1,1-DIPHENYL-2,2,2-TRIFLUOROETHYL SYSTEM SOLVOLYSIS
337
constant rED values of À6.46 Æ 0.24 were obtained for
all the other subsets, ranging from Y = p-Me to 3,5-Cl2.
Obviously, the Y–T correlations for the whole range of
substituents should be non-linear or sharply bilinear in all
subsets. It is therefore remarkable that a precise Y–T
relationship holds for the whole range of symmetrical
substituents (X = Y) subseries 1 where the reactivity
changes enormously.
We conclude that the significant non-linearity of
substituent effect in any Y subset is irrelevant to the
use of the Y–T equation [Eqn. (1)]. The failure in
delineating the substituent effects in these Y subsets is
not due to a deficiency of the Y–T equation but is caused
by an inherent non-linearity of the substituent effects in
the a,a-diaryl system.
The simple additivity relationship, Eqn. (4), against
sX sY instead of 2sX gives a widely spread pattern
(Fig. 1). All the fixed-Y subsets give significant concave
correlations, each of which contacts the correlation line
for subseries 1 at the point X = Y. The tangent r value at
this point of any Y subset should be identical with the
rsym value for the symmetrical subseries. The same
behavior has been observed in other a,a-diarylcarbenium
ion reactions, e.g. in solvolyses of benzhydryl chlor-
ides13,14 and a,a-diarylethyl p-nitrobenzoates (M. Fujio
et al., Unpublished results), and in the bromination and
hydration of a,a-diarylethylenes.7
The non-linear correlations have been treated by a
More O’Ferrall analysis [Eqn. (3)]. The results in Table 4
lead to the same conclusions as those from the Y–T
analysis. The r0 value, i.e. the tangent r value at X = H,
becomes more negative as Y becomes more electron
attracting, and all the correlations are significantly
concave with the same degree of curvature, i.e. with
essentially the same mX coefficient, except for Y = p-
MeO.
A large (2m)Y coefficient in Eqn. (3) indicates a non-
linearity of the Hammett-type relationship, and the
concave correlation for the respective Y-subset should
relate to the anti-Hammond shift of the transition state
coordinate (or a late transition state) for rate-accelerating
substrates, if this might be ascribed to the shift of the
transition state coordinate.8 However, this conflicts with
the conclusion deduced above from the behavior of the r
values for the whole substituent set (Table 3).
In these non-linear correlation analyses, we have used
the reference s values (r = 1.17) defined for symmetrical
subseries 1. However, it is important that in the non-
linear substituent effect correlations for varying fixed-Y
subsets, the r value should vary with the fixed-Y
substituent. Thus for instance, the reactivities of p-
MeS-m-Cl and 3,4-Me2 are the same in the symmetrical
subseries 1, the apparent s values of both substituents
being identical at an r value of 1.17. In subset 3 (Y = p-
MeO), p-MeS-m-Cl is clearly less reactive than 3,4-Me2,
with the r value for this subset being <1.17. On the other
hand, p-MeS-m-Cl is more reactive than 3,4-Me2 in
Y = H and m-Cl subsets, with r > 1.17. Furthermore, in
subsets 7 (Y = m-Cl) and 7a (Y = m-CF3), the reactivities
of p-MeO-m-Cl and p-MeS-m-Cl derivatives are dis-
tinctly higher than those of the p-alkyls, in line with
r = 1.5 in the Y–T correlations for these subsets (Table 3).
These complicated substituent–reactivity relationships
are incompatible with the widely accepted interpretation
of a mechanistic change or a coordinate shift of the
transition state. The non-linearity and/or non-additivity in
the substituent effects observed in our system seem to
arise from a substituent-induced change of the conforma-
tion of the transition state.
Conformation±reactivity relationship
In previous papers,2,3 such complicated non-linearity and
non-additivity behaviors were ascribed to a substituent-
dependent conformation of the incipient carbenium ions.
The reactivity data matrix of the X and Y substituents
in Table 2 can be compared with the MO structural
parameters of the carbenium ions in Table 5. The
reactivities of substrates with X Y or at a limit
(sX À sY)!0 are referred to as inherent substituent
effects of the E-conformation. The reactivities when
X Y are referred to as the inherent substituent effects in
the PT conformation, and those at the limits, where
jsX À sYj becomes highly significant, are regarded as
inherent in the lim PT conformation. In any fixed-Y
subset, the parent conformation of the transition state
varies from the E-conformation when X = Y to the PT
conformation when X Y arrive at the lim PT
conformation at both limits of the substituent set. A
change in the preferred transition state conformation with
the increase in jsX À sYj appears to be the major cause of
the non-linearity of substituent effects.
It is reasonable to assume that a linear Y–T relation-
ship [Eqn. (1)] generally holds for systems where the
transition state conformation remains constant. This is
the only requirement for applying the linear regression
analysis to the present system.
The lim PX correlation (5) should be given for the
PX(TY) arrangement of a given fixed-Y subset:
logꢂkX=kH ꢀPꢂꢁX ꢀPꢂꢁ0 rPÁꢁR ꢂ5;
Y P
P
and the TX correlation for the TX(PY) arrangement of
fixed-Y subset by Eqn. (6):
logꢂkX=kH ꢀT ꢂꢁX ꢀT ꢂꢁ0 rT ÁꢁR ꢂ6:
Y T
T
The two correlation lines should intersect for the
symmetrical X = Y member at (sY)P (sY)T, and the
[log (k ) ]
Y Y PT value at the intersection point should refer
to the reactivity of the X = Y member of lim PT
conformation. The PX(TY) and TX(PY) correlations of a
Copyright 2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 330–342
Fujio, Mizue
