A marcus treatment of rate constants for protonation of ring-substituted α-methoxystyrenes: Intrinsic reaction barriers and the shape of the reaction coordinate

Article abstract of DOI:10.1021/ja071007k

Rate and equilibrium constants were determined for protonation of ring-substituted α-methoxystyrenes by hydronium ion and by carboxylic acids to form the corresponding ring-substituted α-methyl α-methoxybenzyl carbocations at 25°C and I = 1.0 (KCl). The thermodynamic barrier to carbocation formation increases by 14.5 kcal/mol as the phenyl ring substituent(s) is changed from 4-MeO- to 3,5-di-NO₂-, and as the carboxylic acid is changed from dichloroacetic to acetic acid. The Bronsted coefficient a for protonation by carboxylic acids increases from 0.67 to 0.77 over this range of phenyl ring substituents, and the Bronsted coefficient β for proton transfer increases from 0.63 to 0.69 as the carboxylic acid is changed from dichloroacetic to acetic acid. The change in these Bronsted coefficients with changing reaction driving force, ?α/?ΔG°_av = ?β/ ?ΔG°_av = 1/8Λ = 0.011, is used to calculate a Marcus intrinsic reaction barrier of Λ = 11 kcal/mol which is close to the barrier of 13 kcal/mol for thermoneutral proton transfer between this series of acids and bases. The value of α = 0.66 for thermoneutral proton transfer is greater than α = 0.50 required by a reaction that follows the Marcus equation. This elevated value of β may be due to an asymmetry in the reaction coordinate that arises from the difference in the intrinsic barriers for proton transfer at the oxygen acid reactant and resonance-stabilized carbon acid product.

Full text of DOI:10.1021/ja071007k

Published on Web 05/09/2007
A Marcus Treatment of Rate Constants for Protonation of
Ring-Substituted r-Methoxystyrenes: Intrinsic Reaction
Barriers and the Shape of the Reaction Coordinate
John P. Richard* and Kathleen B. Williams
Contribution from the Department of Chemistry, UniVersity at Buffalo, SUNY,
Buffalo New York 14260-3000
Received February 12, 2007; E-mail: jrichard@chem.buffalo.edu
Abstract: Rate and equilibrium constants were determined for protonation of ring-substituted R-methoxy-
styrenes by hydronium ion and by carboxylic acids to form the corresponding ring-substituted R-methyl
R-methoxybenzyl carbocations at 25 °C and I ) 1.0 (KCl). The thermodynamic barrier to carbocation
formation increases by 14.5 kcal/mol as the phenyl ring substituent(s) is changed from 4-MeO- to 3,5-di-
NO2-, and as the carboxylic acid is changed from dichloroacetic to acetic acid. The Brønsted coefficient R
for protonation by carboxylic acids increases from 0.67 to 0.77 over this range of phenyl ring substituents,
and the Brønsted coefficient â for proton transfer increases from 0.63 to 0.69 as the carboxylic acid is
changed from dichloroacetic to acetic acid. The change in these Brønsted coefficients with changing reaction
driving force, ∂R/∂∆G° )∂â/∂∆G° ) 1/8Λ ) 0.011, is used to calculate a Marcus intrinsic reaction barrier
av
av
of Λ ) 11 kcal/mol which is close to the barrier of 13 kcal/mol for thermoneutral proton transfer between
this series of acids and bases. The value of R ) 0.66 for thermoneutral proton transfer is greater than R
) 0.50 required by a reaction that follows the Marcus equation. This elevated value of â may be due to an
asymmetry in the reaction coordinate that arises from the difference in the intrinsic barriers for proton transfer
at the oxygen acid reactant and resonance-stabilized carbon acid product.
addition to the carbonyl group10,11 and to carbocations,8,12 and
bimolecular nucleophilic aliphatic substitution.13,14
Introduction
Marcus theory provides a framework for treating kinetic data
for electron-transfer reactions.1 The Marcus eq 1, which is
central to this theory, predicts a simple relationship between
the activation barriers for electron transfer (∆G†) and the
following quantities: (1) the thermodynamic driving force for
the reaction (∆G°), (2) the intrinsic activation barrier Λ when
∆G° ) 0 for the chemical portion of the reaction, and (3) the
work to bring reactants together into a reactive complex (ωr)
and the negative work done when the product complex separates
to free products (-ωp). This equation predicts nonlinear
logarithmic structure-reactivity relationships between rate and
equilibrium constants for these reactions, and it has been applied
by Marcus to simple organic reactions that exhibit such
structure-reactivity correlations.2,3 Marcus theory has been
refined in attempts to model reaction coordinate profiles for
complex chemical reactions,4-6 and the simple Marcus equation
has been used to rationalize rate data for a variety of organic
reactions including proton transfer at carbon,7-9 nucleophilic
2
∆G° - ωr + ωp
4Λ
∆G° 2
∆G† ) ω + Λ 1 +
(1)
(2)
(
)
r
∆G† ) Λ 1 +
(
)
4Λ
∂2∆G†
∂2∆G°
1
)
(3)
8Λ
Organic reactions that involve extensive electronic reorga-
nization and changes in bonding to the reacting atoms differ
from the electron-transfer reactions that Marcus theory was
developed to treat. The intrinsic barrier to electron transfer can
be modeled as the barrier to reorganization of solvent required
for optimal tunneling of an electron from the donor to acceptor
groups; however, the intrinsic barrier to complex organic
reactions is determined by the relative energies of the reactant
state and a metastable transition state in which there are transient
partial covalent bonds to one of more atoms. There are very
difficult questions about the origin of the barrier to organic
reactions that need to be addressed, but these questions have
(1) Marcus, R. A. J. Chem. Phys. 1956, 24, 966-978.
(2) Marcus, R. A. J. Phys. Chem. 1968, 72, 891-899.
(3) Marcus, R. A. J. Am. Chem. Soc. 1969, 91, 7224-7225.
(4) Chen, M. Y.; Murdoch, J. R. J. Am. Chem. Soc. 1984, 106, 4735-4743.
(5) Murdoch, J. R. J. Am. Chem. Soc. 1983, 105, 2660-2667.
(6) Guthrie, J. P. J. Am. Chem. Soc. 1996, 118, 12878-12885.
(7) Kresge, A. J. Chem Soc. ReV. 1973, 2, 475-503.
(8) Richard, J. P.; Amyes, T. L.; Toteva, M. M. Acc. Chem. Res. 2001, 34,
981-988.
(10) Guthrie, J. P.; Pitchko, V. J. Am. Chem. Soc. 2000, 122, 5520-5528.
(11) Guthrie, J. P. J. Am. Chem. Soc. 2000, 122, 5529-5538.
(12) Guthrie, J. P.; Pitchko, V. J. Phys. Org. Chem. 2004, 17, 548-559.
(13) Albery, W. J.; Kreevoy, M. M. AdV. Phys. Org. Chem. 1978, 16, 87-157.
(14) Lewis, E. S.; Hu, D. C. J. Am. Chem. Soc. 1984, 106, 3292-3296.
(9) Guthrie, J. P. J. Am. Chem. Soc. 1997, 119, 1151-1152.
9
6952
J. AM. CHEM. SOC. 2007, 129, 6952-6961
10.1021/ja071007k CCC: $37.00 © 2007 American Chemical Society

Protonation of Ring-Substituted
R
-Methoxystyrenes
A R T I C L E S
Figure 1. (A) Free-energy profile for a reaction where the work term ωr ) 0, the observed barrier for the thermoneutral reaction is equal to the intrinsic
reaction barrier, and a minimum shift in the position of the reaction transition state with changing reaction driving force is observed. (B) Free-energy profile
for a reaction where there is a large work term ωr, the observed barrier for the thermoneutral reaction is much larger than the intrinsic reaction barrier, and
a substantial shift in the position of the reaction transition state with changing reaction driving force is observed.
