Comparison of pKR values of fluorenyl and anthracenyl cations

Article abstract of DOI:10.1002/poc.511

A value of pK_R = -5.1 for the anthracenonium ion in 50:50 (v/v) aqueous trifluorethanol is reported based on a ratio of measured rate constants k_H for acid-catalysed dehydration of the 9,10-hydrate of anthracene and k_H2O for the reverse hydrolysis of the carbocation (K_R = k_H2O/k_H. Comparison with pK_R = -15.9 for the fluorenyl cation indicates that the latter ion is less stable by more than 10 log units (15 kcal mol^-1). This difference is (a) considerably larger than that between the benzhydryl (pK_R = -11.7) and fluorenyl cations (ΔpK = 4.2), which has been considered too small to indicate antiaromatic character for the fluorenyl cation, and (b) comparable to that between pK_as for the ionization (in DMSO) of fluorene (22.6) and diphenylmethane (32.2), which has been interpreted as implying aromatic character for the fluorenyl anion. It is shown that a difference in stability of anthracene hydrate and 9-hydroxyfluorene makes only a minor contribution to the difference in pK_R values and that the fluorenyl cation is destabilized by ca 10 kcal mol^-1. A smaller difference in pK_as for protonation of fluorenimine (5.85) and benzhydrylimine (7.0) is consistent with the expected moderating effect of an electron-donating substituent on relative carbocation stabilities. Evidence from calculations relating to the antiaromaticity of the fluorenyl cation is reviewed in the light of these measurements. An additional comparison between equilibrium constants for the ionization of aralkylazides (K_az) and alcohols (K_R) reveals the influence of differences in geminal σ-bond interactions for the hydroxy and azido groups in their respective reactants. Copyright

Full text of DOI:10.1002/poc.511

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2002; 15: 529–539
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.511
Comparison of pK values of ¯uorenyl and anthracenyl
R
†
cations
Michael C. Courtney, Aoife C. MacCormack and Rory A. More O'Ferrall*
Department of Chemistry and Centre for Synthesis and Chemical Biology, University College Dublin, Bel®eld, Dublin 4, Ireland
Received 30 January 2002; revised 28 February 2002; accepted 1 March 2002
ABSTRACT: A value of pK = À5.1 for the anthracenonium ion in 50:50 (v/v) aqueous trifluorethanol is reported
R
based on a ratio of measured rate constants k for acid-catalysed dehydration of the 9,10-hydrate of anthracene and
H
k
for the reverse hydrolysis of the carbocation (K = k /k ). Comparison with pK = À15.9 for the fluorenyl
H O
2
R
H O
2
H
R
À1
cation indicates that the latter ion is less stable by more than 10 log units (15 kcal mol ). This difference is (a)
considerably larger than that between the benzhydryl (pK = À11.7) and fluorenyl cations (DpK = 4.2), which has
R
been considered too small to indicate antiaromatic character for the fluorenyl cation, and (b) comparable to that
between pK s for the ionization (in DMSO) of fluorene (22.6) and diphenylmethane (32.2), which has been
a
interpreted as implying aromatic character for the fluorenyl anion. It is shown that a difference in stability of
anthracene hydrate and 9-hydroxyfluorene makes only a minor contribution to the difference in pK values and that
R
À1
the fluorenyl cation is destabilized by ca 10 kcal mol . A smaller difference in pK s for protonation of fluorenimine
a
(5.85) and benzhydrylimine (7.0) is consistent with the expected moderating effect of an electron-donating substituent
on relative carbocation stabilities. Evidence from calculations relating to the antiaromaticity of the fluorenyl cation is
reviewed in the light of these measurements. An additional comparison between equilibrium constants for the
ionization of aralkylazides (K ) and alcohols (K ) reveals the influence of differences in geminal s-bond interactions
az
R
for the hydroxy and azido groups in their respective reactants. Copyright  2002 John Wiley & Sons, Ltd.
KEYWORDS: pK ; fluorenyl cations; anthracenyl cations
R
INTRODUCTION
well established. An equilibrium constant for formation
of the carbocation from the hydrate (Scheme 1) can be
derived from measurements of rate constants for the
It is now well established that the acid-catalysed aroma-
tisation of aromatic hydrates and their methyl ethers
occurs via formation of a carbocation intermediate.
The mechanism of these reactions is illustrated in
Scheme 1 by the dehydration of benzene hydrate. In so
far as it is a major factor controlling reactivity in these
and other reactions the thermodynamic stability of
forward and reverse reactions. The rate constant k
for
H O
2
1–7
reaction of the carbocation with water may be obtained
either (a) by generating stoichiometric concentrations of
10
11
the cation by flash photolysis or radiolysis or (b) by
competitive trapping of non-stoichiometric concentra-
tions of solvolytically produced cations by water and
8,9
2–4,8,12,13
carbocations continues to attract attention.
azide ions based on the azide clock procedure.
The equilibrium constant pK (Àlog K ) is then obtained
R
R
by combining k
with the rate constant k for acid-
H
H O
2
catalysed formation of the cation from the hydrate:
‡
kH2O ‰ROHŠ‰H Š
K ˆ
R
ˆ
ꢀ1†
‡
kH
‰R Š
Scheme 1
In the case of the hydrates of anthracene and naph-
Methods for measuring the stabilities of reactive
carbocations in aqueous solution are now reasonably
thalene, the azide clock method also yields rate constants
2
k for deprotonation of the cations. Combination of these
p
with rate constants kA for protonation of the aromatic
*
Correspondence to: R. A. More O’Ferrall, Department of Chemistry
molecule derived from measurements of hydrogen
14
and Centre for Synthesis and Chemical Biology, University College
Dublin, Belfield, Dublin 4, Ireland.
isotope exchange then yields a pK for the carbocation
a
2
†
from the relationship K = k /k .
Presented at the 8th European Symposium on Organic Reactivity
ESOR-8), Cavtat (Dubrovnik), Croatia, September 2001.
a p A
(
The equilibrium constants pKa and pKR may be
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

5
30
M. C. COURTNEY, A. C. MACCORMACK, R. A. MORE O’FERRALL
combined to yield a third equilibrium constant, pKH2O
,
The purpose of the present work was to compare pKR
values for the anthracenonium ion 3 and fluorenyl cation
4 as a contribution to recent discussions of whether or not
for hydration of the aromatic molecule. This is also
illustrated for benzene hydrate in Scheme 2, although
Scheme 2 shows the 1,4-hydrate of benzene (2) rather
than the 1,2-hydrate shown in Scheme 1.
