Solvent effects on intramolecular electron exchange in the 1,4- dinitrobenzene radical anion

Article abstract of DOI:10.1039/a806679e

The rate constants of the intramolecular electron exchange reaction in the 1,4-dinitrobenzene radical anion in linear alcohols were determined from alternating line-broadening effects in EPR spectra. Rate constants at 293 K range from 2.9 x 10⁹ s^-1 in methanol to 2.7 x 10⁸ s^-1 in octan-1-ol. The rate constant was found to depend on the reverse of the longitudinal correlation time of the solvent, τ(L), as expected for a solvent-controlled adiabatic reaction. Applying Marcus theory and the ellipsoidal cavity model for evaluating λ₀, the amount of transferred charge between nitro groups, z, and the outer-sphere reorganisation energy were determined, z changes from 0.56 at 273 K to 0.52 at 313 K. λ₀ at 293 K changes from 61 kJ mol^-1 in octan-1-ol to 80 kJ mol^-1 in methanol. The activation energies were obtained from the temperature dependence of the rate constants, changing from 26 kJ mol^-1 in methanol to 36 kJ mol^-1 in octan-1-ol. The variation of this energy clearly reflects the increase in the exponential term of τ(L) for the more viscous alcohols. The results for the 1,4-dinitrobenzene radical anion were compared with those previously reported for the radical anion of 1,3-dinitrobenzene. Rate constants are smaller in the former, by three orders of magnitude, due to conjugation of the nitro groups.

Full text of DOI:10.1039/a806679e

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Solvent e†ects on intramolecular electron exchange in the
,4-dinitrobenzene radical anion
1
J. P. Telo,*a G. Gramppb and M. C. B. L. Shohojia
a Instituto Superior T e
Portugal
b Institut f u
T echnikerstrasse 4/I, A-8010 Graz, Austria

cnico, Qu•

mica Orga
ü
nica, Av. Rovisco Pais, P-1096 L isboa Codex,
Ž
r Physikalische und T heoretische Chemie, T echnische Universitat Graz,
Ž
Accepted and transferred from Berichte Bunsen-Gesellschaft 25th August 1998
The rate constants of the intramolecular electron exchange reaction in the 1,4-dinitrobenzene radical anion in
linear alcohols were determined from alternating line-broadening e†ects in EPR spectra. Rate constants at 293
K range from 2.9 ] 109 s~1 in methanol to 2.7 ] 108 s~1 in octan-1-ol. The rate constant was found to depend
on the reverse of the longitudinal correlation time of the solvent, q , as expected for a solvent-controlled
L
adiabatic reaction. Applying Marcus theory and the ellipsoidal cavity model for evaluating j , the amount of
0
transferred charge between nitro groups, z, and the outer-sphere reorganisation energy were determined. z
changes from 0.56 at 273 K to 0.52 at 313 K. j at 293 K changes from 61 kJ mol~1 in octan-1-ol to 80 kJ
0
mol~1 in methanol. The activation energies were obtained from the temperature dependence of the rate
constants, changing from 26 kJ mol~1 in methanol to 36 kJ mol~1 in octan-1-ol. The variation of this energy
clearly reÑects the increase in the exponential term of q for the more viscous alcohols. The results for the 1,4-
L
dinitrobenzene radical anion were compared with those previously reported for the radical anion of 1,3-
dinitrobenzene. Rate constants are smaller in the former, by three orders of magnitude, due to conjugation of
the nitro groups.
dinitrodurene9,10 seemed to conÐrm this idea. However, line-
broadening e†ects due to IEE were recently found in the EPR
spectra of the 2,6-dinitrophenolate radical dianion, where
resonance structures can be drawn delocalising the electron
through the two nitro groups.11
1
Introduction
There is current interest in the kinetics of both intra- and
intermolecular electron transfer reactions, since these are the
fundamental chemical steps in numerous biological processes.
A great investment has been made in the design of organic
molecules for testing electron transfer theories. In particular,
the understanding of intramolecular electron transfer has
evolved to a high degree.1 The veriÐcation of the Marcus
inverted region was Ðrst established for intramolecular elec-
tron transfer reactions.
