J . Phys. Chem. 1986, 90, 3760-3766
3760
Kinetics of Ketonization of Isobutyrophenone Enol in Aqueous Solution. Brernsted Relations and Analysis of Data by Marcus and Lewis-More O’Ferrall Rate Theories P. Pruszynski, Y. Chiang, A. J. Kresge,* N. P. Schepp, and P. A. Walsh Department of Chemistry, University of Toronto, Scarborough College, Scarborough, Ontario M1 C I A4, Canada (Receiced: January 29, 1986)
The enol isomer of isobutyrophenonewas generated in aqueous solution from its alkali-metal enolates, and rates of ketonization of the enol in this solvent were measured under catalysis by HCI, NaOH, H3P04,H2PO4-, six carboxylic acids (RC02H), and six monohydrogen phosphonate anions (RP03H-). Rates of enolization of isobutyrophenonecatalyzed by HCI and NaOH were also determined. These data provide the keto-enol equilibrium constant pKE = 6.48 & 0.02, the enol acidity constant pKaE= 11.78 & 0.01, and the acidity constant of the ketone ionizing as a carbon acid, pKaK= 18.26 f 0.02. The data also give catalytic coefficients for ketonization through carbon protonation of the enol by H3P04and the six RC02H and through carbon protonation of the enolate ion by H2PO4-, the six RC02H, and the six RP03H-. Brernsted relations constructed from the carboxylic acid data are linear, and a = 0.58 & 0.04 for the enol while a = 0.37 & 0.05 for the IO* times more reactive enolate ion. A more extended Brernsted relation for reaction of the enolate, using data for H2PO4- and the six RP03H- in addition to the six RC02H, is curved and shows no sign of an electrostatic difference between the charged and uncharged catalysts. Analysis of this curved plot by Marcus and Lewis-More O’Ferrall rate theories gives intrinsic barriers in the range 2-10 kcal mol-’ and work terms in the range 1-25 kcal mol-’.
Enols are necessary intermediates in a number of important reactions of carbonyl compounds, and knowledge of enol chemistry is essential to understanding and controlling these processes. The direct study of simple enols, however, has been hampered by their generally low equilibrium concentrations and their rapid reversion to keto tautomers. We have shown recently that simple enols can be generated in aqueous solution by the very rapid reaction of alkali-metal enolates with water and that the slower ketonization of enols so produced may be monitored by UV spectroscopy.’ In this paper we describe our application of these techniques to the enol of isobutyrophenone (eq 1).
Ketonization of this enol is accompanied by an especially pronounced UV spectral change, and the system lends itself well to detailed kinetic study. The enol, moreover, is in equilibrium with enolate ion (eq 2), and ketonization proceeds by two separate 0(2) Ph
acid-catalyzed reaction paths, one involving rate-determining carbon protonation of the enol (eq 3) and the other involving carbon protonation of the much more reactive enolate ion (eq 4).
The system therefore provides an opportunity to compare reaction characteristics, such as Brernsted relations, for two substrates of quite similar structure but very different reactivity. The value of such an examination is in this case enhanced by the fact that the keto-enol equilibrium constant for this system and the acid (1) Chiang, Y.; Kresge, A. J.; Walsh, P. A. J . Am. Chem. SOC.1982, 104, 6122-6123; J. Am. Chem. Soc., in press. (2) Chiang, Y.; Kresge, A. J.; Tang, Y. S . ; Wirz, J. J . Am. Chem. SOC. 1984, 106, 6392-639s.
