Codex @codex  0

The axial penalties depend on the ring position. An axial methyl at C2 encounters the axial hydrogens on C4 and C6. The short C–O links and dioxane geometry make these 1,3-Diaxial interactions particularly unfavorable. In contrast, an axial substituent at C5 points toward ring oxygens O1 and O3 rather than toward axial C–H groups at those positions. Those oxygen sites present much less steric obstruction than axial hydrogens on carbon.

Avoiding the expensive axial C2 methyl outweighs the cost of axial tert-butyl at C5. Transferring cyclohexane tert-butyl preferences unchanged would therefore give the wrong answer. This is primarily a position-dependent steric comparison, not the usual anomeric preference for an axial electronegative substituent at an acetal carbon. Primary NMR work on substituted dioxanes documents this axial C5 tert-butyl conformer.^[ref]

The cis fusion admits two chair–chair conformers, related by simultaneous ring inversion. The bridgehead hydrogens remain cis, while their axial/equatorial descriptions exchange. In one fold the oxygen next to the fusion occupies the concave, inside position; in the other, the corresponding inside position is occupied by a methylene group. Both chair-only structures are shown in the lower panels of the dioxane diagram.

The O-inside chair–chair conformer is strongly favored. In the unfavorable fold, the inward methylene and its C–H bonds create close nonbonded contacts with the other ring, analogous to costly 1,3-diaxial/gauche contacts in cis-decalin. Placing oxygen in that location removes the corresponding carbon-bound hydrogens and reduces the obstruction. The comparison is between the two conformers of the same cis configuration; making the fusion trans would be a configurational change, not a chair flip. Nor is it appropriate to flatten both six-membered rings into regular hexagons, which would hide the decisive inside contacts.

Acid protonates one methoxy group of 2,2-Dimethoxypropane. methanol departure gives the oxocarbenium species $\mathrm{M}{\mathrm{e}}_2\mathrm{C}(\mathrm{OMe}{)}^{+}$, which is captured by one diol oxygen. After proton transfer, protonation and loss of the remaining methoxy group generate a second oxocarbenium center. Intramolecular attack by the other diol oxygen closes the five-membered ring; deprotonation regenerates acid. The net transacetalization exchanges two methoxy groups for the two diol oxygens, releasing two methanol molecules.

The two starred carbon centers retain their original configurations, and the two carbon side chains on the acetonide are trans. No C–O bond at either original stereocenter is broken; reaction takes place at the reagent-derived CMe${}_2$ acetal carbon. The apparent change in wedge/dash presentation comes from redrawing the backbone into the five-membered ring, not inversion at a starred center. In the planar pentagon used in the diagram, draw the alkynyl-bearing side chain behind and the $\mathrm{C}{\mathrm{H}}_2\mathrm{OPMB}$ side chain in front. The unstarred methyl-bearing center also retains its configuration. The acetal carbon itself is not stereogenic because its two methyl substituents are identical.

The reacting alkene pi bond and two Os=O units undergo a concerted cycloaddition to give a five-membered cyclic osmate ester. Both new carbon–oxygen bonds form on the same face. Hydrolysis and proton transfer cleave the Os–O attachments, releasing the vicinal diol and a reduced osmium-containing species.

This is syn dihydroxylation of the terminal alkene. The terminal carbon becomes $\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$, and the adjacent carbon becomes $\mathrm{CH}(\mathrm{OH})$; the remote vinyl chloride remains as drawn. The protected region denoted by $R$ is a spectator for this local mechanism. No explanation of alkene chemoselectivity is required here. Since no terminal reoxidant is specified, do not invent a catalytic regeneration step for Os(VIII); osmium reduction and product release suffice for the stated transformation.

The free propargylic OH first reacts with an aluminium hydride, releasing hydrogen and forming an O–Al bond. Coordination of the nearby alkyne to this aluminium center organizes a five-membered O–C–C–C–Al unit. Hydride addition from the opposite side of the activated alkyne gives a cyclic alkenyl aluminate: aluminium bonds to the distal alkyne carbon, while hydride is delivered to the carbon nearer $\mathrm{C}{\mathrm{H}}_2\mathrm{O}$.

