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Primary product isotope effects (PIEs) on L+- and carboxylic acid-catalyzed protonation of ring-substituted α-methoxystyrenes (X-1) to form oxocarbenium ions X-2+ in 50/50 (v/v) HOH/DOD were calculated from the yields of the α-CH3 and α-CH2D labeled ketone products, determined by 1H NMR. A plot of PIE against reaction driving force shows a maximum PIE of 8.7 for protonation of 4-MeO-1 by Cl2CHCOOH (ΔGo = 1.0 kcal/mol). The PIE decreases to 8.1 for protonation of 4-MeO-1 by L3O+ (ΔGo = −2.8 kcal/mol) and to 5.1 for protonation of 3,5-di-NO2-1 by MeOCH2COOH (ΔGo = 13.1 kcal/mol). The PIE maximum is around ΔGo = 0. Arrhenius-type plots of PIEs on protonation of 4-MeO-1 and 3,5-di-NO2-1 by L3O+ and on protonation of X-1 by MeOCH2COOH in 50/50 (v/v) HOH/DOD give similar slopes and intercepts. These were used to calculate values of [(Ea)H − (Ea)D] = −1.2 kcal/mol and (AH/AD) = 1.0 for the difference in activation energy for reactions of A–H and A–D and for the limiting PIE at infinite temperature, respectively. These parameters are consistent with reaction of the hydron over an energy barrier. There is no evidence for quantum mechanical tunneling of the hydron through the barrier. These PIEs suggest that the transferred hydron at the transition state lies roughly equidistant between the acid donor and base acceptor, and contrast with the recently published Brønsted parameters [Richard, J. P.; Williams, K. B. J. Am. Chem. Soc. 2007, 129, 6952–6961], which are consistent with a product like transition state. An explanation for these seemingly contradictory results is discussed.
Brønsted acid-base-catalyzed proton transfer at carbon (eq 1) is an apparently simple, but profoundly important reaction in chemical and biological processes.1 The results of investigations of the effect of changing substituent –X at the base catalyst and –Y at the carbon acid on rate constants for proton transfer provide considerable insight into the bonding changes that occur on proceeding from reactants to transition state. 2–6 This experimental work defines the relative free energies for the formation of a large number of transition states, and has allowed investigators to draw inferences about transition state structure, without the direct observation of these species. By comparison, computational studies have the potential to provide a more detailed description of the reaction coordinate profile and transition state structure for proton transfer at carbon.7–12 However, there is no general agreement about which computational methods are adequate for their intended purpose, particularly for the modeling of acid-base-catalyzed proton transfer at carbon in water. This provides a simple rationale for continued experimental studies on proton transfer at carbon - these are needed to provide the large body of data required to demonstrate that modern computational results are able to reproduce experimental reaction rate and equilibrium constants.
There have been relatively few studies in recent years on kinetic isotope effects on proton transfer at carbon, despite the clear need for experimental data to evaluate the contribution of the pathway for quantum mechanical tunneling to the observed rate constants for these proton transfer reactions.13–18 We recently reported a fast, convenient and general method to determine primary product isotope effects (PIEs) on proton transfer reactions in hydroxylic solvents.19 This method was used to determine PIEs on protonation of ring-substituted α-methoxystyrenes X-1 by lyonium ion (Scheme 1) over a broad range of temperature and thermodynamic driving force (Scheme 1).19 We now report the full details of our experiments to determine PIEs, and extensive new data for protonation of X-1 by carboxylic acids. Our work was initiated with the following goals in mind.
We wanted to increase the number of experimental determinations of isotope effects on protonation of structurally homologous carbon bases, that may be directly compared with the isotope effects determined in computational studies. We have compared these experimentally determined isotope effects with isotope effects calculated using a novel approach based on Kleinert’s variational perturbation theory within the framework of Feynman path integrals.20–22
Primary kinetic isotope effects on Brønsted acid-catalyzed reactions in water are normally estimated from the ratio of second-order rate constants for reactions in HOH and DOD.23 We wanted to show that these primary isotope effects might be determined more easily and accurately from the ratio of H- and D-labeled products of protonation of X-1 in the common solvent of 50/50 HOH/DOD.
We recently reported the effect of changing reaction driving force on the Brønsted structure-reactivity coefficients α and β, determined for variations in the acidity of the carboxylic acid proton donor, and in the basicity of the vinyl ether proton acceptor X-1, respectively.24 We wanted to compare these changes in Brønsted parameters with the corresponding changes in the kinetic isotope effect for the protonation of X-1, in order to more fully define the changes in transition state structure that occur with changing reaction driving force.
Two explanations have been offered to explain the changes in primary isotope effects on hydron transfer at carbon that have been observed to occur with changing reaction driving force:23,25 (a) These changes may be due to changes in the structure of the transition state for the hydron transfer reaction;26,27 or, (b) They may be due to changes in the relative importance of the reaction by hydron transfer over a reaction barrier, which shows a primary KIE of ca 7, compared to the reaction of the hydron by quantum-mechanical tunneling through the barrier, which shows a much larger KIE.25 We have therefore examined the temperature dependence of the PIE on protonation of X-1 by lyonium ion and by a carboxylic acid, in order to evaluate the importance of tunneling.
The procedures for the preparation of 3,5-dinitroacetophenone and ring-substituted α-methoxystyrenes, and the sources for the other reagents used in this work were given in an earlier publication.24 Solvents were used without further purification unless otherwise indicated. Water was first distilled and then further purified with a Milli-Q water apparatus. Deuterium labeled water (99.9% D), DCl (35% w/w, 99.9%D) and KOD (40% wt, >98%D) were purchased from Cambridge Isotope Laboratories.