18–21
the latter ion is antiaromatic.
On the basis of ab initio
calculations and an experimental comparison between
pKR values for the fluorenyl and benzhydryl cations,
18
Amyes et al. concluded that, in contrast to the cyclo-
pentadienyl and indenyl cations, the fluorenyl cation is
not antiaromatic.
Scheme 2
More recently, Jiao et al. have characterized the
fluorenyl cation as ‘non-aromatic’ on the basis of
magnetic criteria. They drew attention to a compensation
between the magnetic properties of the aromatic benzene
In practice, values of pK
accessible for naphthalene, anthracene and benzofuran,
are experimentally
H O
2
for which both the rate constants k
and k have been
H O
2
p
2,3
measured.
More commonly, pK
is derived by
H O
2
20
rings and antiaromatic five-membered ring. From a
comparison with the anthracenyl cation they calculated a
estimating DG° (aq) for the aromatic hydrate and
f
combining it with values for the aromatic molecule and
À1
15
destabilization energy of 8 kcal mol (1 kcal = 4.184 kJ)
water. This is particularly useful in the case of benzene
where the carbocation is too unstable for trapping by
based on an orbital deletion procedure (ODP). This
À1
destabilization is similar to the 10 kcal mol found by
azide ion but the pK can be estimated by combining a
a
themselves and by Amyes et al. from isodesmic
comparisons of the fluorenyl cation with a planarized
benzhydryl cation. In so far as the experimental value of
rate constant for isotope exchange of the tritiated
14
aromatic molecule with a rate constant for deprotona-
tion that approaches the limiting value for relaxation of
8
,16
pK for the benzhydryl cations is affected by reduced
the aqueous solvent.
The latter value is assigned from
R
11
À1
resonance stabilization from the non-planarity of its
rings, it seemed of interest to extend the experimental
comparison to the planar anthracenyl cation.
consideration of this limit (10 s ) and the dependence
on pK of measured rate constants for deprotonation of
a
17
carbocations for which measurements are available.
Having established pK and pK for benzene, the
value of pK is obtained as the sum of pK and pK .
H O
2
The pK value for the anthracenyl cation in Scheme 3
R
a
H O
2
2
cannot be compared directly with that for the fluorenyl
R
a
cation because the latter refers to a 50:50 TFE–H O
This allows us to compare equilibrium constants for
benzene, naphthalene and anthracene as shown in
Scheme 3. In this scheme, the site of protonation of the
2
1
8
solvent mixture. Amyes et al. reported a number of
measurements of k and pK for TFE–H O mixtures
H O
2
R
2
and noted that pK is approximately one unit greater in
R
water than in the mixed solvent. However, few compari-
sons of pK values in H O and TFE–H O have been
R
2
2
reported, and in this paper we describe an extension of the
measurement of pKR for the anthracenyl cation from
water to the TFE–H O mixture. We also report a com-
2
parison of pK s for protonation of benzhydrylimine and
a
9-fluorenimine. In their protonated forms these molecules
may be considered as a-amino-substituted (benzhydryl
and fluorenyl) carbocations.
2
0
Finally, it is worth noting, as recognized Jiao et al.,
Scheme 3
that in principle pK values for the protonated benzene
R
and protonated naphthalene forming 1,4-aromatic hy-
drates in Scheme 3 provide appropriate comparisons for
aromatic molecule is shown by an arrow; the hydrates are
the 1,4-hydrate for benzene and naphthalene and 9,10-
hydrate for anthracene. It can be seen that there is a small
pK measurements for the cyclopentadienyl and indenyl
R
cations. So far, however, the only report of pK for these
R
2
2
variation in pK but that values of pK
exhibit large
H O
2
ions appears to be À40 for the cyclopentadienyl cation
R
differences, reflecting the relative resonance stabilization
energies of the aromatic molecules. These differences are
based on a thermodynamic cycle linking pK to the pK
R
a
of cyclopentadiene via oxidation potentials of the
cyclopentadienyl anion determined by cyclic voltam-
also expressed in the pK values.
a
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

pK
R
VALUES OF FLUORENYL AND ANTHRACENYL CATIONS
531
metry. As pointed out by the authors, this value is subject
to considerable uncertainty.
form the main absorbing product anthracene. Ratios of
rate constants for the reaction of the carbocation with
azide ion, k , deprotonation, k , and nucleophilic reac-
22
az
p
tion with water, k , were evaluated by application of
H O
2
‡
Eqn. (2) based on Scheme 4 (in which R is the
RESULTS
anthracenonium ion).
Anthracenyl cation
1
Aaz
1
1
k ‰N Š
az
3
ˆ A
‡
ꢀ2†
A ꢀk ‡ kH2O†
0
0
p
The principal experimental measurements required for
evaluation of K for the anthracenyl cation in 50:50 (v/v)
R
TFE–H O mixtures are rate constants for the acid-
2
catalysed dehydration of the 9,10-anthracene hydrate,
The absorbances A and A in Eqn. (2) correspond to
az
0
kde, and for attack of water on the carbocation, k . One
H O
2
limiting values at completion of the solvolysis in the
presence and absence of sodium azide. The analysis is
similar to that reported previously for solvolysis in
difference from the reaction of the hydrate in water is that
dehydration in TFE–H O occurs in the absence of added
2
acid. Inhibition of the reaction by added hydroxide, azide
or acetate ions indicates that the reaction involves
specific acid catalysis arising from appreciable ionization
of the trifluoroethanol rather than a general acid-
catalysed reaction. Measurement of first-order rate con-
2
acetonitrile–water mixtures and it was assumed that the
fraction of carbocation reacting with TFE to form a
trifluoroethyl ether was small enough to be neglected.
The ratio of rate constants k /(k ‡ k ) was obtained as
az
p
H O
2
the ratio of slope to intercept from the plot of 1/A versus
az
stants under catalysis by HClO gave the following
À
4
[
N ] shown in Fig. 1. This plot is subject to considerably
3
2
À1
values (10 k/s ) at the indicated acid concentrations
greater scatter than for aqueous acetonitrile mixtures,
2
8
0
.46, 0.00058 M; 5.23, 0.00116 M; 7.64, 0.00163 M;
.65, 0.00203 M; 10.0, 0.0029 M; 12.9, 0.0035 M; 1.85,
possibly because the azide product was not stable but
3,4,23,24
itself underwent solvolysis.
