Solvent-mediated intramolecular electron transfer in U-shaped systems with different 'bite sizes'

Article abstract of DOI:10.1021/ja991895m

The rate of photoinduced charge separation is measured as a function of solvent for four donor (D)-bridge-acceptor (A) systems: DMN[10]DCV, DMN[10nb]DCV, DMN[10cy]DCV, and DMAN[10cy]DCV. In the first three members of this series, the D/A pair is kept constant and contains the strong dimethoxynaphthalene (DMN) donor which enables detection of electron transfer over a wide range of solvent polarity. In the fourth member, DMN is substituted by a dimethoxyanthracene (DMAN) unit, which decreases the driving force for photoinduced charge separation by about 0.58 eV and thereby limits the occurrence of electron transfer to polar solvents. In all systems the bridge is held at a length of 10 σ bonds. The configuration of the bridge is, however, varied to increase its bending in the series, which leads to center-to-center D/A distances decreasing from 13.4 A in the first system to 9.54 A in the second, and 7.50 A in the latter two. In DMN[10nb]DCV, the rate of intramolecular charge separation over 9.54 A is always smaller than that over 13.4 A in DMN[10]DCV, which is in line with a dominant through- bond mechanism that is more efficient via an extended array of σ bonds. However, in DMN[10cy]DCV, the rate is as high as or even higher than that in DMN[10]DCV. Although changes in the driving force are also important, as shown, for example, by the dramatic rate decrease in DMAN[10cy]DCV as compared to that of DMN[10cy]DCV, the high rates observed for DMN[10cy]DCV in polar aromatic solvent as well as in acetonitrile strongly indicate an important contribution of through-solvent interaction across the 7.5 A D/A distance, which in principle allows the intercalation of a single solvent molecule in close contact with both D and A. At the longer distance of 9.54 A in DMN[10nb]DCV, a smaller contribution of through-solvent interaction can still be detected for polar aromatic solvents but not for acetonitrile. The inherently discontinuous distance dependence of through-solvent interaction and its possible interesting dependence on molecular structure and temperature are discussed.

Full text of DOI:10.1021/ja991895m

J. Am. Chem. Soc. 2000, 122, 5075-5081
5075
Solvent-Mediated Intramolecular Electron Transfer in U-Shaped
Systems with Different “Bite Sizes”
Nigel R. Lokan,‡ Michael N. Paddon-Row,‡,* Mattijs Koeberg,† and Jan W. Verhoeven†,*
Contribution from the Laboratory of Organic Chemistry, UniVersity of Amsterdam,
Nieuwe Achtergracht 129, 1018 WS Amsterdam, The Netherlands, and the School of Chemistry,
UniVersity of New South Wales, Sydney 2052, Australia
ReceiVed June 7, 1999. ReVised Manuscript ReceiVed March 9, 2000
Abstract: The rate of photoinduced charge separation is measured as a function of solvent for four donor
(D)-bridge-acceptor (A) systems: DMN[10]DCV, DMN[10nb]DCV, DMN[10cy]DCV, and DMAN[10cy]-
DCV. In the first three members of this series, the D/A pair is kept constant and contains the strong
dimethoxynaphthalene (DMN) donor which enables detection of electron transfer over a wide range of solvent
polarity. In the fourth member, DMN is substituted by a dimethoxyanthracene (DMAN) unit, which decreases
the driving force for photoinduced charge separation by about 0.58 eV and thereby limits the occurrence of
electron transfer to polar solvents. In all systems the bridge is held at a length of 10 σ bonds. The configuration
of the bridge is, however, varied to increase its bending in the series, which leads to center-to-center D/A
distances decreasing from 13.4 Å in the first system to 9.54 Å in the second, and 7.50 Å in the latter two. In
DMN[10nb]DCV, the rate of intramolecular charge separation over 9.54 Å is always smaller than that over
13.4 Å in DMN[10]DCV, which is in line with a dominant through-bond mechanism that is more efficient via
an extended array of σ bonds. However, in DMN[10cy]DCV, the rate is as high as or even higher than that
in DMN[10]DCV. Although changes in the driving force are also important, as shown, for example, by the
dramatic rate decrease in DMAN[10cy]DCV as compared to that of DMN[10cy]DCV, the high rates observed
for DMN[10cy]DCV in polar aromatic solvents as well as in acetonitrile strongly indicate an important
contribution of through-solvent interaction across the 7.5 Å D/A distance, which in principle allows the
intercalation of a single solvent molecule in close contact with both D and A. At the longer distance of 9.54
Å in DMN[10nb]DCV, a smaller contribution of through-solvent interaction can still be detected for polar
aromatic solvents but not for acetonitrile. The inherently discontinuous distance dependence of through-solvent
interaction and its possible interesting dependence on molecular structure and temperature are discussed.