1H-NMR spectra at 500 MHz were recorded on a Varian UNITY INOVA 500 MHz spectrometer as described in earlier work.28,29 The following relaxation times T1 were determined in CDCl3 for the α-CH2D protons of the monodeuteriated ring substituted acetophenones: 3,5-dinitroacetophenone, 3 s; 4-methoxyacetophenone, 3 s; 4-nitroacetophenone, 3 s compounds; and, acetophenone, 4s. 1H-NMR spectra of the products of hydrolysis of X-1 in 50/50 (v/v) HOH/DOD (a mixture of α-CH3 and α-CH2D labeled ketone X-3) were recorded in CDCl3 (30 – 60 transients) with a pulse angle of 90°, an acquisition time of 7–10s, and a relaxation delay of 7T1. All spectra were referenced to CHCl3 at 7.27ppm, and base lines were drift-corrected before integration of the signals due to the α-CH3 and α-CH2D groups.
The concentrations of solutions of strong acids and bases were standardized by titration using phenolphthalein as an indicator. A stock solution of 50/50 (v/v) HOH/DOD, obtained by mixing equal volumes of HOH and DOD, was used to prepare solutions of KCl. A 4.5 M solution of LO− and a 1.0 M solution of LCl in 50/50 (v/v) HOH/DOD were prepared, respectively, by mixing equal volumes of 4.5 M KOH and 4.5 M KOD or of 1.0 M HCl and 1.0 M DCl.
Solutions of CH3COOL in 50/50 (v/v) HOH/DOD were prepared by adding equal molar amounts of CH3COOH and CH3COOD to 50/50 (v/v) HOH/DOD. Other solutions of carboxylic acids in 50/50 (v/v) HOH/DOD were prepared by dissolving the acid RCO2H in 50/50 (v/v) HOH/DOD and then adding a small amount of D2O to balance the acidic hydrogen of RCO2H. These solutions were adjusted to the appropriate [RCO2L]/ [RCO2−] ratio by adding measured amounts of KOL in 50/50 (v/v) HOH/DOD.
The hydrolysis of X-1 was initiated by making a 1/100 dilution of the reactant in acetonitrile into acidic solutions of 50/50 (v/v) HOH/DOD (v/v) (I = 1.0 KCl) to give the following final substrate concentrations: 4-MeO-1, 0.3 mM in 25 mL of 50/50 (v/v) HOH/DOD; H-1, 0.8 mM in 10 mL of 50/50 (v/v) HOH/DOD; 4-NO2-1, 0.09 mM in 50 mL of 50/50 (v/v) HOH/DOD; and, 3,5–di-NO2-1, 0.06 mM in 50 mL of 50/50 (v/v) HOH/DOD.
The halftimes for hydrolysis of X-1 in dilute solutions of LCl were estimated using second-order rate constants determined for hydrolysis in HOH and DOD,24,30 and assuming a linear dependence of the observed rate constant on the deuterium composition of solvent. Acidic solutions of 50/50 (v/v) HOH/DOD were vortexed during the addition of the reactive substrate 4-MeO-1 in order to ensure rapid mixing. In cases where the halftime for the specific acid- and buffer-catalyzed solvolysis in 50/50 HOH/DOD (v/v) was > 1 minute, a 1.0 mL aliquot was transferred to a cuvette immediately after initiation, and the reaction was monitored by UV-spectroscopy.24 The lyonium-ion and buffer-catalyzed reactions of 4-MeO-1 were quenched (see below) after a 1 – 5 minute reaction time, which was at least 10 halftimes for the hydrolysis reaction of 4-MeO-1. The hydrolysis reactions of other X-1 were monitored by UV spectroscopy, and allowed to proceed to at least 50% conversion to ketone product X-3.
These reactions were quenched by extraction of the organic material into 1 – 2 mL of CDCl3 at the following reaction times: H-1, 7 – 10 reaction halftimes; 4-NO2-1, 1 – 7 reaction halftimes, depending upon the buffer catalyst; 3, 5-di-NO2-1, 1 – 5 reaction halftimes, depending upon the buffer catalyst. The organic layer was separated from the aqueous layer using a disposable pipette and then dried by filtration through a short column of MgSO4 directly into an NMR tube. The samples were stored at −15 °C for one or two days, until the analysis for deuterium enrichment of the α-carbonyl methyl group using 1H NMR. It has been shown that the α–hydrogen of a simple methyl ketone are stable to exchange for at least one month under these conditions.31 The reactions at elevated temperatures (> 25 °C) were rapidly cooled to room temperature in an ice bath prior extraction of products into CDCl3.
The ratio of the yields of products of solvolysis of X-1 in 50/50 (v/v) HOH/DOD (I = 1.0 KCl) labeled with an α-CH3 and an α-CH2D group was determined using eq 2, where ACH3 is the area of the singlet due to the -CH3 group and ACH2D is the area for the downfield shifted triplet (JHD = 2 Hz) due to the -CH2D group: MeO-3, δ = 2.553 (CH3), 2.536 ppm, (CH2D); H-3, 2.614 (CH3), 2.598 ppm (CH2D); 4-NO2-3, 2.681 (CH3), 2.665 ppm (CH2D); 3,5-di-NO2-3, 2.777 (CH3), 2.761 ppm (CH2D).
The hydrolysis of X-1 in 50/50 (v/v) HOH/DOD at 25 °C (I = 1.0 KCl) was monitored by UV spectroscopy.24 The observed first-order reaction rate constants and second-order rate constants for Brønsted acid catalysis were determined as described in earlier work.24
The exchange of the α-CH3 hydrogen of X-3 for deuterium in 50/50 (v/v) HOH/DOD (I = 1.0 KCl) was monitored at 25 °C. The exchange reactions were initiated by making a 100-fold dilution of X-3 in acetonitrile into 50/50 (v/v) HOH/DOD (I = 1.0 KCl) to give the following final substrate concentrations and reaction volumes: 4-NO2-3, 0.09 mM in 250 mL solvent; and, 3,5-diNO2-3, 0.08 mM in 250 mL solvent. At timed intervals, 50 mL of the reaction mixture was withdrawn, the organic material was extracted into 1 – 2 mL of CDCl3 and the organic layer was dried as described above.