In this work, the solvent-induced IEE within the conjugated
1,4-dinitrobenzene (1,4-DNB) radical anion is studied in linear
alkanols. The e†ect of the solvent on the kinetics of the reac-
tion is discussed.
Most of the studies of intramolecular electron transfer focus
on photoinduced charge separation, involving di†erent donor
and acceptor moieties to achieve a suitable driving force *G¡.3
Studies on intramolecular degenerated symmetrical electron
exchange reactions with *G¡ \ 0 are rare. Nelsen et al.4
studied the self-exchange within various hydrazine derivatives
by optical and EPR methods. Combination of both methods
made possible the estimation of the coupling matrix element
.5
2 Theory
According to Marcus theory,12h14 the rate constant of an
adiabatic electron transfer reaction is expressed by
k \ l exp([*G*/RT )
(1)
where l is the e†ective nuclear frequency of the reactants. For
a
degenerated intramolecular electron transfer reaction
*G¡ \ 0 and the activation energy is simply given by
H1
2
The kinetics of intramolecular electron exchange (IEE) in
the radical anion of 1,3-dinitrobenzene (1,3-DNB) have been
studied previously by EPR spectroscopy. Rate constants, k,
are ca. 106 s~1 in alcohols and 109 s~1 in aprotic solvents.
The reaction was found to be adiabatic and uniform in the
sense of classic transition state theory.6,7
j ] j
*
G* \ i 4 0 [ H
(2)
12
In intramolecular reactions with aromatic spacers, the overlap
between the orbitals of the donor and acceptor is extensive
and the resonance energy splitting H may be considerably
1
2
It is generally accepted that the absence of direct resonance
between the donor and the acceptor is necessary for the
occurrence of alternating line-broadening e†ects caused by
IEE in the EPR spectra of free radicals. The examples found
in the literature, where the two groups are either in non-
conjugated meta positions, as in the radical anions of 1,3-
DNB and 2,7-dinitronaphthalene (2,7-DNN),8 or sterically
forced out of planarity, as in the radical anion of
larger than RT . Since the activation energies are normally not
very large for adiabatic electron transfer reactions, it is neces-
sary to include H in eqn. (2).
1
2
The inner-sphere reorganisation energy j depends on the
i
changes in the bond lengths between the reactants and the
products. According to Marcus, j can be calculated by eqn.
i
(3), from the changes in bond orders *q between the reactants
j
and products and from the corresponding force constants
Phys. Chem. Chem. Phys., 1999, 1, 99È104
99

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f R, P. In the limiting case of totally excited vibrational states
In the uniform adiabatic regime, the reagents and transition
state are in equilibrium and the system obeys the conditions
of transition state theory. This happens because the solvent
acts as a reversible energy source or sink, providing or
absorbing energy instantaneously to or from the system. If, on
the contrary, relaxation of the solvent occurs on a timescale
larger than that of electron transfer, irreversible reactantÈ
solvent energy dissipation is expected to occur and the rate
constant of the reaction is controlled by the solvent dynamics.
In this solvent di†usion regime, the pre-exponential factor is
given by21,22
j
we have
f R f P
j= \ ;
j
j
(*qj)2
(3)
i
f R ] f P
j
j j
However, the relevant vibrational frequencies are only par-
tially excited at room temperature. A simple correction for the
temperature dependence of j was proposed by Holstein15
i
C
4kT
+u
4kT
D
j (T ) \ ; (j=)
i j +u
tanh
j
(4)
i
j
j
The sum can be substituted by one term with a mean fre-
quency u/2n B 5 ] 1013 s~1. In the range of temperature
under consideration, eqn. (4) can be approximated by a
straight line
l \ 1/q (j /16RT )1@2
(12)
L 0
where q is the longitudinal relaxation time of the solvent.