Scheme 1
not seriously discouraged the use of Marcus theory to describe
experimental rate-equilibrium data. We have followed the lead
of Bernasconi and co-workers15-18 and have shown that the
systematic changes observed in the intrinsic barriers for a broad
range of proton transfer and carbocation-nucleophile combina-
tion reactions provide considerable insight into the factors that
affect the stability of the transition states for these reactions.8
The Marcus intrinsic reaction barrier may be estimated as
the activation barrier for a formally thermoneutral reaction by
assuming that ωr ) ωP ) 0. In this case, the reactant complex
will not differ greatly from free reactants, and the observed
activation barrier will be equal to the change in the energy of
the reactant complex that occurs on moving to the transition
state. A significant work term is sometimes used when fitting
kinetic data to the Marcus equation, but to the best of our
knowledge there have been no systematic attempts in earlier
studies to partition an observed reaction barrier into work done
in formation of a complex between reactants, and the change
in energy as this complex moves to the reaction transition state.
Uncertainty in the significance of this work term has led to
reports of very different values of Λ for similar proton-transfer
reactions at R-methyl ketones and O-alkylated R-methyl
ketones.19-21
The intrinsic barrier Λ for a chemical reaction defines the
steepness of curvature of the reaction coordinate, and this, in
turn, determines the sensitivity of the position of the reaction
transition to changes in thermodynamic driving force. A large,
formal intrinsic barrier Λ requires a reaction coordinate with a
steep ascent to a transition state whose position will shift only
slightly with changing reaction driving force (Figure 1A). The
steepness of the ascent to the transition state decreases with
decreasing Λ, and this will lead to a sharper shift in the position
of the transition state with changing reaction driving force
(Figure 1B).
and KHA is the acidity constant of the Brønsted acid.
The magnitude of the shift in the position of the transition state
(∂R) with changing thermodynamic driving force for the re-
action (∂pKBH, where pKBH is the pKa of the conjugate acid
of the reacting base) is a second-derivative structure-re-
activity effect. This effect is equal to the second derivative of
the Marcus equation and is inversely proportional to the intrinsic
barrier Λ (eq 3).7,22,23 The difference between the observed
barrier for a thermoneutral reaction and the Marcus intrinsic
barrier estimated from an analysis of the second derivative
structure-reactivity effect provides an estimate for the work
term ωr.
We report here a complete set of rate and equilibrium
constants for reversible protonation of ring-substituted R-meth-
oxystyrenes (X-1) by hydronium ion and by substituted car-
boxylic acids to form the corresponding oxocarbenium ions
(Scheme 1). This set of data is used to estimate the intrinsic
reaction barrier Λ from the second-derivative structure-
reactivity term: ∂2 log ∆G†/∂(∆G°)HA∂(∆G°)HB) 1/8Λ.7 The
value of Λ calculated from this structure-reactivity analysis is
similar to the observed activation barrier to thermoneutral proton
transfer. This provides evidence that little work is performed
on moving from free reactants to the complex that undergoes
the proton-transfer reaction. These data also reveal deviations
from ideal Marcus behavior that are pertinent to the use of the
Marcus equation as a descriptor of the reaction coordinate profile
for organic reactions.
The magnitude in the shift of the position of the transition
state with changing thermodynamic driving force can be
evaluated by determining the appropriate second-derivative
structure-reactivity coefficient.7 In the case of proton-transfer
reactions, the approximate position of the transition state is
Experimental Section
Solvents were used without further purification unless otherwise
indicated. Water was first distilled and then further purified with a
Milli-Q water apparatus. Deuterated solvents were purchased from
Cambridge Isotope Laboratories. Methanol and acetonitrile from Fisher
were HPLC grade, and all other solvents used for chemical syntheses
were reagent grade.
defined by the Brønsted coefficient, R ) ∂ log kHA/∂ pKHA
,
where kHA is the second-order rate constant for proton transfer
(15) Bernasconi, C. F. Tetrahedron 1985, 41, 3219-3234.
(16) Bernasconi, C. F. Acc. Chem. Res. 1987, 20, 301-308.
(17) Bernasconi, C. F. Acc. Chem. Res. 1992, 25, 9-16.
(18) Bernasoni, C. F. AdV. Phys. Org. Chem. 1992, 27, 119-238.
(19) Gerlt, J. A.; Gassman, P. G. J. Am. Chem. Soc. 1993, 115, 11552-11568.
(20) Guthrie, J. P. J. Am. Chem. Soc. 1991, 113, 7249-7255.
(21) Toullec, J. J. Chem. Soc., Perkin Trans. 2 1989, 167-171.
(22) Jencks, W. P. Bull. Chim. Soc. France 1988, 218-224.
(23) Richard, J. P.; Amyes, T. L.; Vontor, T. J. Am. Chem. Soc. 1992, 114,
5626-5634.
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6953

A R T I C L E S
Richard and Williams
The following organic compounds were reagent grade from
Aldrich and were used without further purification: 3,5-dinitrobenzoyl
chloride (g98%), 4-methoxyacetophenone (99%), acetophenone
(99%), 4-nitroacetophenone (98%), trimethylorthoformate (>99%),
p-toluenesulfonic acid monohydrate (99%), sodium carbonate, potas-
sium acetate (>99%), potassium phosphate (dibasic trihydrate, 99+%),
potassium phosphate (monobasic, 99%), methoxyacetic acid (98%),
cyanoacetic acid (>99%), and dichloroacetic acid (>99%). Choloro-
acetic acid (>99%) was recrystallized from chloroform. Acetophenone
dimethyl ketal used in product studies was purified by preparative HPLC
to remove small amounts of alkene and ketone impurities. [2-N-
Morpholino]ethanesulfonic acid (MES, 99.5%) was purchased from
Sigma. 3,5-Dinitroacetophenone was prepared from 3,5-dinitrobenzoyl
chloride and diethylmagnesium malonate by following a published
procedure.24
AP ꢀS
[P]
)
(4)
(
(
[S] ) ( )(ꢀ )
(AS)0
P
0
Aalk ꢀket
[alkene]
)
(5)
[ketone]) (A )(ꢀ )
ket
alk
Values of the first-order rate constants (kobsd) for the reactions of
4-MeO-1, H-1, and 4-NO2-1 were determined as the slopes of linear
semilogarithmic plots of reaction progress against time. The reactions
obeyed first-order kinetics for more than three reactions halftimes, and
the values of kobsd were reproducible to (5%. Rate constants for the
reactions of 3,5-di-NO2-1 at pH > 4.6 were determined using the
method of initial rates by monitoring the initial conversion of e6% of
reactant to product and using HPLC to separate the reactant from
product. The values of kobsd were determined as the slopes of linear
plots of [P]/[S]0 against time, where [P] and [S]0 are the concentration
of the product and the initial concentration of the substrate, respectively.
The values of [P]/[S]0 were determined from the peak areas of the
product, AP, and the initial peak area of the substrate at t ) 0, (AS)0 at
250 nm (eq 4), where ꢀS/ꢀP ) 1.44 is the ratio of the extinction
coefficients of the substrate and product at 250 nm determined by HPLC
analysis of known amounts of these compounds. Second-order rate
constants kHA for general acid catalysis were determined as the slopes
of linear plots of kobsd/[H+] against [HA]/[H+]. The values of kHA
determined in wholly separate experiments agree to better than (10%.
Products of Solvolysis of Acetophenone Dimethyl Ketal. The
solvolysis of acetophenone dimethyl ketal to form the alkene and ketone
products was initiated by making a 100-fold dilution of a 0.15 M
solution of the ketal in acetonitrile that contained 0.5 mM fluorene
into water buffered with phosphate at pH 7.0. The products were
separated by HPLC, eluting with methanol/water that contained 10 mM
carbonate buffer at pH 9 and with peak detection at 269 nm. The ratio
of the product yields was determined from the ratio of the HPLC peak
areas Aalk/Aket using eq 5, and ꢀket/ꢀalk ) 0.46 for the ratio of the
extinction coefficients of the acetophenone and R-methoxystyrene
products. The second ratio was determined by HPLC analysis of known
amounts of these two compounds. The product ratio [alkene]/[ketone]
decreased slowly with time, due to acid-catalyzed conversion of the
alkene the acetophenone. 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.
