Non-linearity and non-additivity of substituent effects in solvolysis of 1,1-diphenylethyl p-nitrobenzoates

Article abstract of DOI:10.1246/bcsj.75.1371

The solvolysis rates of 1,1-diarylethyl p-nitrobenzoates and chlorides Y-Ar(X-Ar)CMe-L_G (L_G = OPNB, Cl) have been determined conductimetrically at 25°C in 80% (v/v) aqueous acetone. A linear Yukawa-Tsuno (Y-T) correlation was found for the symmetrical subseries (X = Y), showing a precise additivity relationship for the whole substituent range with ρ_sym = -3.78 and r_sym = 0.77. The unsymmetrical subsets (X ≠ Y) gave statistically less reliable Y-T correlations, the apparent p value decreasing significantly when the fixed substituent Y becomes more electron-donating, which is in line with expectations from the Reactivity-Selectivity Relationship. In the whole dispersion pattern, both strong p-π-donor and electron-withdrawing substituents in any fixed-Y subsets exhibit significant rate-enhancement deviations from the points of X = Y on the reference ρ_sym line, which suggests an anti-Hammond shift of the transition state. However, there was a precise Extended Bronsted Linear Relationship between the pK_R+ values for the hydration of 1,1-diarylethylenes and the rates of solvolysis of the p-nitrobenzoates with a slope of unity (α = 1.03). This is direct, convincing evidence that there is no significant shift of the transition-state coordinate over the whole range of substituent change.

Full text of DOI:10.1246/bcsj.75.1371

c. Jpn.
© 2002 The Chemical Society of Japan
Bull. Chem. Soc. Jpn., 75, 1371–1379 (2002) 1371
e Chemical
ciety of Ja-
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Non-Linearity and Non-Additivity of Substituent Effects in Solvolysis of
1,1-Diphenylethyl p-Nitrobenzoates
Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates
M. K. Uddin et al.
Md. Khabir Uddin, Mizue Fujio,* Hyun-Joong Kim, Zvi Rappoport, and Yuho Tsuno
02
71
79
SJA8
09-2673
457
Institute for Fundamental Research of Organic Chemistry, Kyushu University, Higashi-ku, Fukuoka, 812-8581
(Received December 25, 2001)
The solvolysis rates of 1,1-diarylethyl p-nitrobenzoates and chlorides Y-Ar(X-Ar)CMe-LG (LG = OPNB, Cl) have
been determined conductimetrically at 25 °C in 80% (v/v) aqueous acetone. A linear Yukawa–Tsuno (Y–T) correlation
was found for the symmetrical subseries (X = Y), showing a precise additivity relationship for the whole substituent
range with ρsym = −3.78 and rsym = 0.77. The unsymmetrical subsets (X ≠ Y) gave statistically less reliable Y–T corre-
lations, the apparent ρ value decreasing significantly when the fixed substituent Y becomes more electron-donating,
which is in line with expectations from the Reactivity-Selectivity Relationship. In the whole dispersion pattern, both
strong p-π-donor and electron-withdrawing substituents in any fixed-Y subsets exhibit significant rate-enhancement de-
viations from the points of X = Y on the reference ρsym line, which suggests an anti-Hammond shift of the transition
state. However, there was a precise Extended Brønsted Linear Relationship between the pKR+ values for the hydration of
1,1-diarylethylenes and the rates of solvolysis of the p-nitrobenzoates with a slope of unity (α = 1.03). This is direct,
convincing evidence that there is no significant shift of the transition-state coordinate over the whole range of substituent
change.
01
02
.1
3.2
The Yukawa–Tsuno (Y–T) equation 11 has been successful-
ly applied to the Structure–Reactivity Relationship of a variety
of benzylic carbocation systems2,3 where direct π-delocaliza-
tion of the cationic charge into the ring is possible.
Here (ρX)H, or simply ρH, is the ρX value for the monosubstitut-
ed (Y = H) subset, and q is the coefficient for the Y-dependen-
cy of ρX or (ρX)Y. A general relationship to deal with multiple
substituent effects (Eq. 3) was proposed.5,7–9 It describes the
non-additive effect in terms of different reaction constants for
X and Y substituents, presented in the form of Eq. 3a:
log (k / k0 ) = ρ(σ 0 + r∆σR+)
(1)
Here σo is the normal substituent constant and
+ is the res-
∆σR
(3)
log (kXY / kHH ) = ρH (σX + σY ) + qσXqσY
= ρHσY + (ρH + qσY )σX
onance substituent constant measuring the donor capability of
π-electron donating substituents.1b The parameter r is a mea-
sure of the resonance demand of the given reaction, i.e., the de-
gree of resonance interaction between the aryl group and the
reaction site in the transition state.1–3 Thus the Y–T equation
(3a)
In Eq. 3a the first term ρ Y is a constant for a fixed-Y-subset,
H σ
i.e., Eq. 3a is reduced to Eq. 2. The non-additivity is therefore
taken into account by the last term in Eq. 3, which involves the
coefficient q, described as the interaction constant.7,8a,9 How-
ever, the analyses very often have shortcomings due to the sig-
nificant non-linearity of substituent correlations for any fixed-
Y subsets.
allows one to define the intrinsic
scale inherent in the sys-
σ
tem, and to derive the appropriate ρX as the reference capable
of detecting non-linearity and non-additivity of substituent ef-
fects.
Substituent effects on rates4a and equilibria5 of the heterolyt-
ic formation of benzhydryl and trityl cations6 were analyzed in
terms of a selectivity relationship,7 or of a coordinate-shift of
the transition state.7,8a However, the non-linearity of substitu-
ent effects invalidated the conclusion of such solvolysis. Our
argument against this conclusion for more extensive data sets4c
was presented in our review.3
The non-linearity in the correlations for the fixed-Y-subsets
has been dealt with by the More O’Ferrall equation 4,10
log (kX / kH )Y = (ρo )YσX + (2m)Y (σX )2
(4)
where (ρo)Y is the tangential ρ of the fixed-Y-subset at X = H,
and the coefficient (2m)Y is a susceptibility parameter describ-
ing the degree of curvature of correlations of a given Y-subset.