Eqn. (1) and (12) set an upper limit of ca. 1/q
L
L for the rate of
the reaction.
j (T ) \ j=(m ] nT )
(5)
i
i
with m \ 0.092 and n \ 0.001 36 K~1.16,17
3
Experimental
The outer-sphere reorganisation energy j is associated
0
1,4-DNB (Fluka) was puriÐed by elution with toluene from a
with the reorientation of the solvent molecules along the reac-
tion coordinate. We have shown previously that the ellip-
soidal cavity model is a satisfactory approximation to
short column packed with basic alumina. The solid was
further sublimed and recrystallised from ethanol. The alcohols
(
(
Merck, p.a. or extra pure) were dried with molecular sieves
Union Carbide 3 A, dried at 400 ¡C under vacuum). Tri-
calculate j for IEE reactions in aromatic organic mol-
0
Ž
ecules.6h8 In this model, the molecule is located in an ellip-
ethylamine (Merck) was dried over potassium hydroxide, dis-
tilled and stored over molecular sieves.
soidal cavity surrounded by the solvent, considered as a
dielectric continuum.18,19 The ellipsoid has semi-axes a and b.
If the charge ze is transferred over a distance d, j is given by
Solutions contained, typically, 1È3 mM of the parent com-
pound and 7È10 mM of triethylamine. The solutions were
deaerated with argon, thermostatted at constant temperature
between 250 and 320 K by passing through a glass heat
exchanger, and allowed to Ñow through a quartz Ñat cell
placed in the EPR cavity. The temperature inside the cell was
measured with a Pyrex-coated platinum thermocouple placed
in the upward solution stream immediately above the Ñat part
of the cell. The standard Ñow rate was ca. 0.2 ml s~1. Radicals
were generated by in situ photolysis using an optically focused
high pressure HgÈXe 1000 W lamp. Spectra were recorded
with a Bruker 200D X-band EPR spectrometer.
Under the experimental conditions used, a photoinduced
electron transfer occurs yielding the radical anion of the nitro
compound and the radical cation of triethylamine. The
unstable radical cation of the triethylamine decays fast on the
EPR timescale and is not observed.
0
0
(
e z)2N CA
1
1
B
=
X
j \
0
L
f
[
;
n
0
4ne R
e
e
I (e , e)
0
in
n/1 n in
X
A
1
1
B
=
D
[
[
;
n
(6)
(7)
(8)
e
e
I (e , e )
in
op n/1 n in op
where
and
X \ 2(2n ] 1)[1 [ ([1)n]P2(m)Q (s)/P (s)
n
n
n
n
e
C
s [ P (s)/P (s)
D
I (e , e ) \ 1 [ i
n i
n`1
n
j
e
s [ Q (s)/Q (s)
j
n`1
n
where e is the permittivity of the vacuum and e and e are
the static and optical relative permittivities of the solvent.
0
op
Usually e is taken as the square of the refractive index, e
B
op
op
n2 . Inside the ellipsoidal cavity the relative permittivity in e .
hl
D
in
The commonly used value for this parameter is e B 2, a
RwNO ] NEt ÈÈÈ
Õ
RNO ~~ ] NEt ~`
(13)
in
2
3
2
3
dec.
value of e usual for hydrocarbons. The shape of the ellipsoidal
B
cavity is described by s \ Ja2/(a2 [ b2) and m \ d/R where
f
n
Values of the solvent longitudinal relaxation time were
R \ 2Ja2 [ b2 is the interfocal distance. P (s) and Q (s) are
f
n
obtained from Barthel et al.23 (methanol, ethanol and propan-
the Legendre polynomials of the Ðrst and second kind. A
computer program was developed for calculating j
eqn. (6)È(8).
1
-ol, 298 K) and from Garg and Smith24 (butan-1-ol to octan-
0 from
1-ol, 273 and 293 K). The values of q at 273, 293 and 313 K
not available in the literature, were extrapolated using eqn.