Introduction
all-trans array of σ bonds was confirmed repeatedly.6-9 It was
typically found that the decrease of the rate of electron transfer
(k) with the number of bonds (n) in such an all-trans array can
be described by an exponential (k ∼ exp(-nâ)) with a damping
factor â ) 0.9 ( 0.1 per σ bond under conditions where the
changes in rate are thought to be determined mainly by the
changes in electronic coupling (V), i.e., k ∼ V2. In one instance,
we noted8 that for an extended n ) 8 bridge, removal of the
internal all-trans configuration not only reduced the rate of
electron transfersas expected from the predicted reduction in
The mechanism of long-range electron transfer remains a
topic of active research and discussion. Donor (D)-bridge-
acceptor (A) compounds in which the bridge maintains a well-
defined donor-acceptor distance and relative orientation1-4 have
proven to be of great use in these studies. Especially in com-
pounds where the bridge has an extended structure, it has been
shown unequivocally that through-bridge electronic interaction
plays a dominant role in mediating intramolecular electron
transfer between D and A. While this is not unexpected in the
case of π-conjugated bridges, the dominance of through-bridge
interaction has been found to apply also when extended, rigid,
saturated hydrocarbon bridges are used. In fact, the latter type
of long-range electron transfer has provided some of the most
sensitive and convincing tests of through-σ-bond interaction
(TBI) and its structural dependence. Regarding the latter,
especially the theoretical prediction5 of optimal TBI across an
VTBIsbut also led to a significantly stronger solvent dependence
of that rate. We then tentatively proposed that this may be related
to a relative increase in the contribution of through-solvent
interaction (TSI).
Efforts have been made to determine the importance of TSI
in intermolecular electron-transfer processes in rigid matrixes10,11
(5) Hoffmann, R.; Imamura, A.; Hehre, W. J. J. Am. Chem. Soc. 1968,
90, 1499.
(6) Pasman, P.; Verhoeven, J. W.; Boer, T. J. d. Tetrahedron Lett. 1977,
207.
† University of Amsterdam.
‡ University of New South Wales.
(1) Paddon-Row, M. N.; Jordan, K. D. In Modern Models of Bonding
and Delocalization; Liebman, J. F., Greenberg, A., Eds.; VCH Publishers:
New York, 1988; Vol. 6, pp 115-194.
(2) Closs, G. L.; Miller, J. R. Science 1988, 240, 440.
(3) Jordan, K. D.; Paddon-Row, M. N. Chem. ReV. 1992, 92, 395-410.
(4) Verhoeven, J. W. In Electron TransfersFrom Isolated Molecules to
Biomolecules, Part One; Jortner, J., Bixon, M., Eds.; Advances in Chemical
Physics 106; John Wiley & Sons: New York, 1999; pp 603-644.
(7) Kroon, J.; Verhoeven, J. W.; Oliver, A. M.; Paddon-Row, M. N.
Recl. TraV. Chim. Pays-Bas 1988, 107, 509.
(8) Oliver, A. M.; Craig, D. C.; Paddon-Row, M. N.; Kroon, J.;
Verhoeven, J. W. Chem. Phys. Lett. 1988, 150, 366.