The influence of this
.00464 M; and 2.63, 0.0059 M. These values yield a
subsequent reaction was minimised by extrapolating
absorbances to the time of injection of the anthracenyl
À1 À1
second-order rate constant k = 37.3 M s , which
compares with 9.5 M
de
À1 À1
2
s
in water. In the absence of
acetate into the azide-containing TFE–H O mixture.
2
À3 À1
acid the rate constant is 7.7 Â 10 s .
From Fig. 1, a value of k /(k ‡ k ) = 240 was
az
p
H O
2
The rate constant for the reaction of the anthracenyl
cation with water is based on two independent compari-
sons of the rate of attack by water with the rate of attack
by azide ion. In the first, anthracenyl acetate (6) was
obtained.
A second value of k /(k ‡ k ) was obtained from
az
p
H O
2
measurements of first-order rate constants for the
relatively slow reaction ascribed to solvolysis of the
anthracenylazide. Although this azide was not isolated its
identity was inferred from its formation in the azide
trapping measurements and the fact that the subsequent
solvolysed in 50:50 TFE–H O in the manner described
2
2
previously for water. Solvolysis occurred in the time
taken to record the first measurement of absorbance
À3
following injection of a few microlitres of a 10 M stock
solution in acetonitrile. This absorbance was depressed in
the presence of azide ions in a manner consistent with
nucleophilic trapping of the carbocation intermediate by
azide ions in competition with deprotonation by water to
À
Figure 1. A plot of 1/(Aaz À A ) against [N ] for the
init
solvolysis 9-acetoxy-9,10-dihydroanthracene in 50:50 v:v
3
TFE-H O mixtures at 25°; A and Aaz are initial and ®nal
2
absorbances respectively
init
Scheme 4
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

5
32
M. C. COURTNEY, A. C. MACCORMACK, R. A. MORE O’FERRALL
nucleophilic attack of azide ion on the anthracenyl cation
being diffusion controlled, in so far as, in the reverse of
the ionization reaction, re-formation of the azide will be
faster than diffusive separation of an ion pair. Depro-
tonation within an ion pair is a commonly observed
8,25
phenomenon
and it seems reasonable to suppose that
the reaction competes, albeit inefficiently, with ion-pair
return to the reactant.
The rate expression, based on Scheme 5, is given by
the equation
k ꢀk
‡ k †
1
H2O
p
kobs ˆ k ‡
ꢀ3†
0
k ‰N Š ‡ ꢀk
‡ kp†
az
3
H2O
Figure 2. A plot of ®rst order rate constants for the
(
presumed) solvolysis of 9-azido-9,10-dihydroanthracene
The line drawn through the points in Fig. 2 represents a
À
against [N ] in 50:50 v:v TFE-H O at 25°
À4 À1 À1
3
2
best fit of this equation with k = 2.6 Â 10
M
s ,
1
À4 À1
k = 1.5 Â 10
0
s
and k /(k ‡ k ) = 155. Although
az
p
H O
2
the last value agrees imperfectly with the value of 240
from the trapping experiments, it depends sensitively on
measurements at high azide concentrations which may be
influenced by a failure to keep the ionic strength constant.
A good fit would also be obtained using a larger value of
this ratio. Nevertheless, the values are probably within
their error limits and an average of k /(k ‡ k ) = 200
solvolysis formed anthracene and was subject to a
characteristic common ion rate depression by added
azide ions, as shown in the plot of first-order rate
À
constants against [N ] in Fig. 2.
3
In addition, analysis of the rate depression by azide
ions in Fig. 2 gave a ratio of rate constants k /(k ‡ k
)
az
p
H O
2
az
p
H O
2
consistent with that from the trapping measurements with
anthracenyl acetate. The reaction scheme on which this
analysis was based is shown in Scheme 5. The
was assumed for the calculation of k and k . The level
p H O
2
of agreement between the two measurements is suffi-
ciently good to provide further evidence for the validity
of Scheme 4.
In the usual way, a value for k ‡ k
was derived by
H O
2
p
9
taking k as the diffusion-controlled value of 5 Â 10
az
À1 À1 12,13
À7 À1
M
s .
This gave k ‡ k
= 2.5 Â 10 s .
p
H O
2
Separate values of k and k
could be obtained as
H O
2
p
2
before by adding acid to the solvolysis product and
observing the increase in absorbance from conversion of
any anthracene hydrate formed in the k
pathway to
H O
2
anthracene. Indeed, in TFE–H O this occurs, as already
2
noted, in the absence of acid. We thus obtained the ratio
6
À1 À1
k
/(k ‡ k ) = 0.22 and k
= 5.4 Â 10 M s .
H O
2
p
H O
2
H O
2
The latter value is of a magnitude for which the
assumption that the azide reaction is diffusion controlled
Scheme 5
19
is believed to be correct.
anthracenyl azide (RN ) is subject to reversible ioniza-
We are now in a position to calculate K , the ionisation
3
R
tion followed by attack of water to give a mixture of
anthracene and anthracene hydrate. The rate-depressing
influence of azide ion is expressed through the back
reaction of the anthracenyl cation (R ) to reform the
azide reactant (RN3).
constant of anthracene hydrate, by using Eqn. (1). The
rate constant kde for dehydration of this hydrate in TFE–
H O may be expressed in terms of the rate constant for
2
‡
formation of the carbocation k and k /(k ‡ k ) as
H
H O
2
p
H O
2
in Eqn. (4), which is based on Scheme 6.
