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A puckered conformation with an approximately planar alkene end and a nonplanar saturated part. Bulky substituents commonly favor pseudoequatorial positions.

An aldol reaction between two reactive sites of the same molecule. A tethered enol or enolate attacks a carbonyl group to close a ring; the tether, conformation and competing chemical reactions influence the product.

Number the cyclohexane consecutively, putting the top methylene group at C1 and the two original epoxides at C2/C3 and C5/C6. Both epoxide oxygens are up.

A is a diazidocyclohexanediol, with each epoxide replaced by one azide and one alcohol. A standard successive chair-favored opening gives N3 down at C2 and C5, OH up at C3 and C6. This is the 1,4-diazido/1,4-diol connectivity drawn in the bottom row of the original map.

For each opening, azide attacks from the face opposite oxygen, breaking one C–O bond with inversion at the attacked carbon. protonation of the two resulting alkoxides gives the two OH groups. After the first opening, the preferred conformation of the opened portion must be used for the second trans-diaxial opening; simply imposing one unchanged chair on both steps can select the wrong regioisomer.

The elemental change is addition of two ${\mathrm{N}}_3^{-}$ groups and two work-up protons to ${\mathrm{C}}_6{\mathrm{H}}_8{\mathrm{O}}_2$, giving ${\mathrm{C}}_6{\mathrm{H}}_{10}{\mathrm{N}}_6{\mathrm{O}}_2$. The formula alone would not distinguish alternative positional isomers; the depicted assignment uses the ordinary successive-opening conformational model.

B is the major product: the newly formed OH is the dashed bond in the printed zigzag structure. Retain the existing solid-wedge OH and the configuration at the carbamate-bearing carbon.

zinc coordinates the ketone oxygen and the adjacent hydroxyl oxygen, forming a five-membered O–Zn–O chelate. This constrains rotation around the carbonyl–alpha-carbon bond. In the favored chelated conformation the bulky $\mathrm{CH}(\mathrm{NHC}{\mathrm{O}}_2{\mathrm{R}}^{\prime })\mathrm{C}{\mathrm{H}}_2\mathrm{OR}$ group shields one face of the ketone, while the alpha hydrogen leaves the other more accessible. hydride attacks from that less crowded face, the carbonyl $\pi$ bond opens onto oxygen, and aqueous work-up gives the second alcohol.

Mapping this Cram chelation model back onto the printed zigzag gives B, not A. Merely placing a new OH “on the same side” of an unrotated page drawing is not a valid chelation argument: the reactive chelate and that drawing use different conformations. Zinc-borohydride reductions of alpha-hydroxy ketones are experimentally known to favor the corresponding anti-1,2-diol family under chelation control.^[ref]

The reagent combination can generate zinc borohydride and related zinc-associated reducing species. The stereochemical justification is coordination-controlled facial selectivity; it does not require identifying a unique solution aggregate from the reagent list. The quoted yield is not itself a measurement of a 95:5 diastereomeric ratio.

Label the carbon next to the carbonyl $C_{\alpha }$ and the OH-bearing carbon $C_{\beta }$. The three limiting routes are E1, E1cb and E2 elimination. They differ in whether C${}_{\beta }$–O cleavage, C${}_{\alpha }$–H cleavage, or both occur in the first elementary event. In the following original transition-state structures, dotted lines denote changing bonds, $\delta$ marks developing partial charge, and the bracketed structures carry $‡$. Unmarked skeletal bonds remain present. The dotted line parallel to C${}_{\alpha }$–C${}_{\beta }$ denotes the developing pi bond, in addition to its existing sigma bond.

For E1, C${}_{\beta }$–OH heterolysis occurs first. The electron pair in that bond goes to O, producing $\mathrm{C}{\mathrm{H}}_3\mathrm{COC}{\mathrm{H}}_2{\mathrm{C}}^{+}(\mathrm{H})\mathrm{C}{\mathrm{H}}_3+\mathrm{O}{\mathrm{H}}^{-}$. Its first transition state has a partly broken C${}_{\beta }$–O bond, developing positive charge on C${}_{\beta }$ and negative charge on the leaving O. Next, water uses a lone pair to remove the alpha proton; the C${}_{\alpha }$–H electron pair forms the C${}_{\alpha }$=C${}_{\beta }$ pi bond. This second transition state has partly broken C${}_{\alpha }$–H, partly formed water-O–H, and a partly formed C${}_{\alpha }$–C${}_{\beta }$ pi bond. Positive charge is transferred from the organic cation toward the incoming water/hydronium unit. hydroxide from the first step is a spectator in the second.