The first-order rate constant, kobs (s−1), for the deuterium exchange reaction of the α-CH3 group of X-3 to form the α-CH2D group was determined as the slope of a plot of reaction progress against time over the first 5 – 10% of the reaction (eq 3), where ACH3 is the area of the singlet due to the CH3 group of the reactant and ACH2D is the area for the downfield shifted triplet due to the CH2D group of the product. The second-order rate constant for the carboxylate anion-catalyzed exchange reaction was determined according to eq 4, where [A−] is the concentration of the buffer base for the particular experiment.
This ketal was prepared as a 0.25 M solution in acetonitrile that contained 0.5 mM of the internal standard fluorene. Solvolysis was initiated by making a 100-fold dilution of the ketal into water buffered with potassium phosphate at pH 6.7. The ketone (of 4-NO2-3) and alkene (4-NO2-1) reaction products were separated by HPLC and the product ratio was determined from the ratio of the HPLC peak areas Aalk/Aket, and using εKet/εalk = 0.17 for the ratio of the extinction coefficients of 4-NO2-3 and 4-NO2-1. The product ratio [alkene]/[ketone] decreased slowly with time, due to acid-catalyzed conversion of 4-NO2-1 to 4-NO2-3. The initial ratio of product yields was determined by making a small (< 20%) linear extrapolation to zero time of a plot of Aalk/Aket against time.
A second-order rate constant of kL = 500 M−1 s−1 for hydrolysis of 4-MeO-1 in 50/50 (v/v) HOH/DOD (I = 1.0, KCl) at 25 °C was estimated as the average of the values of kH = 870 M−1 s−1 24 and kD = 170 M−1 s−1 30 for the reactions in HOH and DOD, respectively. The hydrolysis reaction of 4-MeO-1 was examined at lyonium ion concentrations ranging from 3 mM to 11 mM, where the estimated halftimes for hydrolysis is between 0.5 and 0.12 s. These acidic solutions of 50/50 (v/v) HOH/DOD were vigorously vortexed during addition of substrate 4-MeO-1 in order to ensure rapid mixing of the reactant.
Figure 1 shows the partial 500 MHz NMR spectrum, using two different scales for the y-axis, of H-3 that forms as the product of the lyonium-ion-catalyzed reaction of H-1 in 50/50 (v/v) HOH/DOD (I = 1.0, KCl) at 25 °C. These spectra are similar to those reported in earlier determinations of deuterium enrichment of carbon acids using 1H NMR.28,29,31–39 The major peak is the singlet for the α-CH3 group of H-3 formed by reaction with L2OH+, and the smaller peaks are the 0.016 ppm upfield-shifted triplet for the α-CH2D group of H-3 formed by reaction with L2OD+. The observed product isotope effect (PIE)obs for protonation of H-1 is equal to the ratio of the integrated areas of the peaks for the –CH3 and –CH2D groups (eq 2). A small 0.3%/D isotope effect has been reported for partitioning of H- and D-labeled alkanes between methanol/water mixtures and the solid support of a C18 reverse phase HPLC column, with –H showing a slight preference for the hydrophobic environment.40 A small isotope effect on partitioning of the –H and –D labeled X-3 between CDCl3 and water would have been too small to be detected by these experiments, and so this partitioning isotope effect is assumed to be negligible.
The values of (PIE)obs for the L3O+-catalyzed reactions of X-1 in 50/50 (v/v) HOH/DOD (I = 1.0, KCl) at 25 °C are reported in Table S1 of the Supporting Information. Figure 2 shows the values of (PIE)obs determined for hydrolysis of 4-MeO-1 and 3,5-di-NO2-1 in the presence of different [L3O+]. In all cases, the variation in the values (PIE)obs for the reaction of X-1 (X = 4-OMe, 4-H, 4-NO2, 3,5-di-NO2) at different [L3O+] is less than ± 2%. The product isotope effects on protonation of X-1 by lyonium ion [(PIE)L, eq 5 and Scheme 2], calculated as the average of the (PIE)obs determined for reactions at five different [L3O+], are reported in Table 1.
The interpretation of these data would become problematic, if the first-order rate constants for addition of solvent to X-2+ and for deprotonation to form X-1 were similar. This is because the apparent PIE for hydrolysis of X-1 in 50/50 (v/v) HOH/DOD would depend upon the true PIE on protonation of X-1 and a second isotope effect on the partitioning of –CH3 and –CH2D labeled X-2+ between addition of water and deprotonation to reform X-1.41 We have therefore examined the effect of increasing [AcO−] on the yield of the products of solvolysis of 4-nitroacetophenone dimethyl ketal in water that contains 10 mM phosphate buffer at pH 6.7 and 25 °C. The solvolysis gives very low yields of alkene 4-NO2-1 (> 0.1 %). This shows that > 99.9% of the 4-NO2-2+ intermediate of hydrolysis of 4-NO2-1 would partition forward to product under these conditions. The rate constant ratio kAcO/ks = 0.0011 M was determined as the slope of a plot (not shown) of product yields ([4-NO2-1]/[4-NO2-3]) against [AcO−].
Carboxylic acids are very effective catalysts of the protonation of X-1, which is the ratedetermining step for hydrolysis of X-1 to form X-3 (Scheme 1). The values of (PIE)obs for the reactions of X-1 in the presence of carboxylic acid catalysts in 50/50 (v/v) HOH/DOD (I = 1.0, KCl) at 25 °C, determined by 1H NMR analysis, are reported in Table S2 of the Supporting Information.