L
It can be recognised from eqn. (6)È(8) that, in this model, j
0
(21) (see below) and values for H from Fawcett25 (methanol,
ethanol and propan-1-ol) and Garg and Smith24 (butan-1-ol
to octan-1-ol). The values of the solvent polarity parameter c
were calculated at the same temperatures from the corre-
sponding values of the relative permittivity and refractive
index.24,26,27
is not an explicit function of the solvent polarity parameter c,
L
given by eqn. (9)
1
1
1
1
c \
[
B
[
(9)
e
e
n2
e
op
D
However, by calculating j for a given ellipsoid and for the set
0
of solvents used, a simple linear relation between j and c was
0
4 Results and discussion
previously found,6,7
4
.1 EPR spectra
j \ z2pc
(10)
0
EPR spectra of the radical anion of 1,4-DNB were recorded in
linear alcohols, from methanol to octan-1-ol, at temperatures
between 250 and 320 K. For the higher alcohols, the
minimum temperature achieved was ca. 275 K, due to vis-
cosity limitations. All spectra showed temperature-dependent
line-broadening e†ects. The spectra are in the fast region of
exchange, since only one averaged coupling constant is mea-
sured for the two nitrogen atoms. The mean nitrogen coupling
where z is the fraction of transferred charge and p is a param-
eter depending only on the shape of the ellipsoid.
Rips and Jortner pointed out that, for a uniform adiabatic
reaction, the moment of inertia of the solvent molecule, I,
should be included in the pre-exponential factor l, given by20
1
C
2e ] e
6e
D
1@2
l \ 2
n
op (k T /I)
(11)
B
100
Phys. Chem. Chem. Phys., 1999, 1, 99È104

View Article Online
constant at 293 K changes from 3.83 G in methanol to 3.14 G
in octan-1-ol. The continuous decrease of this constant rules
out the possibility of ion pair formation in the less polar alco-
hols. At low temperatures, broadening occurs, not only of the
lines of the nitrogen quintet but also of the lines correspond-
ing to the hydrogens [Fig. 1(c)]. In analogy to the meta
isomer,6,7 this e†ect was interpreted as resulting from the
modulation of the hyperÐne coupling constants by IEE
between the two nitro groups induced by asymmetric solva-
tion, as shown in Scheme 1. Additionally, the spectra show
asymmetric line-broadening e†ects caused by the slow tum-
bling of the radical due to the viscosity of the medium.
The spectra were simulated by solving the appropriate
Bloch equations for a two-jump model. In the fast region of
exchange, the interchangeable coupling constants values are
not accessible experimentally, since only mean constants are
measured. In these cases the coupling constants must be
obtained from spectra in the slow region of exchange (from
ion pairs, for example) or estimated from HMO calculations.
For this purpose, HMO-McLachlan calculations of the spin
densities in the radical anion of 1,4-DNB were performed. The
parameters used were c \ 1.06, c \ 1.67, c \ 1.0 and
CN
NO
CO
d \ 2.2.28 The e†ect of asymmetric solvation was included by
N
using di†erent oxygen Coulomb integral parameters for the
two nitro groups. For the less solvated nitro group a value of
d \ 1.4 was used, whereas for the more solvated nitro group
0
0
d was varied between 1.6 and 1.8. The formulae relating spin
densities and coupling constants were obtained from the liter-
ature.28
The calculations show that the two interchangeable nitro-
gen coupling constants, a and a , have di†erent signs. The
N1
N2
same happens with the interchangeable hydrogen coupling
constants and both these results are independent of the choice
of parameters used in the calculations. The Ñuctuation *a \
N
a
[ a of the calculated nitrogen coupling constants is a
N1
N4
linear function of the averaged constant SaTcalc \ (a ] a )/2
N
1
4
[
eqn. (14)], as found before for the radical anions of 1,3-DNB
and 2,7-DNN.
*
acalc \ 2.40SaTcalc ] 0.18
(14)
N
N
This equation was used to estimate a and a from the
experimental values of SaT . The few values of nitrogen coup-
ling constants reported in the literature for spectra of 1,4-
N1
N4
N
DNB radical anion in the slow region of exchange (in ion
pairs29,30) Ðt eqn. (14) quite well, conÐrming the validity of the
method used to estimate a and a . The same method was
N1
N4
also used to estimate the interchangeable hydrogen hyperÐne
coupling constants.