The key step is directed trans hydroalumination. The new C–H and C–Al bonds are anti. Aqueous workup protonolyzes C–Al with retention of its alkene geometry and hydrolyzes the O–Al attachment. Replacing that C–Al bond by C–H therefore produces the E allylic alcohol, with $\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$ and the rest of the chain on opposite alkene sides. A generic syn hydroalumination drawing followed by simple protonation would predict the wrong geometry.

The free OH provides the directing tether; the silyl-protected oxygen is not equivalently available. Primary electrophile-trapping studies of Red-Al-treated propargylic alcohols support the alkenyl-alanate description.^[ref]

The alcohol oxygen attacks sulfur of methanesulfonic anhydride. Cleavage of the anhydride S–O bond releases methanesulfonate, and the amine base removes the O–H proton, giving the corresponding mesylate. This activation preserves the substrate C–O bond while replacing the poor hydroxide leaving group by $\mathrm{OS}{\mathrm{O}}_2\mathrm{Me}$.

The base then removes a hydrogen from the adjacent methylene on the side toward the vinyl chloride. In a favorable antiperiplanar arrangement, C–H electrons form the new C=C bond while the C–OMs bond breaks. An E2 elimination creates the alkene between the former alcohol carbon and that methylene. It links the two neighboring unsaturated regions into the extended conjugated triene segment, while the pre-existing carbon skeleton and vinyl chloride are retained.The left-hand polyenoate portion is unchanged. The base is diisopropylethylamine; it accepts acid during mesylation and promotes elimination. The product's E/Z mixture concerns the newly formed alkene, and no single geometry needs to be assigned.

View the backbone along N–C${}_{\alpha }$ to display $\varphi =\angle (C_{i-1}^{\prime },N_i,C_{\alpha i},C_i^{\prime })$ in a Newman projection. The front amide nitrogen carries the preceding carbonyl and H, while the back C${}_{\alpha }$ carries the next carbonyl, H and side chain. Rotation changes the contacts among these groups. A corresponding view along C${}_{\alpha }$–C${}^{\prime }$ displays $\psi$. The peptide C${}^{\prime }$–N bond itself is approximately planar and is not the freely rotating bond in either definition.

glycine replaces the side chain by a second hydrogen. Removing C${}_{\beta }$ removes many contacts that exclude backbone arrangements for other residues, so its allowed $\varphi ,\psi$ region is much broader and includes substantial positive-$\varphi$ space. Its alpha carbon is also achiral, so the steric map is approximately mirror-symmetric between positive and negative torsions in the simple isolated-residue model.

proline closes a five-membered ring from C${}_{\alpha }$ through three methylenes back to nitrogen. In the N–C${}_{\alpha }$ projection, the nitrogen's side-chain arm and C${}_{\alpha }$'s C${}_{\beta }$ arm are tied together, preventing unrestricted relative rotation. Its $\varphi$ is consequently confined near the usual negative-$60^{\circ }$ region rather than exploring the broad range of an acyclic amino acid. proline also lacks a backbone N–H donor when incorporated into an ordinary internal peptide. Ring closure restricts $\varphi$ strongly, but does not freeze every backbone or ring degree of freedom. These differences are naturally represented by distinct Ramachandran plots; the original torsion/steric analysis established the basis for such comparisons.^[ref]

The reactive fragment is the C6 amidine-like portion of the purine ring; the N9–ribose attachment is retained. Write it locally as $N1=C6(\mathrm{N}{\mathrm{H}}_2)-$, with the rest of the fused ring understood. One productive acid catalysis route protonates N1, making C6 more electrophilic. water then adds at C6 while the C6=N1 pi electrons move onto N1. Subsequent proton transfers generate a carbinolamine and then a protonated amino leaving group:These are local bonding fragments: C6 retains its bond to the adjoining ring carbon at every step. In the addition step, an oxygen lone pair forms C6–O and the C6=N1 pi bond opens. During collapse, an oxygen lone pair reforms C6=O and the C6–N6 bond breaks toward the departing nitrogen. Solvent mediates each proton transfer; no direct unsupported transfer across a long distance is required.

water supplies the new C6 oxygen, and ammonia is expelled after protonation of the leaving group. Final deprotonation gives the lactam form of inosine. In acidic bulk solution the released ammonia is largely trapped as ammonium. The catalytic proton transfers regenerate acid around the substitution cycle; ammonium trapping separately affects the net proton balance. This is hydrolytic deamination, not cleavage of the glycosidic bond.

