Substituent effects in solvolysis of 1,1-diphenylethyl p-nitrobenzoates. Symmetrically disubstituted and monosubstituted systems

Article abstract of DOI:10.1002/poc.484

The rates of solvolysis of 1,1-diarylethyl p-nitrobenzoates and chlorides were determined conductimetrically at 25 °C in 80% (v/v) aqueous acetone. Applying the Yukawa-Tsuno (Y-T) equation, the symmetrical (X = Y) subseries gave a precise additivity relationship for the whole substituent range with a r_sym value of -3.78 and an r_sym value of 0.77. While any Y subsets gave statistically less reliable Y-T correlations, the apparent ρ value changed significantly depending on the fixed Y substituents; the ρ value decreases with the more electron-donating fixed substituents Y, which is compatible with the Hammond shift of the transition state coordinate. Nevertheless, the concave correlations of the More O'Ferrall non-linearity relationship for any Y subsets are not in line with what is expected from the reactivity-selectivity relationship suggesting an anti-Hammond shift of transition state. However, we found a precise extended Bronsted relationship between the pK_R+ values of 1,1-diarylethylenes and solvolysis rate process with a constant slope of α = 1.03 ± 0.03. This is direct evidence indicating that there is no significant shift of the transition-state coordinate over the whole range of substituent change. Copyright

Full text of DOI:10.1002/poc.484

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2002; 15: 544–549
Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.484
Substituent effects in solvolysis of 1,1-diphenylethyl
p-nitrobenzoates. Symmetrically disubstituted and
monosubstituted systems†
Mizue Fujio,* Md. Khabir Uddin, Hyun-Joong Kim and Yuho Tsuno
Institute for Fundamental Research of Organic Chemistry, Kyushu University, Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
Received 20 October 2001; revised 19 January 2002; accepted 24 January 2002
ABSTRACT: The rates of solvolysis of 1,1-diarylethyl p-nitrobenzoates and chlorides were determined
conductimetrically at 25°C in 80% (v/v) aqueous acetone. Applying the Yukawa–Tsuno (Y–T) equation, the
symmetrical (X = Y) subseries gave a precise additivity relationship for the whole substituent range with a rsym value
of À3.78 and an rsym value of 0.77. While any Y subsets gave statistically less reliable Y–T correlations, the apparent
r value changed significantly depending on the fixed Y substituents; the r value decreases with the more electron-
donating fixed substituents Y, which is compatible with the Hammond shift of the transition state coordinate.
Nevertheless, the concave correlations of the More O’Ferrall non-linearity relationship for any Y subsets are not in
line with what is expected from the reactivity–selectivity relationship suggesting an anti-Hammond shift of transition
state. However, we found a precise extended Brønsted relationship between the pKR values of 1,1-diarylethylenes
‡
and solvolysis rate process with a constant slope of a = 1.03 Æ 0.03. This is direct evidence indicating that there is no
significant shift of the transition-state coordinate over the whole range of substituent change. Copyright  2002 John
Wiley & Sons, Ltd.
KEYWORDS: a-methylbenzhydryl system; substituent effect; Yukawa–Tsuno equation; non-linearity and non-
additivity; coordinate shifts of transition state; extended Brønsted relationship
INTRODUCTION
The non-additivity of rY in multiple-substituent effects
was most simply dealt with using the equation4
It is well known that the kinetic effects of two
substituents on two equivalent aromatic rings are not
additive.1,2 The solvolysis of a,a-di(substituted-pheny-
l)ethyl p-nitrobenzoates also shows a complicated non-
linear correlation of substituent effects. To scrutinize the
non-linearity and non-additivity in the multiple-substi-
tuents effects in this system, the Yukawa–Tsuno (Y–T)
equation has been used as a very effective tool in
correlation analysis:2,3
ꢀY ˆ ꢀH ‡ qꢁY
ꢀ2†
Dubois and co-workers, in their studies on the bromina-
tion of disubstituted diarylethylenes,5 proposed the
following equation,1,5,6 which describes the non-additive
effect in terms of different reaction constants for X and Y
substituents:
‡
logꢀk=k0† ˆ ꢀꢀꢁꢁ ‡ rÁꢁR † ˆ ꢀꢁ
ꢀ1†
logꢀkXY=kHH† ˆ ꢀHꢀꢁX ‡ ꢁY† ‡ qꢁXꢁY
ˆ ꢀHꢁY ‡ ꢀꢀH ‡ qꢁY†ꢁX
ꢀ3†
ꢀ3a†
‡
where s° is the normal substituent constant and ÁꢁR is
the resonance substituent constant measuring the cap-
ability for p-delocalization of electron donor substituents
Non-additivity is therefore taken into account by the qsY
term in Eqn. (3a).1,5,6 The selectivity parameter r for a
reaction series varies appreciably with the reactivities (or
the stabilities of transition states) of the parent substrates.