The asymmetric line-broadening e†ects were simulated by
making the intrinsic linewidth C of each line dependent on its
nitrogen nuclear quantum number M, according to the equa-
tion
C(M) \ A ] BM ] CM2
(15)
Fig. 1 EPR spectra (left-hand side) and computer simulations (right-
hand side) of the 1,4-DNB radical anion in ethanol at di†erent tem-
peratures: (a) spectrum at 293 K and simulation with k \ 1.1 ] 109
The values of the intrinsic line-width parameters A, B and C
and the rate constant of the IEE reaction, k, were adjusted by
Ðtting each experimental spectrum with a computer simula-
tion. Three EPR spectra of the 1,4-DNB radical anion in
ethanol at di†erent temperatures are shown in Fig. 1, together
with their simulations.
s~1,
a
\ 0.759 mT,
a
\ [0.078 mT,
a
\ [0.272 mT,
N1
N4
H2, 6
a
\ 0.053 mT, A \ 11 lT, B \ [0.36 lT and C \ 0.53 lT; (b)
H3, 5
spectrum at 271 K and simulation with k \ 5.1 ] 108 s~1, a
\
N1
\ 0.056 mT,
0
.776 mT, a \ [0.079 mT, a
\ [0.276 mT, a
N4
H2, 6
H3, 5
A \ 11 lT, B \ [1.0 lT and C \ 0.76 lT; (c) spectrum at 246 K and
simulation with k \ 1.9 ] 108 s~1, a \ 0.792 mT, a \ [0.081
N1
N4
mT, a
\ [0.281 mT, a
\ 0.059 mT, A \ 11 lT, B \ [1.8 lT
4
.2 Solvent dependence of the rate constants
H2, 6
and C \ 1.07 lT.
H3, 5
The rate constants for the IEE reaction within the 1,4-DNB
radical anion are shown in Table 1, together with values of the
solvent parameter c and longitudinal relaxation time of the
corresponding solvent, q . For comparison, rate constants for
L
the same reaction in 1,3-DNB radical anion, obtained from
the literature,6,7 are also shown.
The main difficulty in evaluating experimentally the solvent
dependence of the rate constant is to separate the e†ects of the
solvent on the pre-exponential factor and on the activation
energy. The rate constant can be expressed as
ln k \ ln l [ (z2p/4RT )c [ (j /4 [ H )/RT
12
(16)
i
The last term on the right-hand side of eqn. (16) is indepen-
dent of the solvent,31 but the same does not apply for the Ðrst
two terms. In the uniform adiabatic regime, the solvent depen-
dence of l [eqn. (11)] is small compared with the solvent
dependence of j . In this case, eqn. (16) predicts that ln k
0
should decrease with increasing c. Such behaviour is indeed
found for the kinetics of the electron exchange in the 1,3-DNB
Scheme 1
Phys. Chem. Chem. Phys., 1999, 1, 99È104
101

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Table 1 Solvent parameters, rate constants and outer-sphere reorganization energies, at 293 K, and activation parameters for the IEE reaction
in the 1,3-DNB6,7 and 1,4-DNB radical anions (energies in kJ mol~1)
1
,3-DNB~~
1,4-DNB~~
/s~1
Solvent
c
q
/10~12 s
H
k
/s~1
j
*G*
ln A
k
j
*G*
ln A
293
L293
L
293
0 293
293
0 293
Methanol
Ethanol
0.537
0.500
0.476
0.474
0.455
0.444
0.423
0.393
4.85
20.2
44.6
44.8
80
130
182
356
11.8
14.1
15.9
È
19.9
21.6
23.7
26.5
2.7 ] 106
107
100
È
96
È
È
È
È
43
42
È
43
È
È
È
È
29.7
29.4
È
30.1
È
È
È
2.9 ] 109
1.1 ] 109
8.7 ] 108
È
5.1 ] 108
3.8 ] 108
3.7 ] 108
2.7 ] 108
80
74
71
È
68
66
63
61
26 ^ 2
22 ^ 1
26 ^ 2
È
29 ^ 2
30 ^ 3
35 ^ 2
36 ^ 3
36.2
33.8
35.2
È
35.8
36.0
38.2
38.0
2.9 ] 106
Propan-1-ol
Propan-2-ol
Butan-1-ol
Pentan-1-ol
Hexan-1-ol
Octan-1-ol
È
5.0 ] 106
È
È
È
È
È
radical anion (Table 1), which was previously shown to follow
this regime. However, the rate constants for 1,4-DNB radical
anion show an opposite trend. From Table 1, one can notice
an increase in the rate constant with increasing c. As noted
elsewhere,1 such behaviour suggests that the reaction follows
the di†usive adiabatic regime.
