10 Reaction mechanisms : Part (ii) Polar reactions

10 Reaction mechanismsPart (ii) Polar reactions

Kevin N. Dalby

Division of Medicinal Chemistry, College of Pharmacy, University of Texas at Austin,Austin, TX, 78712, USA

This review places an emphasis on papers reporting polar reaction mechanismsin 2002, predominantly in aqueous solutions, where substantial new mechanisticknowledge is presented. Theoretical studies are not generally considered to bewithin the scope of this review.

1 Proton transfer

This section covers reactions where the process of proton transfer is a criticalcomponent of the reaction.

As organic chemists continue to evolve new methods to catalyze chemical reactionsmore mechanistic questions are posed. Liu et al. report further studies on a poly-amine-supported pyridoxamine transaminase mimic 1.1 The system displays goodcatalysis, Michaelis–Menton kinetics and substrate selectivity. Transamination isgenerally susceptible to general acid–base catalysis and thus it was suggested thatgeneral acid–base catalysis exerted by the polymeric partially protonated amine is oneof the reasons for the observed rate enhancement of this system. The catalyst wasmade by covalently attaching pyridoxamine to polyethylenimine that also had hydro-phobic lauryl groups attached to it. Interestingly, for hydrophobic substrates, lauryl-ation of the polymer increases the rate of chemical transformation and decreases Km,possibly by producing a less aqueous reaction environment and by selective binding. Itis estimated that for some substrates this system is some 10000-fold faster than thereaction of simple pyridoxamine with pyruvic acid.

Understanding the strength of hydrogen bonds is fundamental to many questionsin biochemistry. Donati et al. report evidence for an unusually strong intramolecularC–H–O bond in an o-carboranyl β-lactoside 2 in solution.2 The interaction takes placebetween the activated C2–H of the carboranyl cage and the anomeric oxygen ofthe glucose ring of lactose (O�1). The existence of the strong bond was confirmed byab initio quantum mechanical calculations. Reasons for why the bond is observed arediscussed.

The process of enolization underlies many biochemical processes. Several papersreport thermodynamic and kinetic parameters for enolization processes. Eberlin and

DOI: 10.1039/b212015c Annu. Rep. Prog. Chem., Sect. B, 2003, 99, 351–377 351

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View Article Online / Journal Homepage / Table of Contents for this issue

http://dx.doi.org/10.1039/b212015c

http://pubs.rsc.org/en/journals/journal/OC

http://pubs.rsc.org/en/journals/journal/OC?issueid=OC003099

Williams examined the halogenation of the enol tautomer of 2-cyanoacetamide 3.3

The reactions of 2-cyanoacetamide with both bromine and iodine at low halogenconcentration in aqueous acid solution were shown to be first order in halogen and2-cyanoacetamide, suggesting that halogenation (khal) of the enol tautomer 4 is rate-limiting. Furthermore, the observed rate constants for bromination and iodinationwere very similar, indicating that both probably occurred at the encounter limit. Thisassumption enabled a value for the equilibrium constant for enolization of 3 to bedetermined as KE = 6 × 10�10.

352 Annu. Rep. Prog. Chem., Sect. B, 2003, 99, 351–377

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McCann et al. examined the enol–keto tautomerization of 9-anthrol 6 and foundthat the equilibrium constant for keto–phenol tautomerization (KE = [phenol, 6]/[ketone, 5]) is 0.08.4 This was determined from ratios of rate constants for ketoniz-ation of anthrol and phenolization of anthrone in aqueous acetic acid buffers. Acidcatalysis of tautomerization was noted. The H3O

�-catalyzed reaction is subject to asolvent isotope effect of kH/kD = 4.8, consistent with rate-limiting protonation of9-anthrol 6 at carbon C-10 of the anthracene ring.

In Richard’s laboratory second-order rate constants were determined in D2O fordeprotonation of acetamide 7, N,N-dimethylacetamide 8, and acetate anion 9 bydeuteroxide ion and for deprotonation of acetamide 7 by quinuclidine.5 The values ofkB = 4.8 × 10�8 M�1 s�1 for deprotonation of acetamide 7 by quinuclidine (pKBH =11.5) and kBH = 2–5 × 109 M�1 s�1 for the encounter-limited reverse protonation of theenolate by protonated quinuclidine give pKa

C = 28.4 for the ionization of acetamide asa carbon acid. The limiting value of kHOH = 1 × 1011 s�1 for protonation of the enolateof acetate anion by solvent water and kOH = 3.5 × 10�9 M�1 s�1 for deprotonation ofacetate anion by HO� give pKa

C approximately 33.5 for acetate anion. The authorsnote that a downward break in the slope of the plot of log kOH against carbon acidpKa for deprotonation of a wide range of neutral α-carbonyl carbon acids by hydrox-ide ion is the result of a change in the rate-limiting step from chemical proton transferto solvent reorganization. It is noted that α-NH2 and α-OMe groups show similarstabilizing interactions with the carbonyl group, while the interaction of α-O� is only3.4 kcal mol�1 more stabilizing than α-OH.

In a related paper the group report on the formation and stability of several peptideenolates in aqueous solution and compare their properties.6 Using their standard

Annu. Rep. Prog. Chem., Sect. B, 2003, 99, 351–377 353

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approach second-order rate constants kOD (M�1 s�1) were determined in D2O fordeprotonation of several N-terminal α-amino carbons of glycylglycine 12, glycyl-glycylglycine zwitterion 13, glycylglycylglycine anion 14, N-acetylglycine anion 10 andN-acetylglycinamide 11 by deuteroxide ion. The data were used to estimate values ofkHO (M�1 s�1) for proton transfer from these carbon acids to hydroxide ion in H2O.Values of the pKa for these carbon acids ranging from 23.9 to 30.8 were obtained byinterpolation or extrapolation of good linear correlations between log kOH and carbonacid pKa established in earlier work for deprotonation of related neutral and cationicα-carbonyl carbon acids. An interesting point noted by the authors is that the α-aminocarbon at a N-protonated N-terminus of a peptide or protein likely undergoesdeprotonation about 130-fold faster than the α-amino carbon at the correspondinginternal amino acid residue. They also point out how kinetics and thermodynamicsdo not always correlate. For example, the value of kOH for deprotonation of theN-terminal α-amino carbon of the glycylglycylglycine zwitterions 13 (pKa = 25.1) issimilar to that for deprotonation of the more acidic ketone acetone (pKa = 19.3), as aresult of a lower Marcus intrinsic barrier to deprotonation of cationic α-carbonylcarbon acids. This study also shows that while the cationic NH3

� group is generallymore strongly electron-withdrawing than the neutral NHAc group, α-NH3

� andα-NHAc substituents result in very similar decreases in the pKa of several α-carbonylcarbon acids.

