Direct observation of the ionization step in solvolysis reactions: Electrophilicity versus electrofugality of carbocations

Article abstract of DOI:10.1021/ja0765464

Rates and equilibria of the reactions of highly stabilized amino-substituted benzhydrylium ions (Ar₂CH⁺) with carboxylate ions have been determined photometrically in acetone and acetonitrile solutions. Treatment of covalent benzhydryl carboxylates (Ar ₂CH-O₂CR) with aqueous acetone or acetonitrile leads to the regeneration of the colored amino-substituted benzhydrylium ions Ar ₂CH⁺, which do not undergo subsequent reactions with the solvent. One can, therefore, directly measure the first step of S_N1 reactions. The electrofugality order, i.e., the relative ionization rates of benzhydryl esters Ar₂CH-O₂CR with the same anionic leaving group, does not correlate with the corresponding electrophilicity order, i.e., the relative reactivities of the corresponding benzhydrylium ions Ar ₂CH⁺ toward a common nucleophile. Thus, benzhydrylium ions which are produced with equal rates by ionization of the corresponding covalent esters may differ by more than 2 orders of magnitude in their reactivities toward nucleophiles, e.g., carboxylate ions. Variable intrinsic barriers account for the breakdown of the rate-equilibrium relationships. Complete free-energy profiles for the ionization of benzhydryl carboxylates Ar₂CH-O ₂CR are constructed, which demonstrate that the transition states of these ionizations are not carbocation-like. As a consequence, variation of the solvent-ionizing power Y has only a small effect on the ionization rate constant (m = 0.35 to 0.55) indicating that small values of m in the Winstein-Grunwald equation do not necessarily imply an S_N2 type mechanism.

Full text of DOI:10.1021/ja0765464

Published on Web 02/19/2008
Direct Observation of the Ionization Step in Solvolysis
Reactions: Electrophilicity versus Electrofugality of
Carbocations
Heike F. Schaller, Alexander A. Tishkov, Xinliang Feng, and Herbert Mayr*
Department Chemie und Biochemie, Ludwig-Maximilians-UniVersita¨t Mu¨nchen,
Butenandtstrasse 5-13 (Haus F), 81377 Mu¨nchen, Germany
Received August 30, 2007; E-mail: Herbert.Mayr@cup.uni-muenchen.de
Abstract: Rates and equilibria of the reactions of highly stabilized amino-substituted benzhydrylium ions
(Ar2CH+) with carboxylate ions have been determined photometrically in acetone and acetonitrile solutions.
Treatment of covalent benzhydryl carboxylates (Ar2CH-O2CR) with aqueous acetone or acetonitrile leads
to the regeneration of the colored amino-substituted benzhydrylium ions Ar2CH+, which do not undergo
subsequent reactions with the solvent. One can, therefore, directly measure the first step of SN1 reactions.
The electrofugality order, i.e., the relative ionization rates of benzhydryl esters Ar2CH-O2CR with the same
anionic leaving group, does not correlate with the corresponding electrophilicity order, i.e., the relative
reactivities of the corresponding benzhydrylium ions Ar2CH+ toward a common nucleophile. Thus,
benzhydrylium ions which are produced with equal rates by ionization of the corresponding covalent esters
may differ by more than 2 orders of magnitude in their reactivities toward nucleophiles, e.g., carboxylate
ions. Variable intrinsic barriers account for the breakdown of the rate-equilibrium relationships. Complete
free-energy profiles for the ionization of benzhydryl carboxylates Ar2CH-O2CR are constructed, which
demonstrate that the transition states of these ionizations are not carbocation-like. As a consequence,
variation of the solvent-ionizing power Y has only a small effect on the ionization rate constant (m ) 0.35
to 0.55) indicating that small values of m in the Winstein-Grunwald equation do not necessarily imply an
SN2 type mechanism.
Scheme 1
Introduction
Kinetic investigations of solvolysis reactions have been a
major source for the development of electronic theory of Organic
Chemistry.1 In typical SN1 solvolysis reactions (Scheme 1), the
carbocation R+ is formed as a short-lived intermediate, which
undergoes rapid subsequent reactions with the solvent. There-
fore, the rate of the ionization step is usually derived from the
rate of the gross reaction, which is determined by analyzing
the concentrations of the reactants RX or of the products ROSolv
or HX as a function of time.
However, as initially pointed out by Winstein,2 the observed
gross rate constant kobs often is a complex quantity. Since the
SN1 reaction (Scheme 1) may be affected by nucleophilic solvent
participation or accompanied by SN2 processes, there has been
much controversy about the mechanism of solvolysis reactions,
which is still ongoing.3,4
In recent work,5 we have reported the change from the typical
SN1 mechanism (Scheme 1, k1 < ksolv) to the so-called SN2C+
(3) (a) Bentley, T. W.; Schleyer, P. v. R. J. Am. Chem. Soc. 1976, 98, 7658-
7666. (b) Schadt, F. L.; Bentley, T. W.; Schleyer, P. v. R. J. Am. Chem.
Soc. 1976, 98, 7667-7675. (c) Bentley, T. W.; Garley, M. S. J. Phys. Org.
Chem. 2006, 19, 341-349. (d) Bentley, T. W.; Bowen, C. T.; Morten, D.
H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1981, 103, 5466-5475. (e) Richard,
J. P.; Toteva, M. M.; Amyes, T. L. Org. Lett. 2001, 3, 2225-2228. (f)
Tsuji, Y.; Toteva, M. M.; Amyes, T. L.; Richard, J. P. Org. Lett. 2004, 6,
3633-3636. (g) Gajewski, J. J. J. Am. Chem. Soc. 2001, 123, 10877-
10883. (h) Peters, K. S.; Gasparrini, S.; Heeb, L. R. J. Am. Chem. Soc.
2005, 127, 13039-13047.
(4) (a) Sneen, R. A. Acc. Chem. Res. 1973, 6, 46-53. (b) Raber, D. J.; Harris,
J. M.; Schleyer, P. v. R. In Ions and Ion Pairs in Organic Reactions, Vol.
2; Szwarc, M., Ed.; Wiley: New York, 1974; pp 247-374. (c) Katritzky,
A. R.; Musumarra, G.; Sakizadeh, K.; El-Shafie, S. M. M.; Jovanovic, B.
Tetrahedron Lett. 1980, 21, 2697-2699. (d) Katritzky, A. R.; Brycki, B.
E. Chem. Soc. ReV. 1990, 19, 83-105. (e) Jencks, W. P. Chem. Soc. ReV.
1981, 10, 345-375. (f) Ta-Shma, R.; Rappoport, Z. AdV. Phys. Org. Chem.
1992, 27, 239-291. (g) Kevill, D. N. In AdVances in QuantitatiVe Structure-
Property Relationships; Charton, M., Ed.; JAI Press: Greenwich, CT, 1996;
Vol. 1, pp 81-115. (h) Yoh, S.-D.; Cheong, D.-Y.; Lee, C.-H.; Kim, S.-
H.; Park, J.-H.; Fujio, M.; Tsuno, Y. J. Phys. Org. Chem. 2001, 14, 123-
130. (i) Richard, J. P.; Amyes, T. L.; Toteva, M. M.; Tsuji, Y. AdV. Phys.