In order to estimate the shape of the ellipsoidal cavity a
molecular model of the 1,4-DNB molecule based on bond dis-
tances and on van der Waals radii was constructed. The best
Ðt was obtained for an ellipsoidal cavity with semi-axes of
a \ 4.6 A
Ž and b \ 2.7 AŽ . The distance between redox centres
is d \ 5.75 A
Ž
. With these parameters a value of p \ 428 kJ
In the di†usive adiabatic regime, both the pre-exponential
mol~1 is calculated from eqn. (6)È(8) for the set of solvents
used.
factor [eqn. (12)] and j depend on the solvent. However, the
0
solvent dependence of the pre-exponential factor dominates, in
Knowing the value of p, one can calculate the fraction of
the transferred charge z from the slope of eqn. (19). The value
most cases, the equation of the rate constant. The positive
correlation between the rate constants of IEE in 1,4-DNB and
obtained at 293 K, z \ 0.54 ^ 0.07, is shown in Table 2,
exp
c, found in Table 1, occurs because q decreases with c. In fact,
together with the values obtained previously for the radical
L
for the present set of solvents, a good empirical linear corre-
anions of 1,3-DNB and 2,7-DNN. In qualitative terms, z
shows the expected e†ect of the structure of the two radicals.
exp
lation between ln q and c (r \ 0.992 at 293 K), with a nega-
L
tive slope, is obtained
The transferred charge is lower for 1,4-DNB because, in this
radical, the two nitro groups are in a conjugated para position
and the charge, at any instant, is more equally distributed
between the two nitro groups. In the non-conjugated 1,3-DNB
and 2,7-DNN radical anions, the instantaneous di†erence in
charge between the two groups is much higher because the
unpaired electron is almost completely localised in one of the
nitro groups. The same qualitative agreement can be foreseen
in the values of the transferred charge calculated from the dif-
ference in the spin densities on the two nitro groups obtained
from the HMO-McLachlan calculations (Table 2). The theo-
retical calculations do not reproduce well the experimental
values of z in protic solvents, as found before for 1,3-DNB and
ln q \ ac ] b
(17)
L
a \ [29.7 ^ 1.6; b \ [9.8 ^ 0.7 (293 K)
This correlation between q and c was found before for
L
alcohols1 and is responsible, in the present case, for the corre-
lation between k and c with a positive slope. Rate diminution
caused by the increase in the activation energy with c is more
than o†set by the increase of the term ln(1/q ), and the overall
L
e†ect is an increase in the rate constant of the reaction. This
observed behaviour is direct evidence for the role of solvent
relaxation of the reactions dynamics and indicates the pres-
ence of a di†usive regime.
2,7-DNN radical anions.6,7,14 Although the calculated values
4
.3 The amount of transferred charge z and the outer-sphere
reorganisation energy k0
One approach commonly used for separating the solvent
e†ects on l and on j is to correct the rate constant for the
0
anticipated solvent dependence of the pre-exponential factor.
Following this idea, the rate constant can be rewritten as
ln(kq /c1@2) \ 1/2 ln(z2p/16RT ) [ (z2p/4RT c
L
[
(j /4 [ H )/RT
12
(18)
i
A plot of ln(kq /c1@2) versus c should be linear with slope equal
L
to [z2p/4RT . However, this is only true if the parameters q
L
and c do not correlate with each other, otherwise the plot will
Fig. 2 Dependence of the IEE rate constants on the solvent param-
eter c at 293 K, according to eqn. (16).
also reÑect the dependence of q on c. Since, for the present set
L
of solvents, q and c do correlate with each other, eqn. (18)
L
cannot be used.
