Intrinsic barriers for the reactions of an oxocarbenium ion in water

Full text of DOI:10.1021/ja9915293

J. Am. Chem. Soc. 1999, 121, 8403-8404
Scheme 1
8403
Intrinsic Barriers for the Reactions of an
Oxocarbenium Ion in Water
John P. Richard,*,1 Kathleen B. Williams, and Tina L. Amyes
Contribution from the Department of Chemistry,
UniVersity at Buffalo, SUNY, Buffalo New York 14260-3000
ReceiVed May 10, 1999
The nucleophile addition reactions of R-methyl benzyl car-
bocations with Lewis bases are fast and are generally perceived
to be thermodynamically favorable processes.2,3 By contrast with
proton-transfer reactions at carbon,4-6 there has been little
consideration of whether these reactions of unstable carbocations
are intrinsically fast, or whether they are fast simply because they
are energetically favorable. This distinction requires a knowledge
of the intrinsic barrier to the reaction in the absence of a
thermodynamic driving force. We report here intrinsic rate
constants of (kMeOH)o ) 1 × 108 M-1 s-1 and (kp)o ) 450 s-1 for
the nucleophilic addition of methanol to the acetophenone
oxocarbenium ion 2H+ and deprotonation of 2H+ by solvent
water, respectively (Scheme 1). These intrinsic rate constants
correspond to intrinsic barriers of ΛMeOH ) 6.5 kcal/mol and Λp
) 13.8 kcal/mol for the nucleophile addition and proton-transfer
reactions, respectively.
M-1 s-1 and kAcOH ) 0.13 M-1 s-1, respectively. Figure 1 shows
the effect of increasing concentrations of acetate ion on the ratio
of the yields of R-methoxystyrene 2 and acetophenone from the
acid-catalyzed cleavage of acetophenone dimethyl ketal 1 in water
at pH 7.0 (10 mM phosphate buffer) at 25 °C and I ) 1.0 (KCl).14
The data were fit to eq 1 to give kAcO/kHOH ) 0.0034 M-1 for
partitioning of 2H+ between deprotonation by acetate ion to give
2 and nucleophilic addition of solvent water to give, ultimately,
acetophenone.15 This partitioning ratio can be combined with the
value of 5 × 107 s-1 for kHOH,7 to give kAcO ) 1.7 × 105 M-1 s-1
as the absolute rate constant for deprotonation of 2H+ by acetate
ion. The acidity of the oxocarbenium ion 2H+ can then be
calculated as Koxo ) (kAcO/kAcOH)(Ka)AcOH ) 33 M, using p(Ka)AcOH
) 4.60 for acetic acid under our experimental conditions. The
relationship Koxo ) kp/(kH)alk then gives kp ) 2600 s-1 for
deprotonation of 2H+ by solvent water. The equilibrium constant
for elimination of methanol from 1 to give 2 was calculated as
Kalk ) Koxo/Kadd ) 0.018 M (Scheme 1).16
Table 1 summarizes the rate and equilibrium constants for the
formation and reaction of 1, 1H+, 2, and 2H+ in water at 25 °C
(Scheme 1). The literature values7,8 of kMeOH ) 3 × 106 M-1 s-1
and kH ) 1600 M-1 s-1 give Kadd ) 1900 for the addition of
methanol to 2H+ to give 1. The value of pKa ) -6.2 for
protonated acetophenone dimethyl ketal 1H+ was estimated
starting from pKa ) -2.52 for protonated dimethyl ether.9 The
equilibrium constant for the addition of methanol to 2H+ to give
1H+ can then be calculated as (Kadd)H ) Kadd/Ka ) 0.0012 M-1
(Scheme 1). The first-order rate constant for the cleavage of 1H+
(13) The reactions of 2 were monitored by following the appearance of
acetophenone by UV spectroscopy. The protonation of 2 is rate-limiting for
its conversion to acetophenone [Loudon, G. M.; Berke, C. J. Am. Chem. Soc.
1974, 96, 4508-4517].
to give the oxocarbenium ion 2H+ can be calculated as ksolv
)
(14) The products of the cleavage of 1 in water were separated by HPLC
and quantified as described in earlier work [Richard, J. P. J. Am. Chem. Soc.