Org. Chem. 2004, 39, 1-26. (j) Amyes, T. L.; Toteva, M. M.; Richard, J.
P. In ReactiVe Intermediate Chemistry; Moss, R. A., Platz, M. S., Maitland,
J., Eds.; Wiley: New York, 2004; pp 41-68. (k) Tsuji, Y.; Richard, J. P.
Chem. Record 2005, 5, 94-106. (l) Peters, K. S. Acc. Chem. Res. 2007,
40, 1-7. (m) Peters, K. S. Chem. ReV. 2007, 107, 859-873.
(1) (a) Streitwieser, A., Jr. SolVolytic Displacement Reactions; McGraw-Hill:
New York, 1962. (b) Carbonium Ions, Vol. 1-5; Olah, G. A., Schleyer,
P. v. R., Eds.; Interscience: New York, 1968-1976. (c) Ingold, C. K.
Structure and Mechanism in Organic Chemistry, 2nd ed.; Cornell University
Press: Ithaca, NY, 1969. (d) Vogel, P. Carbocation Chemistry; Elsevier:
Amsterdam, 1985. (e) AdVances in Carbocation Chemistry, Vol. 1; Creary,
X., Ed.; JAI Press: Greenwich, CT, 1989. (f) AdVances in Carbocation
Chemistry, Vol. 2; Coxon, J. M., Ed.; JAI Press: Greenwich, CT, 1995.
(2) (a) Winstein, S.; Clippinger, E.; Fainberg, A. H.; Heck, R.; Robinson, G.
C. J. Am. Chem. Soc. 1956, 78, 328-335. (b) For a summary of Winstein’s
contributions, see: Bartlett, P. D. J. Am. Chem. Soc. 1972, 94, 2161-
2170.
(5) Denegri, B.; Minegishi, S.; Kronja, O.; Mayr, H. Angew. Chem. 2004, 116,
2353-2356; Angew. Chem., Int. Ed. 2004, 43, 2302-2305.
9
3012
J. AM. CHEM. SOC. 2008, 130, 3012-3022
10.1021/ja0765464 CCC: $40.75 © 2008 American Chemical Society

Electrophilicity versus Electrofugality of Carbocations
A R T I C L E S
Chart 1. Benzhydrylium Ions Ar2CH+ and Their Electrophilicity
be shown that, in contrast to intuition and earlier assumptions,5
there is no significant correlation between the rates of ionization
of benzhydryl carboxylates and the electrophilic reactivities of
the resulting carbocations.
Parameters E
Experimental Section
Materials. Acetone and acetonitrile were distilled over CaSO4 and
diphenylketene, respectively. Commercially available tetra-n-butylam-
monium acetate and benzoate (Fluka) were used without further
purification. Tetra-n-butylammonium p-nitrobenzoate and 3,5-dini-
trobenzoate were prepared from tetra-n-butylammonium hydroxide and
the nitro-substituted benzoic acids as described previously.10 The
tetrafluoroborate salts of the benzhydrylium ions listed in Chart 1 were
synthesized as reported in ref 9.
Determination of Equilibrium Constants. Equilibrium constants
were measured by UV-vis spectroscopy in acetonitrile as follows: To
solutions of the benzhydrylium tetrafluoroborates in acetonitrile, whose
UV-vis maxima are reported in the Supporting Information, small
volumes of stock solutions of tetra-n-butylammonium carboxylates were
added, and the resulting absorbances were monitored. When the
absorbance was constant (typically after 5 to 15 s), another portion of
stock solution was added. This procedure was repeated four to five
times for each benzhydrylium salt solution.
Determination of the Rates of the Combinations of Benzhydry-
lium Ions with Carboxylate Ions (k-1 in eq 1). Reactions of
carboxylate ions with the colored benzhydrylium ions gave colorless
products. The reactions were followed photometrically at the absorption
maxima of Ar2CH+ by UV-vis spectroscopy using a stopped-flow
instrument (Hi-Tech SF-61DX2 controlled by Hi-Tech KinetAsyst3
software) in single- or double-mixing mode as described previously.9,11
All experiments were performed under pseudo-first-order conditions
(excess of n-Bu4N+RCO2-) at 25 °C in acetonitrile, acetone, or mixtures
of these solvents with water. First-order rate constants kobs were obtained
by least-squares fitting of the absorbance to the monoexponential
function At ) A0 exp(-kobst) + C.
Determination of Ionization Rates (k1 in eq 1). Because benzhy-
drylium carboxylates Ar2CH-O2CR, which are derived from highly
stabilized benzhydrylium ions, cannot be isolated, the double mixing
technique illustrated in Scheme 2 was employed. In the first mixer, a
a Electrophilicity parameter as defined by eq 4 (from ref 9).
mechanism6 (Scheme 1, k1 > ksolv), where ionization is faster
than the subsequent reaction with the solvent. In the latter case,
the intermediate carbocation R+ may accumulate. If the ioniza-
tion equilibrium k1/(k-1[X-]) is favorable, it becomes possible
to investigate the ionization step directly. We will now report
on the direct UV-vis spectroscopic observation of the ionization
of a series of benzhydryl carboxylates (eq 1) derived from the
benzhydrylium ions listed in Chart 1.
solution of Ar2CH+ BF4 in acetonitrile or acetone is combined
-
(stopped-flow instrument Hi-Tech SF-61DX2 controlled by Hi-Tech
KinetAsyst3 software in double-mixing mode) with a solution of 1-100
equiv of nBu4N+RCO2 in the same solvent. The resulting colorless
-
solution is then combined with an equal volume of aqueous acetonitrile
or acetone in a second mixer, which provokes the ionization of the
pregenerated Ar2CH-O2CR. The ionizations are followed photo-
metrically at the absorption maxima of Ar2CH+.
By this protocol we have rapidly collected a large number of rate
constants at different concentrations of n-Bu4N+RCO2 in different
-
solvents. The reported ionization rates were obtained as the average
from at least three different measurements.
Results and Discussion
Equilibrium Constants. As a preliminary to kinetic studies,
we determined the degree of ionization of covalent benzhydryl
In addition, we will report on the direct determination of the
rates of the reverse reactions as well as of some of the relevant
equilibrium constants. By combining these pieces of information
we will arrive at complete free-energy profiles for solvolysis
reactions of benzhydryl carboxylates, which allow us to
determine the intrinsic barriers7,8 for ionization processes. It will
(9) Mayr, H.; Bug, T.; Gotta, M. F.; Hering, N.; Irrgang, B.; Janker, B.; Kempf,
B.; Loos, R.; Ofial, A. R.; Remennikov, G.; Schimmel, H. J. Am. Chem.
Soc. 2001, 123, 9500-9512.
(10) Kirby, J. P.; Roberts, J. A.; Nocera, D. G. J. Am. Chem. Soc. 1997, 119,
9230-9236.
(11) Mayr, H.; Kempf, B.; Ofial, A. R. Acc. Chem. Res. 2003, 36, 66-77.
(12) Pytela, O.; Kulhanek, J.; Ludwig, M.; Riha, V. Coll. Czech. Chem. Commun.