(9) Lawson, J. M.; Craig, D. C.; Paddon-Row, M. N.; Kroon, J.;
Verhoeven, J. W. Chem. Phys. Lett. 1989, 164, 120.
(10) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J. Am. Chem. Soc.
1984, 106, 5057.
10.1021/ja991895m CCC: $19.00 © 2000 American Chemical Society
Published on Web 05/12/2000

5076 J. Am. Chem. Soc., Vol. 122, No. 21, 2000
Lokan et al.
and lately also in liquid solution.12,13 Evidently, competition
between TBI and TSI could be studied by the construction of
D-bridge-A systems containing a rigid but U-shaped bridge.
Such a U-shape on one hand might diminish TBI by the absence
of an all-trans coupling path and on the other hand should
enhance TSI by reducing the direct D/A distance as compared
to the through-bond distance. Recently, several D-bridge-A
systems with a more or less pronounced U-shape have, indeed,
been reported. The first types of U-shaped systems were multi-
chromophoric ones.14-17 Although through-solvent-mediated
charge recombination and charge separation mechanisms were
implicated, the presence of extra chromophores in the bridges
complicates interpretation of the rate data. More recently, also
several bichromophoric systems with a pronounced U shape and
closer approach of D and A have been reported by Zimmt et
al. Especially in two of these with respectively an 11-bond
bridge18 and a 9-bond bridge,19-22 D and A are brought in a
face-to-face orientation with a center-to-center separation across
the “cleft” as close as 10.0 and 7.1 Å, respectively. From a
study of the solvent and temperature dependence of the rates
of photoinduced charge separation in these systems as well as
from theoretical calculations, compelling evidence was found
for significant TSI in electronegatively substituted aromatic
solvents. These results were interpreted from a superexchange
mechanism in which the electron affinity of the solvent plays a
decisive role.18
In these studies, rather “weak” D/A pairs were employed that
require significant solvation assistance to make charge separation
thermodynamically feasible. This implies that the (Marcus)
barrier to electron transfer is inherently high and rather steeply
increases with a decrease of the solvent dielectric constant, thus
severely limiting the range of solvent polarity in which charge
separation occurs and also making its rate strongly limited by
Franck-Condon factors.
Figure 1. Structures of the bichromophores studied and of the model
donors DMN[2] and DMAN[2].
To reduce this problem, we have now studied the D-bridge-A
systems DMN[10]DCV, DMN[10nb]DCV, and DMN[10cy]-
DCV (see Figure 1) containing the rather strong dimethoxy-
naphthalene (DMN)/dicyanovinyl (DCV) donor-acceptor pair.
The latter two systems differ in that the hydrocarbon bridge of
the former possesses a central norbornane group (nb) while the
latter possesses a cyclohexane ring (cy). For comparison, also
the DMAN[10cy]DCV system was studied which contains (see
Figure 1) the less powerful 1,4-dimethoxyanthracene donor unit
employed extensively by Zimmt et al.18-22 Substitution of the
1,4-dimethoxyanthracene donor by 1,4-dimethoxynaphthalene
enhances the driving force for photoinduced charge separation
by about 0.6 eV because it increases the singlet energy from
3.00 to 3.78 eV while the ground-state oxidation potential
increases much less, i.e., from 0.9 to 1.1 V (versus SCE). All
Figure 2. Perspective drawings of DMN[10]DCV, DMN[10nb]DCV,
and DMN[10cy]DCV as modeled with the Sybyl force field (see
Experimental Section) with Rc indicated (hydrogens omitted for clarity).
(11) Miller, J. R. New J. Chem. 1987, 11, 83.
(12) Gould, I. R.; Young, R. H.; Mueller, L. J.; Farid, S. J. Am. Chem.
Soc. 1994, 116, 8176.