Figure 3A shows that there is only a small change in the value of (PIE)obs for protonation of 4-MeO-1 as [LA]T is increased from 0.20 to 0.80 M. This is because the PIEs on the lyonium ion- and on the buffer-catalyzed reactions are similar. The buffer-catalyzed reaction is the major pathway even when concentrations of buffer are low ([PH]LA >> [PH]L and [PD]LA >> [PD]L, eq 7]. The product isotope effects on protonation of 4-MeO-1 by carboxylic acids [(PIE)LA, eq 6)] in 50/50 (v/v) HOH/DOD, determined as the average of the values of (PIE)obs observed at the three highest concentrations of the carboxylic acid catalyst, are reported in Table 1.
Figure 3B shows that the value of (PIE)obs for protonation of H-1 does not change significantly as [LA]T is increased from 0.16 to 0.64 M. This reflects the strong buffer catalysis of protonation of H-1.24 PIEs on protonation of H-1 by carboxylic acids [(PIE)LA] in 50/50 (v/v) HOH/DOD, determined as the average of the values of (PIE)obs observed at the three highest concentrations of the carboxylic acid catalyst, are reported in Table 1.
The general base-catalyzed deuterium exchange reaction of X-3 is normally much slower than the hydrolysis of X-1. For example kA = 7.9 × 10−7 M−1 s−1 42 for deprotonation of acetophenone (H-3) by acetate anion in water, and the rate constant for the deuterium exchange reaction of H-3 in 50/50 (v/v) HOH/DOD will be 4–5 fold smaller, because of the discrimination isotope effect against protonation of the acetophenone enolate by LOD in the mixed solvent. By comparison, rate constants kHA ≥ 6.6 × 10−5 M−1 s−1 were reported for protonation of X-1 in water.24
It would have been difficult to obtain a reliable value of (PIE)LA for the relatively slow protonation of 3,5-di-NO2-1 by CH3CO2L, because the apparent yield of the D-labeled product increased by ca 20% during CH3CO2L-catalyzed hydrolysis in 50/50 (v/v) HOH/DOD. We attribute the additional D-labeled product at later reaction times to a competing acetate anion-catalyzed deuterium exchange reaction of 3,5-di-NO2-3. We have therefore compared directly the rate constants for carboxylate anion-catalyzed deuterium exchange reactions of 4-NO2-3 and 3,5-di-NO2-3 and for carboxylic acid-catalyzed protonation of 4-NO2-1 and 3,5-di-NO2-1 in 50/50 (v/v) HOH/DOD (Table 3). This comparison shows that the ketone product of hydrolysis of 3,5-di-NO2-1 catalyzed by Brønsted acids more reactive than CH3CO2L, or of hydrolysis of aryl vinyl ethers more reactive than 3,5-di-NO2-1 is stable to exchange over several halftimes of the vinyl ether hydrolysis reaction. For example, kHA = 2.8 × 10−4 M−1 s−1 for methoxyacetic acid-catalyzed hydrolysis of 3,5-NO2-1 in 50/50 (v/v) HOH/DOD at 25 °C is 230-fold larger than kA ≈ 1.2 × 10−6 M−1 s−1 for the methoxyacetate anion-catalyzed deuterium exchange reaction of 3,5-NO2-3.
The ratio of –H and –D labeled ketone products for the methoxyacetic acid-catalyzed hydrolysis of 3,5-NO2-1 (Table S2) were determined after ca one reaction halftime, where there can be no significant methoxyacetate acetate anion-catalyzed deuterium exchange reaction of the ketone product. For example, only a 24 minute reaction time was used for hydrolysis of 3,5-NO2-1 in 50/50 (v/v) HOH/DOD that contained 0.80 M MeOAcOH buffer ([HA]/[A−] = 7/3) at 25 °C (Table S2). A control experiment with 0.80 M MeOAcOH buffer, at an even higher pL ([HA] = 0.08 M, [A−] = 0.72 M), showed that only 12% of the α-CH3 groups of 3,5-NO2-3 underwent deuterium exchange after 2400 minutes. A second control showed that identical values (PIE)obs = 5.5± 0.1 were determined for protonation of 3,5-NO2-1 in 0.80 M methoxyacetic acid buffer ([HA]/[A−] = 9) at several times up 1230 minutes, which is 35 halftimes for the hydrolysis reaction (Table S2).
Figure 4 shows the change in (PIE)obs with increasing concentrations of carboxylic acid buffers for the hydrolysis of 4-NO2-1 (Figure 4A) and 3,5-di-NO2-1 (Figure 4B) 1 in 50/50 (v/v) HOH/DOD at 25 °C. The second-order rate constants for the lyonium ion- and buffer-catalyzed reactions in the same solvent are reported in Table 2. The data in Table 2 show that for many of these hydrolysis reactions both the lyonium ion- and buffer-catalyzed pathways contribute to the observed reaction rate constants. Now, the value of (PIE)obs decreases with increasing concentrations of buffer, because (PIE)LA < (PIE)L. Table 1 reports the values of (PIE)LA for protonation of 4-NO2-1 and 3,5-di-NO2-1 by carboxylic acids that were determined from the nonlinear least-squares fit of the data from Figure 4A and 4B to eq 8, using the values of kL and kLA (M−1 s−1) from Table 2, (PIE)L from Table 1, and treating (PIE)LA as a variable parameter. The four terms in eq 8 correspond to the normalized velocities for product formation by the four pathways in eq 7 ([PH]L, [PD]L, [PH]LA and [PD]LA).
The product isotope effect on protonation of 4-MeO-1 by lyonium ion at 278 K, calculated as the average of the (PIE)obs (Table S3) determined for reactions at four different [L3O+], is reported in Table 3. The reactions of 4-MeO-1 at 319 K were examined at four different low concentrations of acetic acid buffer (40% free base) between 3 – 12 mM. The increase in kobs for hydrolysis of 4-MeO-1, from 0.0104 to 0.0165 s−1 as the buffer concentration is increased from 3 – 12 mM (Table S3), corresponds to an increase from 20% to 50% in the contribution of the buffer-catalyzed pathway of the total reaction with the remaining reaction being due to catalysis by L3O+. The value of (PIE)obs = (PIE)L = 6.9 ± 0.1 was found to be independent of buffer concentration (Table S3).We conclude that the PIEs on the lyonium ion and buffer-catalyzed reaction are essentially identical, as was also observed for the acetic acid-catalyzed reaction at 298 K (Table 3).