Inspection of Fig. 2 shows, however, that the rate of
solvolysis of the azide reactant is not fully suppressed at
higher azide concentrations but achieves a significant
limiting value independent of further addition of azide
ions. The magnitude of this limiting rate constant is too
great to be consistent with attack of azide ion as a base on
the free anthracenyl cation, and the behaviour is attri-
buted to deprotonation of the anthracenyl cation by an
azide ion within an ion pair. This is consistent with
‡
kH‰H Š
kp
ÀÀ ÀÀ *
‡
ROH )ÀÀ ÀÀ R ‡ H O À! anthracene
)
ÀÀÀÀ
2
kH
O
2
kH
O
2
Scheme 6
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

pK
R
VALUES OF FLUORENYL AND ANTHRACENYL CATIONS
533
À1 À1
From the measured value of k = 37.3 M
s
we
de
À1 À1
obtain a rate constant k = 47.7 M
s
for carbocation
to obtain
H
formation which may be combined with k
H O
2
5
K = 1.13 Â 10 and pK = À5.1 as in Eqn. (1) (where
R
R
ROH represents the anthracene hydrate).
k k
H
p
kde
ˆ
ꢀ4†
ꢀ
kH2O ‡ kp†
It is not possible to evaluate an ionization constant Ka
for the anthracenyl cation in TFE–H O because a rate
2
constant for protonation of anthracene (from hydrogen
isotope exchange measurements) is lacking for this
solvent. However, one further equilibrium constant can
be derived, for dissociation of the 9-azido-9,10-dihy-
droanthracene to form the carbocation and azide ion. This
Figure 3. LogkOBS-pH pro®le for the hydrolysis of 9-
¯uorenimine at 25°; the dashed line represents limiting
values of logk
for benzhydrylamine
is obtained by combining the rate constant for solvolysis
OBS
À4 À1 À1
of the anthracenylazide, k = 2.6 Â 10
M
s , with
1
the reverse rate constant for reaction of the cation with
azide ion, which is assumed to have the diffusion value of
9
À1 À1 23,24
À14
5
 10 M s .
This yields K = 5.2 Â 10
and
the iminium ion. Between pH 1 and 10 the nucleophile is
water rather than hydroxide. The pK of the iminium ion
eq
pK = 13.3.
a
eq
corresponds to the break in the pH profile close to pH 6.
At low pH there is a further characteristic change from a
pH-independent reaction to a reaction inversely depen-
dent upon pH consistent with a change in rate-determin-
ing step from attack of water on the iminium ion to
expulsion of the amine leaving group from a carbinol-
Fluorenimine
In addition to the study of the anthracenonium ion in
H O–TFE mixtures, measurements of rate constants for
2
Æ
the hydrolysis of 9-fluorenimine (7) to form fluorenone
amine tetrahedral intermediate (T in Scheme 7). The
overall kinetic behaviour for the pH profile is summar-
ized in Eqn. (5), which uses the same notation for rate
constants as Scheme 7. The line drawn through the points
in Fig. 3 represents a best fit of this equation to the
measured first-order rate constants, with k = 1.01 Â
OH
2
À1 À1
À2 À1
1
0 M s , k = 2.63 Â 10 s , k /k = 0.5 M and
0
2
À1
were undertaken to establish a pK for the protonation of
pK = 5.75. These rate constants may be compared with
a
a
its imino nitrogen atom. The hydrolysis was monitored in
aqueous solution from changes in absorbance at 256 nm,
and first-order rate constants were obtained for the
reaction in dilute HCl, dilute NaOH and for buffer
solutions in the pH range 4–9. For the more acidic acetic
acid buffers (the most acidic buffer used) a mild buffer
catalysis was observed, but for more basic buffers rate
constants were independent of buffer concentration. A
plot of logarithms of first-order rate constants against pH
is shown in Fig. 3. The rate constants are extrapolated to
zero buffer concentration for acetic and cacodylic acid
buffers, but otherwise were based on measurements at a
single buffer concentration. The ionic strength was
maintained at 0.5 M with NaCl, except for measurements
with HCl and NaOH, for which no salt was added.
The mechanism of hydrolysis of imines is well
the corresponding values for benzophenoneimine,
2
À1 À1
À3 À1
kOH = 9.0 Â 10 M s , k = 1.3 Â 10
s
and pK =
0
a
26
7.0, measured by Koehler et al. The limiting kinetic
behaviour for this imine is shown by the dashed lines in
Fig. 3.
À
k ‡ k ‰OH Š
k2
0
OH
kobs
ˆ
‡
ꢀ5†
‡
‡
1
‡ K =‰H Š
ꢀk ‰H Š ‡ k †
a
À1
2
The main point of interest here is a comparison of the
pK s for fluorenone and benzophenone imines discussed
a
below. However, it may also be noted that a possible
interpretation of the buffer catalysis at low pH is that
26,27
understood,
and the pH profile shows characteristic
behaviour consistent with the reaction paths shown in
Scheme 7 (in which fluorenimine is denoted by
FlC=NH). At high pH the pH-independent reaction
represents rate-determining attack of hydroxide ion upon
Scheme 7
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

5
34
M. C. COURTNEY, A. C. MACCORMACK, R. A. MORE O’FERRALL
there is an increase in the rate of the partially rate-
The measurements in this paper show that the anthra-
cenyl cation is significantly more stable than the benz-
determining k step of the reaction as a result of general
2
‡
base-catalysed formation of product from the T tetra-
hydryl cation with pK = À5.1 compared with À11.7.
R
hedral intermediate as in the equation.
Comparison of the fluorenyl cation with the anthracenyl
cation therefore increases the difference in pK values to
R
À1
1
0.8 log units or 15 kcal mol . These pK values are
R
shown under the structures of the carbocations below.
DISCUSSION
The measurements described yield equilibrium constants
for the ionization of 9,10-anthracene hydrate (8) and the
corresponding adduct of anthracene with hydrazoic acid
It is noteworthy that the difference in pK values for
the fluorenyl and anthracenyl cations is equivalent to the
R
difference in pK s for the ionization of fluorene and
a
(
9) in 50:50 (v/v) H O–TFE mixtures. In addition, we
2
diphenylmethane to their respective anions. In DMSO
28
these pK s are 22.6 and 32.2, respectively. Although a
a
pK for dihydroanthracene appears not to have been
a
reported, it can hardly be doubted that its value will be
smaller than that for diphenylmethane. If the difference
between fluorenyl and anthracenyl cations is not ascribed
to antiaromaticity then the experimental energy differ-
ence adduced as evidence for the aromaticity of the
fluorenyl anion is smaller than that on which the anti-
aromaticity of the cation is judged to be unimportant.
measured a pK for the protonation of 9-iminofluorene (in
a
water). The results raise two distinct points for discus-
sion. The first is the implications, if any, of the pK values
for ionization of the hydrate and imine for the anti-
aromaticity of the fluorenyl cation. The second is the
interpretation of the relative magnitudes of ionization
constants of alcohols (or hydrates) and alkylazides and,
more generally, of equilibrium constants for the forma-
tion of carbocations from precursors with different
leaving groups. We consider first the question of anti-
aromaticity.