The selectivity parameter ρ for a reaction series shows a
sensitive change when the reactivities (or the stabilities of tran-
sition states) of the parent substrates change. This behavior is
often referred to as adherence to the Reactivity–Selectivity Re-
lationship (RSR),7,8b,11,12 in the sense that there is an inverse re-
lationship between reactivity and selectivity insofar as both are
The earlier data for the solvolysis of benzhydryl
chlorides4a,b indicated that the kinetic effects of multiple sub-
stituent change on different aromatic rings were not additive.
Nishida4a related the reaction constant (ρX)Y, or simply ρY, for
the effect of substituents X in the fixed Y subset to the Y of Y
by Eq. 2.
σ
(ρX )Y = (ρX )H + qσY
(2)

1372 Bull. Chem. Soc. Jpn., 75, No. 6 (2002)
Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates
out extensive studies on its solvolysis. The cation-forming sol-
volysis of this system is mechanistically connected to the re-
versible hydration9 of 1,1-diphenylethylenes which proceeds
via the same intermediate (Scheme 1). Both transition states
should reflect any perturbation of the common intermediate,
and the comparative studies will provide important informa-
tion concerning the behavior of the transition states causing
non-linearity and non-additivity.
In the first paper of this series, we have dealt with the sub-
stituent effects on the solvolysis of the parent, symmetrically
disubstituted system 1 (X = Y) and monosubstituted 2 (Y =
H) subsets, in this α,α-diaryl carbocation-forming reaction.
We have attempted now to gain new insight into the causes of
non-linearity and non-additivity behaviors through ordinary
correlation analyses by using Eqs. 2–5.
Results
Scheme 1.
Solvolysis Rates. The rates of solvolysis of the p-ni-
trobenzoates, 1–4 (Scheme 1) and the corresponding chlorides
were determined conductimetrically at 25 °C in 80% (v/v)
aqueous acetone (80A) at initial concentrations of 10−5 – 10−4
mol dm−3 of the substrates. The reactions displayed accurate
first-order kinetics over 2.5 half-lives and the reproducibility of
the rate constants (kOPNB and kCl) was estimated to be within
1%. The slow solvolyzing derivatives were measured at 45
°C and the data were extrapolated to give the rates at 25 °C us-
ing the linear logarithmic rate relation between 25 °C and 45
°C; log k80A,25 °C = −0.906 + 1.059 log k80A,45 °C. The kOPNB
values were also measured in the faster solvolyzing solvent,
50% (v/v) aqueous acetone (50A) and converted to the rates in
related to shifts in the transition state position.11 Dubois and
co-workers carried out detailed analyses along similar lines for
the bromination of disubstituted X-Ar(Y-Ar)CwCH2 1,1-di-
arylethylenes, demonstrating that the (ρX)Y values significantly
change linearly with σ+ of Y.13 Here again, any regression
analysis displays severe non-linearity of substituent effect cor-
relations of the respective fixed-Y subsets. Nevertheless, the
authors concluded that the selectivities in the electrophilic ad-
ditions are not directly related to the reactivities but to the po-
sition of the transition state.13 They stated that bromination is
a particularly attractive reaction for studying in detail the ori-
gin of Reactivity–Selectivity effects, since it is established that
substituent effects arise both from changes in the stability of
the cationic intermediate and from transition-state shifts,7,8 in
agreement with the RSR,12,14 the Hammond postulate12a and
Marcus effects.15
80% (v/v) aqueous acetone at 25 °C by using log k80A,25 °C
=
−1.037 + 1.142 log k50A,25 °C. The kCl values were obtained for
the highly deactivated derivatives and were converted to kOPNB
by the kOPNB/kCl ratio of 1.03×10−5 derived from the average
rate ratio for 1,1-diphenylethyl derivatives (1(H) and 1(p-Cl)).
Brown’s rate data for 1(H), 2(p-CF3), and 2(3,5-(CF3)2) agreed
with ours within the experimental uncertainty.19 The rate of
the p-MeO-substituted p-nitrobenzoate 2 (p-MeO) reported by
Brown et al. was estimated from the rate of the benzoate using
a ratio of 20.8, which is significantly different from our present
solvolysis data.
The progress of the reaction at this transition state is usually
obtained from the Brønsted α coefficient (Eq. 5) or from other
rate-equilibrium relationships12
log (kXY/kHH) = α(∆pKR+)
(5)
that compare substituent effects on kinetics and thermodynam-
ics.
The solvolysis rates and the activation parameters are sum-
marized in Tables 1–4 together with Brown’s data.
We have recently16–18 investigated the non-linearity and non-
additivity of the substituent effects on the solvolyses of the α-
CF3-diarylmethyl system. Whereas the symmetrical subseries
(X = Y) gave an excellent linearY–T correlation for the whole
substituent range covering a reactivity change of 1012, a precise
simple additivity relationship exists only for the symmetrical
subseries; it generally does not apply for any unsymmetrical
subset (X ≠ Y). These nonlinear and non-additive substituent
effects were ascribed to a substituent-induced conformation
change of the two aromatic rings.
Correlation Analysis of Substituent Effects. The corre-
lation analysis of substituent effects has been routinely carried
out based on the Y–T equation 1, for the symmetrically disub-
stituted 1, monosubstituted 2, and some unsymmetrically dis-
ubstituted 1,1-diphenylethyl p-nitrobenzoates (3 and 4). The
data are summarized in Table 5.
The substituent effects on the solvolysis of the symmetrical
subseries 1 (X = Y) gave an excellent linear Y–T correlation
(Table 5, entry 1 and Fig. 1) for the whole range of substituents
with ρ = −3.78 and r = 0.77, with no noticeable deviation. In
contrast, the correlation of the log (k/k0)OPNB values for the
Similar effects should also be operative in the present α-Me-
system, so that we should take into account here the non-addi-
tivity effect caused by both a substituent-induced conforma-
tional change and by coordinate-shifts of the transition state.