In the present case, one has to combine eqn. (12), (16) and
Table 2 Fraction of transferred charge between the two nitro groups
(
17) to obtain
ln(k/c1@2) \ [[a [ z2p/4RT ]c ] 1/2 ln(z2p/16RT )
(j /4 [ H )/RT [ b
in radical anions of dinitro compounds at 293 K
Radical anion
z
zcalca
exp
[
(19)
2,7-DNNb
1,3-DNBc
1,4-DNB
0.99
0.94
0.54d
0.70
0.73
0.31
i
12
Fig. 2 shows a plot of ln(k/c1@2) versus c for the IEE reaction in
,4-DNB radical anion at 293 K. As predicted by eqn. (19), a
1
linear correlation is obtained experimentally:
a From HMO calculations. b Ref. 14. c Ref. 6, 7. d From the slope of
eqn. (19).
ln(k/c1@2) \ (15.4 ^ 1.8)c ] (13.6 ^ 0.8); r \ 0.967 (20)
102
Phys. Chem. Chem. Phys., 1999, 1, 99È104

View Article Online
are systematically lower than the experimental ones, z
the activation energies *G* are almost perfectly reproduced.
The di†erences between the two values are within 10%.
calc
follows the same trend as z , being lower for 1,4-DNB
exp
radical anion than for the other two radicals.
The outer-sphere reorganisation energies, calculated from
4.6 Temperature dependence of z
z
and eqn. (10), are shown in Table 1 for each solvent at 293
exp
A calculation of the fraction of the transferred charge at 273
and 313 K was performed, using rate constants for the IEE
reaction at these temperatures. The slope of the plots of ln(k/
c1@2) vs. c [eqn. (16)] vary from 20.1 at 273 K to 11.3 at 313 K.
K. For a given solvent, the value of this energy depends, under
the ellipsoidal cavity model, on the amount of transferred
charge z and on the shape of the molecule through the param-
eter p. This parameter is higher for 1,4-DNB than for 1,3-
DNB (p \ 224 kJ mol~1) owing to the more elongated shape
of the former molecule and to the longer distance between
Surprisingly, the calculated z values vary only slightly, from
exp
z
\ 0.56 at 293 K to z \ 0.52 at 313 K. This happens
exp
exp
because the change in the slope of the ln q vs. c relation
parameter ““aÏÏ in eqn. (16)] varies in the same magnitude,
redox centres.32 The experimental values of j for 1,4-DNB
L
0
[
are, however, lower than those for 1,3-DNB, reÑecting instead
from [36.5 at 273 K to [23.8 at 313 K, that is, the change in
the rate constant with temperature is due mainly to the
the higher di†erences in (z )2.
exp
change in q with T and not to the activation term. This is
L
another proof of the di†usive character of the reaction mecha-
nism.
4
.4 Inner-sphere reorganisation energy k and the resonance
i
energy splitting H
12
Since the speciÐc solvation is lower at higher temperatures,
z decreases with increasing temperature. This decrease is less
signiÐcant if the interaction between the solvent and the
radical anion is stronger, as found before for 1,3-DNB and
2,7-DNN radical anions in alcohols as compared with aprotic
solvents.6h8
From the intercept of eqn. (19) the experimental value of (j /4
i
i
[
[
H
H
) can be extracted. At 293 K the calculations yield (j /4
1
2
2
) \ [7.6 kJ mol~1. Calculation of j= from eqn. (3)
1
i
yields j= \ 6.8 kJ mol~1. If we correct this value according to
i
eqn. (5) we get j293 \ 3.3 kJ mol~1. Both these values are
i
much smaller than j . A value of H \ 8.4 kJ mol~1 is
0
12
12
obtained from j293 (H \ 9.3 kJ mol~1 if we use j=). This
i
i
5 Conclusions
relatively high value for the resonance energy splitting is usual
for these type of intramolecular reactions where H
RT .4,33
A
The present data clearly demonstrate the role of solvent
dynamics on the kinetics of IEE in the 1,4-DNB radical anion.