Kresge and Meng compared oxygen and sulfur effects on keto–enol chemistry inseveral benzolactone systems.7 Carbon-acid ionization constants, Ka

C were deter-mined by spectrophotometric titration in aqueous solution for benzo[b]-2,3-di-hydrofuran-2-one 16 (pKa

C = 11.87), benzo[b]-2,3-dihydrothiophene-2-one 17 (pKaC =

8.85), and benzo[b]-2,3-dihydrofuran-2-thione 15 (pKaC = 2.81). Rates of approach to

keto–enol equilibrium were also measured for 15 and 17 in perchloric acid, sodiumhydroxide, and buffer solutions, and the rate profiles constructed from these data gavethe ionization constants of the enols ionizing as oxygen or sulfur acids pKa

O = 5.23 for17 and pKa

S = 2.69 for 15. Combination of these acidity constants with the carbon-acid ionization constants according to the relationship pKa

C/pKaO/S = KE then gave the

keto–enol equilibrium constants pKE = 3.62 for 17 and pKE = 0.12 for 15. The fourth,


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all-sulfur, member of this series, benzo[b]-2,3-dihydrothiophene-2-thione 18, existssolely as the enol in aqueous solution, and only the enol ionization constant pKa

S =3.44 could be determined for this substance; the limits pKE < 1.3 and pKE < 2.1,however, could be set. The unusually high acidities and enol contents of thesesubstances are discussed.

As part of an effort to gain further insight into the intrinsic proton affinitiesof common purine bases in aqueous solution the acidity constants of protonated7,9-dimethylguanine, 7-methylguanosine, 7,9-dimethylhypoxanthine, 7-methylinosine,9-methyladenine, 1,9-dimethyladenine, 7,9-dimethyladenine and 1-methyladenosinewere determined in aqueous solution at 25 �C.8 These studies provide estimates for theacidity of the N1, N3 and N7 sites of the various derivatives.

Dickerson and Janda report catalysis of aldol chemistry by norcotine 19 a nicotinemetabolite.9 They demonstrated that norcotine (2.4 mM) enhances the reaction of4-nitrobenaldehyde 20 with acetone 21 by more than 10-fold. The mechanism remainsto be deduced, but presumably involves general acid–base catalysis.

Sievers and Wolfenden examined the equilibrium of formation of the 6-carbanionof uridine monophosphate, a potential intermediate in the action of orotidine5�-monophosphate (OMP) decarboxylase.10 To evaluate the approximate pKa value ofthe 6-CH group of uridine monophosphate in water they took Richard’s approachand measured the rate of deuterium exchange in the model compound 1,3-dimethyluracil (DMU) 22. The experiments were performed at elevated temperaturesand the results were then extrapolated to room temperature. The pKa of the 6-CH


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group was estimated to be 37, which suggests that the corresponding carbanion doesnot exist as a discrete intermediate in the enzymatic reaction.

2 Hydride transfer

Hydrogen quantum mechanical tunneling has been suggested to play a role in a widevariety of hydrogen-transfer reactions in chemistry and enzymology. The majority ofpublished work on hydride transfer is theoretical in nature and beyond the scope ofthis review. However, some papers pertinent to the experimentalist are included here.

In an interesting paper Kohen and Jensen examined the boundary conditionsfor the Swain–Schaad relationship which are often used as a criterion for hydrogentunneling.11 This is based on the breakdown of the semiclassical prediction for therelationship among the rates of the three isotopes of hydrogen (hydrogen: H, deuter-ium: D, and tritium: T). The semiclassical (no tunneling) limit that is typically used(e.g., 3.34, for H/T to D/T kinetic isotope effects), is based on simple theoreticalconsiderations of a diatomic cleavage of a stable covalent bond. Kohen and Jensenreport a new semiclassical limit (e.g., 4.8 for H/T to D/T kinetic isotope effects), whosebreakdown can serve as a more reliable experimental evidence for tunneling in thecommon mixed-labeling experiment (which they describe).

Mayr et al. examined the reactivity of substituted benzhydryl carbocations 23 with

unsaturated hydrocarbons to determine the hydride donor reactivities of unsaturatedhydrocarbons.12 The kinetics of hydride transfer were found to be almost independentof the solvents or counterions employed. The analysis also shows that compared toSN1 reactions there is only a small substituent effect on the reactivity of hydridedonors. The group also examined the role of intrinsic barriers on rate–equilibriarelationships in hydride transfer reactions,13 using quantum chemical calculations atvarious levels of ab initio and DFT theory. MP2/6-31�G(d,p)//RHF/6-31�G(d,p)


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calculations suggest that electron-releasing substituents in the hydride donors increasethe exothermicity of the reaction, while electron-releasing substituents in the hydrideacceptors decrease exothermicity. In line with Hammond’s postulate, increasing exo-thermicity shifts the transition states on the reaction coordinate toward reactants, asrevealed by geometry parameters and the charge distribution in the activated com-plexes. Interestingly, independent of the location of the transition state on the reactioncoordinate, a value of 0.72 is found for Hammond–Leffler’s α = δ∆G ‡/δ∆ rG � whenthe hydride acceptor is varied, while α = 0.28 when the hydride donor is varied. Thissuggests that the value of α does not report the position of the transition state. It isalso noted that for the degenerate reactions XYC��CH–CH3 � XYC��CH–CH2

� themigrating hydrogen carries a partial positive charge in the transition state and theintrinsic barriers increase with increasing electron-releasing abilities of X and Y. Thus,substituent variation in the donor influences reaction enthalpy and intrinsic barriersin the opposite sense, while substituent variation in the acceptor affects both terms inthe same sense. Thus explaining why substituent effects in the donor are small.

On a similar topic Lee et al. examined the tightness contribution to the Brønsted αfor hydride transfer between NAD� analogues.14 They previously applied Marcustheory of atom and group transfer to hydride transfer reactions and predicted that theBrønsted α depends on the location of the substituent, whether it is in the donor or theacceptor, and the tightness of the critical configuration, as well as the resemblance ofthe critical configuration to reactants or products. The current paper now confirmsthis prediction experimentally for hydride transfer reactions between heterocyclic,nitrogen-containing cations.