1989, 111, 1455-1465]. Ratios of product yields [2]/[acetophenone] were
calculated using eq 4 {[2]/[acetophenone] ) (A2/Aketone)(ꢀketone/ꢀ2)}, where A2/
Aketone is the ratio of the peak areas from HPLC analysis and ꢀketone/ꢀ2 ) 0.46
is the ratio of the extinction coefficients of the two products at 269 nm. The
observed product ratio [2]/[acetophenone] decreases with time due to acid-
catalyzed hydrolysis of 2 to give acetophenone. Therefore, the initial product
ratio was determined by extrapolation to zero time of a linear plot of the
observed product ratios against time determined during reaction of up to 30%
of 1. During this time, the value of [2]/[acetophenone] decreases by ∼30%,
but the difference between the ratio obtained by extrapolation to zero time
and that obtained at the earliest time point was e10%. The values of A2/
Aketone and the value of kAcO/kHOH (M-1) determined from the ratio of product
yields were reproducible to better than (10%.
kHKa ) 2.5 × 109 s-1. This is smaller than the rate constant of
∼1010 s-1 for the thermodynamically favorable deprotonation of
1H+ by solvent water to regenerate 1,11 so that 1 and 1H+ are
essentially at chemical equilibrium during the acid-catalyzed
cleavage of 1. This is in agreement with the conclusions of earlier
studies that 1H+ is an intermediate of the stepwise, specific-acid-
catalyzed hydrolysis of ketals,12 which is the microscopic reverse
of nucleophilic addition of methanol to 2H+ to form 1.
The rate constants for protonation of R-methoxystyrene 2 by
hydronium ion and acetic acid in water at 25 °C and I ) 1.0
(KCl) were determined by published methods13 as (kH)alk ) 80
(15) The derivation of eq 1 assumes that there is no catalysis by acetate
ion of the nucleophilic addition of water to 2H+. An increase in the
concentration of acetate ion from 0 to 0.77 M (I ) 1.0, KCl) results in a
2-fold increase in the observed product rate constant ratio kHOH/kSO3 for
partitioning of 2H+ between the addition of solvent water and the diffusion-
limited addition of sulfite dianion, which is nominally consistent with catalysis
of the addition of water to 2H+ by acetate ion (ref 8). However, this change
in the observed product rate constant ratio is likely a result of a specific acetate
ion salt effect on the relative values of kSO3 and kHOH because (a) acetate ion
catalysis of the addition of water to 2H+ (kHOH ) 5 × 107 s-1, ref 7) should
be less important than catalysis of the addition of water to the more stable
1-(4-dimethylaminophenyl)ethyl carbocation (ks ) 40 s-1 in 50:50 (v/v)
trifluoroethanol/water [McClelland, R. A.; Cozens, F. L.; Steenken, S.; Amyes,
T. L.; Richard, J. P. J. Chem. Soc., Perkin Trans. 2 1993, 1717-1722]), for
which no catalysis by acetate ion was observed.22 (b) The absence of general
acid catalysis of the cleavage of 1 to give 2H+ and methanol (ref 12) requires
that there be no general base catalysis of the addition of methanol to 2H+ in
the reverse direction. This suggests that catalysis of the addition of water,
whose basicity is similar to that of methanol, is negligible.
(1) Tel: (716) 645 6800, ext 2194. Fax: (716) 645 6963. E-mail:
jrichard@chem.buffalo.edu.
(2) Richard, J. P. Tetrahedron 1995, 51, 1535-1573.
(3) McClelland, R. A. Tetrahedron 1996, 52, 6823-6858.
(4) Bernasconi, C. F. Tetrahedron 1985, 41, 3219-3234.
(5) Bernasconi, C. F. Acc. Chem. Res. 1987, 20, 301-308.
(6) Bernasconi, C. F. Acc. Chem. Res. 1992, 25, 9-16.
(7) Amyes, T. L.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7888-
7900.
(8) Young, P. R.; Jencks, W. P. J. Am. Chem. Soc. 1977, 99, 8238-8248.