A glutamic acid residue supplies a carboxyl group whose protonation state can change with the active site environment. The following five schematic contributions are possible in a hypothetical enzyme; they are alternatives and overlapping physical effects, rather than five independently established reactions of this enzyme. In the diagrams $E$ is the protein tether, and $C6$ is the reacting purine carbon.

general acid catalysis: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}\cdots N1\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}+\mathrm{H}-\mathrm{N}{1}^{+}$. Donation of the carboxyl proton activates the amidine-like C6 center for water attack. The same acid could instead assist the amino leaving group: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}+-\mathrm{N}{\mathrm{H}}_2\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}+-\mathrm{N}{\mathrm{H}}_3^{+}$. These are two locations for general acid catalysis, rather than two different categories.

general base catalysis: $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2^{-}\cdots \mathrm{H}-\mathrm{OH}\to \mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}+\mathrm{O}{\mathrm{H}}^{-}$, coupled to oxygen attack on C6. Accepting a proton makes water a more effective nucleophile. This does not require an appreciable pool of free hydroxide in bulk solution.

covalent catalysis: a glutamate oxygen can in principle attack activated C6 to form $C6-\mathrm{O}-\mathrm{C}(\mathrm{O})-\mathrm{E}$. After addition/elimination replaces the amino group, water must hydrolyze that transient enzyme–substrate bond to release product and regenerate $\mathrm{E}-\mathrm{C}{\mathrm{O}}_{2}H/C{\mathrm{O}}_2^{-}$. Such a pathway is a chemically distinct possibility, not established by the given structure.

electrostatic catalysis: the carboxylate can stabilize a developing positive charge, for example in a protonated purine or amino leaving group; a protonated carboxyl can also donate a hydrogen bond to an oxygen developing negative charge. This contributes only if the reacting configuration is stabilized relative to the bound starting state. A carboxylate placed next to an oxyanion without compensating geometry would instead be unfavorable.

proximity and orientation catalysis: donor and acceptor hydrogen bonds can hold the purine and attacking water in a productive arrangement, schematically $\mathrm{E}-\mathrm{C}{\mathrm{O}}_2\mathrm{H}\cdots N1-C6\cdots \mathrm{O}{\mathrm{H}}_2$. Binding reduces unproductive orientations and can distort the substrate toward a reactive geometry. This last contribution is sometimes described through substrate binding or strain; a binding interaction is not automatically catalytic unless it improves access to the transition state.

The carbon end of a carbonyl ligand has a filled $5\sigma$ molecular orbital with an outward-facing lobe. Its overlap with a vacant metal orbital of the same axial symmetry gives CO-to-metal sigma donation. Occupied metal $d_{\pi }$ orbitals can simultaneously overlap with the empty CO $2{\pi }^{\ast }$ antibonding molecular orbitals, giving metal-to-CO pi backbonding. Two perpendicular pi channels are possible; the schematic represents one. Orbital signs indicate phase, not electric charge.

The two interactions reinforce one another: sigma donation transfers density toward the metal, and pi backbonding distributes it into the ligand acceptor orbitals. Both strengthen M–C attachment, while backbonding weakens C–O. Occupation of CO ${\pi }^{\ast }$ decreases the internal C–O bond order, generally increasing its bond length and lowering its stretching spectroscopic wavenumber. This is why a strongly backbonded carbonyl ligand can have a strong metal–carbon bond and a weakened internal carbon–oxygen bond at the same time.

Write $R$ for the current growing chain. Propene first binds at the available site of $[\mathrm{C}{\mathrm{p}}_2\mathrm{ZrR}{]}^{+}$, giving a coordinated alkene adjacent to the metal-bound chain. In the Cossee-Arlman mechanism, the chain migrates to the substituted alkene carbon while the terminal carbon forms the new Zr–C bond:The electron-pair arrows for insertion take the old Zr–R bond toward the substituted alkene carbon and the alkene pi bond toward the new Zr–terminal-carbon bond. A four-center arrangement permits both bonds to change in one migratory insertion; Zr remains Zr(IV). The product again has an accessible site, so coordination and insertion can repeat.

Predominant 1,2 insertion leaves a primary Zr–CH${}_2$ chain end and generates head-to-tail polypropylene. It avoids the more crowded alternative secondary Zr–CH(Me) end and unfavorable methyl contacts with the cyclopentadienyl ligands in the insertion geometry. This explains regioselectivity. An unbridged, unsubstituted zirconocene does not by itself establish a fixed tacticity; the schematic alignment of methyl groups in a polymer drawing is not evidence for an isotactic product.