Accordingly, we had focused on exploring the scope of non-
linearity and non-additivity behavior in the substituent effects
on the solvolysis of the 1,1-diphenylethyl system, and carried
whole set against
+
with the same r value of 0.77 as
σY
σX
that for subseries 1 is poor, as demonstrated in Fig. 2. The
simple additivity relationship (Eq. 6) against Y instead
+
σX
σ
of 2 X, gives a widely spread pattern for the whole set with
σ
partial correlations for different fixed-Y-subsets:

M. K. Uddin et al.
Bull. Chem. Soc. Jpn., 75, No. 6 (2002) 1373
Table 1. Rates of Solvolysis of 1-Aryl-1-phenylethyl Chlorides (Cl) and p-Nitrobenzoates (OPNB) 2 in 80%
Aqueous Acetone
X
a)
a)
kCl×105/s−1
45 °C 25 °C
kOPNB×105/s−1
45 °C 25 °C
692
90.5
∆H‡25 °C
∆S‡25 °C
kcal mol−1
22.0
eu
0.6
1.4
−1.9
−3.3
−2.6
−2.7
2.0
p-MeO
p-MeS
p-MeO-m-Cl
p-Me
63.0
7.00
23.5
23.1
23.1
23.5
23.6
25.5
25.8
24.8
32.3
2.61
15.87
12.94
10.12
5.66
1.28
1.00
0.775
0.354
p-Et
p-t-Bu
p-MeS-m-Cl
m-Me
2.81
0.170
−1.7
−2.8
H
8440
1.52
0.103
7.85×10−2 b)
2.48×10−2 c)
3.11×10−3 d)
1.42×10−3 d)
8.61×10−4 d)
8.95×10−4 b)
1.47×10−4 e)
2.88×10−5 e)
4.31×10−5 b)
p-Cl
0.415
m-Cl
m-CF3
p-CF3
3,5-Cl2
3,5-(CF3)2
132
26.1
14.25
2.79
20.4f)
22.4f)
−7.7f)
−4.6f)
a) 1 cal = 4.184 J. b) Ref. 19. c) Estimated from log k80A,25°C = −0.906 + 1.059 log k80A,45 °C. d) Estimated
from log k80A,25 °C = −1.037 + 1.142 log k50A,25 °C. e) Estimated from chloride reactivities based on the aver-
age ratio of p-nitrobenzoate/chloride = 1.034×10−5 for 1(X = H and X = p-Cl). f) Activation parameters
are those for solvolysis of 1,1-diphenylethyl chlorides.
Table 2. Rates of Solvolysis of 1,1-Bis(substituted phenyl)ethyl Chlorides (Cl) and p-Nitrobenzoates (OPNB) 1 in
80% Aqueous Acetone
a)
a)
kCl×105/s−1
45 °C 25 °C
kOPNB×105/s−1
45 °C 25 °C
1167 111.3
85.5 7.39
9.81
∆H‡25 °C
∆S‡25 °C
X
kcal mol−1
21.6
eu
0.3
−2.0
−4.9
0.7
p-MeS
p-Me
p-MeS-m-Cl
m-Me
p-Cl
p-Br
m-Cl
m-CF3
22.5
23.0
25.2
0.808
4.53
0.294
625
469
9.50×10−2
5.28×10−3 b)
4.85×10−3 c)
6.50×10−5 c)
1.23×10−5 c)
64.4
12.45
6.29
1.187
21.3d)
21.6d)
−6.2d)
−8.8d)
a) See footnote a in Table 1. b) See footnote c in Table 1. c) See footnote e in Table 1. d) See footnote f in Table
1.
Table 3. Rates of Solvolysis of Unsymmetrical 1,1-Diphenylethyl Chlorides (Cl) and p-Nitrobenzoates (OPNB),
3 (Y = p-MeO) and 4 (Y = p-Me), in 80% Aqueous Acetone
a)
a)
kCl×105/s−1
45 °C 25 °C
kOPNB×105/s−1
45 °C 25 °C
∆H‡25 °C
∆S‡25 °C
Y
X
kcal mol−1
22.5
eu
−2.0
2.3
p-MeO
p-Br
305
26.4
9.20
m-Cl
120.2
23.6
m-CF3
6.38
3,5-Cl2
3,5-(CF3)2
m-Cl
3,5-Cl2
3,5-(CF3)2
22.1
12.46
1.22
1.77
0.85
23.2
24.7
−2.4
1.0
p-Me
7.76×10−2 b)
2.66×10−3 c)
7.93×10−4 c)
257
76.7
690
20.1d)
−5.3d)
a) See footnote a in Table 1. b) See footnote c in Table 1. c) See footnote e in Table 1. d) See footnote f in Table 1.

1374 Bull. Chem. Soc. Jpn., 75, No. 6 (2002)
Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates
Table 4. Rates of Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates (OPNB) in 50%
Aqueous Acetone
a)
a)
kOPNB×105/s−1
45 °C 25 °C
∆H‡25 °C
∆S‡25 °C
X
Y
kcal mol−1
20.4
eu
H
p-Me
p-Et
386
374
280
41.7
34.8
26.6
−5.6
−1.3
−2.6
−2.2
−1.2
−5.1
−3.8
21.8
21.6
22.4
23.0
22.4
24.1
p-t-Bu
m-Me
H
86.6
7.56
55.4
21.1
4.51
1.84
p-Cl
m-Cl
m-CF3
p-CF3
p-Cl
2.96
0.217
0.109b)
0.0657b)
0.703
3.36
1.608
0.999
9.92
37.1
4.70
p-Cl
24.4
22.1
24.2
−0.4
−5.0
−2.5
m-Cl
p-Me
m-Me
0.340
a) See footnote a in Table 1. b) Estimated from kOPNB at 45 °C from log k50A,25 °C
−0.839 + 1.069 log k50A,45 °C
=
.
