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E, with the axial anomeric acetate, hydrolyses faster. The tert-butyl substituent strongly favours the chair in which it is equatorial, so the two substrates cannot freely interchange axial and equatorial acetate simply by an inexpensive ring inversion. protonation activates the anomeric acetoxy leaving group. As its C–O bond cleaves to release acetic acid, a lone pair on the endocyclic oxygen donates into the developing anomeric orbital, producing an oxocarbenium ion. water attacks that carbon, and deprotonation gives the cyclic hemiacetal. Attack from either face accounts for the unspecified anomeric configuration of OH in the product.

The axial C–OAc bond in E can adopt antiperiplanar geometry relative to an endocyclic oxygen lone pair. This favourable $n_O\to {\sigma }_{C-O}^{\ast }$ interaction assists departure in the ionization transition state. The corresponding bond in F is poorly aligned in its preferred chair; achieving comparable overlap requires an unfavourable chair change, placing tert-butyl axial, or substantial ring distortion. The distinction is stereoelectronic control of acetal hydrolysis, rather than merely counting steric crowding in the products.

An axial acetal can itself receive ground-state stabilization from the anomeric effect, so “axial means unstable” is not an adequate rate argument. What matters is the relative Gibbs energy of activation for the departing bond and the geometry of lone-pair assistance. Conformationally locked model acetals experimentally demonstrate faster acid-catalysed cleavage of the axially oriented isomer, although their numerical rate ratios should not be transferred to these different substrates.^[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.

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 beta-carbon bond-forming transition state retains the same basic connectivity across this pH range, but the predominant proton-transfer route and enzyme protonation change. Near the acidic end, protonated glutamate can act as a general acid, donating a proton or a strong hydrogen bond to carbonyl oxygen and making C3 more electrophilic; it is less available as the carboxylate general base that activates water. Above its local $p{K}_a$, carboxylate-mediated water activation is favored. Acid catalysis therefore shifts positive-charge stabilization toward a protonated carbonyl, whereas base-assisted attack reduces positive-charge buildup on incoming water. Neither a unique transition-state geometry nor a numerical pH optimum follows from pH alone.

Using a free-solution glutamate side-chain $p{K}_a\simeq 4.2$ only as an illustration, the deprotonated fraction is $[1+10^{p{K}_a-\mathrm{pH}}{]}^{-1}$: about 0.059 at pH 3 and 0.998 at pH 7. An enzyme environment can shift that $p{K}_a$ substantially. The glutamine amide and the hydrocarbon side chains remain in their ordinary forms from pH 3 to 10; arginine guanidinium, with a typical free side-chain $p{K}_a$ around 12.5, remains predominantly positive even at pH 10. Thus the major side-chain switch among those listed is glutamate. At the alkaline end, bulk hydroxide can also contribute to nonenzymatic conjugate addition. A measured pH-rate profile must control substrate stability and enzyme folding before assigning every loss of activity to an active-site titration.

Y91F implicates the Tyr hydroxyl, while E57Q implicates the Glu carboxylic-acid chemistry. Replacing tyrosine by phenylalanine retains an aromatic side chain but removes its hydroxyl, supporting a role for Tyr91 as a hydrogen bond donor that polarizes the steroid C3 carbonyl and stabilizes an enolate-like intermediate or transition state. Its hydroxyl could participate in a proton relay, but inactivity alone does not establish that it supplies the final proton.

Replacing a glutamate residue by glutamine approximately preserves side-chain size while replacing a titratable carboxylic acid by an amide. Loss of activity, combined with the acidic activity range, supports protonated Glu57 as a carbonyl-activating acid and possible proton donor. The two residues can cooperate to stabilize oxygen charge during reduction. The inhibitor-binding structure supports local contacts; it is not a direct picture of a testosterone transition state, and an N–H contact of the aza inhibitor need not occur in testosterone.

To distinguish these chemical roles from indirect effects, compare mutant and wild-type abundance, membrane insertion and folding, cofactor binding, and steroid binding. Measure initial rates with matched enzyme amounts and include no-enzyme and inhibitor-treated wild-type controls. If binding survives but turnover fails, the evidence for a catalytic defect is stronger. The published study combines structure, mutagenesis and modeled testosterone placement, so the proposed residue roles should be distinguished from direct observation of proton trajectories.^[ref]

A dissociative substitution begins with slow CO loss,followed by capture of the incoming ligand in coordination chemistry. A more electron-releasing $L$ increases metal-to-CO pi backbonding in the six-coordinate reactant, stabilizing it and strengthening its M–CO attachments. Removing CO sacrifices a useful pi acceptor from that electron-rich center. Thus the activation free energy for CO dissociation often rises and the substitution slows. Within an otherwise matched series, $k_d\propto \exp [-\Delta G^{‡}/(RT)]$ captures this sensitivity. The rate depends on the relative energies of reactant and dissociation transition state, so the trend is conditional: large changes in steric hindrance, geometry or mechanism can override the electronic effect.