The reactions of 4-MeO-1 at 343 K were examined in the presence of four different concentrations of acetic acid buffer (70% free base) between 3 – 12 mM. The increase in kobs for hydrolysis, from 0.011 to 0.021 s−1 as the concentration of the buffer is increased from 3 – 12 mM (Table S3), corresponds to an increase from 30% to 65% in the contribution of the buffer-catalyzed pathway of the total reaction. The value of (PIE)obs = (PIE)L = 5.87 ± 0.03 determined for these reactions are independent of buffer concentration (Table S3), so that the PIEs on the lyonium ion and buffer-catalyzed reaction are identical within experimental error. A control experiment at 343 K with the ketone 4-MeO-3 in 50/50 (v/v) HOH/DOD that contains 12 mM acetate buffer (70% free base) showed that there was no detectable deuterium exchange over a period of 10 minutes, which is 60-haltimes for the hydrolysis of 4-MeO-1 under these conditions.
Product isotope effects on the reactions of 3,5-di-NO2-1 at 313, 328, 343 and 359 K at different [L3O+] are summarized in Table S3. In all cases (PIE)obs is independent of [L3O+]. The value of (PIE)L for lyonium ion protonation of 3,5-di-NO2-1 at each temperature was calculated as the average of the values (PIE)obs determined at four different [L3O+] (Table 3).
The yields of the H- and D-labeled products formed after ca 10-halftimes of methoxyacetic acid-catalyzed hydrolysis of H-1 in 50/50 (v/v) HOH/DOD (I = 1.0, KCl) and at several different temperatures were determined by 1H NMR. The values of (PIE)obs for experiments at 277 K ([MeOCH2CO2−]/[MeOCH2CO2H] = 9) are summarized in Table S4. The experiments at 321 and 343 K were carried out at [A−]/[AH] = 99, and using a constant concentration of 10 mM acetic acid buffer to maintain pH. There is more than a doubling in kobs for hydrolysis of H-1 at 321 and 343 K as ([MeOCH2CO2−] + [MeOCH2CO2H]) is increased from 0.10 – 0.45 M, but no change in (PIE)obs (±3 %) (Table S4). Therefore, there is no detectable difference in the PIE for reactions catalyzed by the different acids present in solution. The values of (PIE)AL reported in Table 3 for methoxyacetic acid-catalyzed hydrolysis of H-1 were calculated as the average of the values (PIE)obs determined at four different ([MeOCH2CO2−] + [MeOCH2CO2H]) (Table S4). Short reaction times of < 5 minutes were used for the reaction at 343 K in order to guarantee that there was no base-catalyzed exchange of deuterium from solvent into product H-3.
There is good evidence that protonation of X-1 to form X-2+ is effectively irreversible, and the rate-determining step for the hydrolysis of X-1 to form X-3.23,46–48 If so, then the PIEs determined for the hydrolysis of X-1 are equal to the primary isotope effects on protonation of these carbon bases. We have examined the partitioning of X-2+ (Scheme 3) in order to quantify the irreversibility of protonation of these vinyl ethers. The value of kAcO/ks = 0.0011 M reported here for partitioning of 4-NO2-2+ between deprotonation and addition of water (Scheme 3), shows that 4-NO2-2+ formed as an intermediate of protonation of 4-NO2-1 by acetic acid rarely returns to 4-NO2-1. A value of kAcO/ks = 0.0034 M has been reported for the partitioning of H-2+,24 and kAcO/ks = 0.0057 M for partitioning of 4-MeO-2+ may be calculated from ks = 7 × 106 s−1 and kAcO = 4.0 × 104 M−1 s−1.24,48,49 The partitioning of 3,5-NO2-3+ was not examined, because changes from electron-donating to electron-withdrawing ring substituents at X-2+ cause kAcO/ks to decrease (vida infra), so that kAcO/ks < 0.0011 M for partitioning of this oxocarbenium ion.
These data show that hydrolysis of 4-MeO-1 has the greatest tendency towards reversibility. Return to alkene becomes more favorable with decreasing acidity of the acid catalyst, because of a corresponding increase in the basicity of its conjugate base. Even in the most unfavorable case for catalysis by acetic acid, 4-MeO-2+ returns to reactant only ≈ 3/1000 times that it is generated by protonation of 4-MeO-1 by 1.0 M acetic acid ([AH]/A−] = 1.0).