1994, 59, 627-638.
(6) Gelles, E.; Hughes, E. D.; Ingold, C. K. J. Chem. Soc. 1954, 2918-2929.
(7) (a) Richard, J. P.; Amyes, T. L.; Toteva, M. M. Acc. Chem. Res. 2001, 34,
981-988. (b) Bernasconi, C. F. AdV. Phys. Org. Chem. 1992, 27, 119-
238. (c) Bernasconi, C. F. Acc. Chem. Res. 1992, 25, 9-16. (d) Guthrie,
J. P. ChemPhysChem 2003, 4, 809-816. (e) Guthrie, J. P.; Leandro, L.;
Pitchko, V. Can. J. Chem. 2005, 83, 1654-1666.
(13) Chantooni, M. K., Jr.; Kolthoff, I. M. Anal. Chem. 1979, 51, 133-140.
(14) Olmstead, W. N.; Bordwell, F. G. J. Org. Chem. 1980, 45, 3299-3305.
(15) Pilyugin, V. S.; Khrustaleva, L. Y.; Smirnova, S. L.; Ginzburg, M. E. Zh.
Obshch. Khim. 1983, 53, 1391-1395.
(16) Bordwell, F. G.; Branca, J. C.; Hughes, D. L.; Olmstead, W. N. J. Org.
Chem. 1980, 45, 3305-3313.
(8) Bernasconi, C. F. Acc. Chem. Res. 1987, 20, 301-308.
(17) Dippy, J. F. J.; Hughes, S. R. C. Tetrahedron 1963, 19, 1527-1530.
9
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A R T I C L E S
Schaller et al.
Scheme 2. Generation and Subsequent Ionization of Benzhydryl
Carboxylates in a Double-Mixing Stopped Flow Spectrometer
Figure 1. Determination of the equilibrium constant for the reaction of
n-Bu4N+BzO- with (lil)2CH+ BF4- [(1.43-1.46) × 10-5 M] in acetonitrile
at 25 °C. -Aeq ) ꢀ × [Ar2CH+] × d.
Scheme 3
From the initial concentrations, [Ar2CH+]0 and [RCO2-]0, and
the absorbance of Ar2CH+BF4 (A ) ꢀ × [Ar2CH+] × d),
-
-
the equilibrium concentrations [Ar2CH+]eq, [RCO2 ]eq, and
[Ar2CH-O2CR]eq were calculated. Substitution into eq 2 yielded
the equilibrium constants K listed in Table 1.
As the equilibrium constants K defined by eq 2 reflect the
relative Lewis basicities of these carboxylate ions toward
benzhydrylium ions in acetonitirile, while pKa values reflect the
relative basicities of these anions toward the proton (Scheme
4), a comparison between these two quantities is appropriate
(Figure 2).
carboxylates (anions used: AcO-, BzO-, PNB-, and DNB-)
in pure acetonitrile (Scheme 3).
The vertical ordering of the correlation lines provides a direct
comparison of the affinities of the benzoate ions BzO-, PNB-,
DNB- toward benzhydrylium ions and the proton in different
solvents. It is obvious that the benzoates possess a higher affinity
toward the proton in acetonitrile and DMSO than toward
(dma)2CH+ and better stabilized benzhydrylium ions in aceto-
nitrile.
The similarity of the slopes indicates the internal consistency
of the equilibrium constants. They also show that substituents
in the benzoate ions affect their Lewis basicities toward
benzhydrylium ions in the same way as their Brønsted basicities
in acetonitrile and in DMSO.
From the equilibrium constants in Table 1 one can derive
that, at high carboxylate concentration in acetonitrile, the
equilibrium lies further toward the covalent benzhydryl car-
boxylates. Therefore, the rate constants k-1 for the combinations
of the corresponding benzhydrylium ions with carboxylate ions
in acetonitrile should be accessible.
Second-Order Rate Constants for Carbocation Carboxy-
late Combinations. The decays of the benzhydrylium absor-
bances, which were observed after mixing solutions of benzhy-
drylium tetrafluoroborates with more than 6 equiv of tetrabutyl-
ammonium carboxylates, followed single exponentials from
which the concentration-dependent first-order rate constants kobs
were derived. As illustrated in Figure 3, kobs increases linearly
with the concentration of n-Bu4N+ RCO2-, indicating that only
a small percentage of cations can be paired with RCO2-. Since
Figure 1 shows that the benzhydrylium ion absorbance at 632
nm decreases when increasing amounts of tetra-n-butylammo-
nium benzoate (n-Bu4N+BzO-) are added to a solution of
-
(lil)2CH+BF4 in acetonitrile.
Due to the possible coexistence of covalent benzhydryl
carboxylates with different types of ion pairs and free ions, the
mathematical expression for the equilibrium constants may not
be trivial. However, our experiments show that eq 2 provides a
satisfactory description of the equilibria in acetonitrile at the
low concentrations used (ionic strengths from 2.82 × 10-5 to
1.96 × 10-3). The drifts of K with increasing carboxylate
concentration, which were observed in some cases (see Sup-
porting Information), were so small that an explicit treatment
of these effects was not attempted.
[Ar2CH-O2CR]eq
K )
-
[Ar2CH+]eq[RCO2
]
eq
[Ar2CH+]0 - [Ar2CH+]eq
[Ar2CH+]eq([RCO2-]0 - [Ar2CH+]0 + [Ar2CH+]eq)
)
(2)
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3014 J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008

Electrophilicity versus Electrofugality of Carbocations
A R T I C L E S
Table 1. Equilibrium Constants K (M-1) for Reactions of
Benzhydrylium Ions with Carboxylate Ions in Acetonitrile at 25 °C
1
K, M-
a
b
c
Ar2CH+
BzO-
PNB-
DNB-
(lil)2CH+
(6.20 ( 0.40) × 104 (5.79 ( 0.16) × 102
(jul)2CH+ (5.38 ( 1.06) × 104 (5.18 ( 0.11) × 102
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(1.08 ( 0.08) × 104 (1.99 ( 0.25) × 102
(1.13 ( 0.17) × 104 (2.33 ( 0.28) × 102
(3.20 ( 0.10) × 104 (5.48 ( 0.25) × 102
(4.32 ( 0.33) × 105 (5.46 ( 0.16) × 103
a BzO- ) benzoate. bPNB- ) 4-nitrobenzoate. cDNB- ) 3,5-dini-
trobenzoate.
Scheme 4
the ion combinations studied in this work are slow compared
with the diffusional processes which interconvert free ions and
ion pairs, the Curtin-Hammett principle allows us to neglect
the formation of ion pairs prior to bond formation. The second-
order rate constants k-1 can, therefore, be obtained as the slopes
-
of the plots of kobs versus the concentration of n-Bu4N+ RCO2
.