1H NMR spectra were obtained on a Varian Gemini 300, a UNITY
1
INOVA 400, or a UNITY INOVA 500 MHz NMR spectrometer. H
NMR spectra were obtained using CDCl3 as the solvent unless otherwise
stated. Chemical shifts (ppm) were determined using tetramethylsilane
(TMS) as an internal reference at zero ppm. High performance liquid
chromatography (HPLC) was performed using a system described in
earlier work.25,26 Measurements of pH were obtained using a Ross
Combination pH electrode from Orion or a Radiometer Combination
pH electrode.
Syntheses. The procedures for the synthesis of the following
compounds, along with spectroscopic data and analytical data, are given
in the Supporting Information: 4-methoxyacetophenone dimethyl ketal,
4-nitroacetophenone dimethyl ketal, 3,5-dinitroacetophenone dimethyl
ketal, R-methoxy-4-methoxystyrene, R-methoxystyrene, R-methoxy-
4-nitrostyrene, and R-methoxy-3,5-dinitrostyrene.
Kinetic Studies. Reactions were performed in buffered solutions
of H2O at 25 °C with the ionic strength maintained at 1.0 (KCl). The
reactions were initiated by making a 1/100 dilution of the substrate in
acetonitrile to give the following final concentrations: R-methoxy-4-
methoxystyrene, 0.05 mM; R-methoxystyrene, 0.5 mM; R-methoxy-
4-nitrostyrene, 5 µM; R-methoxy-3,5-dinitrostyrene, 0.02 mM. The
substrate solution in acetonitrile used in kinetic analyses by HPLC
contained 2 mM 9-hydroxy-9 methylfluorene as an internal standard
that was used to correct for small errors in injection volume. The
hydrolysis reaction of X-1 (X ) 4-OMe, H, 4-NO2) was followed
spectrophotometrically by monitoring the change in absorbance at the
following wavelengths: 4-MeO-1, 267 nm; H-1, 245 or 269 nm; and
4-NO2-1, 268 nm. The slow reaction of 3,5-di-NO2-1 was monitored
by separation of the product ketone from the substrate by HPLC, with
peak detection at 250 nm.
Results
The reactions of ring-substituted R-methoxystyrenes X-1 to form
the corresponding ring-substituted acetophenone X-3 were monitored
by UV spectroscopy. In all cases the kinetic data can be fit to the rate
law for a first-order reaction. This is consistent with a large body of
data which shows that protonation of the alkene to form X-2+ is the
rate-determining step for the reaction shown in Scheme 1.28-30 Tables
S1-S7 in the Supporting Information report the observed first-order
rate constants for the reactions of X-1 that were used to determine the
second-order rate constants for the reactions catalyzed by Brønsted
general acids and by the hydrogen ion.
The values of the first-order rate constants ko for the reactions of
4-NO2-1 and 3,5-di-NO2-1 were determined for reactions at five
different concentrations of hydronium ion between 0.01 and 0.05 M
(Table S7). Figure 2 shows these data plotted as logarithmic pH rate
profiles. The R-methoxystyrenes H-1 and 4-MeO-1 are too reactive to
conveniently study in unbuffered acidic solutions (-log[H+] e 3). The
observed first-order rate constants for hydrolysis of these vinyl ethers
Literature values for the pKa’s of the carboxylic acids used in this
work are for ionization at I ) 1.0 (KCl).27 For reactions at pH within
one unit of the pKa of the carboxylic acid catalyst, the solutions of
substrate were prepared by making the appropriate dilution of a 1.0 M
solution of the buffer catalyst (I ) 1.0, KCl) with 1.0 M KCl. In many
cases catalysis by Brønsted acids was examined at pH > pKa, using
[2-N-morpholino]ethanesulfonic acid (MES, pKa ) 6.5) to maintain
constant pH. These solutions were prepared by mixing a 0.5 M solution
of the MES buffer (I ) 1.0, KCl) with the carboxylic acid catalyst at
the same pH and ionic strength and diluting the resulting solution with
1.0 M KCl to give a final MES concentration of 20 mM and final
concentrations of 0.05-0.50 M for {[RCO2H + RCO-]}. The pH of
the solution was determined at the beginning and upon completion of
the kinetic experiment, and the change in pH was found in all cases to
be e0.05 units.
(24) Alpha, S. R. J. Org. Chem. 1973, 38, 3136-3139.
(25) Toteva, M. M.; Moran, M.; Amyes, T. L.; Richard, J. P. J. Am. Chem.
Soc. 2003, 125, 8814-8819.
(28) Kresge, A. J.; Chen, H.-L.; Chiang, Y.; Murrill, E.; Payne, M. A.; Sagatys,
D. S. J. Am. Chem. Soc. 1971, 93, 413-423.
(29) Kresge, A. J.; Sagatys, D. S.; Chen, H. L. J. Am. Chem. Soc. 1977, 99,
7228-7233.
(30) Loudon, G. M.; Smith, C. K.; Zimmerman, S. E. J. Am. Chem. Soc. 1974,
96.
(26) Tsuji, Y.; Toteva, M. M.; Garth, H. A.; Richard, J. P. J. Am. Chem. Soc.
2003, 125, 15455-15465.
(27) Fox, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1974, 96, 1436-1449.
9
6954 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Protonation of Ring-Substituted
R
-Methoxystyrenes
A R T I C L E S
Figure 2. pH-rate profiles for the hydrolysis of ring-substituted R-meth-
oxystyrenes X-1 at 25 °C and I ) 1.0 (KCl). Key: (b): Hydrolysis of
4-MeO-1. (1): Hydrolysis of H-1. ([): Hydrolysis of 4-NO2-1. (2):
Hydrolysis of 3,5-di-NO2-1.
Table 1. Second-Order Rate Constants for Acid-Catalyzed
Hydrolysis of X-1 in Water at 25 °C and I ) 1.0 (KCl)
1
b
k
HA (M-1 s-
)
catalyst (pKa)a
4-MeO-1
H-1
4-NO2-1
3,5-di-NO2-1
HOHc (15.7)
3.1 × 10-4
(6 × 10-5 e,f
CH3CO2Hd (4.60)
CH3OCH2CO2Hd (3.33)
ClCH2CO2Hd (2.65)
NCCH2CO2Hd (2.23)
Cl2CHCO2Hd (1.03)
H3O+ c
2.0
18
45
59
570
870 ( 150e,f
0.13 1.2 × 10-3
6.6 × 10-5
7.4 × 10-4
2.3 × 10-3
2.7 × 10-3
4.7 × 10-2
1.0
3.9
5.3
9.5 × 10-3
4.6 × 10-2
6.2 × 10-2
0.72
Figure 3. Effect of increasing [CH3CO2H] on the observed first-order rate
constant, kobsd, for hydrolysis of X-1 at 25 °C and I ) 1.0 (KCl). (A)
Hydrolysis of 4-MeO-1 at pH 6.6 (20 mM MES). (B) Hydrolysis of H-1
at pH 5.7 (20 mM MES). (C) Hydrolysis of 3,5-di-NO2-1 at pH 5.6 (20
mM MES).