Comparison of experimental and calculated
stabilization energies
The energy difference of 15 kcal implied by the pKR
values is close to the difference of 10 kcal in electronic
18
energies calculated by Amyes et al. for the fluorenyl
and planarized benzhydryl cations, especially if account
is taken of the stabilizing inductive effect of the methyl-
ene bridge of the anthracenyl cation. These authors were
reluctant to ascribe the difference to a p-destabilization of
the fluorenyl cation, however, because their calculations
indicated a net p-stabilization of 50 kcal relative to the
(planar) benzhydryl cation and revealed no other evi-
dence of antiaromaticity. They suggested that either there
might be a greater p-stabilization of the fluorenyl relative
to the benzhydryl alcohol or that the energy difference
pK values for anthracenyl and ¯uorenyl cations
R
Ab inito calculations suggest by various criteria, includ-
ing magnetic susceptibility exaltation, nucleus-inde-
2
0,21
pendent chemical shifts (NICS)
and energetic and
18
geometric comparisons with reference compounds, that
the cyclopentadienyl and indenyl cations are anti-
aromatic, whereas the fluorenyl cation is either non-
18
20
18
antiaromatic, ‘non-aromatic’ or borderline in anti-
derives from other sources.
21
aromatic character.
Experimentally it is not possible to distinguish
p-stabilization from s-stabilization or other energetic
18
Amyes et al. compared the stabilities of fluorenyl
and benzhydryl cations and calculated energies, geo-
metries and charge distributions using ab initio calcula-
tions at the 6–31G*/3–21G level. They also measured
effects using pK measurements. However, it is possible
R
to show that the stabilization arising from linking the
benzene rings in fluorene (taken as a model for the
9-fluorenyl alcohol) is significantly less than the
destabilization of the corresponding carbocation. The
stabilization of fluorene relative to dihydroanthracene
may be judged initially from the isodesmic reaction of
pK values for the two ions experimentally and found a
R
difference (DpK ) of 4.2 log units. Because their
R
calculations were based on a planarized structure of the
benzhydryl cation, a more appropriate structure for
comparison with the calculations would appear to be
the planar anthracenyl cation. Indeed this ion was later
À1
Eqn. (7), for which DH = 7.6 kcal mol in the gas phase.
Probably a better measure of this stabilization, however,
is provided by Eqn. (8), in which the cyclohexane and
20
used for comparison in calculations by Jiao et al.
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

pK
R
VALUES OF FLUORENYL AND ANTHRACENYL CATIONS
535
cyclopentane rings of Eqn. (7) are replaced by tetra-
hydronaphthalene and indane, in recognition of the benzo
fusion of the five- and six-membered rings of fluorene
ence reflects stabilization of the anthracenyl cation by the
inductive effect of the methylene group. Nevertheless,
the principal conclusion to be drawn from this analysis is
that the magnitude of the experimental effect matches the
À1
and anthracene. Now the value of DH = 5.4 kcal mol is
15,20
À1
significantly smaller.
This is because benzoannela-
value of DH = 10 kcal mol calculated by Amyes, et
18
20
tion is energetically more favourable for cyclopentane
than cyclohexane. Indeed taking account of the double
benzoannelation in fluorene and anthracene the true
stabilization is probably smaller still, e.g. DH = 3–4 kcal
al. and Jiao et al. It is unlikely that this value needs
correction for strain in the fluorenyl cation because this
should be more than compensated by strain in the central
ring of the anthracenyl cation. Thus there is more strain
associated with replacing single bonds by one or two
À1
mol .
(
conjugated) double bonds in a cyclohexane ring than a
15
cyclopentane ring.
This agreement between experiment and calculation
supports the reality of the destabilization of the fluorenyl
cation. It is possible that the origin of the destabilization
lies in an accumulation of small effects arising from
neglected contributions or approximations, such as the
combination of DH values for the gas phase with DG in
solution or the neglect of geminal interactions of the
hydroxyl groups of the alcohols. However, the more
obvious interpretation is that it represents a p-destabil-
ization energy.
How could such a conclusion be reconciled with
Amyes et al.’s calculation showing a greater p-stabiliza-
tion of the fluorenyl than (planar) benzhydryl cation? As
these authors pointed out, the antiaromaticity of simple
molecules or ions such as cyclobutadiene or the cyclo-
pentadienyl cation is unambiguous and is revealed by
characteristically degenerate highest occupied molecular
orbitals in their planar configurations. For the indenyl
cation the antiaromatic ring is fused to an aromatic ring
and the degeneracy (and simplicity) of the cyclopenta-
dienyl cation is lost. Nevertheless, it is generally agreed
that the indenyl cation is subject to antiaromatic
destabilization.
We can deduce the stabilization of the fluorenyl
relative to the anthracenyl cation by considering the
corresponding isodesmic relationship involving the
indenyl and tetrahydronaphthyl cations shown in Eqn.
17
In the case of the fluorenyl cation the electronic
characteristics of the central five-membered ring are
(
9). If we replace DH° (g) by pK values we obtain a
f
R
measure of the difference in stabilization of the
carbocations relative to their alcohol reactants. This
2
0
overlain by the influence of the two benzene rings. Jiao
20
et al. noted agreement of their own calculations with
amounts to DpK = À11.7, which is equivalent to
R
18
À1
those of Amyes et al. in implying a net ‘nonaromatic’
character for the fluorenyl cation. However, they esti-
mated a delocalization energy in a different manner from
Amyes et al. They compared the effect on fluorenyl and
anthracenyl cations of excluding from the energy
calculation the p-orbital that would accommodate the
positive change if it were fully localized at the 9-position
of the two cations. By this means they estimated a
reduced delocalization energy for the fluorenyl relative to
1
6 kcal mol . If we suppose that stabilization of the
alcohols may be approximated by DH in the gas phase
for the corresponding hydrocarbons, i.e. 3–
À1
4
kcal mol , we find that the fluorenyl cation is
(
isodesmically) destabilized relative to the anthracenyl
À1
cation by 12–13 kcal mol .
À1
the anthracenyl cation of 8 kcal mol . This is in reason-
able agreement with the experimental measurements and
calculations of overall energy differences and suggests
that by the ODP criterion these may be regarded as
mainly antiaromatic in origin.
À1
It is likely that a further 3–4 kcal mol of this differ-
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

5
36
M. C. COURTNEY, A. C. MACCORMACK, R. A. MORE O’FERRALL
Stabilization and NICS values
bons show a less clear correlation between magnetic
properties and stabilization energies than monocyclics.