D-bridge-A systems in Figure 1 contain a 10-bond bridge,
but the curvature of it differs and leads to D/A distances of
13.4, 9.54, and 7.50 Å, respectively (see Figure 2). An X-ray
structure of the ketone precursor to DMN[10nb]DCV (i.e., Cd
(CN)2 replaced by CdO) revealed that this ketone recrystallized
with one molecule of CH2Cl2 in a 1:1 stoichiometry with the
CH2Cl2 molecule lying within the ketone’s molecular cavity.23
(13) Gould, I. R.; Farid, S. Acc. Chem. Res. 1996, 29, 522.
(14) Lawson, J. M.; Paddon-Row, M. N.; Schuddeboom, W.; Warman,
J. M.; Clayton, A. H. A.; Ghiggino, K. P. J. Phys. Chem. 1993, 97, 13099.
(15) Roest, M. R.; Lawson, J. M.; Paddon-Row, M. N.; Verhoeven, J.
W. Chem. Phys. Lett. 1994, 230, 536.
(16) Roest, M. R.; Verhoeven, J. W.; Schuddeboom, W.; Warman, J.
M.; Lawson, J. M.; Paddon-Row, M. N. J. Am. Chem. Soc. 1996, 118,
1762.
(17) Jolliffe, K. A.; Bell, T. D. M.; Ghiggino, K. P.; Langford, S. J.;
Paddon-Row, M. N. Angew. Chem., Int. Ed. Engl. 1998, 37, 916.
(18) Han, H.; Zimmt, M. B. J. Am. Chem. Soc. 1998, 120, 8001-8002.
(19) Cave, R. J.; Newton, M. D.; Kumar, K.; Zimmt, M. B. J. Phys.
Chem. 1995, 99, 17501.
(20) Kumar, K.; Lin, Z.; Waldeck, D. H.; Zimmt, M. B. J. Am. Chem.
Soc. 1996, 118, 243.
Results and Discussion
Table 1 compiles rates of photoinduced charge separation
from the donor singlet excited state at room temperature in
a wide range of solvents for the D-bridge-A systems of
Figure 1.
(21) Gu, Y.; Kumar, K.; Lin, Z.; Read, I.; Zimmt, M. B.; Waldeck, D.
H. J. Photochem. Photobiol. A: Chem. 1997, 105, 189.
(22) Zimmt, M. B. Chimia 1997, 51, 82.
(23) Lokan, N. R.; Craig, D. C.; Paddon-Row, M. N. Synlett 1999, 397.

SolVent-Mediated Intramolecular ET in U-Shaped Systems
J. Am. Chem. Soc., Vol. 122, No. 21, 2000 5077
Table 1. Experimental Rate (kexp) and Estimated Barrier (∆G#) of Photoinduced Charge Separation as a Function of Solvent at Room
Temperature
kexp (×108 s-1) [∆G# (eV)]
dielectric
constant (ꢀ)
refractive
index (n)
solvent
DMN[10]DCV
DMN[10nb]DCV
DMN[10cy]DCV
DMAN[10cy]DCV
TIPB (1,3,5-triisopropyl
benzene)
benzene
2.1 ( 0.1
2.28
1.4882
1.5011
1.3992
1.3524
1.3724
1.4072
1.5515
1.521
19
[0.111]
72
[0.093]
35
[0.096]
51
[0.096]
85
[0.080]
120
[0.066]
141
[0.034]
103
5.9
[0.039]
21.3
[0.033]
8.0
[0.043]
7.5
[0.047]
9.2
[0.038]
18
[0.030]
65
[0.012]
58
187
[0.005]
500
[0.004]
49
[0.010]
49
[0.014]
124
[0.011]
110
[0.008]
665
[0.001]
221
-
[0.210]
-
[0.191]
-
[0.175]
0.07
[0.166]
0.21
[0.147]
0.27
[0.134]
2.0
[0.104]
1.3
DBE (di-n-butyl ether)
DEE (diethyl ether)
EtAc (ethyl acetate)
THF (tetrahydrofuran)
3.10
4.20
6.02
7.58
ODCB (orthodichloro-
benzene)
BzCN (benzylcyanide)
9.93
19.0
[0.036]
a
[0.035]
24
[0.014]
a
[0.013]
7
[0.002]
a
[0.002]
141
[0.102]
9.5
[0.100]
0.3
PhCN (benzonitrile)
ACN (acetonitrile)
25.20
37.50
1.5282
1.3441
[0.073]
[0.037]
[0.011]
[0.133]
a Total electron-transfer quenching of the DMN singlet occurs by this solvent.