This reaction obeys a di†usive adiabatic regime, while the
same reaction in the isomeric 1,3-DNB radical anion in alco-
hols follows a uniform adiabatic reaction behaviour. The dif-
ference reÑects the faster reaction in the 1,4-DNB radical,
where the electron transfer occurs on a timescale where
solvent-relaxation processes controls the reaction rate. For the
1
2
4
.5 Temperature dependence of the rate constants and
activation parameters
The rate constants of the IEE reaction in 1,4-DNB radical
anion at several temperatures were used to calculate the acti-
vation energy of the reaction. One difficulty was to deÐne the
temperature dependence of the pre-exponential factor, eqn.
1,3-DNB radical, solvent relaxation, being much faster than
the electron transfer step, does not a†ect the reaction
dynamics.
The EPR spectra of 1,4-DNB radical anion reported in the
literature in aprotic solvents34 do not show evidence of alter-
nating line-broadening e†ects. In such solvents, the fraction of
(
12). One should note that the longitudinal relaxation time is
approximately proportional to the viscosity and depends
strongly on the temperature through an exponential term
[eqn. (21)]
transferred charge z (and hence j ) is substantially lower than
0
q \ h/kT exp([S /R)exp(H /RT )
in alcohols, due to a lower speciÐc solvation. Since, in most
L
L
L
aprotic solvents, the values of 1/q are higher than in alcohols,
L
\
c/T exp(H /RT )
(21)
the reaction is, under these conditions, too fast to exert dis-
L
cernible alternating line-broadening e†ects on the EPR
spectra.
Including the dependence of q on temperature in the expres-
sion for the rate constant we have
L
The 1,4-DNB radical anion is the Ðrst example where alter-
nating line-broadening e†ects caused by a solvent-induced
IEE reaction are found in the EPR spectra of a free ion conju-
gated aromatic system. Previous examples occurred in spectra
of radicals substituted in non-conjugated meta positions, in
radicals where the two groups are sterically forced out of
planarity or in ion-pairs, in which the counter-ion jumps
simultaneously with the electron.
The classical resonance theory postulates that all the reso-
nance structures have equal energy and that no activation
barrier exists between them. The results presented here show
that, in the case of the 1,4-DNB radical anion, these condi-
tions are not valid if solvation stabilises, by hydrogen
bonding, the structures where the charge is localised in one of
the nitro groups, as compared to those where the charge is in
the aromatic ring.
k \ AT 1@2 exp([*G*/RT )
(22)
(23)
(24)
with
and
j ] j
*
G* \ i 4 0 [ H ] H
12
L
A \ 1/c(j /16R)1@2
0
Although j \ z2pc depends on the temperature by z and c,
0
the temperature dependence of j in eqn. (24) was neglected,
0
since c and z (see below) vary only slightly within the range of
temperatures used and in opposing directions (in methanol
c \ 0.534 at 273 K and c \ 0.539 at 313 K).
The activation parameters of IEE extracted from the slope of
the plots of ln(kT ~1@2) versus 1/T for the various alcohols are
presented in Table 1. The increase in *G* from methanol to
Acknowledgements
octanol clearly reÑects the increase in H for the more viscous
L
solvents, since j and H do not depend on the solvent and
The Ðnancial support of FCT (Fundac
Tecnologia) through its Centro de Processos Qu•
Universidade Tecnica de Lisboa is gratefully acknowledged.
G.G. thanks the EC-Socrates program, the Austrian Academic
Ó
a
8
o para a Cie
ü ncia e
i
12
j
decreases with decreasing c. Adding the value of (j /4

micos da
0
i
[
H
) \ [7.6 kJ mol~1 found before, to j /4 and H for

12
0
L
each solvent, according to eqn. (23), the experimental values of
Phys. Chem. Chem. Phys., 1999, 1, 99È104
103

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17 G. Grampp and W. Jaenicke, J. Chem. Soc., Faraday T rans. 2,
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985, 81, 1035.
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B. S. Brunschwig, S. Ehrenson and N. Sutin, J. Phys. Chem.,
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