The CO trans to a phosphine ligand competes for metal pi donation with a weaker pi acceptor than CO itself, whereas a cis CO has another CO trans to it. The trans-to-phosphine carbonyl can therefore benefit from stronger M–CO pi backbonding; loss of one of the four cis carbonyls is commonly favored. Capture of the incoming phosphine at that vacancy gives the cis bis(phosphine) product. The fourfold statistical availability of cis sites reinforces an electronic preference but does not establish it by itself.

This is the carbonyl cis effect, rather than the square-planar trans effect applied without qualification. A fuller explanation compares the five-coordinate dissociation transition states and their ligand site preferences. Product geometry alone cannot prove which CO first departed, because the intermediate can rearrange before capture. Isotopically labeled CO exchange is a more discriminating experiment; the classic studies explicitly separate this issue from product stereochemistry.^[ref]

The forward and reverse pathways pass through the same transition state. Measured from the cis minimum, the forward barrier is $E_{a,1}$; measured from the trans minimum, the reverse barrier is $E_{a,-1}$. Since $E_{a,-1}=E_{a,1}+2.23\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, the trans minimum lies $2.23\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ below the cis minimum in the elementary energy-profile model:The absolute barrier heights cannot be deduced from their difference. The following original profile uses an arbitrary transition-state height and labels that distinction explicitly.

The ordering is allyl chloride $>$ 1-chloropropane $>$ 2-chloropropane. Iodide is a good nucleophile but a weak base, and polar aprotic solvent acetone favours its SN2 reaction. SN2 reaction and C–Cl cleavage occur in one step; precipitation of sodium chloride can also favour halide exchange without changing the basic steric comparison.

The primary saturated chloride supplies the reference rate. Allyl chloride is also primary, but its neighbouring pi system stabilizes the developing delocalized electronic structure in the substitution transition state. It can therefore react about 64 times faster without requiring a free allylic carbocation. The secondary chloride is sterically crowded at the attacked carbon, making backside approach and the crowded transition state less favourable; its rate is about 0.02 times the primary value. The leaving group and nucleophile are the same in the comparison, so assigning the ordering to different halide leaving groups would be incorrect. If prefactor differences are neglected, $\Delta \Delta G^{‡}=-RT\ln (k/k_{\mathrm{ref}})$ at 333 K gives roughly $-11.5$ and $+10.8\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for the allylic and secondary substrates respectively: modest barrier changes produce large rate ratios.

The products lie below the reactants, while the transition state lies above both. On an energy-versus-reaction-coordinate plot, the forward activation energy is the vertical separation $E_{\mathrm{TS}}-E_{\mathrm{R}}$, not the difference between product and reactant energies. For an exothermic elementary path, $\Delta E=E_{\mathrm{P}}-E_{\mathrm{R}}<0$, and the reverse barrier is $E_{a,-}=E_{a,+}-\Delta E>E_{a,+}$.

The primary chloride undergoes an SN2 reaction; the triphenylmethyl chloride undergoes an SN1 reaction. The primary site is accessible to back-side attack, whereas three phenyl groups make back-side attack at the triphenylmethyl site extremely hindered and stabilize its carbocation through resonance.

For the SN2 reaction, a suitable transition state isThe entering C and leaving Cl lie on opposite sides of the reacting carbon, with partial C–C and C–Cl bonds. The total charge is $-1$. This transition state is not a discrete reaction intermediate.

For the SN1 reaction, the approximately planar $\mathrm{P}{\mathrm{h}}_3{\mathrm{C}}^{+}$ carbocation is a genuine reaction intermediate. Assuming its formation by C–Cl heterolysis is rate determining and trapping is rapid,Thus the limiting rate law is independent of ethanol concentration. The successive attack and proton transfer occur after the slow ionization; a cation-stabilizing environment and efficient trapping underpin this idealized SN1 description.

The first two operations invert the allylic hydroxyl group. Triphenylphosphine adds to the azodicarboxylate, generating the reagent pair that converts the alcohol into an alkoxyphosphonium leaving group. Benzoate displaces it with inversion at carbon, giving the inverted benzoate ester. Methoxide then cleaves that ester by nucleophilic acyl substitution, retaining the newly inverted carbon–oxygen stereochemistry because cleavage occurs at the acyl group, not by substitution at the stereogenic carbon.

The inverted allylic alcohol exchanges with the orthoacetate under acid catalysis. Ethanol loss produces an allyl ketene acetal, schematically $\mathrm{C}{\mathrm{H}}_2=\mathrm{C}(\mathrm{OEt})-\mathrm{O}-(\mathrm{allyl})$. A six-membered suprafacial Johnson-Claisen rearrangement breaks the allylic C–O bond, shifts the ring alkene by one position and forms the new bond from the original alkene terminus to the ketene-acetal CH${}_2$. The result is the $-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_2\mathrm{Et}$ substituent at the carbon that was the remote end of the original double bond. A chair-like transition state placing the larger substituents away from axial crowding explains the stereochemical transfer; the inverted alcohol configuration selects the corresponding face.

Finally, TiCl${}_4$ activates the anomeric methoxy group and methoxide departure creates an oxocarbenium ion. Hydride transfer from triethylsilane replaces that methoxy substituent by hydrogen. The ring oxygen and pendant OTBS group remain intact. The sequence is inversion, stereospecific allylic rearrangement, then reductive removal of the anomeric methoxy group, rather than direct reduction or hydrolysis of the ester introduced by the Claisen step.