For E1cb, water first removes the alpha proton to form a resonance-stabilized enolate plus hydronium:The first transition state has partly broken C${}_{\alpha }$–H and partly formed O${}_{\mathrm{water}}$–H, with developing negative charge delocalized over the alpha-carbon/carbonyl-oxygen system and positive charge on the proton-accepting water unit. The enolate then expels hydroxide: use the carbon-centred contributor to send its alpha-carbon lone pair into C${}_{\alpha }$–C${}_{\beta }$, while the C${}_{\beta }$–O pair goes to oxygen. This second transition state has a partly formed alkene pi bond and partly broken C${}_{\beta }$–O, with negative charge moving from the enolate framework onto the departing hydroxide. hydronium is a spectator in this second step.

For E2, water removes the alpha proton as hydroxide leaves in the same elementary step. Three electron-pair movements are simultaneous: water lone pair to H${}_{\alpha }$, C${}_{\alpha }$–H to the C${}_{\alpha }$–C${}_{\beta }$ pi bond, and C${}_{\beta }$–O to O. Its single transition state therefore contains all three changing bonds: C${}_{\alpha }$–H, water-O–H and C${}_{\beta }$–O, together with the developing pi bond. The departing O becomes negative, the proton-accepting water unit becomes positive, and partial charge at carbon depends on the synchrony of proton loss and leaving-group departure. The reacting conformation should align C${}_{\alpha }$–H and C${}_{\beta }$–O approximately in an antiperiplanar conformation for efficient elimination.

These are formal limiting pathways for the displayed net process, not three claims of equal reaction rates in neutral water. In particular, unassisted loss of OH${}^{-}$ to a secondary carbocation is strongly disfavoured, and water is a weak base for making an enolate. The enolate pathway benefits from resonance stabilization and the final product is a conjugated enone, but actual rate and dominant pathway depend on chemical conditions. The displayed hydroxide and hydronium also rapidly neutralize each other; retaining them separately here tracks which bond cleavage supplied each species. No biological catalysis is needed to describe these chemical mechanisms.

Treat each semiquinonate ligand as a symmetric O,O chelate, with the free radical delocalized over the dioxolene framework. The ideal octahedral donor-connectivity structures are one trans form and two mirror-related cis forms, giving three stereoisomers. Trans refers to the two pyridine N donors, not to the two O atoms of a chelate, which must remain adjacent.

In the diagram, coloured curves join the two O donors belonging to one ligand. For an unambiguous coordinate specification, the trans form has Py at $+z,-z$, with chelate pairs $(+x,+y)$ and $(-x,-y)$. A cis pair has Py at $+z,+x$, with chelates $(-z,+y)$ and $(-x,-y)$; reflecting $y\mapsto -y$ gives the other cis form. Proper rotations cannot superpose those two cis arrangements. Ring conformations and pyridine rotations are not extra donor-connectivity isomers.

The first reagent supplies a vinyl nucleophile, $\mathrm{C}{\mathrm{H}}_2=\mathrm{CH}-$, rather than an allyl group. Two successive conjugate additions install vinyl at C2 and a 2-formylethyl chain at C1. Number the original nitro-bearing alkene carbon C1. Vinylmagnesium bromide attacks the beta carbon C2 of the nitroalkene, shifting the original C1=C2 electrons into a magnesium nitronate. The new C2–vinyl bond remains intact during the second stage; its terminal double bond is not the electrophilic site in that stage.

The carbon end of the nitronate at C1 then attacks the terminal beta carbon of acrolein. Move the acrolein C=C electrons towards its carbonyl and the C=O electrons onto oxygen. This forms the C1–CH2CH2CHO connectivity through an aldehyde enolate; protonation by methanol and tautomerization restore the aldehyde. The nitronate returns to a neutral nitro group as it makes the second C–C bond. Thus the chain is attached through the carbon formerly beta to the acrolein carbonyl, rather than by a direct addition to its aldehyde carbon.