60
85 ( 5f 1.5 ( 0.014f 0.105 ( 0.0013f
a Reference 27. b Second-order rate constant for acid-catalyzed hydrolysis
of X-1 to form the corresponding ketone. Protonation of 1-X is the rate-
determining step for the hydrolysis reaction.27-30 c Determined from the
fit of the data from Figure 2 to a logarithmic form of eq 6. d Determined
from the fit of the experimental data to eq 7. e (s-1). f Standard deviation
from nonlinear least-squares analysis of the data shown in Figure 2.
were determined at near neutral pH in solutions buffered with [2-N-
morpholino]ethanesulfonic acid (MES) [Tables S5 and S6]. The plots
(not shown) of kobsd against buffer concentration were linear and the
rate constants ko (s-1) for the buffer-independent reactions were
determined by extrapolating these linear plots to [B] ) 0. These rate
data are also plotted in logarithmic form in Figure 2. The value of kH
(M-1 s-1) for the reaction of H-1, calculated from the fit of the data in
Figure 2 to a logarithmic form of eq 6 (kw ) 0), is reported in Table
1. The upward break at high pH in the pH rate profile for the reaction
of 4-MeO-1 shows that protonation by water is the dominant reaction
pathway at high pH. Values of kH ) 870 M-1 s-1 and kw ) 3.1 × 10-4
s-1 were determined from the nonlinear least-squares fit of data from
Figure 2 to a logarithmic form of eq 6 (Table 1).
ko ) kw + kH[H+]
(6)
(7)
kobsd/[H+] ) ko/[H+] + kHA([HA]/[H+])
The R-methoxystyrene 4-MeO-1 is too reactive toward specific acid
catalysis to conveniently study at pH ) pKa of alkane carboxylic acid
buffer catalysts. These reactions were studied at pH . pKa in solutions
buffered by MES. The values of kobsd determined at increasing [RCO2H]
are summarized in Table S1 of the Supporting Information. Figure 3A
shows the linear increase in kobsd/[H+] for hydrolysis of 4-MeO-1 in
the presence of increasing [CH3COOH] at pH 6.6 (20 mM MES), 25
°C, and I ) 1.0 KCl; Figure 4A shows the linear increase in kobsd/[H+]
for hydrolysis of 4-MeO-1 at increasing initial [Cl2CHCOOH] at pH
6.7 (20 mM MES), 25 °C, and I ) 1.0 KCl. Values of kobsd/[H+] instead
of simply kobsd are plotted on the y-axes of Figures 3 and 4 in order to
correct for the effect on kobsd of the small (e0.1 unit) change in the
Figure 4. Effect of increasing [CHCl2CO2H] on the observed first-order
rate constants, kobsd for hydrolysis of X-1 at 25 °C and I ) 1.0 (KCl). (A)
Hydrolysis of 4-MeO-1 at pH 6.7 (20 mM MES). (B) Hydrolysis of H-1
at pH 5.6 (20 mM MES). (C) Hydrolysis of 3,5-di-NO2-1 at pH 5.7 (20
mM MES).
initial pH sometimes observed as {[RCO2H] + [RO2-]} is increased
to 0.50 M (Tables S1-S4). Values for the second-order rate constants
kHA for general acid catalysis of the hydrolysis reactions of 4-MeO-1,
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6955

A R T I C L E S
Richard and Williams
Table 2. Equilibrium Constants for the Interconversion of X-1, X-2+, and the Corresponding Dimethyl Ketal (Schemes 1 and 3), Rate
Constants for the Reversible Protonation of X-1, and the Change in Gibbs Free Energy for This Reaction in Water at 25 °C and I ) 1.0
(KCl)
equilibrium constanta
acid catalyst
1 b
alk/M-
c
d
ring substituent
K
(pKR)MeOH
(pKa)ox
log k e
H+
Cl2CHCO2H
CNCH2CO2H
ClCH2CO2H
MeOCH2CO2H
CH3CO2H
4-MeO-
13
-0.81
-2.7
-5.5
-7.8
0.30
k
HA/M-1 s-1 f
2.94
2.6h
2.76
3.49
1.0
1.78
4.3
3.4
-0.143
5.0
1.77
3.70
2.6
0.72
4.5
5.1
-1.21
5.2
1.65
4.0
3.2
0.59
4.7
5.6
-1.34
5.4
9.2
1.26
4.28
4.1
0.00
4.8
6.6
-2.02
5.4
0.30
4.60
5.8
-0.89
5.2
8.3
-2.92
5.8
kA/ M-1 s-1 g
∆G°/kcal/mol
-2.8i
1.93
3.4h
H
17
25
34
-1.5
k
HA/M-1 s-1 f
kA/M-1 s-1 g
∆G°/kcal/mol
-0.4i
0.176
4.3h
4-NO2
3,5-di-NO2
-4.1
-6.3
k
HA/M-1 s-1 f
kA/M-1 s-1 g
∆G°/kcal/mol
3.2i
7.0
-1.33
6.0
8.6
-2.57
5.9
10.1
-3.13
6.5
11.9
-4.18
6.7
k
HA/M-1 s-1 f
-0.98
-2.64
6.3
12.2
kA/M-1 s-1 g
5.3h
∆G°/kcal/mol
6.2i
10
11.6
13.1
14.8
a Equilibrium constants defined in Scheme 3. b Data from ref 21. The value of Kalk for hydration of 3,5-di-NO2-1 was estimated using the Hammett
equation, Falk ) 0.21 calculated from the values of Kalk for hydration of H-1 and 4-NO2-1 (σNO2 ) 0.78) and σ ) 2(0.71) ) 1.42 for the 3,5-di-NO2-
substituents [ref 35]. c See text. d (pKa)oxo ) (pKR)MeOH + log Kalk e Rate constants and the change in standard Gibbs free energy for the conversion of X-1
.
to X-2+. f Rate constants from Table 1. g Calculated from the values of (Ka)ox and kHA using eq 10. h First-order rate constant (s-1). i Calculated for a
dimensionless equilibrium constant determined using a standard state concentration of 1.0 M for the proton-transfer reaction.
determined from the linear least-squares fit of the data to eq 7, are
reported in Table 1.
Brønsted general acid catalysis of the hydrolysis of 3,5-di-NO2-1
was studied at pH 5.6 (20 mM MES), I ) 1.0 (KCl) and 25 °C. The
observed first-order rate constants determined for these reactions are
reported in Table S4. Figure 3C shows the linear increase in kobsd/[H+]
for hydrolysis of 3,5-di-NO2-1 in the presence of increasing [CH3-
COOH]; and, Figure 4C shows the linear increase in kobsd/[H+] for
hydrolysis of 3,5-di-NO2-1 in the presence of increasing [Cl2-
CHCOOH]. Values for the second-order rate constants kHA (Table 1)
for general acid catalysis of the hydrolysis of 3,5-di-NO2-1, determined
from the linear least-squares fit of the data to eq 7, are reported in
Table 1.
The observed first-order rate constants determined for buffer-
catalyzed hydrolysis of H-1 are reported in Table S2. Figure 3B shows
the linear increase in kobsd/[H+] for hydrolysis of H-1 in the presence
of increasing [CH3CO2H] at pH 5.7 (20 mM MES), 25 °C, and I ) 1.0
KCl. Figure 4B shows the linear increase in kobsd/[H+] for hydrolysis
of 1 in the presence of increasing [Cl2CHCO2H] at pH 5.6 (20 mM
MES), 25 °C, and I ) 1.0 KCl. Values for the second-order rate
constants kHA for general acid catalysis of the hydrolysis reactions of
H-1, determined from the linear least-squares fit of the data to eq 7,
are reported in Table 1. The second-order rate constants for the
hydrolysis of H-1 catalyzed by other alkane carboxylic acids are
reported in Table 1.
Figure 5. Effect of increasing the concentration of acetate ion on the ratio
of the yields of H-1 and acetophenone, [H-1]/[ketone], from the acid-
catalyzed cleavage of acetophenone dimethyl ketal at pH 7.0 (10 mM
phosphate buffer) in water at 25 °C and I ) 1.0 (KCl). The solid line shows
the least-squares fit of the data to eq 8. (Inset) Effect of increasing the
concentration of phosphate buffer on [H-1]/[ketone]. The solid line shows
the least-squares fit of the data to eq 8 ([AcO-] ) 0 M).