0022-3654/86/2090-3760$01.50/0
dissociation constant of the ketone may be determined directly; this provides a sound thermodynamic basis for the kinetic comparison. To this end, we have measured rates of ketonization of isobutyrophenone enol catalyzed by the hydronium and hydroxide ions and by a series of undissociated acids, and we have also measured rates of the reverse, enolization reaction catalyzed by hydronium and hydroxide ions. These data give Brcansted relations, which we have analyzed by Marcus3 and Lewis-More O’Ferral14 rate theories. Experimental Section
Materials. Isobutyrophenone enol was generated from the potassium or lithium enolates. The potassium enolate was made by treating isobutyrophenone with potassium h ~ d r i d e and , ~ the lithium enolate was made by treating the trimethylsilyl ether of isobutyrophenone enol with methyllithium.6 This trimethylsilyl ether was prepared from isobutyrophenone and trimethylsilyl chloride;’ it was characterized by its N M R and mass spectrum: ’H N M R (CDCI,) G(TMS) 7.4 (5 H, s), 1.9 (3 H, s), 1.8 (3 H, s), 0.1 (9 H, s); mass spectrum, m / e 220.1290 (M’, calculated 220.1278). Metal enolate stock solutions, ca. 0.2 M in either tetrahydrofuran or dimethoxyethane solvent, were stored under argon in Pierce Reacti Vials fitted with Pierce Mininert Valves; samples for kinetic measurements were withdrawn by hypodermic syringe. Isobutyrophenone used for kinetic measurements was purified by gas chromatography. All other materials were best available commercial grades and were used as received. Aqueous solutions were prepared from deionized H20, purified further by distillation, or from D20(Merck Sharp and Dohme, 99.8 atom % deuterium) as received. Kinetics of Ketonization. Rates of ketonization of isobutyrophenone enol were measured spectroscopicallyby monitoring either the appearance of carbonyl group absorbance at 245 nm or the decrease in vinyl group absorbance at 217 nm; similar rate constants were obtained by the two methods. Determinations in (3) (a) Marcus, R. A. J . Phys. Chem. 1968, 72,891-899. (b) Kresge, A. J . Chem. SOC.Rev. 1973, 4, 475-503. (4) Lewis, E. S.;Shen, C. C.; More O’Ferrall, R. A. J . Chem. SOC.Perkin Trans. 2, 1981, 1084-1088. ( 5 ) Brown, C. A. J . Org. Chem. 1974, 39, 3913-3918. (6) House, H. 0.;Gall, M.: Olmstead, H. D. J . Org. Chem. 1971, 36, 2361-2371. ( 7 ) House, H. 0.;Gzuba, L. J.; Gall, M.; Olmstead, H. D. J . Org. Chem. 1969, 34, 2324-2336.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3761
Ketonization of Isobutyrophenone Enol hydrochloric acid and buffer solutions were made using Cary Model 118C or Model 210 spectrometers with cell compartments thermostated at 25.0 f 0.05 OC. Aqueous acid or buffer solutions contained in 3-mL cuvettes were allowed to come to temperature equilibrium with the cell compartment, and reactions were then initiated by adding a few microliters of substrate stock solution; the amount of organic solvent in the resulting reaction solution was never more than 0.3%. Final concentrations of enol substrate M. were of the order of Rates of ketonization in sodium hydroxide solutions were measured by stopped-flow spectrometry using a Durrum-Gibson instrument operating at 25.0 f 0.05 OC. Substrate and hydroxide ion solutions were mixed in 1:1 ratios by using freshly prepared substrate solutions, made by adding 30 KL of 0.2 M potassium enolate in tetrahydrofuran to 5 mL of 0.004 M aqueous acetic acid: partial neutralization of the acetic acid by the enolate produced an essentially wholly aqueous buffer solution in which the enol had a lifetime of several minutes; this was long enough to perform a number of stopped-flow runs. All of the rate data obeyed the first-order rate law well, and observed first-order rate constants were obtained by least-squares analysis of the relationship between In ( A - A,) or In ( A , - A ) and time. Kinetics of Enolization. Rates of enolization of isobutyrophenone were measured by using bromine to scavenge the enol as it formed. Reactions were conducted under zero-order conditions, with a large excess of ketone, and bromine concentrations were monitored spectrophotometrically. The hydrogen ion catalyzed reaction was studied in HBr solutions with NaBr added to keep the ionic strength constant (0.10 M). Under these conditions, bromine exists largely as the strongly absorbing tribromide ion, and the absorbance of this species at 293 nm was used to follow the reaction. First-order specific rates of enolization were calculated from eq 5, where -dA/dt is the zero-order rate of (5) change of absorbance at 293 nm, t is the extinction coefficient of Br3- at this wavelength, determined here as €293 = 1.65 X lo4 M-' cm-', and K (= 17 M-1)8 is the equilibrium constant for the Brz Br- = Br3- association reaction. Substrate concentrations ([SI) were determined by using the extinction coefficient of iso= 6.19 X lo2 butyrophenone a t 293 nm, determined here as M-' cm-l. In a typical experiment, about 2 KL of isobutyrophenone was dissolved in 10 mL of aqueous HBr/NaBr. A portion of this solution was then transferred to a 3-mL cuvette, and when that had equilibrated with the spectrometer (Cary 118C) cell compartment (25.0 f 0.05 "C), the absorbance at X = 293 nm was measured in order to determine the isobutyrophenone concenM). A b u t 10 KL of bromine solution, enough tration (ca. 1 X to give a stoichiometric concentration in the reaction solution of ca. 1 X M, was then added, and continuous recording of absorbance at X = 293 nm was begun. The reactions were very slow: about 2 days were required for complete bromine consumption, but the absorbance changes were nevertheless accurately zero-order. The hydroxide ion catalyzed enolization of isobutyrophenone was studied under conditions where bromine exists as the hypobromite ion, OBr-, and this reaction was therefore followed by monitoring the absorbance of this ion at X = 330 nm. Zero-order conditions were again used (isobutyrophenone concentrations ca. 1X M and initial stoichiometric bromine concentrations ca. 5X M). First-order observed rate constants were calculated from eq 6, where -dA/dt is the zero-order rate of decrease of
+
absorbance at X = 330 nm and c (= 300 M-I ~ m - ' )is~the extinction coefficient of OBr- at this wavelength. Substrate con(8) Griffith, R. 0.;McKeown, A,; Winn, A. G. Trans. Faraday SOC.1932, 28, 101-107. (9) Jones, J. R. Trans. Faraday SOC.1965, 61, 95-99.