After the first addition, C2 bears the vinyl group while the nitronate carbon C1 remains approximately planar. Approach of the second electrophile to the less crowded face, opposite the adjacent vinyl substituent, gives the new formylethyl chain trans to vinyl. Consequently nitro and vinyl are cis, as depicted: at C1 the chain and nitro group occupy opposite faces. This is a substrate-controlled diastereoselective tandem Michael addition. The reagents and starting material contain no chiral source, so the depicted product represents a racemic pair rather than an enantioselective synthesis. Steric facial selection explains the relative configuration without requiring a uniquely established magnesium aggregate or transition-state conformation.

The bridged, sterically hindered biphenyl framework is twisted and does not rapidly interconvert the two faces of each methylene group on the NMR timescale. Label one hydrogen on each CH2 $H_A$ and the other $H_B$. Replacing $H_A$ versus $H_B$ by a test substituent gives diastereomeric environments, so these hydrogens are diastereotopic and need not have equal chemical shifts even in an achiral solvent. Molecular symmetry relates the two $H_A$ sites to each other and the two $H_B$ sites to each other.

Each methylene hydrogen undergoes geminal coupling to its partner, giving the two doublets, each accounting for two hydrogens overall. Their separation is $0.21$ ppm; at operating frequency ${\nu }_0$ in MHz it corresponds to $0.21{\nu }_0$ Hz. This separation is not the geminal coupling constant, which must be measured from the line spacing within a doublet. If the shift separation is not large compared with that coupling, an AB pattern with second-order distortion is expected rather than ideal first-order doublets. A racemic pair of twisted conformations still has these signals: enantiomers have the same spectrum in an achiral medium, while the two hydrogen environments within each molecule remain different.

In both cases the alkene undergoes concerted oxygen transfer from metachloroperbenzoic acid. The alkene pi bond forms one C–O bond to the terminal peroxide oxygen; electron redistribution forms the second C–O bond, breaks O–O, and transfers the peracid proton to its carbonyl oxygen as the carboxylic acid product forms. This cyclic epoxidation pathway delivers both C–O bonds from one face, without a freely rotating carbon intermediate.

For 1-methylcyclohexene, the two alkene faces are enantiotopic. Attack from opposite faces gives the two mirror-related epoxides, and an achiral peracid in an achiral environment cannot distinguish their Gibbs energies of activation. The product is racemic, 1:1.

For the cis-fused bicyclic alkene, the junction configuration and its puckered ring conformation make approach from the two faces sterically different. The folded saturated ring shields the concave face; oxygen transfer preferentially approaches the more exposed convex face, directed away from that ring. The alternative attack places the incoming peracid closer to the folded skeleton. The 95:5 ratio represents facial diastereoselectivity, while concerted syn oxygen delivery is retained for either product. It should not be explained by free rotation or by one epoxide subsequently changing configuration. For scale only, if this ratio were measured under irreversible kinetic conditions at 298 K, it would correspond to $RT\ln (95/5)\simeq 7.30\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ difference between the competing Gibbs energies of activation; the exam does not specify that temperature.

With triethylamine present, proton transfer from thiophenol produces a more nucleophilic thiolate population. sulfur attacks the anomeric epoxide carbon C1 from the face opposite its epoxide C–O bond. Displacement by backside attack opens the epoxide, breaks C1–O, and leaves the former epoxide oxygen attached to C2. protonation of that alkoxide by thiophenol or triethylammonium gives G: SPh at C1 on the front face and OH at C2 on the back face, a trans relationship. This is inversion at C1 with retention of the C2 C–O bond; there is no need to invert every stereocentre. Rapid protonation also suppresses competing silyl transfer by the alkoxide.

Without added base, neutral thiophenol is less nucleophilic. acid-assisted cleavage at the anomeric epoxide bond can instead be accompanied by donation from the ring oxygen, giving an oxocarbenium ion with charge shared with the ring oxygen. thiophenol capture from the face that puts SPh back on the original epoxide face, followed by deprotonation, gives H with SPh and C2–OH both on the back face, the net-retention pathway. An ion-pair or highly asynchronous opening can provide this outcome; the drawing does not establish a long-lived free carbocation.