Isotope effects on hydron transfer from solvent or from Brønsted acids that undergo fast hydron exchange with solvent can be determined either as the ratio of rate constants (kH/kD) for reactions in HOH and DOD (a KIE),23 or as the ratio of the hydrogen and deuterium labeled products (eq 2) of reaction in 50/50 (v/v) HOH/DOD (a PIE). The KIE on hydron transfer is generally simpler to measure than the PIE, because the kinetic determination does not require analytical methods to distinguish between H- and D- labeled products. On the other hand, the uncertainty in second-order rate constants kL is generally ± 5% so that the uncertainty in the KIE determined from a rate constant ratio will be ca ± 10%. By comparison, the values of (PIE)obs for protonation of X-1 determined by 1H NMR analysis are generally reproducible to better than ±2%. The precision of the measurements of the ratio of 1H NMR peak areas is potentially better than ± 2%.50
The interpretation of the PIEs determined in this work is simpler than interpretation of earlier KIEs on the protonation of vinyl ethers.23 The primary deuterium isotope effect, and the secondary solvent deuterium isotope effect both contribute to the magnitude of the KIE determined from the rate constant ratio kH/kD for reactions in HOH and DOD.51 By comparison, the PIE is obtained from the yields of –H and –D labeled products from a reaction in 50/50 (v/v) HOH/DOD, and provides a direct measure of the relative reactivity of these two isotopes in a common solvent.51
The value of (PIE)L or (PIE)AL (Table 1) for these Brønsted acid-catalyzed reactions is equal to the equilibrium constant for exchange of –H and –D at the transition state for hydron transfer in 50/50 (v/v) HOH/DOD (1/ϕTS, where ϕTS is referred to as the fractionation factor) when x = 0.50 for the mole fraction of –D in solvent (eq 9).52,53 The value of 1/ϕTS defines the relative stability of the –H and –D labeled transition states compared to a common ground state of 50/50 (v/v) HOH/DOD. The kinetic isotope effect (kAH/kAD) is defined by Eyring theory as the ratio of equilibrium constants for conversion of the H- and D-labeled Brønsted acids to the corresponding transition states for protonation of X-1 (, Scheme 4). Eq 10, derived for Scheme 4, shows that the KIE and the PIE are simply related by the equilibrium constant 1/ϕAL for exchange of –H and –D at the Brønsted acid (eq 11).52,53
Eqs 9 and 10 show that the PIE is directly related to the partitioning of –H and –D between a common ground state of 50/50 (v/v) HOH/DOD and the transition state for hydron transfer, while the KIE measures the relative barriers to moving from -H and -D labeled Brønsted acids to the transition state. The PIE and the KIE are different when the H/D enrichment of the Brønsted acid catalyst is different from the enrichment of solvent (ϕAL ≠ 1.0, eq 10), as is the case for L3O+-catalyzed reactions (ϕAL= ϕL3O = 0.69).43,44 The value of (KIE)L for the L3O+-catalyzed reaction provides a measure of the change in the fractionation of –H compared with –D between 50/50 (v/v) HOH/DOD at the reactant compared with the transition state. Correction of the values of (PIE)L in Table 1 for the preferential fractionation of -H from solvent to lyonium ion catalyst (ϕL3O = 0.69) gives the values of (KIE)L reported in this Table. Table 1 also reports values of (KIE)AL for protonation of X-1 by acetic acid, calculated from the (PIE)AL and ϕAL = 0.90 (eq 10).45
We will focus in this paper on the product isotope effects (PIE)L and (PIE)AL, because their changes with changing reaction driving force are due solely to changes in transition state structure, as measured by 1/ϕTS. By comparison, the KIE depends upon ϕAL for the reactant and ϕTS for the transition state, so that changes in reactant ϕAL with changing driving force will affect the KIE (eq 10). Note, for example, that the difference between the KIEs for the lyonium-ion-catalyzed and the acetic acid-catalyzed reactions (Table 1) are partly due to the difference in the fractionation factors for the two Brønsted acid catalysts.
The rate constant ratio kH/kD = 4.0 for L+-catalyzed hydrolysis of H-1 in pure HOH (kH = 85 M−1 s−1)24 and in pure DOD (kH = 21 M−1 s−1)30 at 25 °C and I = 1.0 (KCl) reflects the total changes in bonding at the transferred -L and the two “stationary” -L of L3O+. The primary (KIE)L = 5.7 for protonation of H-1 in 50/50 HOH/DOD (Table 1) shows that the zero-point energy of the transferred -L is largely lost at this transition state (see below); and, when combined with kH/kD = 4.0 gives a value of 4.0/5.7 = 0.70 for the secondary solvent deuterium isotope effect (SDIE) on this reaction. This solvent isotope effect represents the contributions of bonding changes at the nonreacting hydrons to the ratio kH/kD = 4.0. The isotope effect is due to a tightening of the O-L bonds at these “non-reacting” hydrons on proceeding from L2O-L+, where these O-L bonds are weakened by strong hydrogen bonds to solvent, to a transition state that has advanced towards product L-O-L that forms weaker hydrogen bonds to solvent.51,54 A rough estimate of the fractional progress α of the reactants towards the transition state can be obtained using eq 12, where (ϕL3O)2 = 0.48 43,44 is the maximum SDIE for a product-like transition state (α = 1.0).51,54 Substitution of SDIE = 0.70 and (ϕL3O+)2 = 0.48 into eq 12 gives α = 0.48. This corresponds to a transition state that is roughly at the midpoint between reactant L2O-L+ and product L-O-L with respect to changes in the hydrogen-bonding interactions between the solvent and the nonreacting hydrons of L2O-L+
Figure 5A shows Arrhenius-type plots of the PIEs for protonation of 4-MeO-1 and 3,5-di-NO2-1 in 50/50 (v/v) HOH/DOD. The following slopes and intercepts were determined by linear least squares analysis of the data from Figure 5A: 4-MeO-1; slope of -[(Ea)H − (Ea)D]/R = 630 ± 30 K and intercept ln(AH/AD) = −0.048 ± 0.11; 3,5-di-NO2-1, slope of 590 ± 19 K and intercept −0.001 ± 0.06 (the quoted errors are standard deviations). These give values of [(Ea)H − (Ea)D] = −1.25 and −1.17 kcal/mol and (AH/AD) = 1.00 and 0.95, respectively, for protonation of 4-MeO-1 and 3,5-di-NO2-1 by L2OH+ and L2OD+. Figure 5B shows the linear Arrhenius-type plot of (PIE)AL for protonation of H-1 by methoxyacetic acid in 50/50 (v/v) HOH/DOD, constructed using data from Table 3. The slope of this plot is -[(Ea)H − (Ea)D]/R = 595 K ± 30, and the intercept is ln (AH/AD) = 0.02 ± 0.10. These give values of [(Ea)H − (Ea)D] = −1.18 kcal/mol and (AH/AD) = 1.02 for protonation of 4-H-1 by methoxyacetic acid.