However, the analysis has often suffered from
significant non-linearity within a single (X) substituent
effect correlation for the respective Y-fixed subset.1,2,5
The non-linearity in the correlations for respective Y
subsets has been dealt with by the More O’Ferrall
and is defined by ꢁ À ꢁ°.3b Apparent Y–T s values with
‡
an appropriate r are presented by s.
*Correspondence to: M. Fujio, Institute for Fundamental Research of
Organic Chemistry, Kyushu University, Hakozaki, Higashi-ku,
Fukuoka 812-8581, Japan.
E-mail: fujio@ms.ifoc.kyushu-u.ac.jp
†Presented at the 8th European Symposium on Organic Reactivity
(ESOR-8), Cavtat (Dubrovnik), Croatia, September 2001.
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 544–549

SOLVOLYSIS OF 1,1-DIPHENYLETHYL p-NITROBENZOATES
545
equation:7
2
logꢀkX=kH† ˆ ꢀꢀ0†YꢁX ‡ ꢀ2m†YꢀꢁX†
ꢀ4†
Y
where (r0)Y is the tangential r value at X = H of the Y
subset, and the coefficient (2m)Y is a susceptibility
parameter describing the degree of curvature of correla-
tions of given Y subsets.
This behavior is often referred to as adherence to the
reactivity–selectivity relationship (RSR).5,6b,8 There is
generally an inverse relationship between reactivity and
selectivity insofar as both are related to shifts in the
transition-state position.9 The progress of the reaction at
this transition state is usually obtained from coefficients a
of Brønsted or of other rate–equilibrium relationships
that compare substituent effects on kinetics and thermo-
dynamics:10
Scheme 1
‡
systems. The same conformation effects should also be
operative in the 1,1-diarylethyl system, so that we should
take into account the non-additivity effect caused from
substituent-induced change in conformation in addition
to those caused from coordinate shifts of the transition
state.
We have extended our substituent-effect studies to the
non-linearity and non-additivity behaviors in the solvo-
lysis of 1,1-diarylethyl p-nitrobenzoates (Scheme 1). The
solvolytic cation formation of this system should be
connected mechanistically to the hydration12 as a single
reversible process, an E1 elimination process, with a
common intermediate intervening. Both transition states
should reflect any perturbations of the common inter-
mediate, and the comparative studies will provide
logꢀkXY=kHH† ˆ ꢂꢀÁpKR
†
ꢀ5†
We recently investigated11 the non-linearity and non-
additivity in the substituent effects on the solvolyses of a-
CF3-diarylmethyl system. While the simple precise
additivity relationship was found to exist for the
symmetrical (X = Y) subseries, for any unsymmetrical
subsets (X ≠ Y) there were significant non-linearity and
non-additivity of substituent effects for the two aryl rings.
The non-linear and non-additive substituent effects in this
a-CF3 system were explained by the substituent-induced
change in propeller conformation of two aromatic rings.
