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$\mathrm{A}=\mathrm{K}[{\mathrm{B}}_5{\mathrm{H}}_8]$ is nido; $\mathrm{B}=\mathrm{K}[{\mathrm{B}}_6{\mathrm{H}}_{11}]$ and $\mathrm{C}={\mathrm{B}}_6{\mathrm{H}}_{12}$ are arachno. The initial hydride removes an acidic bridging hydrogen as a proton, releasing ${\mathrm{H}}_2$ and retaining the potassium counterion. Addition of one $\mathrm{B}{\mathrm{H}}_3$ unit expands the boron framework; final protonation supplies the neutral hexaborane and KCl. These assignments conserve all the atoms in the displayed sequence, without inserting an unshown dehydrogenation step.

For ${\mathrm{B}}_{\mathrm{n}}{\mathrm{H}}_{\mathrm{m}}^{\mathrm{q}-}$, take one terminal B–H bond per vertex and remove its $2n$ electrons from the valence total. The skeletal electron count is $3n+m+q-2n=n+m+q$. ThusWade's rules assign $n+1$, $n+2$ and $n+3$ pairs to closo, nido and arachno frameworks respectively. A derives from a six-vertex closo octahedron by removal of one vertex, giving a square-pyramidal boron skeleton. B and C have six-vertex open frameworks formally derived from an eight-vertex closo polyhedron by removing two vertices. Their additional hydrogens are distributed over bridging and other open-face positions; counting every hydrogen as an independent terminal B–H vertex would give the wrong classification.

The arachno assignment of $[{\mathrm{B}}_6{\mathrm{H}}_{11}{]}^{-}$ has specific theoretical and NMR support. It should not be replaced by a permanently localized, unrearranged $[{\mathrm{B}}_5{\mathrm{H}}_8{]}^{-}\cdot \mathrm{B}{\mathrm{H}}_3$ picture: the corresponding symmetric adduct participates in fluxional rearrangement rather than being the lowest-energy structure.^[ref]

Only one bromine is replaced by hydrogen. Writing the unchanged protected chain as $R=\mathrm{THPOC}{\mathrm{H}}_2\mathrm{CH}(\mathrm{Me})$, the product is $R\mathrm{CH}=\mathrm{C}(\mathrm{Me})\mathrm{CH}=\mathrm{CHBr}$, retaining the original internal alkene geometry and forming predominantly the $Z$ terminal bromoalkene: bromine and the carbon chain lie on the same side of that new stereodefined double bond. The formula is consequently ${\mathrm{C}}_{13}{\mathrm{H}}_{21}\mathrm{Br}{\mathrm{O}}_2$.

Phosphine dissociation exposes Pd(0), which undergoes preferential oxidative addition into the less hindered C–Br bond, the bromine trans to the carbon chain in the gem-dibromoalkene. hydride transfer from tributyltin hydride replaces the palladium bromide ligand, producing tributyltin bromide and an alkenyl–Pd–H intermediate. reductive elimination joins the alkenyl carbon and hydride, regenerating Pd(0). Retention of the alkenyl geometry through this sequence puts the surviving bromine cis to the chain. The conjugated carbon skeleton and protecting group remain intact; this is not addition of tin hydride across either alkene. The stereoselective monohydrogenolysis is established for this reagent combination.^[ref]

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.

The oxime is reduced at its C=N bond rather than cleaving N–O: hydride addition to the imine carbon followed by protonation gives an N-substituted hydroxylamine. In a chair-like model of the cis-fused ring system, the fused framework and methyl group make the two faces inequivalent. The favoured hydride trajectory accesses the face that places the newly installed C–H bond behind the original drawing and the retained C–NHOH bond in front, giving D. It avoids the more congested trajectory into the folded bicyclic framework; a flat hexagon comparison alone misses this facial distinction.

The existing methyl and junction centres are retained. The selectivity is therefore diastereoselective substrate control, not enantioselectivity from sodium cyanoborohydride, which is achiral. For a racemic starting bicycle the same relative stereochemical preference gives a racemic pair of D enantiomers.

methyl fluorosulfonate alkylates the tertiary isoxazolidine nitrogen, giving a quaternary N-methyl ammonium salt; the methyl remains attached to nitrogen in F. hydride from lithium aluminium hydride then cleaves the N–O bond, releasing the corresponding oxygen as an aluminium-bound alkoxide while restoring neutral tertiary amine nitrogen. Aqueous workup protonates the alkoxide to give the alcohol.

Thus the C–O bond made in the cycloaddition survives as the alcohol-bearing C–O bond, and the formaldehyde-derived methylene survives as the extra carbon between nitrogen and the carbon framework. The N–O bond is the one removed. N-methylation followed by reductive N–O cleavage gives the bridged amino alcohol F without requiring cleavage of its newly formed C–C bond or hydrogenation of a nonexistent residual alkene.

Transfer of a hydrogen nucleus from a donor to an acceptor. Electron-pair bookkeeping distinguishes transfer of ${\mathrm{H}}^{+}$ from transfer of a hydride equivalent.

Zirconocene chloride hydride, $\mathrm{C}{\mathrm{p}}_2\mathrm{Zr}(\mathrm{H})\mathrm{Cl}$, used for hydrozirconation.

Formation of a carbonyl accompanies migration of an adjacent C–H or C–C bond and departure of a leaving group. An alkoxide-assisted hydride migration can convert a suitably aligned halohydrin into a ketone.

Transfer of one electron between species, often converting an enol or enolate into a radical. It must be distinguished from transfer of a two-electron hydride.

$\mathrm{NaB}{\mathrm{H}}_4$, a hydride donor that commonly reduces aldehydes and ketones while leaving ordinary amides unchanged under mild conditions.

The hydride reagent $\mathrm{NaB}{\mathrm{H}}_3\mathrm{CN}$. Its comparatively mild reactivity permits selected imine and iminium reductions.

$\mathrm{NaBH}(\mathrm{OAc}{)}_3$, a hydride reagent often used for iminium-selective reductive amination.

The organotin hydride $\mathrm{B}{\mathrm{u}}_3\mathrm{SnH}$, a hydrogen-atom or hydride source depending on the reaction system.

A hydride reagent that can coordinate nearby oxygen donors while reducing a carbonyl.