NON-EQUILIBRIUM SOLVENT POLARIZATION IN S
2,17 23
N
2 REACTION
321
1
against MeOH taken as the reference solvent.
The
ameter:
coefficients gMeCl were measured only for water, FA,
MeOH and DMF; for other solvents they were estimated
from the linear correlation with the free energy of transfer
0
ꢁ
N
ÁG 48ꢀÆ13E À 45ꢀÆ8
T
À
n 9; r 0:9606; F 83:7; ꢂ 3:1
ꢀ9
of BPh4 ion from water to a given solvent:
RT ln ꢁMeCl 0:20ꢀÆ0:04ÁG ꢀBPh4À 5ꢀÆ1
ꢁ
On the other hand, the resonance energy can be described
approximately by
tr
n 4; r 0:9977; F 429:2; ꢂ 0:19
ꢀ6
ꢀij 0:5ꢀꢁ D ꢁ D
ꢀ10
i
i
j
j
where n is the number of solvents, r the correlation
coefficient, F the value of the Snedecor test, ꢂ the mean
quadratic deviation from the correlation line, 95% errors
of regression coefficients are given in parentheses and the
[neglecting in the original Marcus Eqn. (13d) in Ref. 8
2
the last term 1 À (DG°'/l) because DG°'/l is very small,
as is indicated by the negligibly small quadratic term in
À
0.5
0.5
values DG° (BPh ) were taken from Ref. 20. Homolytic
Eqn. (4) and neglecting the term (ꢁ
i
D
i
)
À (ꢁ
discussed by Marcus ]. Assuming additionally that
= ꢁ = 0.38 in each solvent, as for the symmetric
identity Finkelstein reactions considered by Marcus, one
j
D
j
)
as
tr
4
8
dissociation energies in different solvents were esti-
gas
mated assuming DMeX = DMeX À DG . The resulting
ꢁ
i
j
solv
= 234 and D
gas
gas
8
values (calculated for D
=
MeI
MeCl
À1 21
3
51.5 kJ mol ) are collected in Table 1. From the
can obtain bij = 0.19 (D
i
D
j
) and finally
inspection of that data it is evident that the solvent effect
on DMeX is very small.
0
Ã
ꢁ
ÁG wr l0=4 0:06ꢀDi Dj ÁG =2 ꢀ11
Neglecting the last term in Eqn. (5) and assuming to a
first approximation that w = w , one can express DG°' as
The solvent effect on 0.06(DMeI DMeCl) is negligibly
p
r
À1
the sum of differences between formal potentials, E°
small; 0.06(DMeI D
) is equal to 36 and 35 kJ mol
in aprotic and protic solvents, respectively. The calcu-
MeCl
À
À
(
D
I/I ) À E°(Cl/Cl ), and between bond energies, D
À
MeI
. Formal potentials in aqueous solutions (E° = 1.4
Ã
lated solvent-dependent contributions to ÁG exp(0.5DG°'
MeCl
À
À
and 2.6 V for I and Cl , respectively) were taken from
Ref. 22 and those for other solvents were calculated using
the free energy of transfer of each halogen ion from
water to a given solvent. The differences obtained,
and the sum w l /4) are given in Table 1. It is evident
r
0
that the increase in the activation free energy on going
from aprotic to protic solvents is caused by a very strong
increase in the w l /4 contribution and a 1.8 times
20
r
0
À
À
FDE° = FE°(I/I ) À FE°(Cl/Cl ) are collected in Table
weaker increase in the thermodynamic driving force
1
. The thermodynamic driving force was finally calcu-
0.5DG°' (the last contribution is negative).
lated as
0
ꢁ
ꢁ
À
ꢁ
À
ÁG FE ꢀI/I À FE ꢀCl/Cl D À DMeCl ꢀ7
DISCUSSION
MeI
1
,2
and the values of 0.5DG°' obtained are also collected in
Albery and Kreevoy, in their classical papers on the
Table 1.
methyl transfer reactions, assumed that work terms are
À1
The activation free energy of the S 2 reaction depends
negligibly small (w
r
ꢂ 10 kJ mol in aqueous solution)
N
linearly on the reaction free energy as expressed by the
following equation:
and omitted them. However, the above assumption is not
acceptable if one looks for solvent effects on the
activation barrier. The formation of the encounter pair
of reactants includes at least a partial desolvation of the
0
Ã
ꢁ
ÁG
1:3ꢀÆ0:2ÁG 101ꢀÆ4;
exp
halide ion and therefore w should be dependent on the
solvent acidity described, e.g., by the ET parameter. In
r
N
n 9; r 0:9891; F 316:6; ꢂ 2:2
ꢀ8
general, there is also a contribution to the static
component of the solvent reorganization energy due to
the specific solvation, i.e. the non-continuum solvent
effect. Hupp and Weaver showed that the non-
continuum effect can be taken into account for the
homogeneous outer-sphere ET process for cationic redox
The addition of the quadratic term, as predicted by Eqn.
(
4), is statistically insignificant. However, the slope of the
24
line obtained is about twice the theoretical value of 0.5,
predicted by Eqn. (4). This high value indicates that some
other contribution to the activation barrier depends
linearly on the same solvent properties as the values of
DG°'. The solvent change of the last parameter describes
mainly the solvation of an anionic reactant and product
and thus DG°' should be dependent on the solvent acidity
in the Lewis sense. Indeed, there is the acceptable
couples by the addition to l /4 [described in terms of the
Born model of solvation, cf. Eqn. (13) below] the
0
correction term DG° /(4n 2), where n is the charge
nc
number of a reduced form of a reactant and DG° the free
nc
energy change of the equilibrium specific solvation of a
N
correlation with the Dimroth and Reichardt ET par-
redox couple of interest. The values of DG°nc were
Copyright 2002 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2002; 15: 319–323