Accordingly, our interest has been focused on exploring
the scope of non-linearity and non-additivity behavior in
the substituent effects in the a,a-diarylcarbocation
Table 1. Rates of solvolysis of a,a-diarylethyl p-nitrobenzoates (OPNB) in 80% aqueous acetone at 25°C
Monosubstituted OPNB
Disubstituted OPNB
Substituent
kOPNB Â 105 (sÀ1
)
Substituent
(p-MeS)2
(p-Me)2
(p-MeS-m-Cl)2
(m-Me)2
(p-Cl)2
(p-Br)2
(m-Cl)2
(m-CF3)2
p-MeO p-Br
m-Cl
kOPNB Â 105 (sÀ1
)
p-MeO
p-MeS
p-MeO-m-Cl
p-Me
63.0
111.3
7.39
0.808
7.00
2.61
1.28
0.2938
p-Et
1.00
5.28 Â 10À3
4.85 Â 10À3c
6.50 Â 10À5c
1.23 Â 10À5c
p-t-Bu
p-SMe-m-Cl
m-Me
0.775
0.354
0.170
H
0.103
26.4
7.85 Â 10À2a
2.48 Â 10À2
3.11 Â 10À3b
1.42 Â 10À3b
8.61 Â 10À4b
1.47 Â 10À4c
2.88 Â 10À5c
9.20
p-Cl
m-Cl
m-CF3
p-CF3
3,5-Cl2
3,5-(CF3)2
m-CF3
3,5-Cl2
3,5-(CF3)2
6.38
1.77
0.85
p-Me m-Cl
3,5-Cl2
3,5-(CF3)2
7.76 Â 10À2
2.66 Â 10À3c
7.93 Â 10À4c
a
Ref. 13.
b
Estimated from the rates in 50% aqueous acetone; log k80A = À1.037 ‡ 1.142logk50A
.
c
Estimated from the corresponding chloride reactivities based on the p-nitrobenzoate/chloride ratio = 1.034 Â 10À5
.
Copyright  2002 John Wiley & Sons, Ltd.
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546
M. FUJIO ET AL.
Table 2. Correlation analysis of substituent effects using the Yukawa±Tsuno equation [Eqn. (1)]
No.
System
Substituent (X) range
na
r
r
R
SD
1
2
3
4
5
6
7
8
9
1
2
p-MeS–m-CF3
p-MeO–3,5-(CF3)2
s-EDb
9
À3.78 Æ 0.09
À3.68 Æ 0.08
À4.22 Æ 0.10
À1.97 Æ 0.12
À1.91 Æ 0.10
À3.23 Æ 0.18
À4.61 Æ 0.08
À4.78 Æ 0.26
À5.04 Æ 0.18
0.77 Æ 0.04
0.88 Æ 0.04
(0.36 Æ 0.4)e
(1.33 Æ 0.17)e
(0.87 Æ 0.34)e
(0.99 Æ 0.15)e
0.93 Æ 0.03
1.09 Æ 0.09
1.14 Æ 0.06
0.9990
0.9988
0.9998
0.9978
0.9967
0.9985
0.9995
0.9976
0.9984
0.12
0.10
0.03
0.10
0.07
0.15
0.05
0.11
0.09
14
4
c
3
4
p-MeO–3,5-(CF3)2
8
H–3,5-(CF3)2
p-MeO–3,5-(CF3)2
6
d
6
Y = m-Clf
p-MeO–m-Cl
p-MeO–H
p-MeO–H
10
9
f
Y = 3,5-Cl2
Y = 3,5-(CF3)2
f
11
a
Number of substituents involved.
Including p-MeO, p-MeS, p-MeO-m-Cl and p-MeS-m-Cl.
The rate constant k(p À MeO)2 was estimated by the Y–T correlation (entry 1) for the 1 (X = Y) subseries.
The rate k(p À MeO,p À Me) is estimated by Eqn. (4) for the 3 (Y = p-MeO) subset.
The r value should be statistically indefinite.
b
c
d
e
f
Unpublished data.
important information concerning the behavior of transi-
tion states causing non-linearity and non-additivity.
corresponding chlorides were determined conductime-
trically at 25°C in 80% (v/v) aqueous acetone (80A) at
initial concentrations of 10À5–10À4 mol dmÀ3 of sub-
strates. The rates for highly deactivating derivatives were
only obtained from the chloride rates. The rates for the
chlorides were converted into p-nitrobenzoate reac-
tivities using the rate ratio of p-nitrobenzoate to
chloride = 1.034 Â 10À5. The rates of solvolyses of the
p-nitrobenzoates are summarized in Table 1.