Moreover, as implied above for polycyclic aromatic
molecules showing borderline antiaromatic behaviour, it
may be difficult to assign clearly the origin of electronic
contributions to the destabilization, especially where the
rings are non-equivalent. It seems fair to conclude,
therefore, that the possibility of a mild antiaromatic
destabilization of the fluorenyl cation is not excluded by
2
1
An interesting suggestion by Mills is that the degree of
antiaromaticity of the fluorenyl cation is influenced by
the electronegativity of substituents at the formal charge-
bearing carbon atom, i.e. the 9-position of the fluorenyl
ring. By the criterion of NICS values and proton chemical
shifts a fluorenyl cation with sufficiently electron-with-
drawing substituents such as CF or, most strikingly,
3
20,21
another 9-fluorenyl cation (10), is found to be unambigu-
ously antiaromatic, based on NMR measurements and
high-level Gaussian (including DFT) calculations.
the calculated NICS values.
Ionization of 9-azido-9,10-dihydroanthracene
The measurement of an ionization constant Kaz for
9-anthracenylazide is of interest in the context of a
comparison of the ionization constants of azides and
alcohols. There have been a number of reports of equi-
librium constants for the ionisation of azide derivatives,
2
3,24
notably of arylalkylazides and azido methyl ethers.
These have been based on measurements of a common
ion rate depression by azide ion accompanying solvolysis
of the azide susbstrate. These substrates either have been
synthesized directly or have been formed in situ by
trapping of a carbocation generated from a more reactive
Our own measurement of pK for the protonated
-iminofluorene (11), although not strictly comparable to
a
9
the measurements of pK values, reveals a difference of
R
1
.25 log units from the pK (= 7.0) for protonated
a
benzhydrylimine (12). This small difference is consistent
3,24
solvolytic precursor.
Equilibrium constants have been
obtained by combining a rate constant for the ionization
step with a rate constant for the reverse reaction of the
carbocation with azide ion. For relatively unstable
13
cations this reaction is diffusion controlled.
The equilibrium constants to be compared are the
ionization constant pKaz for the azide and pK for the
R
alcohol. Strictly, pK is a hydrolysis constant for the
carbocation. A more appropriate equilibrium constant for
R
with extensive delocalization of charge from the carbo-
cation centre by the strongly electron-donating amino
susbstituent and a reduction in the difference in stability
compared with the parent ions. An even smaller
comparison with K therefore is that for ionisation of the
az
‡
À
alcohol (i.e. for the equilibrium ROH „ R ‡ OH ),
30
denoted K . Thus 1/Kaz and 1/K measure respectively the
c
c
difference in pK s has been reported for protonation
a
affinities of the azide ion and hydroxide ion for the
of fluorenone (À6.65) and benzophenone (À6.16). As
carbocation. However, as discussed elsewhere, K is
c
expected, the pK = À5.10 for anthrone is less than that
a
30
inversely related to K through the relationship K =
R c
for benzophenone.
K /K where Kw is the autoprotolysis constant of
w
R
Strictly, these results only show that differences in
stabilities of fluorenyl and benzhydryl or anthracenyl
cations are, as expected, saturated by electron-donating
substituents. Nevertheless, formally, they complement
the calculations of NICS values for more unstable
cations.
31
water. Because K is used more widely than K , it is
R
c
KR
‡
‡
R ‡ H O „ ROH ‡ H
2
Kaz
‡
À
RN „ R ‡ N
3
3
In so far as there have been good correlations between
NICS values and energy differences in recognized
examples of antiaromatic molecules, it seems reasonable
to suppose that the energy difference between the parent
fluorenyl and anthracenyl cations in part reflects the same
phenomenon as is responsible for the trend in NICS
‡
‰
ROHŠ‰H O Š
3
K ˆ
R
‡
‰
R Š‰H OŠ
2
‡
À
‰R Š‰N Š
3
K ˆ
az
‰
RN Š
3
21
values. Mills interpreted the trend in NICS values with
-substituent for the fluorenyl cation as indicating that the
À
‡
9
‰ROHŠ ‰N Š‰H3O Š
3
K K ˆ
az
R
unsubstituted cation is close to the borderline of
magnetically detectable antiaromaticity. However, Jiao
‰
RN Š
‰H OŠ
3
2
20
et al. emphasized that polycyclic aromatic hydrocar-
Scheme 8
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

pK
R
VALUES OF FLUORENYL AND ANTHRACENYL CATIONS
537
of the carbocation, it is not necessarily independent of the
solvent.
However, while a change in solvent does change pKaz
and pK it appears that the effects on the two equilibrium
R
constants may be compensating. Thus between water and
5
0:50 TFE–H O, pKR for the anthracenonium cation
2
increases from À5.9 to À5.1, whereas for the same
solvent change pK decreases. This is implied by the
az
lack of solvolysis of the azide in water (and the
supposition that the rate constant for the reverse reaction
remains unchanged at the diffusion value). The less polar
Scheme 9
acetonitrile has the opposite effect on pK as is indicated
R
by a decrease from À6.7 to À7.8 for 2-hydroxy-1,2-
convenient to quantify comparisons in terms of the
dihydronaphthalene on admixture of 25% acetonitrile
2,3
product K K rather than the ratio K /K . Scheme 8
with water.
On the other hand, solvolysis of the
az
R
az
c
summarizes expressions for K , K and K K .
alkylazide must occur more readily in the aqueous
medium (13) (kinetically and presumably thermodyna-
mically), as has been well established, for example, for
az
R
az R
The relevant measurements for comparison are shown
in Scheme 9. Values of pKaz and pK are compared for
R
2
three substrates in (different) mixed or pure aqueous
solvents. The main point of interest for the present
discussion is that whereas pKaz for the three substrates
remains practically the same (13.1 Æ 0.2), pKR varies
from À5.1 to À10, i.e. changes by five powers of ten.
At first sight this behaviour is surprising because the
the comparable solvolysis of the anthracenyl acetate (6).