The observed first-order rate constants determined for buffer-
catalyzed hydrolysis of 4-NO2-1 are reported in Table S3. Table 1
reports values of kHA (M-1 s-1) for general acid-catalyzed hydrolysis
this ketal (Scheme 2). A small, 10-20% decrease in the ratio of the
yields of H-1 and acetophenone determined by HPLC analysis was
observed during the first ∼30% of the specific acid-catalyzed hydrolysis
of acetophenone dimethyl ketal at pH 7.0 (10 mM phosphate buffer
and I ) 1.0, KCl) and 25 °C. The initial product ratios [H-1]/[ketone]
were determined by making short extrapolations to zero time for linear
plots of [H-1]/[ketone] against time.
of 4-NO2-1 determined from the linear least-squares fit of plots of kobsd
/
[H+] against [HA]/[H+]. The hydrolysis reactions of 4-NO2-1 catalyzed
by acetic acid and methoxyacetic acid were studied using these
carboxylic acid catalysts as buffers. The hydrolysis reactions catalyzed
by chloroacetic acid and by cyanoacetic acid were studied in solutions
that contain 20 mM MES buffer (I ) 1.0, KCl) at pH 4.8 and 4.3,
respectively, where MES is a weak buffer. The reactions catalyzed by
dichloroactic acid were studied in solutions buffered with acetic acid
(I ) 1.0, KCl) at pH 4.1.
Figure 5 shows the effect of increasing the concentration of acetate
ion on the ratio of the yields of H-1 and acetophenone from specific
acid-catalyzed hydrolysis of acetophenone dimethyl ketal in water at
pH 7.0 (10 mM phosphate buffer), 25 °C, and I ) 1.0, KCl. There
should be little or no Brønsted general base catalysis of addition of
water to H-2+ because (1) There is no significant Brønsted acid catalysis
of cleavage of the acetophenone dimethyl ketal or Brønsted base
catalysis of addition of methanol to H-2+ in the microscopic reverse
direction.31 (2) General base catalysis of addition of the water or the
The second-order rate constant for the hydronium ion-catalyzed
reaction of acetophenone dimethyl ketal (kH ) 1600 M-1 s-1
fold larger than the rate constant for hydronium ion-catalyzed hydrolysis
of the alkene H-1 (Table 1). Therefore, it was possible to determine
the yield of H-1 that forms during the early stages of the reaction of
)
31 is ∼20-
(31) Young, P. R.; Jencks, W. P. J. Am. Chem. Soc. 1977, 99, 8238-8248.
9
6956 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Protonation of Ring-Substituted
R
-Methoxystyrenes
A R T I C L E S
Scheme 2
basic alcohols ethanol and methanol to the related ring-substituted
1-phenylethyl carbocations is weak or negligible.32,33
(5) The (pKa)oxo of 0.30 for deprotonation of 4-MeO-2+ was
calculated for Scheme 3 from Kalk ) 13,21 (pKR)MeOH ) -0.81, and
The data in Figure 5 were fit to eq 8, derived for Scheme 2 ([Pi] )
0.010 M), to give a slope of kAcO/ks ) 0.0034 M-1. The inset in Figure
5 shows the effect of increasing the concentration of phosphate buffer
on [H-1]/[acetophenone], the products of specific acid-catalyzed
cleavage of acetophenone dimethyl ketal at pH 7.0 in water at 25 °C
and I ) 1.0 (KCl). These data were fit to eq 8 ([AcO-] ) 0 M) to give
(pKa)oxo ) (pKR)MeOH + log Kalk.
(6) The values of (pKR)MeOH for the addition of methanol to 4-NO2-
2+ and to 3,5-di-NO2-2+ were calculated using the Hammett equation,
(pKR)MeOH ) -2.7 for the reaction of H-2+,31 the Hammett reaction
constant F ) 3.6 for addition of methanol to X-1,31 and the Hammett
substituent constants σ ) 0.78 for 4-NO2 and σ ) 2(0.71) ) 1.42 for
3,5-di-NO2.35
(7) The values of (pKa)oxo for deprotonation of 4-NO2-2+ and 3,5-
di-NO2-2+ were calculated for Scheme 3 from the values of Kalk and
(pKR)MeOH (Table 2) and the relationship (pKa)oxo ) (pKR)MeOH + log
a slope and intercept of kPi/ks ) 0.040 M-1 and kHOH/ks ) 5.5 × 10-5
,
respectively.
kHOH kPi[Pi]
k
AcO[AcO]
[H - 1]
[ketone]
)
+
+
(8)
(9)
Kalk
.
ks
ks
ks
(8) The values of the absolute rate constants kA for deprotonation of
X-2+ were calculated from (Ka)oxo and kHA or kH using eq 10 derived
for Scheme 1.
kH
kHOH
)
kHA kAKa
kHOH kAKa
Equation 9 is the relationship between rate constants for pro-
tonation of H-1 and for deprotonation of H-2+ in the reverse direction
(Scheme 1), where Ka is the acidity constant for the Brønsted acid.
The value of kH/kHA ) 650 calculated from the rate constants for the
reaction of H-1 (Table 1) is in good agreement with kHOH/kAKa ) 640
calculated from the values of Ka ) 10-4.6; kHOH/kA ) [(5.5 × 10-5)/
ks]/[(3.4 × 10-3 M-1)/ks] ) 0.016, determined from the fits of data
shown in Figure 5. This agreement between rate constant ratios for
catalysis of proton transfers in the forward and microscopic reverse
directions shows that the rate constants determined in this work are
internally consistent.
(Ka)oxo
)
)
(10)
kH
kHA
Scheme 3
The following procedure was used in combining data reported here
with data from earlier studies21,31 in order to obtain the complete set of
rate and equilibrium constants for Scheme 3 reported in Table 2.
(1) Values for the absolute rate constants for deprotonation of
H-2+ by water (kHOH ) 2750 s-1) and acetate ion (kA ) 1.64 × 105
M-1 s-1) were calculated from the values of the partition rate constant
ratios (above) and ks ) 1 × 107 s-1 for addition of water to H-2+.34
(2) The (pKa)oxo of -1.5 for H-2+ was calculated as log(kHOH/kH) )
2750 M-1 s-1/85 M-1 s-1 for deprotonation of H-2+ and for protonation
of 1 by hydronium ion (Table 1).
Discussion
(3) The (pKR)MeOH of -2.7 for the addition of methanol to H-2+ to
form the dimethyl ketal and H+ was calculated for Scheme 3 from the
values of Kalk ) 17,21 (pKa)oxo ) -1.5 (above), and (pKR)MeOH ) (pKa)oxo
We have probed the extent of the reversibility of protonation
of H-1 by measuring the yields of the alkene and ketone
products that form by deprotonation of H-2+ generated by acid-
catalyzed cleavage of the ketal H-3 (Scheme 2). The slope of
Figure 5 shows that H-2+ generated in the presence of 1.0 M
AcO- at pH 7 is deprotonated about once for every 300 times
that it undergoes nucleophilic addition of water (kAcO/ks )
0.0034 M-1, Scheme 2). Similarly, the intercept of the inset to
- log Kalk
.
(4) The (pKR)MeOH of -0.81 for addition of methanol to 4-MeO-2+
was calculated from (pKR)MeOH ) -2.7 for the reaction of H-2+ and
the 80-fold difference in the equilibrium constants for addition of
methanol to 4-MeO-2+ and H-2+ reported in earlier work.31
(32) Richard, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1984, 106, 1396-1401.
(33) Ta-Shma, R.; Jencks, W. P. J. Am. Chem. Soc. 1986, 108, 8040-8050.
(34) Amyes, T. L.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7888-7900.
(35) Hine, J. Structural Effects on Equilibria in Organic Chemistry; Wiley-
Interscience: New York, 1975; p 66.