3 Acetal chemistry

Three interesting papers examined several aspects of acetal chemistry. Torsionaleffects on the reactivity in glycosyl transfer were reported by Dean et al.15 Theyexamined the rates of hydrolysis of several p-nitrophenyl (PNP) acetals and concludedthat torsional effects in glycopyranosides are significant, but not large. While the foursubstituents in 25 reduce the reactivity in a glycopyranoside by a factor of >107

compared with the parent tetrahydropyranyl acetal 24, most of this is attributed to theinductive influence of the substituents. It is concluded that torsional effects contributea factor of up to 50 towards this total of 107.

In a related study Dean and Kirby examined concerted general acid and nucleo-philic catalysis of acetal hydrolysis as a simple model for lysozyme.16 The mono-anion 26 is the most reactive ionic form of the symmetrical formaldehyde acetal of4-hydroxybenzofuran-3-carboxylic acid. The evidence presented is consistent with amechanism in which the carboxylate anion acts as a nucleophile to assist the general


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acid catalyzed cleavage of the C–O bond to the leaving group: the initial product isthe cyclic acylal 27 and the extra acceleration derived from the participation of theneighboring nucleophile contributes some two orders of magnitude to a total rateenhancement of almost five orders of magnitude over the rate expected for specificacid catalysis.

Rose and Williams report on the effects of detergents on the acid catalyzedhydrolysis of substituted benzaldehyde di-Me acetals 28.17 They provide evidence forcatalysis by association of the acetals with micelles.

4 Elimination reactions

Jia et al. examined the borderline between E1cB and E2 mechanisms using chlorideisotope effects.18a A chlorine leaving group isotope effect was measured for the base-promoted elimination reaction of 1-(2-chloro-2-propyl)indene 29 in methanol at 30 �Cof k35/k37 = 1.0086 ± 0.0007 with methoxide as the base and k35/k37 = 1.0101 ± 0.0001with triethylamine as the base. The large chlorine isotope effects combined with largekinetic deuterium isotope effects of 7.1 and 8.4, respectively, are not consistent with apreviously proposed irreversible E1cB mechanism but with an E2 mechanism with the


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transition states having large amounts of hydron transfer and very extensive cleavageof the bond to chlorine.18b

As part of a continuing study of solvolysis reactions Zeng and Thibblin looked atthe competing processes of base-promoted E1 and E2 reactions of a tertiary substrate4-chloro-4-(4�-nitrophenyl)pentan-2-one 30.19 The solvolysis of 30 in aqueous aceto-nitrile yields the alcohol. 4-hydroxy-4-(4�-nitrophenyl)pentan-2-one 31 and theelimination products 4-(4�-nitrophenyl)-2-oxopent-4-ene 32, (E )-4-(4�-nitrophenyl)-2-oxopent-3-ene 33, and (Z )-4-(4�-nitrophenyl)-2-oxopent-3-ene 34. The possiblemechanisms of alkene formation are discussed. Acetate and other weak bases areproposed to react through either an E2 or E1cB mechanism.

The mechanism of base-promoted HF elimination from 4-fluoro-4-(4-nitro-phenyl)butan-2-one 35 was examined.20 Leaving-group fluorine and secondarydeuterium multiple kinetic isotope effects (KIEs) were determined. The size of thedetermined fluorine KIE is 1.0009 ± 0.0010 when acetate is used as base. The second-ary deuterium KIEs are 1.009 ± 0.017, 1.000 ± 0.018, and 1.010 ± 0.023 for formate,acetate, and imidazole, respectively. This new data is consistent with an E1cBmechanism.

Dey et al. measured several equilibrium constants for dehydration of wateradducts of aromatic carbon–carbon double bonds.21 Equilibrium constants (Kde) arereported for the dehydration of hydrates of benzene, naphthalene, phenanthrene, andanthracene and are found to parallel those of heats of hydrogenation.

Lihs and Caudle examined the kinetics and mechanism of CO2 scrambling in aN-carboxyimidazolidone analogue for N 1-carboxybiotin.22 The N-carboxyimidazol-


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idone anion, 36, was prepared as an analogue for N 1-carboxybiotin, and the kineticsof its CO2-dependent chemistry were studied in polar aprotic media. The objectivewas to assess the viability of unimolecular CO2 elimination from N 1-carboxybiotin asa microscopic step in biotin-dependent carboxyl transfer enzymes. Time-dependentFTIR spectroscopy showed that the lithium salt of 36 undergoes carboxyl exchangewith free carbon dioxide, with kinetics indicative of rate-limiting unimolecular dis-sociation of the N–CO2 bond. Under these conditions, the weak Lewis acid Mg2�

catalyzes the exchange of 36 with free CO2, which appears to be related to the abilityof the metal ion to coordinate to 36. Reaction of the lithium adduct of 36 withcarboxylic acids in DMSO results in acid-dependent decarboxylation of 36 with a ratethat is dependent on the concentration of the acid and its pKa. A common mechanisticframework is presented for both Lewis acid catalyzed carboxyl exchange and acid-dependent decarboxylation that involves initial interaction at the carbonyl oxygen andwhich has the effect of polarizing the nitrogen lone pair toward the imidazolidone ringrather than the carboxyl group. Lewis acid interaction with the carbonyl oxygen thusweakens the N–CO2

� bond and functions as a trigger for dissociation of CO2. In thecontext of biotin-dependent enzymes, this suggests a means by which the kineticallystable N 1-carboxybiotin cofactor intermediate might be triggered for dissociation ofCO2.

Moore and Kluger examined substituent effects in carbon–nitrogen cleavage ofthiamin derivatives.23 The combination of thiamin and benzaldehyde can producebenzoin but also destroys thiamin. The destruction comes from fragmentation of theconjugate of thiamin and benzaldehyde undergoing a process that produces a phenylthiazole ketone and pyrimidine. The key step in this process is cleavage of the C–Nbond between the heterocycles, which occurs by an unknown mechanism. To analyzethe nature of the C–N cleavage step, the rates of fragmentation of a series of phenyl-substituted N1�-methyl-2-(α-hydroxybenzyl)thiamin derivatives 37 were determined.It is concluded that cleavage occurs by a facile process that resembles the outcome of a[1,5] sigmatropic rearrangement, however the mechanism remains elusive.