Table 5. Correlation Analysis of Substituent Effects Using the Yukawa–Tsuno Equation 1
No.
Systems
1 (Y = X)
Substituents (X) range
na)
ρ
r
R
SD
1
2
3
4
5
6
7
8
9
p-MeS –m-CF3
m-correlation
whole range
9
4
14
14
8
6
6
10
9
11
−3.78 0.09
−3.93 0.05
−3.68 0.08
−3.83 0.06
−1.97 0.12
−1.91 0.10
−3.23 0.18
−4.61 0.08
−4.78 0.26
−5.04 0.18
0.77 0.04
0.9990
0.9999
0.9988
0.9990
0.9978
0.9967
0.9985
0.9995
0.9976
0.9984
0.12
0.04
0.10
0.09
0.10
0.07
0.15
0.05
0.11
0.09
2 (Y = H)
1 + 2
3 (Y = p-MeO)
0.88 0.04
0.76 0.03
equivalent classb)
whole rangec,d)
H – 3,5-(CF3)2
whole ranged)
p-MeO – m-Cl
p-MeO – H
(1.33 0.17)e)
4 (Y = p-Me)
(Y = m-Cl)f)
(0.99 0.15)e)
0.93 0.03
1.09 0.09
1.14 0.06
(Y = 3,5-Cl2)f)
(Y = 3,5-(CF3)2)f)
10
p-MeO – H
a) Number of substituents involved. b) Equivalent class comprises all X in the subseries 1 (X = Y), and p-Et, p-t-Bu,
m-Me, p-Cl, and m-Cl for 2 (Y = H). c) The rate k(p-MeO)2 is estimated by Y–T Eq. for 1 (X = Y) subseries (entry 1). d)
The rate k(p-MeO,p-Me) is estimated by Eq. 4 for 3 (Y = p-MeO) (Table 6, entry 4). e) The r value should be statistically
indefinite. f) Unpublished.
log (k/k0)X,Y = ρsym
(
+
)
σY
(6)
duced (ρX)Y value was obtained, though the r value might not
be statistically very reliable (Table 5, entry 5). A similar corre-
lation with a reduced (ρX)Y was obtained also for 4 (Y = p-
Me) (Table 5, entry 7). In contrast, each of those subsets of
variable X with fixed strong electron-withdrawing Y (Y = m-
Cl, 3,5-Cl2, and 3,5-(CF3)2), correlates linearly by Eq. 1 with
significantly higher (ρX)Y and r values than 1 (Table 5, entries
8–10), when the regression analysis includes additional points
from unpublished data.20
While the Y–T correlation may be sometimes statistically a
little uncertain or nonlinear, evidently the apparent (ρX)Y value
for Y–T correlations of variable X-substituents changes signif-
icantly for a fixed Y-substituent. A qualitative trend of inverse
linear change of (ρX)Y, which tends to be more negative as Y
becomes more electron-withdrawing, is apparent (Table 5).
These results suggest that different Y–T correlations (Eq. 3a)
with different r values for Y- and X-substituted aryls are re-
quired for dealing with the non-additivity behavior in the
present reaction.
σX
While Eq. 6 holds precisely (with ρsym = −3.83, rsym = 0.76)
for the closely limited substrates (Table 5, entry 4) where the
two aryl-substituents X andY are essentially kinetically equiv-
alent, there is a significant deviation from additivity when
σX
is different from Y of the fixed-Y, thus indicating the impor-
σ
σX σ
tance of the q
Y term in Eq. 3. In a typical case, the wide-
range additivity correlation cannot include the plots of the
monosubstituted subset 2; both strong p-π-donor and electron-
withdrawing substituents exhibit significant rate-enhancement
deviations (Fig. 2). The resulting concave plot, whose two ex-
tremes are bent back upward from the reference line, appears
to be typical of any subset with a variable X- and a fixedY-sub-
stituent in the α,α-diaryl system.3
For the monosubstituted subset 2, however, a nearly precise
Y–T correlation is obtained with a slightly lower (ρX)Y value
of (−3.68) and a higher r (0.88) than 1 (Table 5, entry 3 and
Fig. 3). For the 3 (Y = p-MeO) subset where log kX for X =
p-MeO was estimated from the Y–T correlation for subseries 1
(Table 5, entry 1 and Fig. 1), a good Y–T correlation with a re-
All the fixed-Y subsets give significantly concave correla-
tions, each of which contacts the tangential correlation line de-

M. K. Uddin et al.
Bull. Chem. Soc. Jpn., 75, No. 6 (2002) 1375
Fig. 1. Y–T plot for the solvolysis of symmetrically disubsti-
tuted 1,1-diphenylethyl p-nitrobenzoates 1(X = Y) in 80%
aqueous acetone at 25 °C: Closed circles for 2σo, open cir-
cles for 2σ+, and open squares for 2σ , respectively.
Fig. 2. Plots of log (kXY/kHH) for the solvolysis of 1,1-di-
phenylethyl p-nitrobenzoates against σX + σY with rsym
= 0.77.
fined by symmetrical subseries 1 at the point X = Y (Fig. 2).
A nonlinear correlation analysis has been carried out for the re-
spective Y-subsets using the More O’Ferrall equation (Eq. 4).
The curved correlations for 2 (Y = H), 3 (Y = p-MeO), 4 (Y
= p-Me), and when Y = m-Cl, were treated by Eq. 4 using the
lowed to shift to the point of contact (X = Y), all the correla-
tions for the Y-subsets should have an identical shape, with
(ρo)Y = ρsym
.
Discussion
same
scale (at rsym = 0.77) as was used for the symmetri-
The correlation results in Table 5 indicate that the apparent
(ρX)Y values of the Y–T correlations for Y-subsets with vari-
able X-substituents change significantly with Y, in an approxi-
mate trend of a linear decrease of (ρX)Y as Y for the respective
subsets becomes more electron-donating. The observed de-
pendence of ρX values upon the fixed-Y-substituents appears to
be in accord with the changes caused for an early transition-
state expected from the Hammond–Leffler rate-equilibrium re-
lationship (or extended Brønsted relationship).12
This elegant conclusion, however, relies heavily upon the
validity of the Y–T correlations for the respective Y-subsets.