centrations were determined from the weight of isobutyrophenone stock solution used to make up the reaction mixtures; the isobutyrophenone concentration in this stock solution was also determined by weight. In a typical experiment, 1.00 mL of ketone stock solution was weighed into a cuvette and this was allowed to come to temperature equilibrium (25.0 f 0.05 "C) with the spectrometer (Cary Model 210) cell compartment. Reaction was then initiated by adding 0.40 mL of OBr-/HO- solution (containing enough NaBr to bring the ionic strength of this solution up to 0.35 M), and continuous recording of absorbance at X = 330 nm was begun. When the reaction was finished, the cuvette was weighed again to determine the exact amount of brominating solution added; substrate and sodium hydroxide concentrations were then calculated from the combined weighings.
Results Ketonization Rates. Rates of ketonization of isobutyrophenone enol were measured in aqueous hydrochloric acid solutions over the concentration range 0.004-0.04 M; the data are summarized in Table S1.Io Observed first-order rate constants were accurately proportional to acid concentration, and least-squares analysis gave the hydronium ion catalytic coefficient kH+= 2.14 f 0.04 M-' s-1. Rates of ketonization of isobutyrophenone enol were also measured in sodium hydroxide solutions over the concentration range 0.007-0.10 M; these data are summarized in Table S2.I0 They show hydroxide ion catalysis of the ketonization reaction at low hydroxide ion concentrations and saturation of this catalysis at high hydroxide ion concentrations. This is the expected behavior in this pH it derives from a rapid acid-base reaction between hydroxide ion and the enol, whose position of equilibrium shifts from enol to enolate as the hydroxide ion concentration increases, followed by rate-determining ketonization of the enolate through proton transfer from water (eq 7). The rate law for this
scheme, given in eq 8, requires (kobsd)-lto be a linear function
of [H+] (eq 9), from whose slope and intercept parameters both (9) the rate constant for ketonization of enolate catalyzed by water, kb, and the enol acidity constant, KaE, may be evaluated. The data do conform to this requirement, and linear least-squares analysis gives k b = 69.3 f 0.8 s-I, KaE = (1.67 f 0.04) X 10-l2, and pKaE = 11.78 f 0.01.'1~12 Rates of ketonization were also measured in buffer solutions of six carboxylic acids (CNCH2CO2H, C1CH2CO2H, C H 3 0 CHZCO2H,H C 0 2 H , CH3COZH,and C2HSC02H),six monohydrogen phosphonate anions (CC13P03H-, CHCI2PO3H-, CH2CIP03H-, HOCH2P03H-, CH3PO3H-, and (CH3)3CP03H-), H3P04, and HZPOd-; these data are summarized in Table S3.I0 In these buffer solutions, the ketonization reaction showed both general acid and general base catalysis. This is consistent with the dual-channel reaction scheme of eq 3 and 4, with general acid catalysis required for direct ketonization of the enol and general base catalysis required for ketonization of the enolate. The latter (IO) Supplementary material; see paragraph at the end of this paper regarding availability. (1 1) This equilibrium constant is a concentration quotient which refers specifically to concentrations at an ionic strength of 0.10 M. (1 2) Hydrogen ion concentrations needed for this analysis were calculated from the hydroxide ion concentrations by using Qw = 1.59 X M2 as the [H'] [HO-] ion product of water at 25 "C and ionic strength 0.10 M. This value is based upon ionic activity coefficients recommended by Bates.I3 (1 3) Bates, R. G. Determinationof p H . Theory and Practice; Wiley: New York, 1973; p 49.
3762 The Journal of Physical Chemistry, Vol. 90, No. 16. 1986
Pruszynski et al.
, 2
00
4
6
[HCOZH ]
/
8
10
01 0
12
I
I
I
2
4
6
[Ht]-l/
M
Figure 1. Relationship between buffer acid concentration and observed first-order rate constants for the ketonization of isobutyrophenone enol in formic acid buffer solutions at constant buffer ratio: kobsd = (1.15 f 0.04) X (3.03 f 0.05) X 10-*[HC02H].