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5 Reactions of carbocations

The mechanism of glycopyranosyl and 5-thioglycopyranosyl transfer reactions insolution have been thoroughly reviewed by Bennet and Kitos.24

A study investigating the hydrogen bonding and catalysis of solvolysis of4-methoxybenzyl fluoride 38 was reported by Toteva and Richard.25 Values of k0 =8.0 × 10�3 s�1 and kH = 2.5 × 10�2 M�1 s�1, respectively, were determined for thespontaneous and the acid-catalyzed cleavage of 4-methoxybenzyl fluoride 38 to formthe 4-methoxybenzyl carbocation 39. Values of kF = 1.8 × 107 M�1 s�1 and kHF = 7.2 ×104 M�1 s�1 were determined for addition of F� and HF to 4-methoxybenzylcarbocation for reaction in the microscopic reverse direction. Evidence is presentedthat the reversible addition of HF to 39 to give 38 � H� proceeds by a concertedreaction mechanism. The relatively small 250-fold difference between the reactivitiesof fluoride ion and neutral HF toward 39 is attributed to the tendency of the strongaqueous solvation of F� to decrease its nucleophilic reactivity and to the advantagefor the concerted compared with the usual stepwise pathway for addition of HF.There is no significant stabilization of the transition state for cleavage of 38 fromgeneral acid catalysis by 0.80 M cyanoacetate buffer at pH 1.7.

Kresge’s laboratory report an investigation into the properties of two quinonemethides.26 o-Quinone α-phenylmethide 42 was generated as a short-lived transientspecies in aqueous solution by flash photolysis of o-hydroxy-α-phenylbenzyl alcohol40 and its rate of decay was measured in various aqueous solutions. It was concludedthat hydration of 42 back to its benzyl alcohol precursor occurs by acid-, base-,and uncatalyzed routes. The acid-catalyzed reaction gives the solvent isotope effectkH�/kD� = 0.34, which indicates that this reaction occurs via rapid pre-equilibriumprotonation of the quinone methide on its carbonyl oxygen atom followed by rate-determining capture of the ensuing carbocationic intermediate by water, a conclusionsupported by the saturation of acid catalysis in concentrated HClO4 solution.o-quinone α-(p-anisyl)methide 43 was also generated by flash photolysis of the corre-sponding benzyl alcohol 41 and of the p-cyanophenol ether of this alcohol as well,


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and its rate of decay was also measured in various aqueous solutions. Acid-, base-,and uncatalyzed hydration reaction routes were again found, and solvent isotopeeffects as well as saturation of acid catalysis, this time in dilute HClO4, confirmed apre-equilibrium mechanism for the acid-catalyzed reaction.

The same laboratory also reported an investigation of p-quinone methide 45.27

Flash photolysis of p-hydroxybenzyl acetate 44 in aqueous perchloric acid solutionand formic acid, acetic acid, biphosphate ion, and tris(hydroxymethyl)methyl-ammonium ion buffers produced p-quinone methide 45 as a short-lived species thatunderwent hydration to p-hydroxybenzyl alcohol in hydronium ion catalyzed (kH� =5.28 × 104 M�1 s�1) and uncatalyzed (kuc= 3.33 s�1) processes. The inverse nature of thesolvent isotope effect on the hydronium ion-catalyzed reaction, kH�/kD� = 0.41, indi-cates that this process also occurs by rapid and reversible protonation of the quinonemethide on its carbonyl carbon atom, followed by rate-determining capture of thep-hydroxybenzyl carbocation by water. p-quinone methide also underwent hydroniumion-catalyzed and uncatalyzed nucleophilic addition reactions with chloride ion,bromide ion, thiocyanate ion, and thiourea. The solvent isotope effects on the hydro-nium ion-catalyzed processes again indicate that these reactions occurred by pre-equilibrium mechanisms involving a p-hydroxybenzyl carbocation intermediate, andassignment of a diffusion-controlled value to the rate constant for reaction of thiscation with thiocyanate ion led to KSH = 110 M as the acidity constant of oxygen-protonated p-quinone methide.

Ruane et al. examined the properties of a series of N-arylbenzonitrilium ions47 (Ar–C��N�–Ar�) in aqueous 20% acetonitrile.28 The cations were generated byphotoheterolysis of benzimidate esters Ar–CZ��N–Ar� (Z = OC6H4-4-CN) with4-cyanophenoxide as the photochemical leaving group 46. Rate constants for thereaction with water (kw), azide ion (kaz) and hydroxide (kOH) were measured. Thecation Ph–C��N�–Ph is only 50-fold shorter lived in water compared to Ph–C��N�–iPr;thus the effect of replacing an N-alkyl group with N-Ph is modest. These two cations


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are also shown to have similar lifetimes to iminium analogs, e.g., Ph–CH��N�(Me)–Ph.Thus, addition of water to analogous sp and sp2 hybridized systems occurs at a similarrate, and the increased steric access to the nitrilium plays at most a modest role. Rateconstant ratios kaz/kw, are constant at approximately 104, with values of kaz well belowthe diffusion limit, even for the most reactive nitrilium ions. This is very differentbehavior from that of carbocations and arylnitrenium ions of similar lifetimes inwater. For these cations the rate constants kaz would be at or at least approaching thediffusion limit.

6 Through space or through bond effects and isomerizations

This section covers reactions where through space or through bond effects are import-ant. Malnar et al. examined the solvolysis of several 1,1-dimethyl-4-alkenyl chloridesand concluded that there is significant π-participation.29 For example, tertiary 1,1-di-methyl-4-alkenyl chloride 48 solvolyzes with significantly reduced secondaryβ-deuterium kinetic isotope effect and has a lower entropy and enthalpy of activationthan the saturated analogue 50. A transition structure was computed at the MP2(fc)/6-31G(d) level of theory which suggested that the reaction proceeds through a latetransition state with considerably pronounced double bond participation and a sub-stantially cleaved C–Cl bond. The doubly unsaturated compound 49 (1,1-dimethyl-4,8-alkadienyl chloride) solvolyzes with further reduction of the isotope effect, and adrastically lower entropy of activation, suggesting that the solvolysis of 49 proceedsby way of extended π-participation, i.e., the assistance of both double bonds in therate-determining step.

In a theoretical study Segurado et al. present new evidence for through-spacetransmission of substituent effects in benzene derivatives.30 Notably, electrostaticinteraction energies between dipolar substituents and dipolar or charged reaction siteswere re-examined because at short interaction distances and given orientations, the


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point-dipole approximation is shown to introduce significant errors. Exact expressionswere derived for correcting current equations for both interaction types, including theKirkwood–Westheimer equation.