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6957

A R T I C L E S
Richard and Williams
Table 3. Structure-Reactivity Coefficients for Acid-Catalyzed Protonation of X-1 and Absolute Rate Constants ks (s-1) for Addition of Water
to the Oxocarbenium Ion Reaction Intermediate X-2+ for Reactions at 25 °C and I ) 1.0 (KCl)
1
a
c,d
a
c.f
ring substituent
ks/s-
∆Ga°v
R b,c
∂R/
∂∆Gav
°
carboxylic acid
∆Ga°v
â e
∂R/∂∆Ga°v
4-MeO-
H
4-NO2
3,5-di-NO2
3.5 × 106
2.7
5.7
8.8
0.67 ( 0.04
0.74 ( 0.03
0.78 ( 0.03
0.77 ( 0.03
0.0113 ( 0.0041
Cl2CHCO2H
CNCH2CO2H
ClCH2CO2H
MeOCH2CO2H
CH3CO2H
5.4
7.0
7.6
8.0
0.632 ( 0.0028
0.667 ( 0.019
0.660 ( 0.021
0.676 ( 0.038
0.689 ( 0.027
0.0114 ( 0.0026
5 × 107
9 × 108
1.4 × 1010
11.7
10.2
a The average change in ∆G°, calculated from the data in Table 2. b The Brønsted coefficient, determined as the slopes of the correlations shown in
Figure 7A. c The quoted error is the standard deviation of the slope determined by linear least-squares analysis. d The second-derivative structure-reactivity
coefficient, calculated as the slope of the correlation shown in Figure 7B. e The Brønsted coefficient, determined as the slopes of the correlations shown in
Figure 6A. f The second-derivative structure-reactivity coefficient, calculated as the slope of the correlation shown in Figure 6B.
Figure 5 shows that H-2+ is deprotonated by water in an
unbuffered solution about once for every 18,000 times that it
undergoes nucleophilic addition of water (kHOH/ks ) 5.5 × 10-5).
We conclude that deprotonation of H-2+ is a very rare event in
comparison with nucleophilic addition of water. This reflects
the larger Marcus intrinsic kinetic barrier to deprotonation
compared to that of nucleophilic addition of water.36
Lifetimes of Reaction Intermediates. Young and Jencks
have studied the specific acid-catalyzed reactions of 4-Me-1
and 4-methylacetophenone dimethyl ketal in the presence of
sulfite dianion.31 Each reaction in the presence of a specified
[SO32-] gives the same yield of sulfite adduct, with rates that
are zero-order in [SO32-]. This shows that these substrates
undergo acid-catalyzed reactions through the common inter-
mediate Me-2+ that is trapped by addition of SO32-. Absolute
Figure 6. (A) Brønsted correlations of second-order rate constants log kHA
(M-1 s-1) for protonation of X-1 in water at constant ionic strength of 1.0
maintained with KCl. The slope of these plots is equal to the Brønsted
coefficient â for proton transfer. Key: (b): Acetic acid catalyst. (1):
Methoxyacetic acid catalyst. (9): Chloroacetic acid catalyst. (2): Cy-
anoacetic acid catalyst ((), dichloroacetic acid catalyst. (O): Hydronium
ion catalyst. (B) Change in the Brønsted coefficient â for protonation of
X-1 with changing thermodynamic driving force. The solid line is the least-
squares fit determined using data for carboxylic acid catalysts.
rate constants ks (s-1) for addition of solvent to X-2+ were
estimated from the product rate constant ratios kSO3/ks and kSO3
) 5 × 109 M-1 s-1 for diffusion-limited addition of sulfite to
X-2+. These rate constants were revised when it was determined
that kSO3 is 2-fold smaller than the rate constant for a diffusion-
controlled reaction.34 Rate constants for addition of water to
4-NO2-2+ and to 3,5-di-NO2-2+ estimated using log ks ) 7.7
for the reaction of H-2+,31 the Hammett reaction constant of
F+ ) 1.6 for addition of water to X-2+,31 and the appropriate
Hammett substituent constant σ are reported in Table 3.35
The rate constant of ks ) 1.4 × 1010 s-1 estimated for the
reaction of 3,5-di-NO2-2+ is below the limiting rate constant
of 1 × 1011 s-1 for a reaction whose rate is controlled by
reorganization of the solvation shell that surrounds 3,5-di-NO2-
2+ but is similar to that for diffusional steps.37-41 Therefore,
solvent in the initial solvation shell is predicted to react with
3,5-di-NO2-2+ at a rate competitive with diffusion-controlled
exchange of solvent from this shell with other nucleophiles. The
largest rate constant for deprotonation of X-2+ by an alkane
carboxylate ion estimated in this work is kA ) 5 × 106 M-1
1), (Ka)oxo ) 0.50 M for deprotonation of 4-MeO-2+ by water,
and the relationship kHO ) (kw)(Ka)oxo/Kw. This provides
evidence that there is little or no chemical barrier to this proton-
transfer reaction, which is downhill by almost 20 kcal/mol.
Brønsted Correlations. Linear free-energy relationships
between rate and equilibrium constants are an invaluable tool
for the study of organic reaction mechanisms. The reactions
examined here were chosen because they provide for a large
∼15 kcal/mol range of driving force for proton transfer by
making small changes in the structure of the reactants at site(s)
distant from that for proton transfer. The minimal changes, with
changing reaction driving force, in the interaction between the
acid catalyst and carbon base reduces the ambiguity in the
interpretation of the structure-reactivity correlations reported
here.
s-1 for deprotonation of 3,5-di-NO2-2+ by CH3CO2 (Table
-
2). This is far below the diffusion-controlled limit of 5 × 109
M-1 s-1. We conclude that there is a chemical barrier to
deprotonation of all of these R-methyl oxocarbenium ions by
added buffer anions. A value of kHO ) 1.5 × 1010 M-1 s-1 for
deprotonation of 4-MeO-2+ by hydroxide ion can be calculated
from kw ) 3.1 × 10-4 s-1 for protonation of 4-MeO-1 (Table
Figure 6A shows Brønsted correlations of second-order rate
constants log kHA (M-1 s-1) for general acid-catalyzed hydrolysis
of X-1 by rate-determining protonation of X-1 (Scheme 1),
where the relative basicity of the R-methoxystyrene X-1 (Table
2) is plotted on the x-axis. The slopes of these correlations for
the reactions catalyzed by different carboxylic acids are reported
in Table 3 as the Brønsted coefficients â. Figure 7A shows
related Brønsted correlations of second-order rate constants log
(36) Richard, J. P.; Williams, K. B.; Amyes, T. L. J. Am. Chem. Soc. 1999,
121, 8403-8404.
(37) Giese, K.; Kaatze, U.; Pottel, R. J. Phys. Chem. 1970, 74, 3718-3725.
(38) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371-374.
(39) Kaatze, U.; Pottel, R.; Schumacher, A. J. Phys. Chem. 1992, 96, 6017-
6020.
k
HA (M-1 s-1) for general acid-catalyzed hydrolysis of X-1 by
a group of alkane carboxylic acid catalysts. The slopes of these
(40) Paradisi, C.; Bunnett, J. F. J. Am. Chem. Soc. 1985, 107, 8223-8233.
(41) Toteva, M. M.; Richard, J. P. J. Am. Chem. Soc. 1996, 118, 11434-11445.
9
6958 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Protonation of Ring-Substituted
R
-Methoxystyrenes
A R T I C L E S
the same for a balanced transition state in which there is equal
development of the interaction between the partial negative
charge at the carboxylate oxygen and the alkyl substituent(s)
and also of the interaction between partial positive charge at
the benzylic carbon and the phenyl ring substituent(s).
The imbalance at [X-1‚HA]† shows that the apparent
transition-state charges at the reacting acid and base are different.