RESULTS
Solvolysis rates
The rates of solvolysis of the p-nitrobenzoates and the
Correlation analysis of substituent effects
The correlation analysis of substituent effects was carried
out based on the Y–T equation [Eqn. (1)] as a routine
procedure. The results are summarized in Table 2. The
substituent effects on the solvolysis of symmetrical
subseries 1 (X = Y) gave an excellent linear Y–T
correlation for the whole range of substituents with a r
value of À3.78 (for single sX) and an r value of 0.77;
correlation coefficient R = 0.9990 and SD = 0.12. For
subset 2, a precise Y–T correlation can be obtained with a
r value À3.68 and r = 0.88. For the 3 (Y = p-MeO) subset
a good Y–T correlation with a reduced r value was
obtained, but the r value was not statistically definite. A
similar correlation with a reduced r was obtained also for
4 (Y = p-Me). On the other hand, the subsets Y = m-Cl,
3,5-Cl2 and 3,5-(CF3)2 were correlated linearly by Eqn.
(1) with significantly higher r and r values. While the Y–
T correlations for any subsets are statistically lightly less
certain or sometimes indefinite, the apparent rY value for
the Y–T correlations of variable X substituents changes
significantly depending upon fixed Y substituents.
Non-linear correlation analysis
Figure 1. Plots of log (kXY/kHH) for the solvolysis of 1,1-
diphenylethyl p-nitrobenzoates against ꢁꢀX ‡ ꢁꢀY with
r = 0.77; solid circles represent the symmetrical subseries 1
(X = Y)
Figure 1 demonstrates a poor correlation of the
log(k/k0)OPNB values against ꢁꢀX ‡ ꢁꢀY with the r scale
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 544–549

SOLVOLYSIS OF 1,1-DIPHENYLETHYL p-NITROBENZOATES
Table 3. Analysis of substituent effects by Eqn. (4)
547
Subset (Y)
na
6b
14
6
8
(r0)Y
(2m)Y
R
SD
(m-Cl)
2(H)
4(p-Me)
3(p-MeO)
À4.92 Æ 0.16
À4.08 Æ 0.06
À3.62 Æ 0.14
À2.61 Æ 0.04
0.53 Æ 0.79
0.54 Æ 0.11
0.43 Æ 0.22
0.69 Æ 0.06
0.9984
0.9992
0.9987
0.9995
0.09
0.08
0.14
0.05
a
b
Number of substituents involved.
Substituents range: p-Me–m-Cl.
of 0.77 identical with rsym for the symmetrical subseries.
The following simple additivity relationship against
ꢁꢀX ‡ ꢁꢀY instead of 2ꢁꢀX does not hold as a whole but
gives a widely spread pattern with branched correlations
for the respective Y subsets:
the Hammond–Leffler rate-equilibrium relationship (or
extended Brønsted relationship).10
This elegant conclusion, however, relies heavily upon
the validity of the Y–T correlations defined for the
respective Y subsets. The Y–T correlation given for
subset 3 (Y = p-MeO) should be that for the electron-
withdrawing range of substituents and the r value should
be almost meaningless. The situation should be the same
in the case of 4 (Y = p-Me). In the case of electron-
withdrawing Y subsets, on the other hand, the correlation
was assigned only for the electron-donating range, and
there is no evidence for the same r value applying to the
other range of substituents.
Whereas the symmetrical subseries where X = Y gives
an excellent linear correlation against 2ꢁꢀX over the whole
range of substituents, the simple additivity relationship in
Eqn. (6) against ꢁꢀX ‡ ꢁꢀY no longer holds and gives a
wide dispersion pattern as in Fig. 1 when ꢁꢀX are entirely
different from ꢁꢀY. This characteristic dispersion pattern
of the additivity relationship has been generally observed
for multiple substituent effects in typical a,a-diarylcar-
benium ion formation processes, and presumably a
‘concave plot’ where both the head and the tail are bent
back upwards from the reference line should be the best
description of the shape of the correlation inherent in the
substituent effect of the respective subsets.