Some plots of kobs against the carboxylate concentrations show
considerable intercepts on the ordinate as illustrated on pp S25-
S26 in the Supporting Information. In pure acetonitrile and
acetone, i.e., solvents which do not react with the benzhydrylium
ions under consideration, this situation is observed when the
cation anion combinations reach an equilibrium. The observed
rate constants for reversible reactions equal the sum of forward
and backward reactions as expressed by eq 3.18
-
kobs ) k1 + k-1[RCO2 ]
(3)
For the reaction of (ind)2CH+ BF4- with n-Bu4N+ PNB- in
acetonitrile the intercept of the plot of kobs against the carboxy-
late concentration is 11.1 s-1 (see Supporting Information). This
value closely resembles the ionization rate constant k1 ) 9.07
s-1 calculated from the ratio of the ion combination rate constant
k-1 ) 9.80 × 104 M-1 s-1 and the equilibrium constant K )
1.08 × 104 M-1 (Table 1). As expected, the ionization rate
constants derived from the intercepts of the ion combination
reactions are less precise when the intercepts are small compared
Figure 2. Comparison of the equilibrium constants (25 °C) for reactions
of benzhydrylium ions with benzoate (BzO-), 4-nitrobenzoate (PNB-), and
3,5-dinitrobenzoate (DNB-) ions with the pKa values of the corresponding
carboxylic acids in different solvents (AN: acetonitrile). a pKa(in AN) )
20.3 (benzoic acid, from ref 12), 18.7 (4-nitrobenzoic acid, from ref 13),
and 16.9 (3,5-dinitrobenzoic acid, from ref 13). b pKa(in DMSO) ) 11.0
(benzoic acid, from ref 14), 9.0 (p-nitrobenzoic acid, from ref 15), and 7.3
(3,5-dinitrobenzoic acid, from ref 16). c pKa(in H2O) ) 4.2 (benzoic acid,
from ref 17), 3.4 (p-nitrobenzoic acid, from ref 17), 2.8 (3,5-dinitrobenzoic
acid, from ref 17).
with kobs
.
In aqueous solvents, the kinetics of the reactions of benzhy-
drylium ions with carboxylate ions often did not show a
monoexponential decay of the carbocations due to the revers-
ibility of the carbocation anion combinations and the competing
reactions of the carbocations with the solvents. However, in
cases where monoexponential decays of the carbocation absor-
bances were observed, rate constants for the combinations of
benzhydrylium ions with carboxylate ions could be determined
(Table 2). In Table 2 values of rate constants given in
parentheses are approximate, with typical errors of 8-10%.
In previous work,9,11,19 we have shown that reactions of
carbocations with nucleophiles can be described by eq 4,
trophile-independent nucleophilicity parameters. Figure 4 cor-
relates some of the second-order rate constants listed in Table
2 with the previously reported electrophilicity parameters of
benzhydrylium ions9,11 and shows that the reactions of the
(18) (a) Maskill, H. The InVestigation of Organic Reactions and Their
Mechanisms; Blackwell Publishing: Oxford, 2006. (b) Schmid, R.;
Sapunov, V. N. Non-Formal Kinetics; Verlag Chemie: Weinheim, 1982.
(19) (a) Mayr, H.; Patz, M. Angew. Chem. 1994, 106, 990-1010; Angew. Chem.,
Int. Ed. Engl. 1994, 33, 938-957. (b) Mayr, H.; Ofial, A. R. In Carbocation
Chemistry; Olah, G. A., Prakash, G. K. S., Eds.; Wiley: Hoboken, NJ,
2004; pp 331-358. (c) Mayr, H.; Ofial, A. R. Pure Appl. Chem. 2005, 77,
1807-1821.
log k ) s(N + E)
(4)
where k is the second-order rate constant, E is a nucleophile-
independent electrophilicity parameter, and N and s are elec-
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J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008 3015

A R T I C L E S
Schaller et al.
Figure 4. Correlation of second-order rate constants k-1 (at 25 °C) for the
combination of benzhydrylium ions with carboxylate ions in different
solvents. A ) acetone, AN ) acetonitrile, W ) water.
Figure 3. Linear correlation of the observed pseudo-first-order rate
constants kobs for the reaction of (jul)2CH+ (c0 ) 9.99 × 10-6 M) with
BzO- in acetonitrile (25 °C) with the concentration of n-Bu4N+BzO-.
Table 3. Nucleophilicity Parameters (25 °C) of Carboxylate Ions in
Different Solvents
Table 2. Second-Order Rate Constants k-1 for Reactions of
Benzhydryl Cations Ar2CH+ with Carboxylates at 25 °C
-
a
a
RCO2
solvent
N25
s25
-
a
1
RCO2
solvent b
Ar2CH+
k-1, M-1 s-
AcO-
AN
16.90
12.71b
12.5c
16.82
11.3c
15.30
18.74
14.9c
18.8c
0.75
0.68b
0.60c
0.70
0.72c
0.76
0.68
0.71c
0.62c
AcO-
AN
(lil)2CH+
1.51 × 105
3.21 × 105
1.46 × 106
(3.42 × 106)
5.79 × 106
1.17 × 105
1.15 × 105
6.87 × 105
(8.67 × 104)
(2.06 × 103)
5.43 × 103
6.75 × 104
5.51 × 104
9.79 × 103
7.59 × 103
1.12 × 105
9.33 × 104
6.07 × 104
1.27 × 105
4.48 × 105
3.91 × 105 c
1.05 × 106
(8.93 × 103)
1.20 × 105
1.26 × 105
7.79 × 105
9.80 × 104
2.46 × 105
7.46 × 105
2.00 × 106
9.29 × 105
1.96 × 106
6.97 × 106
4.01 × 105
4.39 × 106
3.70 × 106
(1.56 × 106)
(3.50 × 106)
(7.06 × 106)
10W90A
20W80A
AN
10W90AN
AN
A
AN
A
(jul)2CH+
(ind)2CH+
(thq)2CH+
(lil)2CH+
BzO-
PNB-
DNB-
A
10W90AN
(dpa)2CH+
(mfa)2CH+
(pfa)2CH+
(pfa)2CH+
(pyr)2CH+
(dma)2CH+
(mpa)2CH+
(mor)2CH+
(mpa)2CH+
(mor)2CH+
(dpa)2CH+
(mfa)2CH+
(lil)2CH+
20W80AN
10W90A
a Note that for the sake of compatibility with the heterolysis rate constants
determined in this work (see below) all rate constants k-1 were measured
at 25 °C (not at 20 °C as for other electrophile-nucleophile combinations),
and for that reason the index “25” is added to the N and s parameters.
bAdditional k-1 values from Table 4 were used (see also Figure 6). cValues
from correlations of lower quality.
20W80A
AN
substituted benzhydrylium ion (mpa)2CH+ behaves similarly,
whereas (mor)2CH+reacts more slowly than expected. We have
previously observed analogous deviations of the reactions of
these carbocations with a variety of nucleophiles in protic
solvents.20 Possibly, the phenylamino substituted benzhydrylium
ions (mpa)2CH+ and (dpa)2CH+ are less efficiently solvated in
protic solvents than benzhydrylium ions without phenylamino
groups and, therefore, are more electrophilic in protic solvents
than derived from their electrophilicity parameters which were
determined in dichloromethane.
In pure acetone, acetate and benzoate react so fast with
benzhydrylium ions that we were not able to determine the
nucleophilicity parameters N and s of these anions in acetone.