+
requirement stems from the fact that, at the acidities of the buffers used, the substrate exists essentially completely in the enol form; reaction through the enolate thus involves prior ionization of the enol (eq IO), which gives the rate an inverse dependence on [H+],
I
I
a
12
10
IO3 M-'
Figure 2. Relationship between hydrogen ion concentration and the rate of change of observed first-order rate constants with general acid concentration at constant [H'] for the ketonization of isobutyrophenone enol in formic acid buffers: ( a k O b , d / ~ [ H A ] ) [ ~=+ (1.24 1 f 0.06) X (5.61 f 0.12) X 10"/[H+].
+
3,
/
I
/
I
I
I
I
1
,
I
I
I
and that, coupled with the general acid catalysis required for the rate-determining carbon protonation step, appears operationally as general base catalysis. The complete rate law which applies to the ketonization reaction in buffer solutions is given in eq 11. It consists of rate constants kobsd = (kll + kH+[H+l + kHAIHAl)[H+l/([H+l + KaE) + (k'o k',+[H+] ~ ' H , [ H A ] ) K , ~ / ( [ H + ] KaE) (11)
+
+
for carbon protonation of the enol by water, k,, hydrogen ion, kH+, and general acid, kHA, plus another set of rate constants for the analogous reactions of enoiate ion ( k b , k',+, and HA); each of these sets of rate constants is multiplied by a fraction which expresses the portion of substrate present as enol or enolate. In the present buffer solutions, [H+] was always much greater than ,K : and this rate law can therefore be simplified to the expression shown in eq 12. kobsd
= ko
+ kH+[H+] + ~ H A [ H A+] kbKaE/[H+] +
k'H+KaE+ ~ ' H A K , ~ [ H A ] / [ H +(12) ]
The present rate measurements in buffers were performed in series of solutions of varying buffer concentration but constant buffer ratio and constant ionic strength; this served to hold [H+] constant along a solution series for all but the most acidic buffers. The rate law of eq 1 2 requires a linear dependence of kobsd upon [HA] at constant [H'] (eq 13), and this proved to be the case; (kobsd)[H+]= a
+ b[HA1
(13)
Figure 1 gives an example of this relationship for formic acid buffers with a buffer ratio of one. The slopes of this relationship ( b of eq 13) determined at different values of [H+] should in turn be a linear function of l / [ H + ] (eq 14), and this also proved to b = ( ~ ~ O ~ S ~ / ~ [ H A=] )kHA [ H+ + ]~ ' H A & ~ / [ H +(]1 4 )
be the case. Figure 2 shows an example using data for all of the formic acid buffers studied; the intercept of this plot gives kHCOIH = (1.24 & 0.06) X lo-* M-' s-l , and the slope plus the known value of KaEgives k'HC02H= (3.37 f 0.1 1) X lo6 M-' s-l. The results
TABLE I: Summary of Rate Constants for the Ketonization of Isobutyrophenone Enol and Enolate in Aqueous Solution at 25 OC"
k/M-' catalyst H+ CNCH2CO2H CICH2C02H CH30CH2C02H HCO2H CHlC02H C,H,CO,H CllCPO1HC12CHPO3HCICHZPO3HHOCH2POIHCHjPOIH(CH,),CPO3HH2P04H2O
PK, 2.47' 2.87' 3.57d 3.7Y 4.76 4.889 4.93h 5.60h 6.59h 7.36h 8.00h 8.7Ih 2.15' 7.2W
enol 2.14 5.99 X 4.45 X 1.09 X 1.24 X 2.98 x 1 0 - ~ 2.68 X IO-'
2.59
X
s-'
enolate 3.03 x 5.17 X 4.57 X 2 42 X 3.37 X 7.73 x 7.39 X 8.19 X 5.39 x 1.90 x 8.89 x 4.21 x 5.18 x
103
IO6 IO6 IO6 lo6 io5 lo5 IO' 105 105 104 104 103
lo-' 1.24 X 10' 6.93 X I O '
"Ionic strength = 0.10 M. *Feates, F. S . ; Ives, D. J . G. J . Chem. SOC.1956, 2798-2812. 0.5 for the late transition states of endoergic reactions in which the proton is more than half transferred. It is of interest to determine whether or not the present reactions support this hypothesis. Ketonization of the enolate ion (eq 23) is a simple one-step
I
I
Pruszynski et al.