The individual correlation of any Y subset appears to
be a non-linear (concave) correlation, which may be
delineated using the More O’Ferrall equation [Eqn. (4)].7
The tangent (r0)Y for the respective Y subset which has
essentially the same physical significance as the apparent
rY value in the Y–T correlation varies in the same way as
the latter: The (r0)Y becomes more negative as the Y
substituent becomes more electron attracting. The
variation of (r0)Y will be related to the Hammond shift
of the transition state if the variation can be ascribed to
the coordinate shift of the transition state.7,10
A positive (2m)Y coefficient in Eqn. (4) implies an
assignment of a ‘concave correlation’ for any Y subset:
the shape of the plot should be related to the anti-
Hammond shift of the transition state coordinate (or the
late transition state) for accelerating substrates. This
clearly conflicts with what has been deduced from the
behaviors of other selectivity indices. Most seriously, it
conflicts with the so-called saturation effect that would be
generally expected from the More O’Ferrall theory.7,10
log ꢀk=k0†
ˆ ꢀsymꢀꢁꢀX ‡ ꢁꢀY†
ꢀ6†
X;Y
While the limited substrates where the two substituents X
and Y are essentially kinetically equivalent are involved
in Eqn. (6), we find a significant deviation when ꢁꢀX is
entirely different from ꢁꢀY of the fixed substituent Y. As
seen in Fig. 1, all the Y subsets result in significant
concave correlations, each of which contacts with the
tangential correlation line defined by symmetrical
subseries 1 at the point X = Y. A non-linear correlation
analysis was carried out for respective Y subsets with the
More O’Ferrall equation [Eqn. (4)]7 in terms of the same
ꢁꢀ scale (at r = 0.77), and the results are summarized in
Table 3.
The tangent (r0)Y values are, to a good approximation,
proportional to the corresponding r values of the Y–T
correlations in Table 2, and both show the same
dependence upon Y substituents; the (r0)Y value
becomes more negative as the Y substituent becomes
more electron withdrawing. On the other hand, the (2m)Y
coefficient remains constant at 0.5 for Y substituents; the
coefficient with a constant value indicates the same shape
of curvature for all the Y subset correlations, while the
positive sign should constrain the shape of a significantly
bent-back curvature for all subsets as seen in Fig. 1.
DISCUSSION
The correlation results in Table 2 indicate that the
apparent rY values of the Y–T correlations for Y subsets
with variable X substituents change significantly depend-
ing upon fixed Y substituents, and that there is a
qualitative trend of a linear decrease in the r value as
the fixed substituent Y for the respective subsets becomes
more electron donating. The observed dependence of rY
values on the second (fixed) Y substituents appears to
accord with the changes caused by the early shift of the
transition-state coordinate which would be expected from
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 544–549

548
M. FUJIO ET AL.
Figure 3. Linear relationship between log ksolv for the
solvolysis of 1,1-diphenylethyl p-nitrobenzoates and the
Figure 2. Plots of log k/k0 for the solvolysis of 1,1-
diphenylethyl p-nitrobenzoates and logK/K0 values for the
corresponding carbocations against ꢁꢀX ‡ ꢁꢀY with r = 0.77;
open circle represent solvolyses and solid circles equilibria
corresponding log KR
‡
values; log (kXY/kHH)OPNB =
À(1.03 Æ 0.03)DpKR
‡
The characteristic dispersion of this non-additivity
relationship appears to be general in many solvolysis
processes of a,a-diarylcarbocation formation, among
which the reaction of particular importance in the present
study is the protonation equilibria of a,a-diarylethy-
lenes.12 Despite the wide dispersion pattern for the
respective Y subsets of the additivity correlation against
pKR , they all satisfy the rate–equilibrium relationship in
‡
Eqn. (7) with the same Brønsted coefficient a = 1.03; if
any linear substituent effect correlation holds for an
individual Y subset, Eqn. (8) should also be satisfied with
the same a coefficient for the rate–equilibrium system:
ꢀꢀk† ˆ ꢂꢀꢀt†
ꢀ8†
Y
Y
ꢁꢀX ‡ ꢁꢀY, we found that the scattered plots of the pKR
‡
values against ꢁꢀX ‡ ꢁꢀY of a,a-diarylethylenes, as a
whole, can be superimposed precisely upon the corre-
sponding plots of the non-additivity relationship of p-
nitrobenzoates as in Fig. 2. This finding naturally points
to the existence of a precise extended Brønsted relation-
ship:10
then,
log ꢀk=k0† ˆ ꢂ logꢀK=K0†
(8a)
Y
Y
The Brønsted relationship in Eqn. (8a) should include any
constituent Y subsets, regardless of whether the Ham-
mett-type correlations of the subsets are linear or not.