While subsets 3 (Y = p-MeO) and 4 (Y = p-Me) gave Y–T
correlations of excellent precision level, the apparent (ρX)Y val-
ues were based only on the electron-withdrawing range of sub-
stituents and their r-values which are based on a single p-MeO
group are statistically indefinite. Analogously, for the elec-
tron-withdrawing Y-subsets, the correlation encompasses the
electron-donating range, and there is no evidence that the same
(ρX)Y value applies to the range of other substituents. It is
noteworthy that analogous results were found for the bromina-
tion of 1,1-diarylethylenes.3,13 The conclusion deduced above
simply arises from the fact that the Y–T equation gives an ex-
cellent linear correlation for subset 2 (Fig. 3). The partial cor-
σX
cal subseries 1. Similarly treated were the nonlinear correla-
tions for other subsets, as summarized in Table 6.
In Table 6, the tangent (ρo)Y values change widely from sub-
set to subset. They are roughly of the same magnitude, or to a
good approximation proportional to the (ρX)Y values for the
corresponding Y–T correlations in Table 5. Most important,
both show the same dependence upon Y; the more electron-
withdrawing Y is, the more negative the (ρo)Y value is. The
(2m)Y coefficient remains constant at 0.5 for the subsets of dif-
ferent fixed-Y-substituent, indicating the same degree of curva-
ture and the same shape of bent-back curvature for all subsets,
as seen in Fig. 2.
The concave correlation line for these fixed-Y-subsets and
the linear correlation for the symmetrical subseries touch at the
point X = Y when the fixed-Y is in the middle of substituent
range. In other cases, the correlation curve merges with the
line of the symmetrical subseries' correlation at the point X =
Y when Y is located at the ends of the substituent range stud-
ied. The tangent ρ value at the contact point X = Y of any Y
subsets should be nearly the same as the ρsym value for the
symmetrical subseries. Thus, provided that the zero-point (X
= H) in the
scale of any Y-subsets’ correlation may be al-
σX

1376 Bull. Chem. Soc. Jpn., 75, No. 6 (2002)
Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates
Fig. 3. Y–T plot for the solvolysis of monosubstituted 1,1-
diphenylethyl p-nitrobenzoates 2 (Y = H): Closed circles
for σo, open circles for σ+, and open squares for σ , re-
spectively.
Fig. 4. Plots of log (kXY/kHH) for the solvolysis of 1,1-diphen-
ylethyl p-nitrobenzoates and log (KXY/KHH) values against
σX + σY with r = 0.77: Open circles for solvolyses and
solid circles for equilibria.
relations for (a) strong π-donor substituents and for (b) elec-
tron-withdrawing substituents, are clearly different, indicating
a non-linearity of the Y–T correlation for this subset.
back upward from the reference line, is the best description of
the shape of the correlation for the substituent-effect of the re-
spective subsets. The individual correlation of any Y subset is
concave and may be treated by the More O’Ferrall equation
(Eq. 4). The tangent (ρo)Y value for the respective fixed Y-sub-
set which has essentially the same physical meaning as the ap-
parent (ρX)Y value in the Y–T correlation, varies similarly to
the latter: It becomes more negative when Y becomes more
electron-attracting. This variation can be referred to as a Ham-
mond shift of the transition state, provided that it is due to the
coordinate-shift of the transition state.11,12
The positive (2m)Y coefficient in Eq. 4 implies an assign-
ment of a “concave plot” for any Y-subset: The shape of the
plot should be related to the anti-Hammond shift of the transi-
tion state coordinate (or the late transition state) for rate-accel-
erating substrates. This conflicts with deductions from the be-
havior of other selectivity indices, especially with the so-called
saturation effect that is expected from the More O’Ferrall theo-
ry.5,10,11 This, in turn, leads to the conclusion that the signifi-
It is therefore remarkable that the symmetrical subseries
1(X = Y) gives an excellent linear correlation against 2
σX
over the whole-range of substituents. However, the simple ad-
ditivity relationship, Eq. 6, against Y holds only for a
+
σX
severely limited range, but it gives a wide dispersion pattern as
in Fig. 2 when differs significantly from Y for the fixed-
σ
σX
σ
substituent Y. This characteristic dispersion pattern of the ad-
ditivity relationship has been generally observed for multi-sub-
stituent effects in many typical α,α-diaryl carbocation forming
processes,3 such as the solvolysis of ArArꢀC(CF3)X system,16–18
the ionization equilibria (pKR+) and nucleophile-recombination
reactions of ArArꢀAr C+,6 the hydrolysis and alcoholysis of
the diarylmethyl systems,4,5 and the hydration9 and
bromination13 of ArArꢀCwCH2.7,8
From analogy with the behavior of closely related systems,
a “concave plot,” where both extreme ends of the plot are bent
Table 6. Analysis of Substituent Effects by Eq. 4
No.
System
Y
na)
(ρo)Y
(2m)Y
R
SD
1
2
3
4
m-Cl
H
p-Me
p-MeO
10
14
6
−5.03 0.30
−4.04 0.05
−3.58 0.13
−2.58 0.04
0.50 0.68
0.51 0.09
0.40 0.21
0.67 0.06
0.9919
0.9994
0.9988
0.9996
0.21
0.07
0.14
0.04
2
4
3
8
a) Number of substituents involved.

M. K. Uddin et al.
Bull. Chem. Soc. Jpn., 75, No. 6 (2002) 1377
different solvents were used for the solvolysis and the equilib-
ria measurements. We emphasize that, while any Y-subset
shows a different dependence upon the X-substituents in either
the solvolysis or the pKR+, they all satisfy the rate-equilibrium
relationship (7) with a single α; i. e., both the susceptibility
and the degree of curvature of the nonlinear correlation of any
Y-subset are the same for the rates and the equilibria. Hence,
the Brønsted relationship (8a),
log (k/ko)Y = α log (K/Ko)Y
(8)
should embrace any Y subsets, regardless of whether their
Hammett-type correlations are linear or not. If a linear corre-
lation holds for any individual Y-subset, Eq. 8a should also be
satisfied with the same α-coefficient for the rate-equilibrium
system of the subsets.