We suggest that this is due to a reduction in the destabilizing
inductive transition-state interaction between electron-withdraw-
ing phenyl ring substituent(s) and positive charge at the partly
cationic benzylic carbon, because of the attenuation of the
unfavorable interaction by enhanced stabilizing resonance
electron donation from the R-methoxy group. This will increase
the charge at the R-methoxy oxygen and the separation of this
charge from electron-deficient ring substituent(s).44-46 The
resulting reduction in the polar interactions between these centers
would cause a decrease in the Brønsted coefficient â relative
to R, because R reflects the normal expression of polar
interactions between substituents at the carboxylic acid and the
reacting acidic oxygen. A similar attenuation of the large
inductive destabilization of methoxybenzyl carbocations caused
by strongly electron-deficient groups at the benzylic carbon (e.g.,
R-CF3) provides a relatively simple rationalization for the small
effects of these groups on the rate constants for nucleophilic
addition to R-substituted 4-methoxybenzyl carbocations.45-47
Related imbalances, most substantially larger than the imbal-
ance reported here, have been observed for deprotonation of
carbon acids by electronegative bases to form resonance-
stabilized carbanions.17,18 There is good theoretical evidence
consistent with the existence of these transition-state imbalances
in carbanion-forming reactions48 and a simple physical explana-
tion for their occurrence.3,49
Figure 7. (A) Brønsted correlations of second-order rate constants log kHA
(M-1 s-1) for protonation of X-1 in water at constant ionic strength of 1.0
maintained with KCl. The slope of these plots is equal to the Brønsted
coefficient R for proton transfer. Key: (b): X ) 4-MeO-. (1): X ) H-.
(9): X ) 4-NO2-. (2): X ) 3,5-di-NO2-. Open symbols are for the
reactions catalyzed by H3O+. (B) The change in the Brønsted coefficient R
for protonation of X-1 with changing thermodynamic driving force.
correlations for the reactions of different X-1 are reported in
Table 3 as the Brønsted coefficients R.
The Brønsted coefficients for chemical reactions provide a
measure of the effect of changing polar substituents on the
equilibrium constant for a reference chemical reactionswhere
there is a full unit change in the charge on proceeding from
reactant to productsrelative to the substituent effect on the rate
constants for a second chemical reaction such as protonation
of X-1.42 A Brønsted coefficient of close to 1.0 would show
that the change in effective charge “seen” by the polar
substituent on proceeding from reactant to transition state is
similar to the unit change in charge for the reference reaction.
A Brønsted coefficient of close to 0.0 shows that there is little
or no change in this effective charge on proceeding to the
transition state, while intermediate Brønsted coefficients are
consistent with partial proton transfer at the transition state.42
The relationship between the magnitude of the Brønsted
coefficient and the fractional transfer of the proton on proceeding
to the reaction transition state is not known, but a linear
correlation between the two quantities is generally assumed.
The observation here of a small, but significant increase in the
Brønsted coefficients R and â with increasing thermodynamic
barrier to protonation of X-1 is consistent with a shift to a later,
more productlike transition state with increased negative charge
at the Brønsted acid catalyst and increased positive charge at
the carbon base. This corresponds to a normal Hammond-type
effect.43
The Second-Derivative Structure-Reactivity Effect. The
slope of the least-squares line through the data in Figure 6B is
equal to ∂â/∂∆G° ) 0.011 ( 0.0026 (standard deviation) and
av
the slope of the least-squares line through the data in Figure
7B is equal to ∂R/∂∆G° ) 0.011 ( 0.0041 (standard devia-
av
tion). There is good agreement between the slopes of the
correlations from Figures 6B and 7B, as required for these cross-
correlation coefficients.50 The difference in the uncertainty of
the slopes of the correlations from Figures 6B and 7B is
discussed below. These data are consistent with an earlier
Transition-State Imbalance. Figure 6B shows the change
in the Brønsted coefficient â with the change in ∆G° , the
av
arithmetic average of the changes in ∆G° for protonation of
four different 1-X by a single carboxylic acid, and Figure 7B
shows the change in the Brønsted coefficient R with the change
estimate of a limit of ∂R/∂∆G° e 0.026 for protonation of a
av
in ∆G° for protonation of a single 1-X by a series for five
av
(44) Amyes, T. L.; Stevens, I. W.; Richard, J. P. J. Org. Chem. 1993, 58, 6057-
6066.
carboxylic acids. The y-intercepts of 0.66 for Figure 7B and
0.58 for Figure 6B provide estimates of the Brønsted coefficients
R and â, respectively, for thermoneutral proton transfer from
the acid catalyst to the basic carbon. These coefficients will be
(45) Richard, J. P. J. Am. Chem. Soc. 1989, 111, 1455-1465.
(46) Richard, J. P. Tetrahedron 1995, 51, 1535-1573.
(47) Richard, J. P.; Amyes, T. L.; Bei, L.; Stubblefield, V. J. Am. Chem. Soc.
1990, 112, 9513-9519.
(48) Bernasconi, C. F.; Wenzel, P. J. J. Am. Chem. Soc. 1994, 116, 5405-
5413.
(42) Hupe, D. J.; Jencks, W. P. J. Am. Chem. Soc. 1977, 99, 451-464.
(43) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334-338.
(49) Kresge, A. J. Can. J. Chem. 1974, 52, 1897-1903.
(50) Jencks, D. A.; Jencks, W. P. J. Am. Chem. Soc. 1977, 99, 7948-7960.
9
J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007 6959

A R T I C L E S
Richard and Williams
Figure 8. Two hypothetical reaction profiles which might be used to rationalize the observation of a relatively late transition state for thermoneutral
protonation of X-1 by alkane carboxylic acids. (A) Reaction profile for which the chemical barrier to the proton-transfer step is uphill, but the overall
reaction is thermoneutral, because the negative work associated with the breakdown of the product complex (ωp) is greater than the positive work associated
with the formation of the reactant complex (ωr ≈ 0). (B) Asymmetric reaction profile which shows a shallow curvature close to the reactants and a much
steeper curvature close to the products.
more structurally diverse series of vinyl ethers.51
determined for the electrostatic cross-correlation coefficient (-τ)
in studies on the formation of hydrogen bonds between
substituted phenoxide anions and alkane ammonium ions in
water54 suggests that such electrostatic effects may mask a
change in structure-reactivity coefficients for protonation of
vinyl ethers that arise from a shift in the position of the reaction
transition state.
log ko ) 12.8 - Λ/1.36
(11)
The slopes ∂R/∂∆G° ) ∂â/∂∆G° ) 1/8Λ ) 0.011 of the
av
av
correlations from Figures 6B and 7B are consistent with an
intrinsic barrier of 11 kcal/mol for a reaction coordinate that
can be described by Marcus theory (eqs 1-3). The range of
intrinsic barriers consistent with these data is 8-18 kcal/mol,
calculated for the larger error limit of ( 0.0041. By comparison,
a value of Λ ) 13 kcal/mol can be calculated from the intrinsic
rate constant of log ko (M-1 s-1) ) 3.2 for protonation of
4-MeO-1 by using eq 11. This intrinsic rate constant was
determined by making a short linear extrapolation to ∆G° ) 0
of a plot of log kHA against ∆G°. We conclude that these data
are consistent with a reaction in which there is little work done
on reactants in the formation of the reaction complex so that
ωr ≈ ωP ≈ 0 (eq 1) for formation of a complex similar to that
formed by simple diffusional encounter of 1-X and carboxylic
acid catalysts.