0RCO2H
t
-
RCOZ t
H:h
(23)
Ph
reaction whose equilibrium constant is equal to the acidity constant of the catalyzing acid divided by the acidity constant of isobutyrophenone. The latter has been determined here as pKaK= 18.26, and for a catalyst at the midpoint of the present Bransted correlation pKa = 3.68; this leads to an equilibrium constant which corresponds to AGO = -20.3 kcal mol-'. Ketonization of the enol is a two-step process whose first and rate-determining step is shown in eq 24. This reaction may be formulated as the sum of the three I
-5
1
I -3
I
-4
I
I
1-3
RC02H t
-2
Log ( q K o / P )
Figure 4. Bronsted relations for the ketonization of isobutyrophenone enol and enolate ion catalyzed by a series of carboxylic acid in aqueous solution at 25 OC: (0)enolate, log (PHA/p)= 7.607f 0.188+ (0.371 f 0.053)log (qK,/p); (A)enol, log ( k H A / p = ) 0.048 f 0.128 + (0.577 f 0.036)log ( q K , / p ) .
xyh-
RCO;
t
Myh'
(24)
processes given in eq 25-27, and its equilibrium constant is RChH
RCOz- t H+
(25) (26)
just a keto-enol equilibrium whose equilibrium constant may be expressed as the ratio of rate constants for the first step times the equilibrium constant for the second step; the latter is equal to the autoprotolysis constant of water, K,, divided by the acidity constant of the enol, KaE,and KE = (koH-Ek',J(K,/KaE). Since kd and KaEare known from the ketonization rate measurements in sodium hydroxide solutions, KE may once again be evaluated; the PKE = 6.48 f 0.02. This result is KE = (3.34 f 0.19) X is in excellent agreement with the value obtained from measurements made in acid solutions; the weighted average of the two pKE = 6.48 f 0.02. results is KE = (3.33 f 0.17) X This keto-enol equilibrium and the acid dissociation of the enol make up two steps of a thermodynamic cycle (eq 22) whose third
,
,OH
'
'Ph
therefore equal to the product of those for these three processes. The acidity constant of the catalyst is once again pKa = 3.68, and K for the enol-ketone equilibrium of eq 26 is the reciprocal of the keto-enol equilibrium constant measured here as PKE = 6.48. An equilibrium constant for oxygen protonation of isobutyrophenone (eq 27) has not been measured, but a good value is available for acetophenone: pK = 4.16.*O Isobutyrophenone might be expected to be slightly more basic than this, and pK = 4.0 would not seem to be an unreasonable value. This leads to an equilibrium constant for the overall process of eq 24 which corresponds to AGO = 1.2 kcal mol-'. This analysis thus shows that the ketonization of isobutyrophenone enolate ion with a = 0.37 is a strongly exoergic reaction and that the rate-determining step in the ketonization of the enol with a = 0.58 is a moderately endoergic reaction. The present investigation thus provides at least qualitative support for the idea that Bransted exponents measure the extent of proton transfer at the transition states of the reactions to which they refer. Marcus and Lewis-More OFerrall Rate Theories. The relationship between Brernsted exponents and free energy of reaction may be examined further by using the Marcus rate equation shown in eq 28.3 This expression relates the free energy of activation
+
leg is the ionization of the ketone as a carbon acid. The equilibrium constant for this third process, KaK,may therefore be calculated from the other two constants; the result is KaK= (5.54 pKaK= 18.26 f 0.02. f 0.31) X
Discussion Brtamted Relations. Figure 4 shows Brtansted relations for the ketonization of isobutyrophenone enol and enolate ion, each catalyzed by the same set of six carboxylic acids. The Bransted exponent for the reaction of the enol is a = 0.58 0.04, and that for reaction of the enolate ion is a = 0.37 f 0.05. Brtansted exponents are believed to provide information about transition-state structure for the reactions to which they refer.Ig In particular, for processes such as the present ketonizations which involve simple proton transfer from oxygen acids to carbon, a might be expected to measure the extent of proton transfer at the transition state, with a < 0.5 for the early transition states of exoergic reactions in which the proton is less than half transferred
*
(19) Kresge, A. J. In Proron Trunsfer Reactions; Caldin, E. F., Gold, V., Eds.; Chapman and Hall: London, 1975; Chapter 7.