Hegarty et al. examined the rate-determining inversion in the isomerization ofisoimides to imides and azides to tetrazoles and observed intermediates on thereaction pathway.31 Reaction of N-alkyl- and N-trifluoroalkylbenzimidoyl chlorides inthe presence of either acetate or azide ion leads initially to the formation of thecorresponding isoimides 51 and imidoyl azides 52 (both of which could be observedspectroscopically). These are formed via nucleophilic trapping of the nitrilium cationsin aqueous organic solutions. Subsequently these imidoyl acetates and azidesrearrange to the more stable imides or tetrazoles. These rearrangements are character-ized by a low dependence on solvent polarity and insensitivity to added salts,indicating that the rate-determining step is the isomerization of the initially formedZ-isomer of the imine to the E-isomer (imine nitrogen inversion) rather than thesubsequent N O acyl group transfer or cyclisation. The Hammett r value (�0.4),obtained for the rearrangement of the imidoyl azides to the tetrazoles, compares wellto other systems where the rate-determining step (nitrogen inversion) was similar.Nitrogen inversion in these imine systems is therefore significantly slower (ca. 10-foldrelative to an Et group) in the presence of the trifluoroethyl group on nitrogen.

Chen et al. examined the substituent effects on the thermal cis to trans isomeriz-ation of 1,3-diphenyltriazenes 53.32 The geometric isomerization is catalyzed bygeneral acids and general bases as a result of acid/base-promoted 1,3-prototropicrearrangements. Acid catalysis becomes more prominent as the electron-donatingcharacter of the para substituent increases, while base catalysis becomes more import-ant as the electron-withdrawing character of the para substituent increases. In addi-tion, the rate ascribed to the interconversion of neutral cis rotamers through hinderedrotation around the nitrogen–nitrogen single bond is found to decrease as the electron-withdrawing character of the para substituent increases. Rates of interconversion ofneutral cis rotamers are also found to decrease with decreasing solvent polarity, whichis indicative of the involvement of a polar transition state. On the other hand, kineticinvestigations of the acid-catalyzed decomposition of target triazenes are consistentwith an A1 mechanism.

7 Acyl transfer at carbon

A number of years ago Capon reported that the amino group of 54 (where X = H) didnot participate in catalysis at acidic and basic pH. Fife now reports that at intermedi-ate pH this is not the case.33 For the hydrolysis of the trifluoroethyl, phenyl, and


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p-nitrophenyl esters of 2-aminobenzoic 54 the most likely mechanism involves intra-molecular general base catalysis by the neighboring amine group. The amino group isreported to result in a 50–100-fold rate enhancement.

The addition of OH�, CN�, and N3� to a series of aryl benzoates in 20 mol%

DMSO displayed non linear Hammett plots.34 A mechanism involving a tetrahedralintermediate with curvature resulting from a change in rate-determining step wasdiscounted in favor of an alternative explanation. This explanation involves ground-state stabilization through resonance interaction between the benzoyl substituent andthe electrophilic carbonyl center in the two-stage mechanism. Linear fits to theYukawa–Tsuno equation was provided as evidence to support the hypothesis.

Phosphate-catalyzed hydrolysis of a series of aryl benzoates 55 and 56 has beenstudied spectrophotometrically.35 The reaction is reported to proceed via the irrevers-ible formation of acyl phosphate where the formation of a tetrahedral species byattack of the HPO4

2� on the ester CO group is rate limiting.Pseudo-first-order rate constants have been measured spectrophotometrically for

reactions of O-4-nitrophenyl thionobenzoate 57 with a series of primary and acyclicsecondary amines.36 Plots of kobs vs. amine concentration are linear for the reaction of57 with primary amines. The slope of the Brønsted-type plot for the reaction of 57with primary amines decreases from 0.77 to 0.17 as the amine basicity increases,indicating that the reaction proceeds through a zwitterionic addition intermediate inwhich the rate-determining step changes from the breakdown of the intermediate tothe reaction products to the formation of the intermediate as the amine basicityincreases. On the other hand, for reactions with all the acyclic secondary aminesstudied, the plot of kobs vs. amine concentration exhibits an upward curvature,suggesting that the reaction proceeds through two intermediates, e.g., a zwitterionicaddition intermediate and an anionic intermediate.

Kirby et al. report on the remarkable properties of 59 and the zwitterionic tetra-hedral addition product 58, which is the preferred form in polar solvents and in thecrystal.37 Chemical analysis confirms that the equilibrium 58 59 lies well to the leftin more polar solvents and the cyclic form 58 is not a fully developed zwitterion.


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Hoffman et al. undertook a study on α-lactams to determine the origins ofthe observed regioselectivity of their reactions with nucleophiles.38 They showthat sterically stabilized α-lactams 60 react by two distinct acid-catalyzed pathways.Protonation on oxygen results in nucleophilic attack at the acyl carbon and gives C-2products, while protonation on nitrogen leads to nucleophilic attack at the C-3 carbonand yields C-3 products. The authors hope that the mechanism thus developed will beuseful for understanding the changes in rates and product distributions in the reac-tions of sterically stabilized α-lactams with nucleophiles as well as other α-lactams sothat a more coherent picture of α-lactam reactivity can be developed.

The hydrolysis of several secondary aryl N-pyridylcarbamates 61 was studied overthe pH range from 12 to 13.7.39 The pH–rate profile points to an E1cB mechanism,involving a pre-equilibrium deprotonation of the nitrogen atom to form an anion thatundergoes rate-limiting decomposition into pyridyl isocyanate and a phenoxide ion.The observed substituent effect (ρ = 2.45) is in accordance with rate-determiningdeparture of the phenoxide group from the anion intermediate formed in apre-equilibrium step.

The hydrolysis of phenylureas 62 is affected by temperature, pH and buffer concen-tration.40 Kinetic evidence suggests that the formation of phenyl isocyanate, the initialproduct, occurs via an intermediate zwitterion. Depending on pH and buffer concen-trations the zwitterion can be produced through three parallel routes: at lowpH, specific acid–general base catalysis, followed by slow deprotonation of a N atomby a general base; at high pH, specific basic–general acid catalysis, followed by slowprotonation of a N atom by a general acid; at intermediate pH the reaction proceedsthrough a proton switch promoted by buffers. Bifunctional acid–base buffers are veryefficient catalysts. At high buffer concentration, as well as at pH < 3 or > 12, the


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breakdown of the zwitterion is rate-determining. The results are discussed in relationto recently published papers reporting different pathways.