If the change in solvent is not the main factor causing
the discrepancy between changes in K and K , then the
R
az
differences arise chiefly from variation in Kbond, rather
than the solvent sensitive but substrate independent
HN
3
ionisation constant of hydrazoic acid, Ka . Hence they
arise from differences in stabilities of the substrates RN3
and ROH. If we consider first the highly negative value of
pKR for the ionization of propionaldehyde hemiacetal
(15), it seems clear that this must arise from the
stabilising geminal interaction between the two oxygen
relative magnitudes of Kaz and K (strictly the product
R
K K ) should be independent of the stability of the
az
R
carbocation. The origin of the behaviour is best assessed
if K K is rewritten in terms of two further equilibrium
az
R
HN
3
constants, Ka , the ionization constant of hydrazoic
atoms of the reactant. This stabilization amounts to about
À1
7
kcal mol
and would contribute 5 log units to a
32
HN3
difference between pKR and pKaz.
Although the
Ka
‡
À
3
magnitude of the geminal interaction of OMe and N in
15 is not certainly known, such interactions can vary
3
HN À) ÀÀÀÀ *À H ‡ N
3
)
ÀÀÀ
widely and that between OH and CN (for example) is
À1 32
unfavourable by 7 kcal mol . What evidence there is
is consistent with the N –MeO interaction being
considerably less favourable than MeO–MeO.
Kbond
3
33
ÀÀÀ*
RN ‡ HOH )ÀÀÀ ROH ‡ HN
3
3
)
ÀÀÀ
Turning to the difference of 2.7 log units between pKR
values for anthryl and naphthyl substrates (13 and 14), we
may draw on recent estimates of the energy difference
between substitution of a hydroxyl group for a hydrogen
atom at the appropriate carbon atoms of 9,10-di-
Scheme 10
15
acid (HN ), and Kbond, the equilibrium constant for the
bond exchange reaction’ between OH and N leaving
hydroanthracene and 1,2-dihydronaphthalene. A dif-
3
À1
‘
ference of DG(aq) = 1.8 kcal mol
was estimated in
3
groups shown in Scheme 10. The latter constant is a
measure of the relative strengths of bonds between
oxygen and nitrogen and hydrogen on the one hand and
oxygen and nitrogen and carbon on the other. By
comparing Schemes 8 and 10, it can be seen that the
relationship between the two pairs of equilibrium
favour of the 2-hydroxy-1,2-dihydronaphthalene, reflect-
ing a more favourable hydroxyl–alkyl than hydroxyl–
phenyl interaction. This is consistent with the direction of
the observed difference in pK s. Again, little is known of
R
the corresponding geminal interactions of an azido group
but we may speculate that the interaction of an azide with
the phenyl groups in 9-azido-9,10-dihydroanthracene is
more stabilizing than with a hydroxyl group.
One objective of the above analysis was to explore the
possibility of using measurements of pKaz to derive
HN
3
constants is K K = KbondKa
.
az
R
Before focusing on the bond exchange equilibrium, it
may be recalled that the equilibrium constants in Scheme
9
were measured in different solvents, specifically
aqueous trifluoroethanol, aqueous acetonitrile and water.
values of pK for alcohols for which direct measurements
R
Although the value of K K is independent of the nature
are lacking. The issues discussed are pertinent to the
az
R
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

5
38
M. C. COURTNEY, A. C. MACCORMACK, R. A. MORE O’FERRALL
general problem of interrelating pK values for ionisation
reactions involving different leaving groups. The attrac-
tion of establishing such relationships is that in favour-
able cases equilibrium constants can be derived from
solvolysis measurements in aqueous solution in the same
solid, leaving the unreacted fluorenone in solution.
Neutralization of the hydrochloride with aqueous ammo-
nia yielded the imine, which was crystallized from
tolnene–methanol to give yellow needles (22.5 g, 41%
36
1
yield): m.p. 123.5–124.5°C (lit. 124°C); H NMR
24
way as for the azides discussed above, i.e. by com-
bining the solvolysis rate constant with a rate constant for
the reverse reaction which is assumed to be diffusion
(CDCl ), ꢀ 7.14–8.27 (m, 8H, fluorenyl rings), 10.32 (s,
3
1H, NH).
34
controlled. Then if an equilibrium constant for one
leaving group becomes available, others may be deduced.
However, in the absence of relevant thermodynamic
measurements, more information on (equilibrium con-
stants for) s-bond interactions of the leaving groups will
be required to make the necessary interpolations. In
principle this information may be accessible from cal-
Kinetic and equilibrium measurements. Kinetic
methods for the measurement of rate constants for
dehydration of anthracene hydrate and solvolysis of
9-acetoxy-9,10-dihydroanthracene in water or water–
acetonitrile mixtures have been described, as have
product analyses and trapping experiments with azide
2
ion. Similar methods were used for the TFE–H O
2
35
culations.
solvent mixtures.
Determination of the ratio of aromatic product to
hydrate formed from solvolysis of 9-acetoxy-9,10-di-
hydroanthracene was based on differences in absorbance
at 251 nm between the beginning of the solvolysis
reaction (estimated from injection from a stock solution
EXPERIMENTAL
Instrumentation and reagents. NMR measurements
were made with a Jeol JNMGX270 spectrometer
of the substrate into non-solvolysing acetonitrile), Ainit,
1
13
operating at 270 MHz for H NMR and 68 MHz for
NMR. UV–Vis spectra were recorded using Phillips PU
600, Bausch and Lomb Spectronic and Perkin-Elmer
C
the absorbance at the completion of the reaction, A , and
0
the absorbance following addition of a small amount of a
strong acid to effect conversion of anthracene hydrate to
anthracene, Amax. In principle, some trifluorethyl ether
would also be formed in the solvolysis but inspection of
the dependence of the product ratio of alcohol and
trifluoroethyl ether upon pKR for the carbocation in
previous studies suggested that the amount would be
8
Hitachi 124 spectrophotometers, with thermostatting of
cell compartments at 25.0 Æ 0.1°C for kinetic measure-
ments. Reagents, including the solvent trifluoroethanol,
were normally purchased from Aldrich and used without
purification; acetonitrile was of HPLC grade. Water for
kinetic measurement was doubly distilled.
18
small enough (<5%) to be neglected. The ratio of
anthracene to hydrate in the solvolysis products (and thus
kp/k ) is then given by (A À Ainit)/(Amax À A ) and was
Synthesis. The preparation of 9-hydroxy-and 9-acetoxy-
H O
0
0
2
2
9
,10-dihydroanthracene has been described previously.
based on the following measurements of A and A
:
max
0
Fluorenimine was prepared by the method of Hilbert and
Pinck, with the variations described below.