AG* = AGo*(l + AGo/4AGo*)2
(28)
of the proton transfer reaction, AG*, to its overall free energy change, AGO, through the intrinsic barrier AGO*. The Brtansted exponent is taken to be equal to the derivative dAG*/dAGo, and the rate of change of a with AGO is then given by the second derivative of AG* with respect to AGO (eq 29). da/dAGo = 1 /8AGo*
(29)
On the assumption that the ketonization of isobutyrophenone enol and that of the enolate ion belong to the same reaction series, eq 29 may be used to estimate the intrinsic barrier for this process from the differences in a and AGO for these two substrates. The result is AGO* = 12 kcal mol-], with a probable uncertainty (standard deviation) of ca. 5 kcal mol-'. This value is not in(20) Cox, R. A,; Smith, C. R.; Yates, K. Can. J . Chem. 1979, 57, 2952-2595.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3765
Ketonization of Isobutyrophenone Enol
TABLE 11: Rate Theory Parameters for the Ketonization of Isobutyrophenone Enolate Ion in Aqueous Solution at 25 OC
7t
Marcus
Q I X
13 points
12 points
AGO'
2.1f0.6 7.9 f 0.4 25.0 f 3.1
5.1f2.7 6.2 f 1.1 20.6 f 6.7
W'
.I
-
parameter"
WP
I
Lewis-More O'Ferrall 13 points 12 points 4.2f1.2 5.8 f 0.7 22.9 f 3.2
10.2f5.4 1.1 f 3.4 15.5 f 7.4
" In kcal mol-'.
I -9
-8
I -7
I -5
I
-6
I -4
I
-3
I -2
-I
Log ( q K o / p )
Figure 5. Bronsted relation for the ketonization of isobutyrophenone enolate ion catalyzed by RCOIH (0)and RP03H- (A)in aqueous solution at 25 "C: (---) fit using all points; (-) fit omitting (CHJ3CP03H-.
consistent with AGO*= 8 kcal mol-' determined for the ionization of a variety of carbonyl and nitro compounds from rate equilibrium and isotope effect correlations.21 Marcus and other rate theories require Bransted plots to be curved, but those of Figure 4 appear not to be so. This is undoubtedly because the carboxylic acid catalysts employed cover a limited range of acid strength and thus provide an insufficiently large interval of AGO for curvature to be detected. The range of catalyst acid strength can be increased by including data for the phosphonate anions, and the resulting Bransted plot, shown in Figure 5 , is indeed curved.22 The two kinds of catalyst used in this Brransted plot differ in charge type, and they might therefore give data which disperse into two separate correlation^.^^ Such behavior has in fact been observed for the mechanistically similar hydrolysis of some vinyl ethers catalyzed by these same two sets of acids, and the dispersion has been explained in terms of an attractive electrostatic interaction between the negative charge of the anionic catalyst and a positive charge being generated on the substrate in this reaction, which lowers the free energy of the transition state.24 In the present case, however, the substrate is negatively charged and the electrostatic effect will be repulsive rather than attractive; the charges will therefore move apart, and the electrostatic effect will be minimized. This minimization is apparently strong enough to suppress dispersion completely, for the data show no difference between the two kinds of catalyst. The carboxylic acid and phosphonate anion data were therefore combined and used together for fitting to rate theories. In this treatment the usual three-step representation of the proton-transfer process (eq 30-32) was used, and it was assumed that rate S
w' + H A Fz S*HA
(30)
AG'
S H A eSH.A wp
SH-A S SH
(31)
+A
equilibrium relations apply only to the actual proton-transfer step, eq 31; i.e. the energy required to form reaction complexes from and products (wp) was taken to be independent of reactants (w') catalyst acid strength. Use of the Marcus expression (eq 28) for the proton-transfer step led to the parameters listed in the second and third columns (21) Kresge, A. J. Acc. Chem. Res. 1975, 8, 354-360. Kresge, A. J. In Isotope Effects on Enzyme-Catalyzed Reactions; Cleland, W. W., O'Leary, M. H., Northrup, D. B., Eds.; University Park Press: Baltimore, MD, 1976; Chapter 2. (22) This plot is for the enolate reaction only because catalysis of ketonization of the enol by RPOBH-could not be detected. (23) Bell, R. P. Acid-Base Catalysis; Oxford University Press: London, 1941; p 8 5 . Kresge, A. J.; Chiang, Y. J . Am. Chem. SOC.1973, 95, 803-806. (24) Chwang, W. K.; Eliason, R.; Kresge, A. J. J . Am. Chem. Sot. 1977, 99,805-808. Kresge, A. J.; Chwang, W. K. J . Am. Chem. Sot, 1978, 100, 1249-1 253.