According to Table 2 the acetate ion is 2-3 times more reactive
than benzoate in acetonitrile and approximately 15 times more
reactive than 4-nitrobenzoate. Only one carbocation, (dma)2CH+,
could be used to derive that p-nitrobenzoate is 5 times more
nucleophilic than 3,5-dinitrobenzoate in acetonitrile. As the slope
parameters s are similar, these differences are also reflected by
N, and one can deduce from Table 3 that 4-nitrobenzoate and
3,5-dinitrobenzoate are approximately 2-3 orders of magnitude
more nucleophilic in acetone than in acetonitrile. In aqueous
acetone (10W90A and 20W80A) the N value for acetate is 4.2
to 4.4 units smaller than that in pure acetonitrile.
BzO-
(jul)2CH+
(ind)2CH+
(thq)2CH+
(mor)2CH+
(dpa)2CH+
(mfa)2CH+
(pfa)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
10W90AN
AN
PNB-
A
(jul)2CH+
(ind)2CH+
(dma)2CH+
(mpa)2CH+
(mor)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
DNB-
AN
A
a AcO- ) acetate, BzO- ) benzoate, PNB- ) 4-nitrobenzoate, DNB-
) 3,5-dinitrobenzoate. bA ) acetone, 10W90A ) 10% water and 90%
c
acetone (v/v), AN ) acetonitrile. At 20 °C.
carbocations Ar2CH+ with carboxylate ions generally follow
eq 4.
From these correlations one can derive N and s parameters
(eq 4) for the carboxylate ions in different solvents (Table 3).
For some benzhydrylium ions systematic dispersions are obvi-
ous. As shown in Figure 4, (dpa)2CH+ generally reacts faster
than predicted by its E-parameter. The phenylmethylamino
Kinetics of Ionization of Benzhydryl Carboxylates. As
described in Scheme 2, solutions of covalent benzhydryl
(20) (a) Minegishi, S.; Kobayashi, S.; Mayr, H. J. Am. Chem. Soc. 2004, 126,
5174-5181. (b) Phan, T. B.; Mayr, H. Can. J. Chem. 2005, 83, 1554-
1560.
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3016 J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008

Electrophilicity versus Electrofugality of Carbocations
A R T I C L E S
Table 4. Ionization Rate Constants k1 of Benzhydryl Derivatives in Different Solvents (25 °C)
1
1
nucleofuge
solvent
Ar2CH+
k
1 [s-
]
nucleofuge
solvent
Ar2CH+
k
1 [s-
]
AcO-
20W80AN
(lil)2CH+
3.63
BzO-
40W60AN
(lil)2CH+
1.19 × 101
6.79 × 101
5.16
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
1.97 × 101
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
2.23
5.87
8.57
1.77
2.45 × 101
3.60 × 101
7.62
40W60AN
6.90
20W80A
40W60A
10W90A
20W80A
4.97
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
3.99 × 101
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
1.97 × 101
4.52
2.89
1.34 × 101
2.20 × 101
4.54
7.14
9.83
3.49
10W90A
20W80A
2.34a
1.93 × 101
9.50 × 101
1.38 × 101
3.63 × 101
5.05 × 101
1.27 × 101
5.22 × 101
1.63 × 102
2.59 × 101
5.59 × 101
6.59 × 101
2.06 × 101
1.03 × 102
3.53 × 102
5.58 × 101
1.56 × 102
3.82 × 101
7.02 × 102
1.76 × 102
1.06 × 103
2.53 × 102
4.80 × 102
0.49 b
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
1.09 c
1.85 d
1.08
2.24
8.37
1.40
3.36
4.95
2.22
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
PNB-
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
40W60A
1.36 × 101
6.15 × 101
9.41
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
(lil)2CH+
(jul)2CH+
(ind)2CH+
(pyr)2CH+
(dma)2CH+
(pyr)2CH+
(dma)2CH+
(pyr)2CH+
(dma)2CH+
(dma)2CH+
2.49 × 101
3.59 × 101
9.30
BzO-
20W80AN
9.58
40W60A
10W90A
20W80A
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
4.49 × 101
5.16
DNB-
1.47 × 101
2.11 × 101
4.28
a
k-1 ) 1.85 × 102 M-1 s-1
.
b k-1 ) 4.50 × 102 M-1 s-1
.
c k-1 ) 9.41 × 102 M-1 s-1
.
d k-1 ) 2.73 × 103 M-1 s-1
.
Scheme 5. Heterolysis of (jul)2CH-OAc in 20W80A
carboxylates and tetrabutylammonium carboxylates in acetone
or acetonitrile were produced in the first mixing step of a
stopped-flow double-mixing experiment. When these solutions
were combined with aqueous acetone or aqueous acetonitrile
(second mixer in Scheme 2) the regeneration of the colored
benzhydrylium ions was observed photometrically. The appear-
ance of the benzhydrylium absorbances generally followed
single exponentials (eq 5) from which the rate constants kobs
were derived. A typical example is shown on page S34 of the
Supporting Information.
formation of the carbocations which do not undergo subsequent
reactions with the solvent (Scheme 5).
The formation of persistent solutions of carbocations is in
accordance with the estimated rate constants for the reactions
of these carbocations with the leaving group and the solvent.
For the ionization of (jul)2CH-OAc in 20W80A a rate constant
of k1 ) 8.37 s-1 was determined (Table 4). With N25 and s25
values for the acetate ion in 20W80A (12.5 and 0.60, Table 3)
and the electrophilicity parameter for (jul)2CH+ (E ) -9.45,
Chart 1), one calculates k-1 ) 67 M-1 s-1 by using eq 4. For
the highest concentration of tetra-n-butylammonium acetate
present in the ionization experiments ([AcO-] ) 3.88 × 10-4
obst
[Ar2CH+] ) [Ar2CH+]eq(1 - e-k
)
(5)
Thus, unlike typical solvolyses of R-X substrates, where
ionization rates are determined indirectly, in this work the
appearance of the carbocations Ar2CH+ is directly observed.
As all ionization experiments of this investigation had to be
performed in the presence of variable concentrations of the
carboxylate ions ([n-Bu4N+RCO2-] < 6 × 10-4 M-1), the effect
of the ionic strength on the ionization rates was studied
systematically. As shown on pages S48 to S50 of the Supporting
Information, the salt concentrations relevant for these studies
(<6 × 10-4 M-1) did not affect the ionization rates by more
than 12%.
For most heterolysis reactions described in Table 4, constant
end absorbances Aend which are independent of [RCO2-], as
well as ionization rate constants k1 which are independent of
[RCO2-], were observed. One can, therefore, conclude that the
heterolyses described in Table 4 proceed with quantitative
M) one obtains k-1[AcO-] ) 2.6 × 10-2 s-1, i.e., k1
.
k-1[AcO-] corresponding to a quantitative ionization process.
From the nucleophilicity parameters of the solvent mixture
20W80A (N ) 5.77, s ) 0.87)5 and E ((jul)2CH+) ) -9.45)
one calculates (eq 4) a rate constant of 6.29 × 10-4 s-1 for the
reaction of (jul)2CH+ with the solvent. This is in line with the
observation that the benzhydrylium ion (jul)2CH+ does not
undergo fast subsequent reactions with the solvent. Analogous
calculations can be performed to rationalize why none of the
carbocations generated under the conditions described in Table
4 is rapidly intercepted by the solvent.