0.45, 0.53; 0.46, 0.53; and 0.48, 0.54. In each case Ainit
was 0.16.
36
Addition of sodium azide to the solvolysis reaction led
Fluorenimine (7). Fluorenone (50.0 g, 0.278 mol) was
heated slightly above its melting-point (82°C) and
gaseous ammonia, dried by passage through a calcium
oxide tower, bubbled through the melt for 7 days, using a
bubbler with a sintered-glass end to give a large gas–
liquid surface area. Formation of the imine was detected
by thin-layer chromatography on silica [chloroform:
R (ketone) = 0.8; R (imine) = 0.3] although extensive
hydrolysis occurred (even on neutral alumina plates).
The reaction could be crudely monitored by the increase
in bath temperature necessary to maintain the melt in the
molten state, since the melting-point of the imine product
to a reduction in absorbance of the product from A to
0
Aaz. As described above, a ratio of rate constants for
trapping the solvolytic intermediate (presumed to be the
anthracenonium ion) by azide ion and water is obtained
À
from a plot of 1/(A À A ) against [N ], as shown in
az
init
3
Fig. 1. The measured values of A at the indicated
az
concentration of azide ion were: 0.51, 0 M; 0.38,
0.0015 M; 0.38, 0.0020 M; 0.37, 0.0030 M; 0.34,
0.0040 M; 0.295, 0.0045 M; and 0.30, 0.0060 M. In all
cases Ainit was 0.16.
f
f
Following the trapping by azide ion a further increase
in absorbance was observed which was attributed to
solvolysis of the azide trapped product 9-azido-9,10-
dihydroanthracene. Rate constants for this process
(
124°C) is higher than that of fluoreneone (82°C).
Completion of the reaction was difficult to attain because
of accumulation in the melt of water produced during the
reaction and because the solubility of the ammonia falls
with increasing temperature.
4
À1
(10 k s ) were measured at the indicated concentra-
obs
À
tions of azide ion and plotted against [N ] in Fig. 2:
3
3.42, 0.0015 M; 3.12, 0.002 M; 3.59, 0.003 M; 2.86,
0.004 M; 3.09, 0.0045 M; 2.60, 0.006 M; 2.51, 0.010 M;
2.10, 0.015 M; 1.99, 0.020 M; 1.66, 0.040 M; 1.57,
0.060 M; 1.52, 0.080 M; and 1.52, 0.1 M.
The melt was allowed to solidify and then dissolved in
chloroform and shaken with dilute hydrochloric acid. The
fluorenimine hydrochloride precipitated as an orange
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 529–539

pK
R
VALUES OF FLUORENYL AND ANTHRACENYL CATIONS
539
The hydrolysis of fluorenimine was monitored spectro-
photometrically from the increase in absorbance at
7. Boyd DR, McMordie RAS, Sharma ND, More O’Ferrall RA, Kelly
SC. J. Am. Chem. Soc. 1990; 112: 7822–7823.
8
. Richard JP, Amyes TC, Lin S-S, O’Donoghue AC, Toteva MM,
Tsuji Y, Williams KB. Adv. Phys. Org. Chem. 2000; 34: 67–115.
2
56 nm, lmax for the fluorenone product. First-order rate
constants were measured in aqueous HCl, sodium
hydroxide and acetate, cacodylate, N-methylmorpholine
and trimethylamine buffers. For the buffers the ionic
strength was maintained at 0.5 M with NaCl but no NaCl
was added to the HCl or NaOH solutions. For the acetate
and cacodylate buffers rate constants were extrapolated
to zero buffer concentration. The following first-order
9. McClelland RA. Tetrahedron 1996; 52: 6823–6858.
0. McClelland RA, Kanagasapathy VM, Banait NS, Steenken S. J.
Am. Chem. Soc. 1989; 111: 3966–3972.
1
1
1
1
1. Steenken S, McClelland RA. J. Am. Chem. Soc. 1989; 111: 4967–
4973.
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06: 1361–1372.
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Am. Chem. Soc. 1991; 113: 1009–1014.
3
À1
14. Cox RA. J. Phys. Org. Chem. 1991; 4: 233–241.
rate constants (10 k s ) were measured at the indicated
pHs: 0.97, pH 0; 11.2, pH 1; 24.7, pH 2; 23.0, pH 4.22;
1
5. Dey J, O’Donoghue AC, More O’Ferrall RA. J. Am. Chem. Soc. in
press.
2
7
4.0, pH 4.83; 21.0, pH 5.30; 11.6, pH 5.98; 1.23, pH
.12; 0.47, pH 7.63; 0.178, pH 8.35; 0.115, pH 9.89; 0.98,
16. Toteva MM, Richard JP. J. Am. Chem. Soc. 1996; 118: 11434–
1
1445.
1
7. More O’Ferrall RA, O’Donoghue AC, McDonnell CA, MacCor-
mack AC. In Modern Problems in Organic Chemistry, vol. 13.
Kostikov R (ed). St. Petersburg University Press: St. Petersburg, in
press.
pH 12; 0.87, pH 13; and 1.12, pH 14.
À
Weak buffer catalysis in 4:1 AcOH–AcO buffers
ionic strength 0.5 M, pH 4.22) was indicated by
(
1
8. Amyes TL, Richard JP, Novak M. J. Am. Chem. Soc. 1992; 114:
2
À1
measurements of first-order rate constants (10 k s ) at
8
032–8041.
the indicated acetate ion concentrations: 2.63, 0.04 M;
19. Allen AD, Sumonja M, Tidwell TT. J. Am. Chem. Soc. 1997; 119:
371–2375, and references cited therein.
2
2
.74, 0.06 M; 2.96, 0.08 M; and 3.0, 0.1 M. These give an
2
0. Jiao H, Schleyer PvR, Mo Y, McAllister MA, Tidwell TT. J. Am.
Chem. Soc. 1997; 119: 7075–7083.
apparent second-order rate constant with respect to
À1 À1
acetate ion of 0.08 M s . Corresponding rate constants
21. Mills WS. J. Am. Chem. Soc. 1999; 121: 11690–11696.
22. Breslow R, Mazur S. J. Am. Chem. Soc. 1972; 95: 584–585.
À
in 1:1 and 1:4 AcOH–AcO buffers were 0.06 and
2
3. Amyes TL, Stevens IW, Richard JP. J. Org. Chem. 1993; 58:
057–6066.
À1 À1
0
.03 M s .
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2
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