Stoichiometry gives H = $\mathrm{Ph}(\mathrm{TMP}{)}_3\mathrm{CuL}{\mathrm{i}}_3$, formally F plus two LiTMP units. A compatible ring connectivity is $\mathrm{Ph}-\mathrm{Cu}-{\mathrm{N}}_1-\mathrm{Li}-{\mathrm{N}}_2-\mathrm{Li}-{\mathrm{N}}_3-\mathrm{Li}$, closed through a lithium–phenyl interaction. The TMP attached to copper, N${}_1$, remains chemically distinct; N${}_2$ and N${}_3$ belong to the more labile lithium-amide part.

Reversible detachment and reattachment of a symmetric $(\mathrm{LiTMP}{)}_2$ segment can exchange its two amides and reassign which Li occupies the phenyl-contacting or nitrogen-bridging positions. It can therefore exchange all three Li sites and the two Li-associated TMP groups while retaining the Cu-bound TMP group. Fast TMP-ring conformational inversion can further average methyl environments without exchanging entire ligands. These are different kinds of motion; simple ring inversion alone cannot explain exchange of the lithium sites. Such a dissociative interpretation is consistent with the experimentally studied lithium-rich aggregate, but the exchange pattern does not determine a unique transition state or prove that every bond breaks in one concerted event.

acetone first forms a proline enamine by reversible iminium formation and alpha-deprotonation. The enamine attacks the aromatic aldehyde in a hydrogen-bonded arrangement involving the catalyst's carboxylic acid. hydrolysis of the resulting iminium releases the beta-hydroxyketone and regenerates proline. The usual L-proline arrangement gives the $R$ secondary alcohol.

The sterically crowded aryl–amide axis is selected at the same bond-forming step: rapid rotation in the aldehyde permits the catalyst to react preferentially with the conformer that puts the smaller carbonyl-oxygen side of the amide towards the approaching aldol transition structure and the bulky diisopropylamino side away. A chair-like enamine–aldehyde model minimizes the interaction of the amide with the catalyst-side axial hydrogen; reversing the amide orientation creates the less favourable diastereomeric transition state. Replacing planar CHO by tetrahedral CH(OH)CH${}_2$COMe then raises the rotation barrier and traps the axis. This is a dynamic kinetic resolution, not resolution of two configurationally stable starting atropisomers.

To specify the predicted major axis without relying on a flat bond-line formula, look from the aromatic ipso carbon towards the amide carbonyl carbon. Put the higher-priority aryl path, the trimethylsilyl-bearing ortho side, at nine o'clock. The preferred model puts the carbonyl oxygen at approximately six o'clock and the diisopropylamino group at twelve o'clock. This is $S_a$ using the near-to-far high-priority convention; oxygen outranks nitrogen at the far end. Coupled with the alcohol assignment, the model predicts $(R,S_a)$. The drawing defines the configuration even if an alternative viewing direction is used. The dynamic-resolution mechanism is established by the primary aldol study; the product-axis assignment here is a stereochemical-model prediction for the printed substrate.^[ref]

A potential-energy profile plots the potential energy of the reacting system along a specified path from reactants through a transition state to reaction products. It is a particular kind of energy profile. For an elementary reaction, a suitable reaction coordinate parametrizes the path; a multi-step reaction mechanism needs the coordinates of its successive steps. See the IUPAC Gold Book: potential-energy profile.

A reaction intermediate is formed during a reaction mechanism and consumed in a subsequent step, cancelling from the net chemical equation. It can accumulate, as I does in the consecutive first-order reaction mechanism. A reaction intermediate can also connect transformations in energy coupling. Unlike a catalyst, it need not be present before conversion begins.^[ref]

A reaction intermediate is distinct from a transition state: the former can persist between steps, whereas the latter describes passage through a barrier. The existing potential energy surface and energy profile provide the configuration-space picture; the time-dependent concentration of an intermediate instead measures an ensemble of reacting entities. Low concentration or short lifetime can make detection difficult, so failure to detect a proposed reaction intermediate is not by itself proof of absence. Conversely, detecting a chemical species does not establish that it carries the proposed route to the final reaction products; it could belong to a competing route.

A transition state describes configurations at the barrier between reactants and reaction products in an elementary reaction. It is a crossing region, rather than a stable substance that accumulates in a bottle. The IUPAC definition characterizes these configurations by equal probabilities of proceeding toward reactants or reaction products: ^[ref]. Lowering the barrier relative to the starting configuration can increase a reaction rate, even when the overall change in Gibbs free energy is unchanged.

Transition state theory relates an elementary reaction's rate constant to a Gibbs energy of activation. The Eyring expression used in the catalyst example assumes every passage counted at the transition state succeeds. More generally, a factor accounting for unsuccessful passage multiplies it. Comparing barriers alone gives the quoted speedup only when the remaining prefactors agree. Free-energy profiles can depend on temperature, so the example's values at $300\mathrm{K}$ do not determine a temperature curve. See the IUPAC Gold Book: transition state theory.