The average value of [(Ea)H − (Ea)D] = −1.2 kcal/mol determined from these Arrhenius-type plots is remarkably close to the value of -1.21 kcal/mol for the difference in zero-point energy for ground state hydrons at LO-H and LO-D (Δzpe), calculated from “first principles” using eq 13,55 where νH = 3400 is the IR stretching frequency for the LO-H bond 56 and νH/νD = 1/1.35 is the ratio of stretching frequencies for LO-H and LO-D bonds.55 This provides good evidence that most or all of the zero-point-energy of the solvent LO-L bond is lost at the transition state for protonation of X-1 by Brønsted acids.
Figure 3B, Figure 4A and 4B for the reactions of H-1, 4-NO2-1, and 3,5-di-NO2-1, respectively, provide the following insight into the relationship between the magnitude of the PIE and the reaction driving force.
The value of (PIE)L for catalysis by lyonium ion (y-intercept, Figure 3 and Figure 4) is generally equal to or larger than value of (PIE)obs = (PIE)AL for reactions in the presence of large concentrations of carboxylic acid catalysis; and, the values of (PIE)AL decrease with increasing pKa of the carboxylic acid catalyst. This shows that these PIEs generally decrease as the proton transfer reaction becomes more unfavorable thermodynamically. On the other hand, the difference between (PIE)L for catalysis by L3O+ and (PIE)AL for catalysis by methoxyacetic acid increases as the reactivity of the vinyl ether substrate is decreased by electron-withdrawing ring substituents. For example, (PIE)L = 8.2 and (PIE)AL = 7.6, respectively, for protonation of H-1 by L3O+ and methoxyacetic acid, while (PIE)L = 7.3 and (PIE)AL = 5.1 for protonation of 3,5-di-NO2-1 by the same two acids.
These trends are also shown in the logarithmic plot (Figure 6) of isotope effects against the change in the reaction standard Gibbs free energy (ΔG° = −RTlnKeq, Scheme 5),24 where the range of values of ΔG° on the x-axis is 16 kcal/mol.24 The solid symbols in Figure 6 are PIEs, and the open symbols are KIEs that were calculated from the PIE using eq 10. Note that similar PIEs for reactions in 50/50 HOH/DOD are observed for L+- and carboxylic acid-catalyzed reactions of similar driving force. This confirms that the difference in the KIEs determined for protonation of X-1 by L+- and carboxylic acids in pure HOH and DOD is due essentially entirely to difference in secondary solvent deuterium isotope effects on proton transfer (see above).
Figure 6 shows that the maximum PIE of ca 8.7 is observed for the nearly thermoneutral (ΔG° = 1.0 kcal/mol) protonation of 4-MeO-1 by Cl2CHCOOH. There is a falloff in this isotope effect to 8.1 for thermodynamically favorable protonation of 4-MeO-1 by L3O+, and a falloff to 8.0 for protonation of H-1 by CNCH2COOH as the reaction becomes thermodynamically favorable (ΔG° = 5.1 kcal/mol). The result is a broad region that runs from ΔG° = −2.8 kcal/mol to ΔG° = 5.1 kcal/mol where the change in PIE with changing reaction driving force is relatively small (0.7 units). There is then a steeper change in PIE with changing driving force, as shown by the decrease in the (PIE)L = 8.0 for protonation of H-1 by cyanoacetic acid to (PIE)AL = 5.1 for protonation of 3,5-di-NO2-1 by methoxyacetic acid (Figure 4B) as ΔG° increases from 5.1 to 13.1 kcal/mol.
An isotope effect maximum at ΔG° ≈ 0 kcal/mol similar to that shown in Figure 6 has been reported in earlier studies of the KIEs on Brønsted base-catalyzed deprotonation of –H and –D labeled α-carbonyl carbon acids.57 The rate constants ratio kH/kD for lyonium ion-catalyzed hydrolysis of substituted vinyl ethers in HOH and DOD also show a maximum at intermediate reactivity.23 However, the values of ΔG° for these reactions were not determined. The scatter in the earlier experimental data is much greater than for Figure 6 and this resulted in very poorly defined isotope effect maxima. For example, nearly the same value of kH/kD = 2.6 is observed for specific acid-catalyzed hydrolysis of 4-methylene-1,3-dioxane (kH = 6.5 M−1 s−1) and methyl trans-propenyl ether (kH = 0.072 M−1 s−1), despite the ca 100-fold difference in the second-order rate constants for these reactions.23 The extensive scatter in these earlier plots of KIE against reaction driving force represents partly or entirely the very large structural diversity of reactants in comparison with structurally homologous substrates X-1.
The complete equations for kinetic isotope effects published by Bigeleisen and Mayer58 can be used to rationalize both small and large kinetic isotope effects, and changes in these isotope effects.59 Two explanations have been proposed to explain the changes in primary kinetic isotope effect responsible for bell-shaped plots of primary isotope effects against reaction driving force, and the centering of the isotope effect maximum on ΔGo = 0.25
(1) The change in the primary isotope effect may reflect a change in the fraction of the zero-point energy of the reactant A-H bond that is maintained in the symmetrical stretching vibration at the transition state (Scheme 6), as described by Melander and Westheimer.26,27 Equal force constants for the partial bonds of A and B to –L are expected at the transition state for thermoneutral proton transfer (ΔGo = 0, Scheme 6), so that there should be no net movement of -L associated with this symmetrical stretch, and no effect of an –H for –D substitution on this stretching frequency. Hammond-type movement of hydron -L toward the acid catalyst or base acceptor will be observed,60 respectively, for a change to thermodynamically favorable hydron transfer (ΔGo << 0, Scheme 6), where the hydron is bonded most tightly to A, or to thermodynamically unfavorable transfer (ΔGo >> 0) where the hydron is bonded most tightly to B. In both cases, a part of the zero-point energy of the reactant A-L bond is maintained at the symmetrical stretching vibration, which will show a larger frequency for the light isotope –H compared with –D.