9
J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008 3017

A R T I C L E S
Schaller et al.
Figure 5. Correlation of the observed rate constants for the ionization of
(pyr)2CH-OAc (1.00 × 10-5 M), (thq)2CH-OAc (8.70 × 10-6 M), and
(ind)2CH-OAc (1.00 × 10-5 M) in 10W90A with the concentration of
n-Bu4N+AcO- (at 25 °C).
Figure 7. Correlation of ionization rate constants of Ar2CH-O2CR in
different solvents (given as (v/v); W ) water, A ) acetone, AN )
acetonitrile) at 25 °C.
faster than the ion recombinations (k1 . k-1[RCO2-]), only the
ionization constants k1 were derived from these experiments.
The ionization rate constants of different benzhydrylium
carboxylates are compared in Figure 7. Though some of the
correlations of Figure 7 are only of moderate quality, the
positions of the different correlation lines clearly show a
decrease of the leaving group abilities in the series PNB-
>
BzO- > AcO- as well as an increase of the ionization rates
with higher water content in the solvent mixtures.
Transition States of the Ionizations. In 1948 Winstein and
Grunwald reported that rates of the SN1 solvolyses of neutral
RX substrates in different solvents can be described by the linear
free energy relationship (eq 6).21
Figure 6. Correlation of the combination rate constants for the reactions
of Ar2CH+BF4- with n-Bu4N+AcO- in 10W90A (log k-1 ) 8.60 + 0.68E).
log (k/k0) ) mY
(6)
A different situation is encountered when the heterolysis
reactions of the benzhydryl acetates are studied in 10W90A.
Now, the final absorbances decrease with increasing acetate ion
concentration and the observed first-order rate constants kobs
increase with increasing acetate ion concentration as depicted
in Figure 5, indicating the reversibility of the ionization
processes.
In this relationship, k and k0 are rate constants for solvolysis
of RX in a given solvent and in 80% aqueous ethanol,
respectively. Winstein and Grunwald selected the solvolysis of
tert-butyl chloride as a reference reaction (m ) 1) for establish-
ing Y as a measure of the ionizing power of a solvent (relative
to 80% aqueous ethanol). The slope m of a plot of log (k/k0)
against Y thus measures the sensitivity of a reaction to the
ionizing power of the solvent. Values of m close to 1.0 were
found for numerous SN1 solvolysis reactions,21,22 and m values
below 0.5 were considered as evidence for SN2 reactions. The
value of m therefore was suggested as a criterion for distin-
guishing the two mechanisms.
Figure 8 compares plots of log(k/k0) against Y for typical SN1
solvolyses of the parent benzhydryl chloride and its p,p-dimethyl
derivative23,24 with the corresponding plots for the amino-
substituted benzhydryl carboxylates studied in this work.
While the slopes for benzhydryl chloride (m ) 1.07) and p,p-
dimethylbenzhydryl chloride (m ) 1.02) are those expected for
rate-limiting ionization processes, much smaller slopes are found
Because the observed first-order rate constants kobs of
reversible processes reflect the sum of the forward and the
backward reactions (eq 3),18 the ionization rate constants k1 were
obtained as the intercepts of the plots of kobs versus the
concentration of n-Bu4N+AcO- (Figure 5). The slopes of these
plots yield k-1, i.e., the second-order rate constants for the
combination reactions of the carbocations with the acetate ions.
The consistency of this evaluation is shown by Figure 6,
where the rate constants k-1 obtained from ion combination
reactions (Table 2) and from the ionization reactions are directly
compared with each other. While k-1 for (pyr)2CH-OAc has
been determined by both methods, for the other systems only
one method could be employed. As required by eq 4, all rate
constants for the ion combinations are on the same correlation
line.
(21) (a) Grunwald, E.; Winstein, S. J. Am. Chem. Soc. 1948, 70, 846-854. (b)
Fainberg, A. H.; Winstein, S. J. Am. Chem. Soc. 1956, 78, 2770-2777.
(22) Bentley, T. W.; Llewellyn, G. Prog. Phys. Org. Chem. 1990, 17, 121-
158.
(23) Denegri, B.; Streiter, A.; Juric, S.; Ofial, A. R.; Kronja, O.; Mayr, H.
Chem.sEur. J. 2006, 12, 1648-1656; Chem.sEur. J. 2006, 12, 5415.
(24) (a) Double determination of k1 for (p-MeC6H4)2CH-Cl in 40W60A in this
work: k1(25 °C) ) 0.916 s-1. (b) Solvolysis rate constant k1(25 °C) for
(Ph)2CH-Cl in 40W60A from: Liu, K.-T.; Lin, Y.-S.; Tsao, M.-L. J. Phys.
Org. Chem. 1998, 11, 223-229.
A slight increase of kobs with increasing concentration of
carboxylate ions was also observed for some heterolyses of
benzhydryl acetates and benzoates in 20W80A (see Supporting
Information). Since, in these cases, the ionizations were much
9
3018 J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008

Electrophilicity versus Electrofugality of Carbocations
A R T I C L E S
Figure 9. Simplified free energy profiles (25 °C) for ionizations of
benzhydrylium derivatives in 80% aqueous acetone (encounter complexes
not specified).
constant at 25 °C listed in Table 4. Even though the N25 and s25
values given for acetate in 80% aqueous acetone in Table 3 are
not very precise, the calculated rate constant of 29.5 M-1 s-1
(for (lil)2CH+ + OAc-, 20W80A) can be expected to be reliable
within a factor of 1.5 because application of eq 4 requires only
a short extrapolation beyond the experimental range studied in
Table 2 (Ar2CH+ + OAc-, 20W80A). Substitution of this rate
constant into the Eyring equation yields ∆Gq ) 64.6 kJ mol-1
(25 °C). Though the standard free energy ∆G° of the ionic
(lil)2CH+ OAc- is thus calculated slightly above that of the
covalent compound (Figure 9), the ionization equilibrium is fully
on the side of the ions at low concentrations of acetate anions,
as observed during the experiments described in Table 4. The
right part of Figure 9 thus describes an ionization process with
a transition state which is in between a covalent ester and ionic
products. As the transition state is not carbocation-like, a small
value of m results (Figure 8). One implication of this result is
that m cannot generally be employed to differentiate SN1 and
SN2 processes.
Figure 8. Correlation of rate constants for ionization of some benzhydryl
derivatives with solvent ionizing power Y (k1 for Ar2CH-Cl in 10W90A
and 20W80A from ref 23; k1 for Ar2CH-Cl in 40W60A from ref 24.
Slopes: (pyr)2CH-DNB ) 0.39, (dma)2CH-DNB ) 0.35, (jul)2CH-OAc
) 0.54, (dma)2CH-OAc ) 0.35, (p-MeC6H4)2CH-Cl ) 1.02, (Ph)2CH-
Cl ) 1.07).
for the benzhydryl carboxylates (m ) 0.35-0.54) despite the
fact that these rate constants also refer to rate-limiting ionization
processes.
Philicity-Fugality Relationships: The Role of Intrinsic
Barriers. A further consequence of the non-carbocation-like
transition states of these ionization processes are the dramatically
different orders of electrofugalities (Figure 7) and electrophi-
licities (Chart 1, Table 2).