As reported earlier,24 the variation of rate with solvent is
modest for the extended system DMN[10]DCV, notwithstanding
the large changes in driving force predicted to be brought about
by changing the solvent dielectric constant between ꢀ ≈ 2.2
and 37. This is interpreted to indicate both a virtually solvent-
independent electronic coupling of the TBI type (VTBI) and an
almost solvent independent Franck-Condon factor (see below).
It is well known that one should be careful with interpreting
rates only in terms of changes in the total electronic coupling
(V) because changing the solvent (and/or the distance) may also
change the Franck-Condon factor. Within the framework of
basic electron transfer theory, the latter translates into the Marcus
barrier (∆G#), and the rate of nonadiabatic electron transfer can
be written as
that the refractive index remains constant. For photoinduced
charge separation in solvents with n2 ) 2, the condition under
which this occurs is given,29 to a good approximation, by
Rcopt ) 7.2/[Eox(D) - Ered(A) - E00 + λin + 6.81/r] (2)
In eq 2, Eox(D) and Ered(A) represent the one-electron redox
potentials (in volts) of D and A as measured in a polar solvent
such as acetonitrile, E00 the energy (in electronvolts) of the
locally in D or A excited state, λi the internal reorganization
energy (in electronvolts), and r (in angstroms) the average ionic
radius.
For the DMN/DCV donor-acceptor pair, the values Eox(D)
) 1.1 V, E00 ) 3.78 eV, Ered(A) ) -1.7 V, r ) 4.5 Å, and λin
) 0.6 eV apply.24 Equation 2 then gives Rc ) 6.35 Å. This
opt
k ) [2π3/2V2 exp(-∆G#/kBT)]/(h2λkBT)1/2
(1)
implies that electron transfer in DMN[10cy]DCV (Rc ) 7.5 Å)
should be close to barrierless in all solvents. In Table 1, this is
further illustrated by calculating the barrier explicitly in each
solvent, taking into account its dielectric constant and its
refractive index and employing the well-known dielectric
continuum models29 with again the average ionic radius set at
4.5 Å and a constant internal reorganization energy set at 0.6
eV.24 For DMN[10cy]DCV, a very small barrier is then, indeed,
estimated, irrespective of the solvent employed. Unavoidably,
the barrier increases with Rc and at the same time becomes more
solvent dependent in DMN[10nb]DCV and DMN[10]DCV (see
Table 1).While in all three DMN/DCV systems the estimated
barriers are quite small, it should be realized that even small
barriers have a significant kinetic effect, which starts to exceed
an order of magnitude for DMN[10]DCV upon going to low-
polarity solvents. We stress that under such conditions the
separation of barrier effects from electronic coupling effects in
determining the rate of electron transfer (see eq 1) becomes
progressively more difficult.
In eq 1, h is Planck’s constant, kB Boltzmann’s constant, and λ
the reorganization energy.
Thus, not only changes in V but also changes in ∆G# have a
dramatic influence on the rate and thereby frustrate extraction
of V from electron-transfer rates. In principle, this can be
remedied by determining ∆G# from temperature-dependent
studies, but the interpretation of these has turned out to be
complex due to the changes of the solvating properties of
solvents with temperature.25 It is therefore not amazing that,
e.g., quite different V values are derived26,27 from a single set
of temperature-dependent rate data employing different solvation
models.28
As we have pointed out before,29 for each D/A combination
there exists a unique distance (Rcopt) at which ∆G# becomes
zero, irrespective of the solvent dielectric constant, provided
(24) Oevering, H.; Paddon-Row, M. N.; Heppener, M.; Oliver, A. M.;
Cotsaris, E.; Verhoeven, J. W.; Hush, N. S. J. Am. Chem. Soc. 1987, 109,
3258.