(ρk)Y = α(ρt)Y
(8a)
Whatever the reason of the non-linearity and non-additivity
behavior of any selectivity parameter, such as (ρk)Y, (2m)Y, and
(ρo)Y, the constant α coefficient serves as convincing evidence
for the absence of a coordinate-shift of the transition state in
this rate process. The changes in (ρk)Y with the subsets is inde-
pendent of coordinate-shifts of the transition state in the rate
process studied.
For the hydration of 1,1-diarylethylenes where the interme-
diate carbenium ion is identical with that for the present sol-
volysis, we expect a close pattern of the kinetic substituent ef-
fect, without the effect associated with coordinate-shifts of the
transition state. The same expectation may be extended to the
bromination of 1,1-diarylethylenes, for which a quite similar
dispersion pattern to the additivity correlation in Fig. 2 was
Fig. 5. A linear relationship between log ksolv for the solvoly-
sis of 1,1-diphenylethyl p-nitrobenzoates and the corre-
sponding log KR+ values; log (kXY/kHH
0.03) ∆pKR+.
)
= −(1.03
OPNB
cant non-linearity observed in correlations of the Y-subsets
does not arise from the coordinate-shift of transition state. As
the More O’Ferrall coefficient (2m)Y remains approximately
constant irrespective of the Y subset, the deviation from the
linear correlation remains the same, implying no change in the
position of the transition state.
This complicated Substituent–Reactivity Relationship is in-
compatible with the expectation from the RSR and the details
are also incompatible with the conventional interpretation of a
coordinate-shift of the transition state as a single effect.
The characteristic dispersion of this non-additivity relation-
ship appears to be general in many α,α-diaryl carbenium ion-
forming processes. Among them, highly relevant for the
present study is the protonation equilibria of 1,1-diarylethyl-
enes. Despite the extensive dispersion pattern with branches
found, although the susceptibility parameters, e.g., ρsym
=
−3.43 and rsym = 0.56 for the symmetrical olefins (X = Y),
are slightly lower than those of the solvolysis. So far a great
importance was attached only to the favorable dependence of
the apparent ρX values on the fixed Y-substituents. Dubois and
co-workers concluded therefrom7 that the non-additivity in the
bromination reaction arose not only from changes in the stabil-
ity of the cationic intermediate but also from a significant coor-
dinate-shift of the transition state, in contrast with our conclu-
sion. Further comparative study of both reactions is required
to clarify the major cause of this characteristic non-additivity
pattern.
The characteristic dispersion pattern of the non-additivity
relationship has been observed also for the α-CF3-diarylmethyl
system;16–18 the observed variation of the selectivity ρX within
any given Y-subset displayed a dependence of ρX upon the ex-
tent of deviation from the symmetrical propeller conformation
of the aryl groups in the α,α-diaryl carbocations (or in the cor-
responding transition states). Thus the significant non-lineari-
ty and non-additivity observed in the α-CF3 system were as-
cribed to a substituent-dependent conformational change rath-
er than to a coordinate-shift of the transition state.
for respective Y-subsets of the correlations against
+
,
σY
σX
we have found that these plots of the literature pKR+ values
against for 1,1-diarylethylenes, can be surprisingly
+
σX
σY
precisely superimposed upon the non-additivity plot of the sol-
volysis of p-nitrobenzoates (OPNB) in Fig. 4. This finding is
equivalent to a precise extended Brønsted relationship (7):12
log (kXY/kHH OPNB
)
= −(1.03 0.03)∆pKR
+
(7)
which is demonstrated in Fig. 5 as a linear relationship with a
single slope between log (kXY/kHH OPNB for the solvolysis and
∆pKR+ values. We hesitate to ascribe mechanistic significance
to the derived value of Brønsted α coefficient of 1.03, since
Although we presently prefer not to speculate on the reason
for the significant non-linearity and non-additivity, the nonlin-
ear Y–T correlations in the 1,1-diphenylethyl system may also
result from a substituent-dependent varying conformation of
)

1378 Bull. Chem. Soc. Jpn., 75, No. 6 (2002)
Solvolysis of 1,1-Diphenylethyl p-Nitrobenzoates
Table 7. Physical and Analytical Data of 1,1-Diarylethyl Alcohols and p-Nitrobenzoates
Substituents
Mp
°C
Carbon/%
Hydrogen/%
Nitrogen/%
X
Y
Found
Calcd
Found
Calcd
Found
Calcd
Alcohol
p-MeO
H
H
H
p-MeS
p-Me
H
H
H
H
m-Me
H
H
H
H
H
p-Cl
H
Liq.
Liq.
78.40
68.49
73.66
65.67
84.49
84.63
84.61
84.95
64.65
84.50
84.87
84.73
72.39
67.66
72.32
63.18
63.30
57.52
73.20
64.38
58.63
68.62
61.02
78.92
68.57
73.73
66.16
84.91
84.87
84.91
84.99
64.62
84.91
84.87
84.81
72.26
67.66
72.26
62.94
62.94
57.49
73.02
64.07
58.63
68.57
60.62
7.11
5.93
6.61
6.14
7.48
7.57
8.23
8.65
5.33
7.94
7.62
7.10
5.65
4.94
5.68
4.63
4.70
3.70
6.23
5.18
4.05
5.79
4.80
7.06
5.75
6.60
6.25
8.02
7.60
8.02
8.72
5.42
8.02
7.60
7.12
5.63
4.92
5.63
4.53
4.53
3.62
6.13
5.02
4.05
5.75
4.75
p-MeO-m-Cl
p-MeS
p-MeS
p-Me
p-Me
p-Et
p-t-Bu
p-MeS-m-Cl
m-Me
m-Me
H
m-Cl
m-CF3
p-Cl
Decompa)
107–108
Liq.