of Table 11. The fit based upon the full set of 13 catalysts (six R C 0 2 H , six RP03H-, and H2P04-) gave a reasonable value of w' but produced a very low value of AGO*and a very high value of wp. It can be argued that the data for t-BuPO,H-, which make up the point farthest to the left in Figure 5, should be omitted from the correlation: steric problems, absent in the case of other smaller catalysts, may have affected the rate of reaction here, and because of the position of this point, this would have a disproportionate effect on the outcome of the calculation. Leaving this point out does raise AGO*and lower wp somewhat, but the changes are small and the striking difference between w' and wp still remains. Low values of AGO*require the barrier for proton transfer in the forward direction, AGf', to drop rapidly with increasing exoergicity of the proton-transfer step, and they also require the barrier for proton transfer in the reverse direction, AGr*, to decrease correspondingly quickly with increasing endoergicity of this step. When these barriers become comparable to those for reversal of the reaction complex forming steps, proton transfer ceases to be fully rate-determining. In such situations, Brmsted plots based upon observed rate constants take on additional curvature, and parameters derived from correlations by using such data are not fully characteristic of the proton-transfer step; in particular, AGO* tends to be too low and w' and wp tend to be too high.25 It is possible that the present data are affected in this way. Another possible reason for the low values of AGO*obtained in these correlations derives from the quadratic nature of the simple Marcus expression (eq 28). This feature limits the applicability of the theory to values of AGO which lie in the range f4AGo*. It would seem more realistic to give AGO a wider range with f m as asymptotic limits, and Marcus has in fact proposed such a relati~nship.~"This same desirable feature is present in the mathematically more tractable hyperbolic expression put forward by Lewis and More O'Ferrall (eq 33). For the same amount of
AG* =
E 2 +
[ (y) +
(AGo*)2]1'2
(33)
Bransted plot curvature, Lewis-More OFerrall theory gives values of AGO*twice as great as those produced by Marcus theory, and application of the Lewis-More OFerrall equation to the present data gave the results listed in the last two columns of Table 11. Although AGO*is now respectably large and wp has been reduced to what is perhaps a not unreasonable value, w' has become very small and a disparity between w' and wp still remains. Some disparity, however, might not be unexpected. Proton transfers to and from carbon, such as those taking palce in the present reactions, probably occur directly rather than by a Grotthuss chain mechanism involving proton jumps down intervening solvent molecules.26 The oxygen acid and base catalysts used in the present study are of course solvated in aqueous solution, and the reactive sites of these species will therefore have to be desolvated in the course of reactant complex formation. For catalysis of the ketonization reaction by carboxylic acids, this involves removal of water from an uncharged molecule for reaction in the forward direction and removal of water from a negatively charged ion for reaction in the reverse direction. For catalysis by phosphonate anions, on the other hand, water will have to be (25) Murdoch, J. R. J . Am. Chem. Sot. 1972, 94, 4410-4418; J . Am. Chem. Sot. 1980, 102, 71-78. (26) Bednar, R. A.; Jencks, W. P. J . Am. Chem. Sot. 1985, 107, 7 126-7 134.
J. Phys. Chem. 1986,90, 3166-3774
3766
removed from a singly charged ion in the forward direction and from a doubly charged ion in the reverse direction. In each case, therefore, the reverse reaction will involve desolvation of the more heavily charged species, which will require more energy. It is thus not unreasonable that wp should be larger than w'.
Acknowledgment. We are grateful to the Natural Sciences and Engineering Research Council of Canada and the donors of the
Petroleum Fund, administered by the American Chemical Society, for their financial support of this research, Registry No. Isobutyrophenone enol, 4383-10-2.
Supplementary Material Available: Tables Sl-S6 of rate data for the enolization of isobutyrophenone and the ketonization of isobutyrophenone enol in aqueous solution at 25 OC (26 pages). Ordering information is given on any current masthead page.
Phenomenological Manifestations of Large-Curvature Tunneling in Hydride-Transfer Reactions Maurice M. Kreevoy,* Draien Ostovit, Donald G. Truhlar,* Chemical Dynamics Laboratory, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
and Bruce C. Garrett Chemical Dynamics Corporation, Columbus, Ohio 43220 (Received: February 7, 1986)
An important consequence of recent dynamical theories of tunneling is that, because of large curvature of the reaction path in a typical H, H ' , or H-transfer, light-isotope transfer occurs in more extended nuclear frameworks than heavy-isotope transfer. This is incorporated here into a modified version of the Marcus phenomenological theory relating reaction rate constants to equilibrium constants. It leads to Bronsted slope parameters that depend on the isotope transferred. The new theoretical formulation is tested on experimental data for hydride and deuteride transfer between nicotinamide adenine dinucleotide analogues and on computational data for hydrogen-atom and deuterium-atom transfer between pseudoatoms. The experimental kinetic isotope effects (KIE's) are shown to vary with reaction equilibrium constant (Kij) in a way that is quantitatively consistent with the theory. The critical configurations generated by the calculations vary from the saddle point and from each other in the way anticipated by theory. However, the calculated KIE values are a rather scattered function of because the tunneling corrections are large and somewhat system specific. Overall, we believe that this combination of experimental and calculated results provides considerable support for the idea that large-curvature tunneling needs to be considered in hydrogen-transfer reactions.