How can one explain that reactions with rate-limiting
ionization have m values similar to those of SN2 reactions? In
previous work,25 we have demonstrated that the rates of the
reactions of (Ph)2CH+ and (p-MeC6H4)2CH+ with chloride and
bromide ions in 20W80AN are diffusion limited. Consequently
the combination rates of these ions must also be diffusion
controlled in the less polar solvents 20W80A and 10W90A. The
principle of microscopic reversibility requires transition states
for the reverse reactions which correspond to the carbocations
(Figure 9, left).
With this information, we can now construct the free energy
diagrams for the ionization of (p-MeC6H4)2CH-Br and (lil)2CH-
OAc in 80% aqueous acetone. The Eyring equation allows one
to calculate ∆Gq ) RT ln(kBT/hk) ) 74.9 kJ mol-1 (25 °C)
from the solvolysis rate constant of (p-MeC6H4)2CH-Br in 80%
aqueous acetone (4.65 × 10-1 s-1, from ref 23). As the reverse
reaction is diffusion controlled, we substituted k-1 ) 1010 M-1
s-1 into the Eyring equation and arrived at a formal barrier of
16 kJ mol-1 for the reverse reaction (Figure 9).
Table 5 compares electrophilicities and electrofugalities of
different benzhydrylium ions. Because it was not possible to
identify a single carboxylate ion, for which rate constants for
the reactions with all benzhydrylium ions could be measured,
the relative reactivities toward p-nitrobenzoate and benzoate ions
were considered and the reactivity of (thq)2CH+ (krel ) 12.3)
was employed to link the two series of data. It is found that the
-
electrophilic reactivities of benzhydrylium ions toward ArCO2
decrease by more than 2 orders of magnitude in the series from
(dma)2CH+ to (lil)2CH+. The same order of electrophilicities
has previously been observed in reactions of these carbocations
with more than 100 other nucleophiles.
The relative electrofugalities of benzhydrylium ions follow
a completely different order. The (dma)2CH+ cation which reacts
130 times faster with carboxylate ions than (lil)2CH+ (Table 5,
top) is formed with exactly the same rate as that of the latter
carbocation by heterolysis of the corresponding benzhydrylium
acetate in 80% aqueous acetone (Table 5, bottom). Figure 7
shows that the electrofugality order of benzhydrylium ions
shown in Table 5 is consistently found for ionizations of various
For the ionization of (lil)2CH-OAc in 80% aqueous acetone,
∆Gq ) 71.0 kJ mol-1 can be calculated from the ionization
(25) Minegishi, S.; Loos, R.; Kobayashi, S.; Mayr, H. J. Am. Chem. Soc. 2005,
127, 2641-2649.
9
J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008 3019

A R T I C L E S
Schaller et al.
Table 5. Comparison of Relative Electrophilicities and Relative Electrofugalities of Benzhydrylium Ions
a From Table 2. b From Table 4.
q
Table 6. ∆Gq, ∆G°, and ∆G0 (in kJ mol-1) for the Ionization of
covalent benzhydryl acetates and benzoates in a variety of
solvents.
Ar2CH-O2CR at 25 °Ca
AcO in
AcO in
BzO in
AN
PNB
DNB
The fact that m- and p-substituents in the amino-substituted
benzhydrylium ions exert completely different effects on the
rates of formation and consumption of these carbocations implies
that forward and backward reactions cannot be described by
the same Hammett substituent parameters. The σ+ values for
the different amino groups, which have previously been derived
from nucleophilic additions to these benzhydrylium ions, should
therefore be considered with caution.9
It is generally assumed that stabilized carbocations, which
are rapidly formed in heterolysis reactions, show low reactivities
toward nucleophiles. On the other hand, less stabilized car-
bocations are supposed to form slowly in SN1 processes and
react rapidly with nucleophiles. Extensive work by Richard on
trifluoromethyl substituted carbocations had already shown that
this simple relationship does not hold universally, which was
attributed to differences in intrinsic barriers.7,8,26,27 While, in
Richard’s systems, structural variations were made in direct
vicinity to the reaction center, we now find that changes in
intrinsic barriers may also be caused by substituent variation at
positions more remote from the reaction center.
Ar2CH+
10W90A
20W80A
in AN
in AN
(lil)2CH+
∆Gq
∆G°
∆G0
∆Gq
∆G°
71.0
6.4c
67.8
67.7
5.1c
73.1d
27.4
58.6
70.9d
27.0
56.6
66.0e
15.8
57.8
63.1e
15.5
55.1
67.5d
23.0
55.4
65.4 d
23.1
53.2
65.2d
25.7
51.5
69.2d
32.2
51.9
q
(jul)2CH+
(ind)2CH+
(thq)2CH+
(pyr)2CH+
(dma)2CH+
70.9
10.8b
65.4
74.8
16.9b
66.0
72.8
16.8b
64.1
71.5
17.4b
62.5
72.8
21.1b
61.8
q
∆G0
∆Gq
∆G°
65.1
72.2
11.9c
66.1
70.1
11.8c
64.1
69.0
12.5c
62.6
71.0
16.8c
62.4
61.1e
13.1
54.4
59.3 e
13.5
52.4
59.3e
15.6
51.2
62.4e
21.3
51.1
q
∆G0
∆Gq
∆G°
q
∆G0
∆Gq
∆G°
q
∆G0
∆Gq
∆G°
q
∆G0
a
Note that K defined by Scheme 3 and eq 2 refers to the ion
combination, i.e., the reverse of ionization reaction. For that reason, ∆G°
for the ionization process is given by +RT ln K. b K derived from
experimental k1 and k-1
.
c K derived from experimental k1 and calculated
(eq 4) k-1 .
.
d k1 derived from experimental K and k-1 e k1 derived from
How can we explain the fact that the order of electrophilicity,
as reflected by the second-order rate constants for the combina-
tion of benzhydrylium ions with carboxylate ions (Table 2), does
not correlate at all with the order of electrofugality which is
reflected by first-order rate constants of ionization of benzhydryl
carboxylates (Table 4). Why is (lil)2CH+, the least electrophilic
benzhydrylium ion of the series, not generated rapidly by the
heterolytic process but is formed relatively slowly?
experimental K and calculated (eq 4) k-1
.
q
and the intrinsic barrier ∆G0 , which is defined as the activation
free energy of a process with ∆G° ) 0. If the work term in the
Marcus equation is omitted, eq 7 can be used to calculate ∆Gq
q
from the reaction free energy ∆G° and the intrinsic barrier ∆G0 .
∆Gq ) ∆G0q + 0.5∆G° +((∆G°)2/16∆G0 )
(7)
q
The Marcus equation28 expresses the activation free energy
of a reaction by a combination of the reaction free energy ∆G°
For about half of the combinations of electrophiles and
nucleophiles given in Table 6, rate and equilibrium constants
are available from Tables 1, 2, and 4, which are converted into
∆G° and ∆Gq values and are listed in Table 6. Substitution of
(26) (a) Richard, J. P. J. Am. Chem. Soc. 1989, 111, 1455-1465. (b) Amyes,
T. L.; Stevens, I. W.; Richard, J. P. J. Org. Chem. 1993, 58, 6057-6066.
(c) Richard, J. P.; Williams, K. B.; Amyes, T. L. J. Am. Chem. Soc. 1999,
121, 8403-8404.