The constant a coefficient irrespective of the Y subsets
should suffice as direct convincing evidence for the
absence of coordinate shifts of transition states in this rate
process. Changes in (rk)Y with subsets should be
independent of coordinate shifts of transition states in
the present rate process. Whatever the cause of non-
linearity and non-additivity behaviors of any selectivity
parameters, (rk)Y, (2m)Y, (r0)Y, etc., in the present
solvolysis rate process, the constant a coefficient does not
allow them to be ascribed to the substituent-induced
coordinate shifts of the transition state.
‡
log ꢀkXY=kHH
†
ˆ Àꢀ1:03 Æ 0:03†ÁpKR
ꢀ7†
OPNB
which is demonstrated in Fig. 3 as a linear relationship
between log (kXY/kHH OPNB for the solvolysis and DpKR
)
‡
values with a constant slope. The exceptionally large
deviation of the (p-Me)2 substrate may presumably be
attributed to experimental error. The observed value of
the Brønsted coefficient a of close to unity may be
coincidental, since the solvents are different between the
solvolysis and the equilibrium.
While any Y subsets show different dependences upon
X substituents (Fig. 2) for either the solvolysis or the
For the hydration reaction of 1,1-diphenylethylenes
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 544–549

SOLVOLYSIS OF 1,1-DIPHENYLETHYL p-NITROBENZOATES
549
where the intermediate carbenium ion is identical with
that for the present solvolysis, we may expect a closely
similar pattern of the kinetic substituent effect, without
the effect associated with coordinate shifts of the
transition state. The same expectation may be extended
to the bromination of 1,1-diphenylethylenes, since a
similar characteristic dispersion pattern of the additivity
correlation was found for the bromination of diphenyl-
ethylenes. Nevertheless, Dubois and co-workers con-
cluded6 that the non-additivity in the bromination
reaction arose not only from changes in the stability of
the cationic intermediate but also significantly from
coordinate shifts of the transition state.1
The characteristic dispersion pattern of this non-
additivity relationship has been observed also in the a-
CF3-diarylmethyl system;11 the observed variation of the
r value within any given Y subset just displayed the
dependence of the selectivity (r) on the deviation from
the symmetrical propeller conformation of diaryl carbo-
cations (or of the corresponding transition states). Thus
the significant non-linearity and non-additivity were
concluded to be caused by a conformational change of
the transition state with varying substituents, and not
caused by coordinate shifts of the transition state.
dependence of the selectivity r and r parameters on
second substituents Y.
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1997; 70: 1403–1411; (b) Fujio M, Morimoto H, Kim HJ, Tsuno
Y. Bull. Chem. Soc. Jpn. 1997; 70: 3081–3090; (c) Fujio M, Kim
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Although are not prepared at this time to speculate
about the cause of significant non-linearity and non-
additivity, evidently the coordinate shift of the transition
state is not the main cause of the significant scattering
behavior in this system. The non-linear Y–T correlations
in the present system is most probably caused by varying
conformations of the transition state. Further studies are
in progress in order to clarify the conformational
12. Goethals G, Membrey F, Ancian B, Doucet JP. J. Org. Chem.
1978; 43: 4944–4947.
13. Brown HC, Ravindranathan M, Peters EN. J. Org. Chem. 1977; 42:
1073–1076.
Copyright  2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 544–549