1. Introduction
In recent years there has been a rapid development of theory for hydrogen-transfer reaction~.I-~Theory now suggests that tunneling is significant in most hydrogen-transfer reactions (hydrogen atom, proton, and hydride ion) and that the heavy-atom framework in which this tunneling takes place is generally different from that which characterizes the saddle point of the potential energy surface connecting reactants and products.14 The geo(1) (a) Marcus, R. A,; Coltrin, M. E. J . Chem. Phys. 1977,67,2609. (b) Garrett, B. C.; Truhlar, D. G.; Grev, R. S.;Magnuson, A. W. J . Phys. Chem. 1980,84, 1730. ( c ) Truhlar, D. G.; Isaacson, A. D.; Skodje, R. T.; Garrett, B. C. J . Phys. Chem. 1982, 86, 2252. (d) Skodje, R. T.; Truhlar, D. G.; Garrett, B. C. J. Phys. Chem. 1981,85, 3019. J . Chem. Phys. 1982, 77, 5955. (2) (a) Ovchinnikova, M. Ya. Chem. Phys. 1979, 36, 85. (b) Babamov,
V. K.; Marcus, R. A. J . Chem. Phys. 1978, 74, 1790. (c) Babamov, V. K.; Lopez, V.;Marcus, R. A. J . Chem. Phys. 1983.78.5621. Chem. Phys. Lett. 1983, 202, 507. J . Chem. Phys. 1984,80, 1812. (d) Abusalbi, N.; Kouri, D.; Lopez, V.; Babamov, V. K.;Marcus, R. A. Chem. Phys. Lett. 1983, 203,458. (e) Nakamura, H.J . Phys. Chem. 1984,88, 4812. ( f ) Coveny, P. V.; Child,
M. S.;R h e l t , J. Chem. Phys. Lett. 1985, 220, 349. ( 9 ) Nakamura, H.; Ohsaki, A. J. Chem. Phys. 1985,83, 1599. (h) Babamov, V. K.; Lopez, V. J . Phys. Chem. 1986, 90, 215. (3) (a) Garrett, B. C.; Truhlar, D. G.; Wagner, A. F.; Dunning, T. H., Jr. J . Chem. Phys. 1983, 78, 4400. (b) Bondi, D. K.; Connor, J. N. L.; Garrett, B. C.; Truhlar, D. G. J . Chem. Phys. 1983, 78, 5981. (c) Garrett, B. C.; Truhlar, D. G. J . Chem. Phys. 1983, 79,4931. (d) Garrett, B. C.; Abusalbi, N.; Kouri, D. J.; Truhlar, D. G. J . Chem. Phys. 1985, 83, 2252. (4) See also: Marcus, R. A. J . Chem. Phys. 1966, 45, 4493; 1969, 49, 2617. Bowman, J. M.; Kuppermann, A.; Adams, J. T.; Truhlar, D. G. Chem. Phys. Lett. 1973, 20, 229. Kuppermann, A,; Adams, J. T.; Truhlar, D. G. Abstr. Pap. Int. Con$ Phys. Electron. At. Collisions 1973. 8, 149. Kuppermann, A. Theor. Chem. ( N . Y.)1981, 6A, 79.
metrical dislocation of the dominant tunneling path from the saddle point is particularly large for the case of a hydrogen, proton, or hydride ion being transferred between two much heavier atoms or groups; this may be considered to arise from the large curvature of the reaction path in mass-scaled coordinates in such ~ y s t e m s . ~ ? ~ In the present paper we attempt to adapt recent large-curvature-tunneling theory to exhibit some of its possible consequences for reactions of complex molecules in solution. In particular we focus on the consequences of the fact that, because tunneling is more facile for hydrogen than for deuterium, there are significant differences between the heavy-atom framework at the critical configuration for hydrogen transfer and that for deuterium transfer. Thus the critical configuration of a reaction-defined as the most probable structure for crossing the transition-state dividing surface that separates reactants and products-is different for hydrogen and deuterium transfer, and this isotopic shift can be treated analogously to a chemical substituent effect. For reactions of complex molecules in solution, reliable, realistic potential surfaces are not available, so comparison of calculated and observed rates of individual reactions does not provide a direct test of dynamical approximations. However, it is possible, especially for organic reactions in solution, to systematically vary the structure of the reactants and, thereby, of rate and equilibrium constants, by a series of very small steps, making the rate and equilibrium constants almost continuous functions of structural parameters. Thus it is possible to experimentally determine the derivatives of kinetic parameters with respect to the standard free energy of reaction, AGO, or, equivalently, with respect to the reaction equilibrium constant. It is attractive to test theoretical
0022-3654/86/2090-3766$01.50/00 1986 American Chemical Society