(9) Following the methodologies of Fox and Jencks (ref 10a) and
Funderburk et al. (ref 10b), the acidity of 1H+ can be estimated starting from
pKa ) -2.52 for protonated dimethyl ether (ref 10c) and using an average of
the values of FI ) -8.4 (ref 10a) and FI ) -9.1 [Taylor, P. J. J. Chem. Soc.,
Perkin Trans. 2 1993, 1423-1427], which correlate the pKa of alcohols of
structure R1R2CHOH with the value of σI for the substituents R. The values
of σI ) 0.12 for RdPh and 0.30 for RdOMe [Charton, M. Prog. Phys. Org.
Chem. 1981, 13, 119-251] then give pKa ) -6.2 for 1H+.
(10) (a) Fox, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1974, 96, 1436-
1449. (b) Funderburk, L. H.; Aldwin, L.; Jencks, W. P. J. Am. Chem. Soc.
1978, 100, 5444-5459. (c) Bonvicini, P.; Levi, A.; Lucchini, V.; Modena,
G.; Scorrano, G. J. Am. Chem. Soc. 1973, 95, 5960-5964.
(11) Eigen, M. Angew. Chem., Int. Ed. Engl. 1964, 3, 1-72.
(12) Cordes, E. H.; Bull, H. G. Chem. ReV. 1974, 74, 581-603.
(16) This is in fair agreement with Kalk ) 0.06 M obtained by combining
the value of Kalk determined for the elimination reaction in methanol and the
free energies of transfer of the reactants and products from methanol to water
[Toullec, J. J. Chem. Soc., Perkin Trans. 2 1989, 167-171]. The value of
Koxo ) 33 M reported here also shows a similar agreement with the value of
65 M determined by a different indirect method in this earlier study.
10.1021/ja9915293 CCC: $18.00 © 1999 American Chemical Society
Published on Web 08/31/1999

8404 J. Am. Chem. Soc., Vol. 121, No. 36, 1999
Communications to the Editor
Table 1. Rate and Equilibrium Constants for the Formation and Reaction of 1, 1H+, 2 and 2H+ in Water (Scheme 1)a
reaction
equilibrium constant
rate constants
Kalk/[MeOH]
Kalk ) 0.018 Mb
Ka ) 1.6 × 106 Mc
Koxo ) 33 Md
1 y
1H+ y
z 2
+
]
Ka/[H
z 1
+
Koxo/[H
]
kp ) 2600 s-1 e
2H+ y
z 2
(kH)alk ) 80 M-1 s-1
+
Kadd[MeOH]/[H
]
Kadd ) 1900f
kMeOH ) 3 × 106 M-1 s-1 g
2H+ y
z 1
kH ) 1600 M-1 s-1 h
kMeOH ) 3 × 106 M-1 s-1 g
ksolv ) 2.5 × 109 s-1 j
(Kadd)H[MeOH]
(Kadd)H ) 0.0012 M-1 i
2H+ y
z 1H+
a At 25 °C and I ) 1.0 (KCl), unless noted otherwise. A discussion of the uncertainties and standard errors in the rate and equilibrium constants
reported in this table is given in the Supporting Information. b Calculated as Kalk ) Koxo/Kadd
.
c Estimated from pKa ) -2.52 for dimethyl ether, as
f Calculated as
described in ref 9. d Calculated as Koxo ) (kAcO/kAcOH)(Ka)AcOH, see text. e Calculated as kp ) Koxo(kH)alk ) (kAcO/kAcOH)(Ka)AcOH(kH)alk
.
Kadd ) kMeOH/kH. g Data from ref 7. h Data from ref 8. i Calculated as (Kadd
)
) Kadd/Ka. j Calculated as ksolv ) kHKa.
H
(5-7) × 109 M-1 s-1 for the diffusion-limited reactions of
carbocations.19 We conclude that the thermoneutral nucleophilic
addition of methanol to the oxocarbenium ion 2H+ is an
intrinsically fast reaction. By contrast, the deprotonation of 2H+
by solvent water through transition state 4 is a much slower
process.
Figure 1. The effect of increasing concentrations of acetate ion on the
ratio of the yields of R-methoxystyrene and acetophenone, [2]/[acetophe-
none], from the acid-catalyzed cleavage of acetophenone dimethyl ketal
1 in water at pH 7.0 (10 mM phosphate buffer) at 25 °C and I ) 1.0
(KCl). The solid line shows the least-squares fit of the data to eq 1 of
the text. The slope of this line is kAcO/kHOH ) 0.0034 M-1 for partitioning
of the oxocarbenium ion 2H+ between deprotonation by acetate ion and
nucleophilic addition of solvent water.