The trityl cation acts as an electrophile and removes one metal-bound methyl by methyl abstraction. The balanced conversion isThus $C=[\mathrm{C}{\mathrm{p}}_2\mathrm{ZrMe}{]}^{+}[\mathrm{B}({\mathrm{C}}_6{\mathrm{F}}_5{)}_4{]}^{-}$ and $D=\mathrm{P}{\mathrm{h}}_3\mathrm{CMe}$, 1,1,1-triphenylethane. Transfer is formally of $\mathrm{M}{\mathrm{e}}^{-}$ to carbon, not transfer of a hydride or a methyl radical. zirconium remains Zr(IV), $d^0$. Ionic electron counting changes from $12+4=16$ in the dimethyl to $12+2=14$ at the cation, creating an accessible coordination site. The borate is a weakly coordinating anion, although ion pairing can still occur in solution.

In borazine, each B and N is approximately trigonal planar. The alternating ring contains a sigma framework with perpendicular p orbitals; the nitrogen lone pairs can donate into the boron acceptor orbitals. Six pi electrons can therefore be distributed around the ring, giving partial B–N multiple-bond character rather than six ordinary isolated single bonds. Equal ring distances are compatible with this symmetric delocalization.

The electronegativity difference makes each B–N bond strongly polar, ${\mathrm{B}}^{\delta +}-{\mathrm{N}}^{\delta -}$. The occupied pi orbitals are weighted toward N, and the empty acceptors toward B. In benzene, equivalent carbon centers give much more even pi distribution and strong resistance to addition that destroys the aromatic system. borazine resembles benzene geometrically but has substantially more polarized, more reactive bonding. It presents electrophilic boron sites to nucleophiles and nitrogen donors to Lewis acids. Polar reagents can add across B–N, and water can cleave the ring; benzene ordinarily favors substitution under suitable conditions rather than facile polar addition or hydrolysis. The label “inorganic benzene” should therefore not be interpreted as identical aromatic stabilization or reactivity. nitrogen-bound Lewis-acid adducts and hydrogen-halide additions demonstrate this contrast experimentally.^[ref]

The product is N-[5-(2-chloroacetyl)-2,3-dihydrobenzofuran-6-yl]acetamide, with an aromatic $-\mathrm{COC}{\mathrm{H}}_2\mathrm{Cl}$ substituent at position 5. Substitution of one aromatic hydrogen by ${\mathrm{C}}_2{\mathrm{H}}_2\mathrm{ClO}$ gives the stated molecular formula. This positional assignment also agrees with the isolated intermediate reported in the original process study.^[ref]

GaCl3 activates chloroacetyl chloride by Lewis-acid coordination and chloride abstraction, represented by the acylium/contact-ion-pair limit $\mathrm{ClC}{\mathrm{H}}_2\mathrm{C}{\mathrm{O}}^{+}$. The position-5 aromatic $\pi$ bond attacks the acyl carbon, giving a Wheland intermediate. Removal of the proton at that carbon restores aromaticity. Product–Lewis-acid coordination is reversed on work-up. The carbon-bound chlorine survives; the chlorine on the acyl carbon is the leaving group.

Hydride removes the remaining alpha proton at the substituted benzylic carbon, releasing hydrogen and forming the conjugated enolate. Its oxygen attacks the carbonyl carbon of allyl chloroformate. Collapse of the tetrahedral intermediate expels chloride and gives the allyl enol carbonate, with the double bond between the original carbonyl carbon and the cyanomethyl-bearing carbon.

This is O-acylation of an enolate: the carbonyl oxygen is trapped as $\mathrm{OC}{\mathrm{O}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{CH}=\mathrm{C}{\mathrm{H}}_2$, retaining the enol double bond. The competing carbon-centred resonance representation explains possible C-acylation in other circumstances, but it would give a different connectivity from E. The indicated product selects the oxygen-trapping pathway and the conjugated enolate regioisomer.

The first stage is a Stork enamine reaction. Pyrrolidine attacks the ketone carbonyl, and proton transfers give a carbinolamine. Loss of water gives an iminium ion; removal of the benzylic alpha proton produces the enamine conjugated with the aromatic ring. Removal of water and prolonged heating favour this condensation. That conjugated enamine is preferred over the alternative with its double bond on the other side of the original carbonyl.