There is a Hammond effect on protonation of X-1 by substituted carboxylic acids. This results in a 0.10 unit increase in the Brønsted parameter α for catalysis by carboxylic acids as the thermodynamic barrier for proton transfer is increased by 9 kcal/mole by changing the substituent at X-1 from 4-MeO- to 3,5 di-NO2.24 This Hammond-type shift in the position of the reaction transition state provides a simple explanation for the decrease in the PIE with the increasing thermodynamic barrier to proton transfer.
(2) It has been proposed that the contribution of tunneling increases with the size of the tunneling cross section; and, that this cross section is a maximum for thermoneutral hydron transfer, but decreases in size as ΔGo for proton transfer becomes either positive or negative.25 This would cause the isotope effect to change from a large tunneling-enhanced value for thermoneutral proton transfer, to the smaller values for more activation limited thermodynamically favorable or unfavorable proton transfer.
The value of [(Ea)H − (Ea)D] = −1.2 kcal/mole calculated from the slopes of the Arrhenius-type plots shown in Figure 5 is roughly equal to the difference in the zero-point energy of the ground-state LO-L bond. This is consistent with a reaction in which the zpe of the hydron is lost at the potential energy maximum for the transition state.. The ratio of (AH/AD) = 1.0 for the preexponential factors is also consistent with a semiclassical model for proton transfer, where the rate constants for reaction of A–H and A–D approach the same limiting value at very high temperatures. The ratio of (AH/AD) = 1.0 is inconsistent with a reaction in which there is significant quantum mechanical tunneling of the light, but not the heavy isotope.61–63 In this case, there should be a sharp increase, with increasing T, in the rate of the activation-limited reaction of A–D relative to the rate of the (partly) tunneling-limited reaction of A–H. This would give rise to a sharp decrease in the PIE with increasing T, so that extrapolation of the ln PIE to 1/T = 0 would show a negative y-intercept. A unit ratio for the preexponential term is also inconsistent with significant tunneling for the reactions of both –H and –D. The isotope effect on a reaction where both isotopes tunnel through the barrier will show a small or negligible temperature-dependence, so that extrapolation of ln PIE to 1/T = 0 would give a positive y-intercept.61–63 We conclude that protonation of X-1 by Brønsted acids in water appears to proceed mainly by a mechanism where the reactions of both -H and –D pass over a maximum on the potential energy surface, instead of tunneling through the energy barrier.
The primary deuterium isotope effect maximum observed for thermoneutral protonation of X-1 is consistent with a transition state for proton transfer in which the hydron remains stationary during the symmetrical stretch shown in Scheme 6. 26,27 This corresponds to a transition state in which bond cleavage at the carboxylic acid and bond formation to carbon are each ca 50% of that observed for the overall proton transfer reaction (Figure 7).
By comparison, the structure reactivity parameters α = 0.66 and β = 0.58 ( Scheme 7)24 estimated for thermoneutral protonation of X-1 by substituted carboxylic acids are significantly greater than the values of α = β = 0.50 predicted by simple Marcus theory. 6,65 These Brønsted parameters are consistent with the development of an effective transition state charge of −0.66 at the carboxylic acid catalyst and of +0.58 at the carbon acid base,66,67 where the charges are normalized relative to values of -1 for the ionization substituted carboxylic acid and of +1 for protonation of X-1 to form the oxocarbenium ion X-2+.
We propose that there is a balanced transition state for proton transfer, as suggested by the position of the isotope effect maximum, and that the Brønsted structure-reactivity parameter α ( Scheme 7) overestimates the fractional proton transfer from the acid catalyst. This would be the case if the total change in effective charge on proceeding from free reactants to the ion pair product complex is greater than the change of −1.0 assumed for ionization of carboxylic acids in water,64 and if solvation of the developing carboxylate anion (Ksol, Figure 7) lags behind proton transfer to the carbon base.4,5,68 This is shown in Figure 7, where formation of hydrogen bonds between solvent and the carboxylate anion reduces the charge at the oxygen anion, so that Ksol for anion solvation increases with increasing pKa of the carboxylic acid catalyst. A value of αsol = −0.20 has been estimated for conversion of complexes between substituted quinuclidines and activated phosphate monoesters (e.g. 2,4-dinitrophenyl phosphate) to the free solvated quinuclidine.64 A similar value of αsol = −0.20 for formation of hydrogen bonds to the carboxylate anion would give a total absolute effective charge of (1 − αsol) = 1.20 at RCO2− in the ion-pair complex (Figure 7).65 In this case, the effective change in charge at the carboxyl(ate) oxygen on moving from reactant to transition state (α = 0.66, Scheme 7) would be only slightly greater than 50% of the total charge of 1.2 at the product complex: αnor = αobs/(1 − αsol) = 0.66/1.20 = 0.55. This is closer to the value of 0.50 predicted by Marcus theory for a thermoneutral proton transfer reaction.
We have compared these experimentally determined isotope effects with isotope effects calculated using a novel approach based on Kleinert’s variational perturbation theory within the framework of Feynman path integrals.20–22 There is generally good agreement between the results of experiments and calculations, and the computational results provide additional deeper insight into origin of these primary isotope effects.
This paper is dedicated to Yvonne Chiang and A. Jerry Kresge. We acknowledge the National Institutes of Health (GM 39754) for generous support of this work.
Supporting Information Available: Table S1 – S4 of observed product isotope effects, (PIE)obs, for reactions of X-1 in 50/50 (v/v) HOH/DOD that contains different concentrations of lyonium ion or Brønsted acid catalysts, and at different reaction temperatures. This material is available free of charge via the Internet at http://pubs.acs.org.