The distinction is configuration, not a mandatory fixed chair. For the closely matching trisilylated substrate, the primary study obtained both anomers with thiophenol alone, and established an unusual inverted chair for the alpha thioglycoside by NMR and crystallography. Thus H should be explained as an accessible product, not asserted to be the sole product or necessarily to have axial SPh in its preferred conformation.^[ref]

water stabilizes the planar amide more strongly relative to the twisted rotational transition region, increasing the free-energy barrier. nitrogen lone-pair donation into the carbonyl gives the C–N bond partial double-bond character through amide resonance, represented byamide bond rotation between the two amide conformations requires loss of favourable overlap. Near a strongly twisted geometry the nitrogen lone pair is less conjugated with C=O, and the charge-separated resonance in chemistry contribution is reduced. Polar water, a hydrogen bond donor, preferentially stabilizes the planar starting structures, including their polar carbonyl/resonance distribution, compared with this less conjugated rotational region. chloroform provides less of that differential stabilization. What controls the rate is the difference between the starting minimum and the transition state, not the absolute stabilization of either one in isolation.

For a first-order interpretation of the half-lives, the characteristic rate constants areThus the interconversion is 25 times slower in water. With comparable Eyring equation prefactors at the same temperature,which is about $8.0\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ at $298\mathrm{K}$. This temperature is illustrative because none is specified for the measurements.

The two endpoint conformations remain minima separated by a twisted barrier in each solvent. The profiles are schematic, with arbitrary absolute barriers; the half-life ratio supports the relative kinetic comparison. If the quoted half-lives describe relaxation of a reversible cis/trans mixture, $k_{\mathrm{obs}}=k_f+k_r$, so the ratio directly concerns relaxation rates. Assigning the full $RT\ln 25$ difference to one microscopic forward barrier additionally requires comparable equilibrium populations or directional-rate information.

Successive Si–O links have the same local bonding role, unlike the unequal links selected by an alternating phosphazene conformation. The polysiloxane backbone is described primarily by polar Si–O sigma bonds, with local oxygen lone-pair interactions rather than a localized single/double-bond sequence. There is therefore no alternating Si–O bond-order pattern that requires two characteristic distances. Equal chemical environments give equal bond lengths in the ideal repeating structure; local strain or packing can perturb individual distances.

The unequal P–N distances reflect unequal local bonding interactions in the alternating-chain conformation, rather than an extended conducting P=N pi system. nitrogen is much more electronegative than phosphorus, so the backbone sigma bonds are strongly polar. nitrogen lone-pair density can also donate into appropriately oriented antibonding P–substituent orbitals: negative hyperconjugation, schematicallyThe strengths of these interactions depend on the orientation of the donor and acceptor orbitals. In a planar cis–trans backbone, the P–N links are not all geometrically equivalent. Different overlap and charge redistribution give alternating greater and smaller effective P–N bond orders, hence shorter and longer bonds. A formal alternating P=N/P–N drawing is a useful shorthand for this inequality, but does not imply that isolated textbook single and double bonds are present with no electronic communication.

The historical island picture captures the limitation of pi interaction to local P–N–P regions rather than a continuous band along the whole chain. A modern description need not invoke strong phosphorus $3d$–nitrogen $2p$ bonding; polar bonding and donation into sigma-star orbitals provide the useful explanation. Calculations on oligomers found bond alternation for planar cis–trans conformations but not for optimized helices. Bond alternation is therefore conformation dependent, not a universal consequence of the repeat formula alone.^[ref]

The depicted trans-fused $A$ is chiral; cis-fused $B$ is achiral as a configurational species. The unsaturated ring makes the two sides of the fused system constitutionally different. At the trans junctions of $A$, the mirror image cannot be superposed by a proper rotation; there is no surviving mirror plane or inversion center that exchanges the two distinct rings correctly. A twofold rotational relationship is compatible with chirality and does not remove it. This is why simply importing the chirality conclusion for fully saturated trans-decalin would be unsafe.

For $B$, interchange of the two junction ends relates the opposite local stereochemical senses. An individual folded cis conformer may look chiral, but ring inversion interconverts its mirror-related conformations without changing junction configuration. The configurations therefore describe a meso/achiral species rather than a persistent enantiomeric pair. The conformational sketches below distinguish the rigid trans arrangement from the two accessible cis folds; the alkene ring is represented schematically as a half-chair-like unit.

For both substrates, the alkene pi bond attacks bromine and polarizes/breaks Br–Br. A bromine lone pair completes a three-membered bromonium ion, and bromide subsequently attacks a carbon from the opposite face, cleaving that C–Br bridge bond. The two new C–Br bonds are anti. A free carbocation that rotates before capture is not needed.