Liq.
Liq.
Liq.
Liq.
Liq.
81.0
Liq.
Liq.
Liq.
Liq.
Liq.
Liq.
Liq.
Liq.
101
Liq.
49
p-Cl
3,5-Cl2
3,5-(CF3)2
p-Me
H
m-Cl
3,5-Cl2
3,5-(CF3)2
m-Cl
3,5-Cl2
p-MeO
p-Nitrobenzoates
H
p-Cl
m-Cl
m-CF3
p-CF3
H
H
H
H
H
135.0decompb)
72.53
66.01
64.80
63.64
63.72
72.61
66.06
66.06
63.62
63.62
4.97
4.33
4.19
3.91
3.90
4.93
4.22
4.22
3.88
3.88
4.03
3.62
4.05
3.32
3.47
4.03
3.67
3.67
3.37
3.37
115
118
95
122c)
a) Decomp at temp above 35 °C. b) Lit.19 mp 135 °C decomp. c) Lit.19 mp 121.5–122 °C.
1,1-Bis(p-methylphenyl)ethyl Alcohol. To magnesium turn-
ings (1.74 g, 71.5 mmol) under nitrogen atmosphere, p-bromotol-
uene (11.12 g, 65.0 mmol) in 30 mL dry ether was added dropwise
at room temperature, and the mixture was stirred for 3 h. A solu-
tion of ethyl acetate (2.64 g, 30 mmol) in 30 mL dry ether was
slowly added to the Grignard reagent solution and the mixture was
stirred for an additional 3 h at room temperature. To the ice-bath
cooled reaction mixture, aqueous NH4Cl (3.38 g, 63.2 mmol) was
added dropwise over 20 min and then the mixture was extracted
with ether. The extract was washed with aq NaCl solution and
dried over anhydrous MgSO4. After evaporation of the solvent,
the residue (5.90 g) was flash chromatographed on silica gel 60
(230–400 mesh, Merck) to give the alcohol as a colorless liquid
(1.84 g, 26% yield). Other bis-substituted alcohols were synthe-
sized similarly.
the transition state. In order to investigate this effect on the se-
lectivity parameters ρX and r on the fixed-substituents Y, we
have extended our investigations to widely varying Y substitu-
ent systems. This will be reported in the following papers.
Experimental
All melting points are uncorrected. 1H NMR spectra in CDCl3
were recorded on a JEOL JNM-A500 FT-NMR spectrometer op-
erating at 500 MHz and the chemical shifts are given in ppm (δ)
downfield from TMS as an internal standard. The NMR data were
deposited as Document No. 75031 at the Office of the Editor of
Bull. Chem. Soc. Jpn.
Materials. Monosubstituted 1,1-diphenylethyl alcohols were
prepared by the reaction of acetophenones with appropriate Grig-
nard reagents in dry ether. Symmetrically disubstituted alcohols
were prepared by treating ethyl acetate with the Grignard re-
agents. 1,1-Diphenylethyl p-nitrobenzoates were prepared from
the lithium alkoxide and p-nitrobenzoyl chloride in tetrahydrofu-
ran according to the general procedure reported by Brown and Pe-
ters.21 The chlorides were prepared by reacting the alcohols with
SOCl2 in dry benzene at 0 °C.16a,17 The physical properties of the
tertiary alcohols and p-nitrobenzoates are summarized in Table 7.
1-(m-Chloro-p-methoxyphenyl)-1-phenylethyl Alcohol.
A
solution of acetophenone (3.60 g, 30 mmol) in 30 mL dry ether
which was slowly added to the solution of a Grignard reagent pre-
pared from magnesium (0.87 g, 35.75 mmol) and o-chloro-p-bro-
moanisole (7.20 g, 32.5 mmol) in 30 mL dry ether was stirred for
3 h at room temperature. The mixture was then quenched by aq
NH4Cl (1.69 g, 31.6 mmol) at ice bath temperature and extracted
with ether. The combined organic layer was washed with aq NaCl

M. K. Uddin et al.
Bull. Chem. Soc. Jpn., 75, No. 6 (2002) 1379
solution, dried over anhydrous MgSO4, and evaporated under re-
duced pressure. The residue (7.41 g) was flash chromatographed
on silica gel to give the alcohol as a colorless liquid (5.37 g, 75%
yield). Other unsymmetrically substituted alcohols were synthe-
sized similarly from the appropriate acetophenones and the Grig-
nard reagent.
References
a) Y. Yukawa and Y. Tsuno, Bull. Chem. Soc. Jpn., 32, 971
(1959). b) Y. Yukawa, Y. Tsuno, and M. Sawada, Bull. Chem. Soc.
Jpn., 39, 2274 (1966).
1
2
Y. Tsuno and M. Fujio, Chem. Soc. Rev., 25, 129 (1996).
Y. Tsuno and M. Fujio, Adv. Phys. Org. Chem., 32, 267
3
(1999).
4
1,1-Bis(p-methylthiophenyl)ethyl p-Nitrobenzoate. To the
corresponding alcohol (1.45 g, 5 mmol) in 5 mL of THF, 15% bu-
tyllithium in hexane (5 mL, 7.5 mmol) was added dropwise at 0
°C under nitrogen and then the mixture was stirred for 3 h. A so-
lution of p-nitrobenzoyl chloride (0.93 g, 5 mmol) in 5 mL THF
was added slowly to the mixture at −30 °C, the mixture was
stirred for 30 min, and then allowed to warm to room temperature
with stirring for an additional 3 h. The reaction mixture was
quenched by slowly adding ice-cooled water (13 mL) and extract-
ed with ether. The ether extract was washed with ice-cold 5% aq
NaHCO3, and then with aq NaCl solution, dried over anhydrous
MgSO4, and kept in solution in dry ether. Since the p-nitroben-
zoates were unstable and formed olefins, they were used directly
for kinetic measurements immediately after evaporation of the
solvent. Other esters were synthesized similarly.
a) S. Nishida, J. Org. Chem., 32, 2692, 2695, 2697 (1967).
b) J. R. Fox and G. Kohnstam, Proc. Chem. Soc., 1964, 115. c) M.