The reactions of methyl 4-nitrophenyl carbonate 63 with a series of secondaryalicyclic amines and quinuclidines, methyl 2,4-dinitrophenyl carbonate 64 withquinuclidines and 1-(2-hydroxyethyl)piperazinium ion, and phenyl 2,4-dinitrophenylcarbonate 65 with secondary alicyclic amines are subjected to a kinetic investigation inaqueous solution.41 The Brønsted-type plot (log k(N) vs. amine pKa) for the reactionsof secondary alicyclic amines with 63 is biphasic with slopes β = 0.3 (high pKa region)and β = 1.0 (low pKa region) and a curvature center at pKa = 9.3. This plot is consistentwith a stepwise mechanism through a zwitterionic tetrahedral intermediate and achange in the rate-determining step with amine basicity. The Brønsted plot for thequinuclidinolysis of 63 is linear with slope β(N) = 0.86, in line with a stepwise processwhere breakdown of the tetrahedral intermediate to products is rate limiting. A previ-ous work on the reactions of secondary alicyclic amines with 64 was revised by includ-ing the reaction of 1-(2-hydroxyethyl)piperazinium ion. The Brønsted plots for thereactions of quinuclidines and secondary alicyclic amines with 64 and secondaryalicyclic amines with 65 are linear with slopes β = 0.51, 0.48, and 0.39, respectively,consistent with concerted mechanisms. Since quinuclidines are better leaving groupsfrom zwitterionic intermediates (T±) than isobasic secondary alicyclic amines, yield-ing a less stable (T±), it seems doubtful that the quinuclidinolysis of 65 is stepwise, aspreviously reported.

The reactions 4-methylphenyl 4-nitrophenyl carbonate 66, 4-chlorophenyl4-nitrophenyl carbonate 67, 4-methylphenyl 2,4-dinitrophenyl carbonate 68, and4-chlorophenyl 2,4-dinitrophenyl carbonate 69 with a homogeneous series ofphenoxide anions are subjected to a kinetic investigation in aqueous solution.42 TheBrønsted-type plots for the nucleophilic rate constants (kN) are linear, with slopesβ = 0.48 66, 0.67 69, 0.41 68, and 0.32 69. The magnitude of these slopes and theabsence of a curvature in the Brønsted plot at pKa = 7.1 for the 67 reactions areconsistent with concerted mechanisms (one step). The carbonates 68 and 69 are morereactive than 66 and 67, respectively, toward phenoxide nucleophiles. This can beexplained by the presence of a second nitro group in the nucleofuge of the dinitroderivatives, which (i) leaves their carbonyl carbon more positively charged, makingthem better electrophiles, and (ii) makes 2,4-dinitrophenoxide a better leaving groupthan 4-nitrophenoxide. The 4-chloro derivatives are more reactive than the corre-sponding 4-methyl derivatives. This should be due to the greater electron withdrawalof 4-chloro than 4-methyl, which makes the former carbonyl more electrophilic.Comparison of the concerted phenolysis of 68 with the stepwise reactions of second-ary alicyclic amines with the same substrate indicates that substitution of a secondary


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alicyclic amine group in a zwitterionic tetrahedral intermediate by a phenoxy groupgreatly destabilizes the intermediate. An equation is deduced for log k(N) in terms ofthe basicity of the nucleophile, the non-leaving moiety, and the leaving group. Thisequation shows that for these reactions, the sensitivity of log k(N) to the basicity ofthe non-leaving moiety (β(nlg) = �0.27) is very similar to that of the nucleofuge(β(lg) = �0.25).

Rates of addition in aqueous solution of RCOOH (R = CH3-, CH3OCH2-, ClCH2-,Cl2CH-) to 70 [Ar = C6H5-, 3-ClC6H4-, 4-CH3OC6H4-, 3,4-Cl2C6H3-, 2,4-(CH3O)2-C6H3-] yielding a transient O-acylisourea, have been measured as a function of pH.43

Relative activities indicate a reaction mechanism in which a carboxylate anion adds toa mono- or di-protonated arylcarbodiimide. Only a weak dependence of reactionvelocity upon basicity of carboxylate nucleophile is noted (Brønsted β value ofapproximately 0.2).

8 Acyl transfer at sulfur

A novel mechanism of alkaline hydrolysis was noted for the sultam 71.44 The alkalinehydrolysis of N-α-methoxycarbonyl benzyl-β-sultam 71 occurs through an E1cB typemechanism (shown below). Evidence for this is the unusually faster 1000-foldhydrolysis of 71 than the corresponding carboxylate, the rapid D-exchange at theα-carbon, the pH rate profile, which indicates pre-equilibirum CH ionisation andthe formation of benzoyl formate as a product. This represents a novel pathway forthe hydrolysis of a β-sultam catalyzed by hydroxide.

The reactivity and the mechanism of reactions of β-sultams with nucleophiles wasalso assessed.45 Ethane-1,2-sultam which has a pKa of 12.12 ± 0.06 at 30 �C shows apH-dependence reflecting this so that the observed pseudo first-order rate constant atpHs above the pKa are pH independent. No neighboring group participation by carb-oxylates was detected in the hydrolysis of either N-carboxybenzylethane-1,2-sultamor N-(hydroxyaminocarbonylmethyl)-2-benzylethane-1,2-sultam. Oxyanions, but notamines or thiols, react with N-benzoylethane-1,2-sultam 72 in water by a nucleophilicring opening reaction confirmed by product analysis and kinetic solvent isotopeeffects. A Brønsted plot for this reaction has two distinct correlations with βnuc = 0.52


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and 0.65 for weak and strong bases, respectively, although a statistically corrected plotmay indicate a single correlation.

9 Acyl transfer at phosphorus

2002 saw several reports of mechanistic studies on phosphoryl transfer reflecting itsimportance in numerous areas of biology. This section has been organized into threeareas, corresponding to phosphate monoester, diester and triester chemistry.