(27) Richard, J. P.; Toteva, M. M.; Crugeiras, J. J. Am. Chem. Soc. 2000, 122,
1664-1674.
(28) (a) Marcus, R. A. J. Phys. Chem. 1968, 72, 891-899. (b) Albery, W. J.
Annu. ReV. Phys. Chem. 1980, 31, 227-263.
9
3020 J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008

Electrophilicity versus Electrofugality of Carbocations
A R T I C L E S
Figure 11. Gibbs free energy profiles (25 °C) for the reactions of the acetate
ion with benzhydrylium ions in 20W80A.
obviously holds also for intrinsic barriers which are derived from
calculated rate constants (eq 4), because intrinsic barriers derived
from experimental and calculated rate constants show exactly
the same regularity in Figure 10.
Figure 10. Correlation of intrinsic barriers for the ionization of benzhydryl
carboxylates in different solvents. The corresponding lines for (jul)2CH+
and (dma)2CH+ coincide with those of (ind)2CH+ and (pyr)2CH+, respec-
tively, and have not been drawn.
It is evident that compounds with benzo-annulated five-
membered rings, i.e., (lil)2CH+ and (ind)2CH+ have higher
intrinsic barriers than their six-membered ring analogues
(jul)2CH+ and (thq)2CH+, respectively (see structures in Chart
1). While we presently do not understand the reason for the
different intrinsic barriers for the different ring sizes, it is
obvious that these differences are responsible for the breakdown
of the rate-equilibrium relationships.
these values into the Marcus eq 7 yields the intrinsic barriers
∆G0 , which are also listed in Table 6.
q
The high reliability of eq 4 to calculate rate constants for the
reactions of benzhydrylium ions with nucleophiles also allows
us to derive rate constants for the combinations of benzhydry-
lium ions with carboxylate ions in different solvents, which
cannot directly be measured, from the N and s parameters in
Table 3.
As reported in Table 6 and illustrated in Figure 11, the
ionizations of (lil)2CH-OAc and (jul)2CH-OAc have similar
reaction free energies ∆G°. Because (jul)2CH-OAc has a lower
intrinsic barrier than (lil)2CH-OAc, (jul)2CH-OAc ionizes 3.7
times faster and at the same time (jul)2CH+ reacts 2.3 faster
with nucleophiles than (lil)2CH+ in 20W80A (Figure 11).
Similar rate ratios are found for other carboxylates. Analogously
the ionizations of (ind)2CH-OAc and (thq)2CH-OAc have
similar values of ∆G°, and the higher electrophilic reactivity
of (thq)2CH+ (Figures 4 and 6) as well as the higher ionization
rates of the (thq)2CH-esters compared with the (ind)2CH-esters
(Figure 7) are again caused by different intrinsic barriers (Figure
11).
Accidentally, the ionizations of (ind)2CH-O2CR and (jul)2CH-
O2CR have almost the same intrinsic barriers (Table 6). The
higher ionization rate of (jul)2CH-O2CR as well as the lower
electrophilic reactivity of (jul)2CH+ are, therefore, a consequence
of the better stabilization of the (jul)2CH+ ion compared with
(ind)2CH+. As we are presently unable to predict the relative
magnitudes of the intrinsic barriers, we cannot generally derive
information about relative carbocation stabilities from kinetic
data, unless the reverse reaction (ion recombination) occurs
without a barrier.
A graphical comparison of the intrinsic barriers is shown in
Figure 10. As the intrinsic barriers for the ionizations of
(ind)2CH-O2CR and (jul)2CH-O2CR as well as those for
(pyr)2CH-O2CR and (dma)2CH-O2CR are very similar, Figure
10 presents only data for the first compound of these pairs.
One can see that, for all benzhydrylium derivatives, the
intrinsic barriers increase by approximately 9-10 kJ mol-1 when
changing from dinitrobenzoates and p-nitrobenzoates in aceto-
nitrile to acetates in aqueous acetone. Since the differences
between intrinsic barriers for benzoates, p-nitrobenzoates, and
3,5-dinitrobenzoates of each of the benzhydrylium systems in
CH3CN are relatively small (∼1 kJ mol-1, Table 6), one has to
assume that the higher barriers for the reactions of acetates in
aqueous acetone are predominantly due to the change of
solvents. Most likely, the increase of the intrinsic barriers in
aqueous solvents reflects the higher energy of reorganization
of the water molecules to solvate the ions.8,29 In line with these
numbers, Richard reported an intrinsic barrier of 61 kJ mol-1
for the reactions of the acetate anion with the tritylium ion in
water.27
Most intriguing is the order of intrinsic barriers for the
different benzhydrylium systems. In all cases (different solvents
and different nucleofuges) we find the ordering (lil)2CH+
>
(ind)2CH+ ≈ (jul)2CH+ > (thq)2CH+ > (pyr)2CH+ ≈ (dma)2-
CH+ (Figure 10). If one assumes a 10% error in the experi-
mentally determined rate and equilibrium constants and an
Conclusion
From the excellent correlation between the averaged elec-
trophilic reactivities of the carbocations toward a large variety
of nucleophiles and the ethanolysis rate constants of the
corresponding alkyl chlorides we had previously concluded that
carbocation electrophilicity is inversely related to electrofugal-
ity.5,23,30
q
accumulation of the errors, the maximum absolute error of ∆G0
would be 1 kJ mol-1. The equal ranking of the different
compounds in Figure 10 indicates that the relative magnitudes
of the intrinsic barriers ∆G0q are even more accurate. An error
limit of <1kJ mol-1 for the relatiVe magnitudes of ∆G0
q
(30) Mayr, H.; Patz, M.; Gotta, M. F.; Ofial, A. R. Pure Appl. Chem. 1998, 70,
1993-2000.
(29) Bernasconi, C. F. Tetrahedron 1985, 41, 3219-3234.
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J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008 3021

A R T I C L E S
Schaller et al.
This opinion now requires revision. Obviously, the inverse
relationship between electrophilicity and electrofugality holds
only for carbocations which are less stabilized than 4,4′-
dimethoxy benzhydrylium ions though even in this range some
exceptions have been reported. If better stabilized carbocations
are considered (in this work amino-substituted benzhydrylium
ions), ionization rates are largely controlled by differences in
intrinsic barriers, and simple rate-equilibrium relationships break
down. Further work must focus on the origin of the intrinsic
barriers.
Acknowledgment. Dedicated to Professor Sema L. Ioffe on
the occasion of his 70th birthday. We thank Prof. T. W. Bentley
and Dr. A. R. Ofial for discussions and the Deutsche For-
schungsgemeinschaft (Ma 673-20) and the Fonds der Chemis-
chen Industrie for financial support.
Supporting Information Available: Details of kinetic experi-
ments. This material is available free of charge via the Internet
at http://pubs.acs.org.
JA0765464
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3022 J. AM. CHEM. SOC. VOL. 130, NO. 10, 2008