Fujio et al., unpublished result.
5
J. Mindle and M. Vecera, Collect. Czech. Chem. Commun.,
37, 1143 (1972). J. Mindle and M. Vecera, Collect. Czech. Chem.
Commun., 36, 3621 (1971).
6
N. C. Deno and A. Schriesheim, J. Am. Chem. Soc., 77,
3051 (1955). N. C. Deno and W. L. Evans, J. Am. Chem. Soc., 79,
5804 (1957). C. D. Ritchie, Can. J. Chem., 64, 2239 (1986). R.
A. McClelland, V. M. Kanagasabapathy, N. S. Banait, and S.
Steenken, J. Am. Chem. Soc., 111, 3966 (1989). R. A.
McClelland, V. M. Kanagasabapathy, N. S. Banait, and S.
Steenken, J. Am. Chem. Soc., 113, 1009 (1991).
7
8
M. F. Ruasse, Adv. Phys. Org. Chem., 28, 207 (1993).
a) J. E. Dubois, M. F. Ruasse, and A. Argile, J. Am. Chem.
1,1-Bis[m(trifluoromethyl)phenyl]ethyl Chloride.
To the
corresponding alcohol (0.83 g, 2.5 mmol) in 4 mL of dry benzene
containing dry pyridine (0.20 g, 2.5 mmol), SOCl2 (5.95 g, 50
mmol) was added dropwise at 0 °C and the reaction mixture was
stirred for 30 min. The solvent was evaporated under reduced
pressure and the residue was dissolved in dry benzene. The pre-
cipitated pyridinium salt was filtered, and the solvent was evapo-
rated under reduced pressure. The same procedure was repeated
by adding new dry benzene in order to remove completely the ex-
cess SOCl2 and salts. Since the chlorides were very unstable and
formed an appreciable amount of olefins, they were used directly
for kinetic measurements immediately after evaporation of the
solvent. Other chlorides were prepared similarly from the corre-
sponding alcohol.
Solvents. Commercial acetone was refluxed with KMnO4 for
6 h and distilled. The distillate was dried over anhydrous Na2CO3
and redistilled. HPLC grade distilled water (Chameleon reagent)
was distilled immediately before use. 80% (v/v) and 50% (v/v)
aqueous acetone mixtures for the solvolysis studies were prepared
by mixing the corresponding volumes of acetone and water at 25
°C.
Kinetic Measurements. The solvolysis rates were deter-
mined conductimetrically as reported previously17 at initial con-
centrations of ca. 10−5 for p-nitrobenzoates and 10−4 mol dm−3
for chlorides. CM-60S and CM-50AT (Toa Electronics Ltd.) con-
ductivity meters were equipped with an interval time unit and
printer and those of CM-60V, CM-40G, and CM-40V were con-
nected to a high speed personal computer. Solvolysis was fol-
lowed in a thermostatted bath controlled within 0.01 °C by tak-
ing at least 100 readings at appropriate intervals during 2.5 half-
lives, and an infinity reading after 10 half-lives. The experimental
errors in the respective runs were generally less than 1.0% and re-
producibility of the rate constants was within 1.5%. The first-
order rate plots were satisfactorily linear over 2.5 half-lives with a
correlation coefficient > 0.99997.
Soc., 106, 4840 (1984). b) M. F. Ruasse, A. Argile, and J. E.
Dubois, J. Am. Chem. Soc., 106, 4846 (1984).
9
G. Goethals, F. Membrey, B. Ancian, and J. P. Doucet, J.
Org. Chem., 43, 4944 (1978).
10 M. O’Brien and R. A. More O’Ferrall, J. Chem. Soc.,
Perkin Trans. 2, 1978, 1045.
11 D. J. McLennan, Tetrahedron, 34, 2331 (1987).
12 a) G. S. Hammond, J. Am. Chem. Soc., 77, 334 (1955). b)
J. E. Leffler and E. Grunwald, “Rates and Equilibria of Organic
Reactions,” Wiley, New York (1963). c) E. S. Lewis, C. C. Shen,
and R. A. More O' Ferrall, J. Chem. Soc., Perkin Trans. 2, 1981,
1084.
13 J. E. Dubois, A. F. Hegarty, and E. D. Bergmann, J. Org.
Chem., 37, 2218 (1972). A. F. Hegarty, J. S. Lomas, W. V. Wright,
E. D. Bergmann, and J. E. Dubois, J. Org. Chem., 37, 2222
(1972).
14 C. D. Johnson, Tetrahedron, 36, 3461 (1980). B. Giese,
Angew. Chem., Int. Ed. Engl., 16, 125 (1977).
15 R. A. Marcus, J. Phys. Chem., 72, 891 (1968). J. R.
Murdoch, J. Am. Chem. Soc., 94, 4410 (1972). G. W. Koppel and
A. J. Kresge, J. Chem. Soc., Chem. Commun., 1973, 371.
16 a) M. Fujio, H. Morimoto, H.-J. Kim, and Y. Tsuno, Bull.
Chem. Soc. Jpn., 70, 1403 (1997). b) M. Fujio, H. Morimoto, H.-
J. Kim, and Y. Tsuno, Bull. Chem. Soc. Jpn., 70, 3081 (1997).
17 M. Fujio, H.-J. Kim, H. Morimoto, S.-D. Yoh, and Y.
Tsuno, J. Phys. Org. Chem., 12, 843 (1999).
18 M. Fujio et al., to be published in J. Phys. Org. Chem.
19 H. C. Brown, M. Ravindranathan, and E. N. Peters, J. Org.
Chem., 42, 1073 (1977).
20 M. K. Uddin, M. Fujio, and Y. Tsuno, to be published in J.
Phys. Org. Chem.
21 H. C. Brown and E. N. Peters, J. Am. Chem. Soc., 97, 1927
(1975).