(2) The difference in the uncertainty of the slopes of the
correlations shown in Figure 6B (∂â/∂∆G° ) 0.011 ( 0.0026)
av
and in Figure 7B (∂R/∂∆G° ) 0.011 ( 0.0041) reflects the
av
apparent downward curvature for the latter correlation. Such
apparent curvature may simply be due to the uncertainty in the
experimental data. However, the curvature is caused mainly by
the large 0.07 unit change in R for the 4-OMe for 4-H
substitution at X-1 (Table 3); and this large change may be
observed because the strongly resonance electron-donating
4-MeO- group causes a significant increase in the Marcus
intrinsic reaction barrier Λ compared to the reaction of other
X-1,55 similar to the exalted value of Λ observed for deproto-
nation of the 1-(4-methoxyphenyl)ethyl carbocation.56 Such a
specific increase in Λ for protonation of 4-MeO-1 would cause
a decrease in R that reflects the tendency of reactions with very
large intrinsic barriers to react through central transition states
with R ) â ) 0.50. This would correspond to a third-derivative
structure-reactivity effect.33 These effects have been extensively
documented for related reactions.8,23,33,57 The effect would cause
the observed value of ∂R/∂∆G° ) ∂â/∂∆G° ) 0.011 to
Two other effects, in addition to a formal shift in the position
of the reaction transition state, may contribute to the observed
value of ∂R/∂∆G° ) ∂â/∂∆G° ) 0.011.
av
av
(1) There may a change in these Brønsted coefficients that
opposes the change from a Hammond-type shift in the structure
of the transition state that arises from changing electrostatic
interactions between substituents at the vinyl ether and the
carboxylic acid reactants.52-54 For example, the interaction
between the electron-deficient 3,5-nitro groups at 3,5-di-NO2-1
and electron-rich or electron-deficient groups at the carboxylic
acid catalyst are stabilizing (v kHA) and destabilizing (V kHA),
respectively, compared to the interactions with the hydrogen at
4-H-1. Such a change in rate constants for weakly and strongly
acidic catalysts will have the effect of causing a decrease in
the Brønsted coefficient R. The value of -(∂R/∂KBH) ) -0.013
av
av
overestimate the shift in the position of the transition state from
a Hammond effect and would compensate for any opposing
contribution of the electrostatic term τ discussed above.
The following Marcus parameters for protonation of vinyl
ethers by hydronium ion have been reported in earlier work:
(1) Λ ) 4 kcal/mol, ωr ) 13 kcal/mol, and ωP ) 11 kcal/mol,
obtained from the very poorly defined fit of a small set of six
rate constants for protonation of X-1 by H3O+ to an equation
that contains three variable parameters21 and (2) Λ ) 4 kcal/
mol and ωr ) 10 kcal/mol that were obtained by an analysis of
the change in the solvent kinetic deuterium isotope effect with
changing vinyl ether reactivity for lyonium-ion catalyzed
(51) Murray, C. J.; Jencks, W. P. J. Am. Chem. Soc. 1990, 113, 1880-1889.
(52) Hine, J. J. Am. Chem. Soc. 1972, 94, 5766-5771.
(53) Rothenberg, M. E.; Richard, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1985,
107, 1340-1346.
(54) Stahl, N.; Jencks, W. P. J. Am. Chem. Soc. 1986, 108, 4196-4205.
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6960 J. AM. CHEM. SOC. VOL. 129, NO. 21, 2007

Protonation of Ring-Substituted
R
-Methoxystyrenes
A R T I C L E S
hydrolysis of a broad range of vinyl ethers.29 This second
analysis was carried out in the absence of the determination of
the thermodynamic driving force ∆G° for proton transfer to form
the oxocarbenium ion.58 A value of Λ ) 4 kcal/mol requires a
cross correlation coefficient of ∂R/∂∆G° ) ∂â/∂∆G° ) 0.031
that is substantially larger than the value of 0.011 determined
in this work. We conclude that if there is a sharp change in the
position of the transition state for a reaction with Λ ) 4 kcal/
mol, then the effect of this change on the observed Brønsted
coefficients R and â is masked by a large electrostatic term τ
that causes an opposing change in the magnitude of these
coefficients (see above).
Thermoneutral Proton Transfer. The y-intercepts of 0.66
for Figure 7B and of 0.58 for Figure 6B are equal to the
Brønsted coefficients R and â, respectively, when ∆G° ) 0 for
proton transfer from the acid catalyst to the basic carbon. These
Brønsted coefficients are both greater than the value of R ) â
) 0.50 predicted by Marcus theory for thermoneutral proton
transfer.7 A value of R > 0.50 for thermoneutral proton transfer
might be explained by one of the two reaction coordinate profiles
shown in Figure 8.
as stabilizing electrostatic interactions between the oppositely
charged ions. In any case, we are not able to offer a physical
explanation for any large difference in the respective work done
to form reactant and product complexes and consider this to be
unlikely explanation for the large Brønsted coefficients observed
for thermoneutral proton transfer.
av
av
(2) The exalted value of R for thermoneutral proton transfer
is consistent with a smaller curvature along the free-energy
surface near the reactants, where the primary motion is stretching
of the O-H bond of a carboxylic acid, compared with the energy
surface near the products, where the primary motion is stretching
of the C-H bond of the R-alkoxy carbocation (Figure 8B). Such
an asymmetric reaction coordinate is in keeping with the notion
that it may be constructed as a hybrid of (a) the energy surface
close to the reactants, which is dominated by proton transfer at
oxygen and shows shallow curvature expected for a reaction
with a small intrinsic barrier59 and (b) the energy surface near
the products, which is dominated by proton transfer at carbon
and shows steep curvature expected for this reaction with a large
intrinsic barrier.17,18
Concluding Remarks
(1) The data are consistent with a reaction profile (Figure
8A) in which the chemical barrier to the proton-transfer step is
uphill, but the overall reaction is thermoneutral because the
negative work associated with the breakdown of the product
complex (ωp) is greater than the positive work associated with
the formation of the reactant complex (ωr). Extrapolation of
the correlation from Figure 7B gives R ) 0.50 when proton
transfer to a hypothetical X-1 is favorable by 14 kcal/mol. For
a symmetrical reaction (Figure 8A), this corresponds to 14 kcal/
mol greater work done in the formation of the product compared
to that for the reactant complex from free species. There may,
indeed, be work associated with the desolvation of the product
ions RCO2- and X-2+ when they are brought together to form
the reaction complex, but part or all of this may be “recovered”
This discussion collides with the limits of what might be
learned about the transition-state structure and reaction coor-
dinate profile for protonation of X-1 from systematic analyses
of rate-equilibrium relationships. These limits are best extended
through computational studies, which reproduce experimental
structure-reactivity coefficients and provide additional insight
into questions that are not easily resolved by experiment.
Acknowledgment. This paper is dedicated to the memory of
William P. Jencks. We acknowledge the National Institutes of
Health (GM 39754) for generous support of this work.
Supporting Information Available: Details of procedures for
the synthesis of 4-methoxyacetophenone dimethyl ketal, ac-
etophenone dimethyl ketal, 4-nitroacetophenone dimethyl ketal,
3,5-dinitroacetophenone dimethyl ketal, R-methoxy-4-methoxy-
styrene, R-methoxystyrene, R-methoxy-4-nitrostyrene, and
R-methoxy-3,5-dinitrostyrene; Tables S1-S7 of observed first-
order rate constants (kobsd) for hydrolysis of X-1 in solutions
that contain HCl or carboxylic acids. This material is available
free of charge via the Internet at http://pubs.acs.org.
(55) Any effect which causes a change in the Brønsted coefficient for the reaction
of 4-MeO-1, such as a change in the intrinsic reaction barrier or a change
to a concerted reaction mechanism, will be very difficult to detect as
curvature that is caused by the change in the position of a single data point
on the correlations shown in Figure 6A. This effect will be easier to detect
on the correlations shown in Figure 7A, because all of the deviant rate
constants are present on the single Brønsted correlation for the reaction of
the deviating compound 4-MeO-1.
(56) Richard, J. P.; Amyes, T. L.; Lin, S. S.; O’Donoghue, A. C.; Toteva, M.
M.; Tsuji, Y.; Williams, K. B. AdV. Phys. Org. Chem. 2000, 35, 67-115.
(57) Sørenson, P. E.; Jencks, W. P. J. Am. Chem. Soc. 1987, 109, 4675-4690.
(58) The value of the Brønsted coefficient â for protonation of X-1 by H3O+
lies on the correlation between â and reaction driving force determined
for protonation of X-1 by carboxylic acids (Figure 6B). This provides
evidence that there is not a large difference in the value of intrinsic barrier
Λ for the reaction of these different types of Brønsted acids.
JA071007K
(59) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1-72.
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