(25) Kroon, J.; Oevering, H.; Verhoeven, J. W.; Warman, J. M.; Oliver,
A. M.; Paddon-Row, M. N. J. Phys. Chem. 1993, 97, 5.
(26) Zeng, Y.; Zimmt, M. B. J. Phys. Chem. 1992, 96, 8395.
(27) Kumar, K.; Kurnikov, I. V.; Beratan, D. N.; Waldeck, D. H.; Zimmt,
M. B. J. Phys. Chem. A 1998, 102, 5529.
For the DMAN/DCV combination, eq 2 predicts that Rcopt is
as small as 4.2 Å, and as can be seen from Table 1, the
attenuation of the electron transfer by barrier effects must be
very dramatic in all solvents (about 2 orders of magnitude in
polar solvents and exceeding 3 orders of magnitude in low-
polarity solvents) for DMAN[10cy]DCV, even at the short
distance of 7.5 Å. In fact, charge separation is calculated to
(28) Matyushov, D. V. Chem. Phys. 1993, 174, 199.
(29) Kroon, J.; Verhoeven, J. W.; Paddon-Row, M. N.; Oliver, A. M.
Angew. Chem., Int. Ed. Engl. 1991, 30, 1358.

5078 J. Am. Chem. Soc., Vol. 122, No. 21, 2000
Lokan et al.
Figure 3. Rates of photoinduced charge separation in DMN[10nb]DCV, DMN[10cy]DCV, and DMAN[10cy]DCV relative to that in DMN[10]-
DCV as found experimentally, kexp (A), and after correction to “zero barrier” conditions, kopt (B).
become significantly endergonic for DMAN[10cy]DCV in low-
polarity solvents, and experimentally we found it quite difficult
to detect significant effects of electron transfer on the fluores-
cence in nonpolar solvents and were only able to estimate its
rate with reasonable confidence in diethyl ether and in higher
polarity media (see Table 1).
DCV should be more effective than that in DMN[10nb]DCV,
but of course there is a significantly lower barrier in the former
(see Table 1) that accounts for at least a part of the rate increase.
This barrier-related effect should, however, be most pronounced
in low-polarity solvents and decrease to a lower and almost
constant effect at higher polarities. That is clearly not in line
with the observations, and therefore an additional effect, such
as a solvent-dependent contribution of VTSI, may already be
invoked for DMN[10cy]DCV from this inspection of the
experimental rates. The experimental rates for DMAN[10cy]-
DCV are too low to draw any conclusion by direct comparison
with the DMN/DCV systems and furthermore extend over a
smaller polarity region, but again we note that the rate ratios
plotted in Figure 3A show a strong solvent dependence that
crudely resembles that of the other bent systems.
To reveal more quantitatively the eventual changes in V
occurring as a function of structure and solvent, we have
corrected the experimental rates to “zero barrier conditions”. It
should be stressed that these barriers are notoriously difficult
to obtain experimentally, especially because changes in solvent
parameters with temperature play such a complicating role in
most common organic solvents employed here,28,29 and that also
upon calculational derivation of the barriers the solvation model
employed as well as its parametrization31 plays a critical role.
The dielectric continuum model we employed here requires only
a few parameters but has been found25 to reproduce quite well
the experimentally determined barrier in cases where the
temperature-dependent behavior of the rate is uncomplicated.
Of course, the dielectric continuum model does not take into
account any specific solvent/solute interactions, and even so
its outcome depends rather critically upon the choice of
We now first qualitatively discuss the experimental rate data
compiled in Table 1, and for this purpose we have plotted in
Figure 3A the rates of the bent systems relative to that of DMN-
[10]DCV in each solvent (note that for the DMN/DCV systems,
no rates in PhCN can be measured because this strongly
electron-accepting solvent itself fully quenches the singlet
excited state of DMN). