kinetic enolate. Reduce the resulting ketone selectively with $\mathrm{NaB}{\mathrm{H}}_4$ while retaining the ester, hydrolyse the ester, then acidify and promote intramolecular esterification with water removal. The hydroxy acid closes to the required six-membered lactone. There is no specified stereochemical relationship to enforce, but a stereochemically pure target would require an additional selectivity or resolution step.

The five-membered enone-like carbon framework can be obtained by an intramolecular aldol condensation ofEnolization at an internal methylene next to one ketone followed by attack on the opposite ketone closes a five-membered ring. dehydration leaves one acetyl group attached to one alkene carbon and one methyl group on the other. The two nitrile-bearing carbons remain adjacent and their original cis relationship is retained if epimerization is avoided.

Now reverse a reductive ozonolysis: the diketone arises by opening a six-membered cyclohexene whose alkene carbons each carry Me. That cyclohexene is the Diels-Alder reaction product of 2,3-dimethylbuta-1,3-diene and maleonitrile. The latter is the supplied cis dinitrile. The stereospecificity of the cycloaddition puts the two CN groups on the same face.

Thus the forward plan is Diels–Alder addition, reductive ozonolysis, then five-membered aldol ring closure and dehydration. Use a reductive ozone work-up that stops at the diketone. During the final step, avoid prolonged strongly basic heating because the carbons bearing CN can be deprotonated and epimerized. Achiral reagents give the racemic pair with the required cis relationship; resolution would be necessary if only the depicted enantiomer were required. The diene supplies six carbons and maleonitrile supplies four, accounting for all ten carbons without an unexplained carbon deletion.