In trans-fused $A$, the fixed conformation makes the alternative anti-opening pathways diastereomeric. A chair-like, trans-diaxial opening is favored over a geometrically strained alternative that requires a twist/boat-like arrangement of the six-membered ring. The Fürst-Plattner rule describes this conformational preference. One depicted enantiomer of $A$ therefore gives essentially one dibromide diastereomer, with the two bromines occupying the trans-diaxial arrangement in its favored chair. If a racemic sample of $A$ were used, its other enantiomer would of course give the mirror product as well.

For cis-fused $B$, the accessible mirror-related folds and the equivalent anti pathways produce mirror-related dibromides with equal rates in an achiral environment. Adding the two bromines destroys the symmetry that made the starting configuration achiral. $B$ gives a racemic dibromide pair. The racemate follows from equivalent enantiomer-forming pathways, not from a loss of anti stereospecificity.

The relevant quantity is the H–C–C–H dihedral angle, through the Karplus relation, rather than the labels cis and trans alone. Couplings tend to be larger near eclipsed or antiperiplanar arrangements and smaller nearer a right angle. The observed value averages the accessible conformations.

In A, the saturated five-membered ring is puckered. A preferred envelope-like conformation can place the trans hydrogens closer to an antiperiplanar arrangement, giving a slightly larger coupling than the cis pair. In B, the double bond restricts ring geometry toward a flatter arrangement: the cis hydrogens are more nearly eclipsed, whereas the trans pair has an oblique dihedral angle. The cis coupling is then larger. Approximate Newman projections illustrate these trends; exact angles cannot be recovered from four coupling constants without a calibrated relation and conformational populations.

Use a cyclohexene half-chair, not a fully puckered saturated-cyclohexane chair. The alkene carbons and their directly attached bonds form the approximately planar end; the saturated part puckers. Put the $\mathrm{C}(\mathrm{OH})(\mathrm{C}{\mathrm{H}}_3{)}_2$ substituent pseudoequatorial at the opposite saturated methine to avoid a crowded pseudoaxial arrangement. Its methine proton is correspondingly pseudoaxial. This is a preferred conformation; the achiral spectra do not assign an absolute configuration.

The terminal ureidopyrimidinone groups supply the association sites. Their urea/pyrimidinone NH donors and carbonyl/ring-nitrogen acceptors can form a self-complementary array of four hydrogen bonds between two UPy units. Joining the two terminal units of one molecule by this noncovalent association closes the ring.

The ether-containing arms provide flexibility and spacing; they are not covalently joined together during ring formation. The ring is therefore a supramolecular conformation of the existing molecule, rather than a new covalent ether macrocycle.

DMSO is a strong hydrogen-bond acceptor. It competes for the NH donors of the UPy units and solvates the association sites, weakening their mutual hydrogen bonding.

For A, the intermolecular chains should shorten or dissociate, reducing the association-driven viscosity. For B, the intramolecular ring should become less populated, increasing the fraction of open conformations. Sufficient DMSO also weakens rings of A and any intermolecular associations of B. The covalent molecular skeletons remain intact.

The extent depends on DMSO fraction and the association free energies in the mixed solvent. solvent viscosity itself also changes, so the prediction concerns the supramolecular contribution rather than an unconditional numerical value for total solution viscosity.

Use two-dimensional NOESY, or ROESY where molecular tumbling makes NOESY less favorable, to look for through-space correlations between proton sites on the two ends that are brought together in the closed conformation. Assign resonances first and compare predicted ring contacts with an open reference or model.

The nuclear Overhauser effect involves NMR cross-relaxation through magnetic dipole–dipole coupling. Its strong approximate $r^{-6}$ dependence makes it sensitive to short interproton distances. A NOESY cross-peak therefore reports spatial proximity, including between sites far apart along the covalent skeleton; it is not a NMR scalar coupling transmitted along that skeleton.

Run a dilution series: end-to-end contacts that persist at concentrations where intermolecular association is negligible support intramolecular ring closure. Hydrogen-bonded NH chemical shifts and diffusion measurements can support the assignment, but neither alone proves ring topology. A flexible open chain can transiently bring ends together, and intermolecular contacts can also give NOEs. Several geometry-consistent cross-peaks, concentration behavior and controlled mixing times make the case much stronger than one peak.