9.1 Monoester

Kinetic isotope effects are reviewed for the uncatalyzed reactions of phosphate andsulfate monoesters and for a number of enzymic phosphoryl transfer reactions.46

Knowledge of the pKa of phosphoranes is important for a mechanistic interpret-ation of phosphate ester hydrolysis and has long been a topic of considerable interest.This year saw two groups report estimates for the pKa of phosphoranes using differentapproaches. Notably, both estimates agree well with those reported previously. Davieset al. used a bond length–pKa correlation based on crystal structures of cyclohexanolderivatives to derive their estimates.47 Using this approach they obtained values of13.5 ± 1.5 and 8.62 ± 1.87, respectively, for the apical and equatorial OH groupsof tetracyclohexyloxyhydroxyphosphorane 73. In addition they also performed anab initio molecular dynamics calculation which gave similar values of 14.2 and 9.8 forthe corresponding first ionizations of pentahydroxyphosphorane 74. In a separatereport Lopez et al. used partly empirical continuum dielectric methods to determinepKa’s of ethylene phosphorane 75.48 They calculated a first pKa for the equatorial OHof 7.9 and a second pKa of 14.3.

The reactivity of the phosphate monoester monoanion 76 in aqueous solution wasreinvestigated by Bianciotto et al. by examining the free energy profiles for the dissoci-ative pathway of CH3OPO3H

��H2O hydrolysis.49 Their quantum mechanical calcu-lations (density functional theory (B3LYP)) and optimizations performed with apolarizable continuum model (PCM) solvation model support the existence of thetautomeric form 77 as an intermediate. While collapse (via P–O bond cleavage) of thezwitterion is thought to be rate-determining in solution, the calculations do not allowa distinction to be made between a concerted or stepwise (with a metaphosphateintermediate) addition of a nucleophilic water molecule to the zwitterion.

In a similar study the first step in the catalytic mechanism of a protein tyrosinephosphatase, the transfer of a phosphate group from the phosphotyrosine substrate toa cysteine side chain of the protein to form a phosphoenzyme intermediate, wasstudied by combining density functional calculations of an active-site cluster withcontinuum electrostatic descriptions of the solvent and the remainder of the protein.50


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Calculations of the energy barriers and geometries along a reaction pathway sup-ported transition state structure 78. This corresponds to a dissociative pathwaythrough a dianionic-substrate, with early proton transfer from Asp-129 to the leavinggroup oxygen atom and no metaphosphate intermediate.

Ab initio methods were also used to examine the enzymatic mechanism of guano-sine triphosphate hydrolysis in the Cdc42/Cdc42GAP complex.51 Calculations focusedon the nucleophilic addition of a water molecule to the γ-phosphate phosphorusatom. A large model system was used to model the electrostatic field of the biologicalcomplex at the reactants. The predicted H-bond pattern of the nucleophilic waterruled against the possibility that it directly transfers its proton to the γ-phosphate ashas previously been proposed by a number of groups (see discussion within). Thecalculations appear to suggest that the nucleophilic water becomes acidic enoughto transfer a proton to the weakly basic Gln-61 prior to nucleophilic attack, thussuggesting a highly unusual mechanism of specific base catalysis.


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Rate comparisons of D314N Csk-promoted phosphotransfer using a series offluorotyrosine-containing peptide substrates reveal a near zero β(nuc), consistent witha dissociative mechanism of phosphotransfer.52 This result (in combination with pre-vious studies from Cole’s laboratory) argues against a hydroxy nucleophile-to-phosphate proton transfer occurring prior to an associative transition state ofphosphoryl transfer.

Acyl phosphate monoesters are intermediates in many biochemical acylation reac-tions, such as those involving aminoacyl adenylates. The hydroxide-dependenthydrolysis rate in the europium complex is about 105 times that of free substratewith hydroxide and thus worthy of investigation. Thus, the mechanism of lanthanidecatalyzed benzoyl methyl phosphate hydrolysis was examined.53 A mechanism thataccounts for the kinetic data involves bidentate coordination of the metal ion by theacyl phosphate through phosphate and carbonyl oxygens 79, lowering the energy ofthe tetrahedral addition intermediate and the associated transition states. Thedependence of the metal ion catalyzed process on the concentration of hydroxide ionis consistent with coordinated hydroxide acting as a nucleophile.

Forconi and Williams reported how catalysis of phosphate monoester hydrolysisby an intramolecular OH group becomes much more effective when combined withcatalysis by a dinuclear metal ion complex.54 They report that while 80 is hydrolyzed10-fold faster than 81, 84 and 83 are hydrolyzed 50000-fold and 5000-fold faster than82 respectively. Catalysis is proposed to occur according to the mechanism shown for84. Interestingly, there appears to be little driving force for proton transfer at the rate-limiting transition state, which suggests that the observed catalysis is in conflict withJencks’ libido rule. The theoretical basis for the high catalytic efficiency is lacking andrequires further investigation.

Two reports appeared concerned with environmental effects on phosphate mono-ester stability and reactivity. Previous work by Kirby and co-workers revealed a


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significant acceleration of the rate of hydrolysis of p-nitrophenyl phosphate by addeddipolar solvents such as DMSO. Hengge and co-workers reanalyzed the reaction for aseries of phosphate esters with more basic leaving groups. Both experimental andcomputational results are consistent with a desolvation-induced weakening of theP–O ester bond in the ground state for most aryl phosphate esters. Notably the reactiv-ity of Ph and Me phosphates is not enhanced by the addition of DMSO and in facttheir hydrolysis reactions are actually slowed.55

Cheng et al. used vibrational spectroscopy to study bonding in monosubstituteddianionic phosphates, both to learn more about their basic properties and to assess theability of vibrational spectroscopy to provide a probe of the local environment experi-enced by the phosphoryl group.56 A broad linear correlation of the bridging P–O(R)bond length and the pKa of the substituent alcohol. was observed indicating that theP–O(R) bond changes by approximately 0.04 Å with alcohol substituents that vary inpKa by approximately 12 units, suggesting that phosphoryl group bonding responds ina subtle but regular manner to changes in the local environment. The addition ofDMSO elongates the bridging bond. The results suggest that the change in the bridg-ing bond energy is small compared to the changes in energy that accompany theobserved reactivity differences of phosphate monoesters. Electrostatic interactionsprovide a common driving force underlying both bond lengthening and the observedrate increases.

9.2 Diester

Hanes et al. tried to isolate the hydroxy-pentaoxy-phosphorane 85. Hydroxy-pentaoxy-phosphoranes are believed to be transient intermediates formed during thehydrolysis of various phosphoesters. Kinetic analyses support the existence of suchcompounds, although they have not been isolated. In an attempt to create a stable


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example, two equivalents of a ligand possessing a very high effective molarity wereattached to a central phosphorus.57 Instead of obtaining the hydroxyphosphorane 85,analysis by 31P and 19F NMR spectroscopy and X-ray crystallography showed theproduct to be the phosphotriester 86.