A qualitative explanation for the existence of a significant
intrinsic barrier for carbocation-nucleophile combination reac-
tions such as the addition of methanol to 2H+, is that the
stabilization of the transition state 3 due to the developing C-O
bond is smaller than the opposing increase in energy from the
loss of stabilizing electron donation from the R-oxygen and
R-phenyl groups to the benzylic carbon.2 The falloff in stabilizing
electron donation to the benzylic carbon of carbocations such as
2H+ on proceeding to the transition state 3 may be relatively large
because2,3,20 (a) there is a fractional loss of stabilization from
electron donation that is roughly equal to the fraction of C-O
bond formation at 3; and (b) stabilization of the carbocation from
π-overlap with R-substituents is further reduced by the movement
away from a planar geometry at the partly sp3-hybridized benzylic
carbon of 3.20,21 Whatever the explanation for the magnitude of
ΛMeOH ) 6.5 kcal/mol, this experimental intrinsic barrier for the
addition of methanol to 2H+ will serve as a benchmark against
which to test developing theoretical work to model these intrinsic
barriers.
ko
kAcO
[2]/[acetophenone] )
+
[AcO-]
kHOH kHOH
(1)
1
1.36
1.36log K 2
log k )
17.44 - Λ 1 -
(2)
(3)
{
(
) }
4Λ
Λ
1.36
log ko ) 12.8 -
Table 1 shows that, despite the 6 kcal/mol larger thermody-
namic driving force for the deprotonation of 2H+ to give 2 (∆G°
) -2.1 kcal/mol) than for the nucleophilic addition of methanol
to give 1H+ (∆G° ) 4.0 kcal/mol), there is a 1200-fold larger
rate constant for the latter reaction. The rate and equilibrium
constants for these reactions of 2H+ were substituted into the
Marcus equation17 (eq 2, derived at 298 K) to give ΛMeOH ) 6.5
( 0.5 kcal/mol as the intrinsic barrier for the hypothetical
thermoneutral nucleophilic addition of methanol to 2H+, and Λp
) 13.8 ( 0.1 kcal/mol as the intrinsic barrier for the hypothetical
thermoneutral deprotonation of 2H+ by solvent water. These
Acknowledgment. We acknowledge the National Institutes of Health
Grant GM 39754 for its generous support of this work.
Supporting Information Available: A discussion of the uncertainties
and standard errors in the rate and equilibrium constants reported in Table
1, and in the intrinsic barriers and rate constants ΛMeOH, Λp, (kMeOH)o,
and (kp)o. This material is available free of charge via the Internet at
http://pubs.acs.org.
intrinsic barriers correspond to intrinsic rate constants of (kMeOH o
)
) (1.1 ( 0.9) × 108 M-1 s-1 and (kp)o ) 450 ( 60 s-1 (eq 3).18
The value of (kMeOH)o for addition of methanol to 2H+ is larger
than ko ) 1 × 107 M-1 s-1 for thermoneutral protonation of the
dicyanomethyl carbanion by secondary amines, a prototypical fast
proton transfer at carbon,4 and only ∼60-fold smaller than kd ≈
JA9915293
(19) McClelland, R. A.; Kanagasabapathy, V. M.; Banait, N. S.; Steenken,
S. J. Am. Chem. Soc. 1991, 113, 1009-1014.
(20) Kresge, A. J. Can. J. Chem. 1974, 52, 1897-1903.
(21) Bernasconi, C. F.; Wenzel, P. J. J. Am. Chem. Soc. 1994, 116, 5405-
5413.
(22) (a) Ta-Shma, R.; Jencks, W. P. J. Am. Chem. Soc. 1986, 108, 8040-
8050. Richard, J. P.; Jencks, W. P. J. Am. Chem. Soc. 1984, 106, 1396-
1401.
(17) Marcus, R. A. J. Phys. Chem. 1968, 72, 891-899.
(18) The quoted errors are standard errors. The calculation of the standard
errors in the values of ΛMeOH, Λp, (kMeOH)o, and (kp)o is discussed in the
Supporting Information.