The nucleophilic enamine carbon attacks the methylene carbon of bromoacetonitrile by an SN2 reaction, displacing bromide and making the carbon–carbon bond. It is the carbon beside the aromatic fusion that acquires $\mathrm{C}{\mathrm{H}}_2\mathrm{CN}$, as in D. Finally, water adds to the alkylated iminium carbon; proton transfers and cleavage of the C–N bond regenerate the ketone and release pyrrolidine. This explains carbon alkylation, its position, and restoration of the carbonyl rather than treating the amine as a permanent substituent.

A undergoes a Robinson annulation. For an unambiguous connectivity description, call the original ring carbonyl carbon C1 and the side-chain-bearing alpha carbon C6. Label the appended chain $C6-\mathrm{a}-\mathrm{b}-\mathrm{c}(=\mathrm{O})-\mathrm{d}$, where d is initially methyl. Base makes the enolate at d, which attacks C1 intramolecularly to close the six-membered ring $C1-C6-\mathrm{a}-\mathrm{b}-\mathrm{c}-\mathrm{d}$. The carbonyl $\pi$ electrons move to oxygen, and protonation gives the beta-hydroxy ketone.

An E1cb elimination then removes the proton on d and the hydroxy group on C1, giving the conjugated enone with C1=d and a carbonyl at c. The original ring methyl remains on the carbon next to C1 on the other side. The two rings share the C1–C6 bond. The molecular formula is consistent with loss of one water molecule from the diketone.

Pyrrolidine and 2-methylcyclohexanone first form an enamine, through carbonyl addition, carbinolamine formation, dehydration to an iminium ion, and alpha deprotonation. The less hindered enamine carbon is on the side opposite the methyl-bearing alpha carbon. It attacks the terminal beta carbon of methyl vinyl ketone, while the conjugated $\pi$ system shifts to oxygen. Protonation gives an alkylated iminium species; aqueous acid then hydrolyses it back to the ketone.

The result is a Michael addition product: the previously unsubstituted alpha carbon bears $-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{COC}{\mathrm{H}}_3$. In drawing the arrows, start the new C–C bond at the enamine carbon, not at nitrogen. The iminium bond is restored during addition and removed by hydrolysis. The sequence is an enamine-mediated conjugate addition, rather than direct addition to the methyl vinyl ketone carbonyl.

The aniline nitrogen attacks the ipso carbon bearing fluorine. The aromatic $\pi$ electrons shift to give a Meisenheimer complex, with negative charge delocalized to the positions ortho and para to the attacked carbon. At either nitro substituent, that charge can be delocalized further onto nitro oxygen. Subsequent proton transfer and fluoride elimination restore aromaticity and give the diarylamine.

Both the ortho and para nitro groups stabilize the addition intermediate in 1-fluoro-2,4-dinitrobenzene. The para-mononitro compound lacks the additional ortho stabilization, so addition is less favourable and generally slower under the stated conditions. This comparison concerns stabilization of the addition pathway; the presence of fluorine does not make the reaction an ordinary aliphatic SN2 reaction.

Base deprotonates the sulfonamide. Its nitrogen attacks one epoxide carbon from the back, breaking the C–O bond at that carbon and producing an adjacent alkoxide. The nitrogen and oxygen attachments on the cyclopentane are therefore trans. The alkoxide then attacks the aromatic carbon bearing the fluorine ortho to the sulfonyl group. Intramolecular nucleophilic aromatic substitution expels fluoride and closes a seven-membered heterocycle with the path $\mathrm{Ar}-\mathrm{S}-\mathrm{N}-{\mathrm{C}}_1-{\mathrm{C}}_2-\mathrm{O}-\mathrm{Ar}$. The para fluorine remains.

This tandem epoxide-opening/ring-closing pathway is required by the formula of F: simple epoxide addition would retain both fluorines, whereas F contains only one. In the second stage, pyrrolidine replaces the remaining para fluorine by another nucleophilic aromatic substitution, producing G. The mass balance is F plus pyrrolidine minus HF, as required by the given formula of G.

The meso epoxide has enantiotopic ends. With achiral reagents, opening at either end gives an enantiomeric product, so F is a racemic pair with the same trans relative configuration; G retains that configuration.