Phosphodiester hydrolysis has been the subject of intense study due to itsimportance in biology. Despite numerous mechanistic studies, comparatively littleis known about the nucleophiles in these reactions. To determine whether hydrox-ide acts as a nucleophile or a general base in the hydrolysis of thymidine-5�-p-nitrophenyl phosphate, solvent deuterium isotope effects, ionic strength effects,and the 18O isotope effects on the solvent nucleophile (18knuc) were determined.58

The kD2O for hydroxide-catalyzed phosphodiester hydrolysis is slightly inverse(0.9 ± 0.1) suggesting that a proton transfer does not occur in the transitionstate. A significant effect is observed with hydroperoxide, demonstrating that oxy-anions can act as nucleophiles in the reaction. Additionally, the ionic strengthdependencies of hydroxide and hydroperoxide catalysis are indistinguishable,suggesting that they act by the same mechanism. Finally, the 18knuc for thehydroxide-catalyzed reaction is 1.068 ± 0.007, well in excess of the equilibrium 18Oisotope effect between water and hydroxide (1.040 ± 0.003). Together, the dataare most consistent with direct nucleophilic attack by hydroxide. From the observed18knuc and the known equilibrium component, the kinetic component of the isotopeeffect was calculated to be 1.027 ± 0.010. This large kinetic component suggeststhat little bond order to the nucleophile occurs in the transition state. In conclusionthe data suggests direct nucleophilic attack by hydroxide with an early transitionstate 87.


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The catalysis of phosphate diester transesterification reactions by metal ionsremains an active area of research. Brown and Neverov have reviewed metal ioncatalyzed methanolysis of esters, reactive amides and phosphate diesters.59

Andersson et al. discuss the mechanism of the metal ion promoted hydrolysis ofApppA and m7GpppG focusing on several Zn2� and Cu2� complexes that were usedas catalysts. Comparison of rate constants of hydrolysis of ApppA obtained in theabsence and in the presence of metal ions revealed that the catalytic activity of metalion complexes is significant. A rate enhancement of more than four orders of magni-tude was observed in the presence of 2 mM metal ion complexes. The rate of the metalion promoted reactions depends on the concentration of metal ion hydroxo com-plexes, indicating that a hydroxo ligand of the metal ion catalyst is involved in thereaction. A hydroxo ligand of a phosphate-bound metal ion acts as a nucleophile inthe hydrolysis reaction, but they also indicated that the role of a metal ion catalyst ismore complicated than this.60

The lanthanide ion based macrocyclic complexes 88 (Ln = La3�, Ce3�, Pr3�, Nd3�,Eu3�, Gd3�, Tb3� and Lu3�) were designed to mimic the hydrophobic nature ofribonucleases. The lanthanide ions induce the formation of a hydrophobic cavity thatcan bind the phosphate diester 89. The complex gives rise to a large order (3417-fold)of magnitude enhancement in the hydrolytic cleavage of 89.

Isotope effects in the nucleophile and in the leaving group were measured togain information about the mechanism and transition state of the hydrolysis ofmethyl p-nitrophenyl phosphate complexed to a dinuclear cobalt complex 90.61

The complexed diester undergoes hydrolysis about 1011 times faster than the


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corresponding uncomplexed diester. The kinetic isotope effects indicate that this rateacceleration is accompanied by a change in mechanism. A large inverse 18O isotopeeffect in the bridging hydroxide nucleophile (0.937 ± 0.002) suggests that nucleophilicattack occurs before the rate-determining step. Large isotope effects in the nitrophenylleaving group (18Olg = 1.029 ± 0.002, 15N = 1.0026 ± 0.0002) indicate significantfission of the P–O ester bond in the transition state of the rate-determining step. Thedata indicate that in contrast to uncomplexed diesters, which undergo hydrolysisby a concerted mechanism, the reaction of the complexed diester likely proceedsvia an addition–elimination mechanism. The rate-limiting step is expulsion of thep-nitrophenyl leaving group from the intermediate, which proceeds by a late transitionstate with extensive bond fission to the leaving group. This represents a substantialchange in mechanism from the hydrolysis of uncomplexed aryl phosphate diesters.

Anslyn and co-workers evaluated the cooperativity between a zinc ion andguanidinium groups in the hydrolysis of RNA.62 The Zn–hydroxide form of complex91 is thought to be the active catalyst in ApA hydrolysis. When zinc is bound to form91 the activity is 0.08 h�1. In the absence of zinc no activity can be detected, whilecompounds 92 and 93 which lack guandinium groups have activities of 0.009 h�1 and0.000024 h�1 respectively. It is suggested that this represents significant cooperativity.It appears that inherent in this assumption is that structural changes in the catalystsdo not affect ApA binding.

9.3 Triester

The hydrolysis of diethyl 8-dimethylaminonaphthyl-1-phosphate 94 is catalyzed bythe neighboring dimethylammonium group, with a rate acceleration, compared withdiethyl naphthyl-1-phosphate, of almost 106.63 The effective pKa of the naphtholateleaving group is reduced from 9.4 to 3.4 by partial protonation in the transition state.


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The reaction is catalyzed by oxyanion nucleophiles, and it is shown that a commonnucleophilic mechanism, enhanced by general acid catalysis by the neighboring di-methylammonium group, accounts for all the observed reactions. The efficiency ofgeneral acid catalysis depends on the extent of negative charge development on theleaving group oxygen in the transition state for P–O cleavage, and the strength of theintramolecular hydrogen bond in reactant and transition state.

As stated by Kirby the interpretation of buffer catalysis data is always subject to adegree of uncertainty, because changing the concentration of the catalyst neces-sarily changes the medium. Marriott and Kirby report how solvent effects perturb thekinetics of hydrolysis of 4-nitrophenoxymethyl uridine 3�-phosphate.64 They showthat in the case of catalysis by imidazole, a bell-shaped dependence on the bufferratio is explained in terms of a solvent effect on the background, hydroxide-catalyzedreaction. In addition six other amine bases with pKa = 7 ± 1 are studied and show that,in this system, non-linear behavior is the norm rather than the exception.

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10 Reaction mechanisms : Part (ii) Polar reactions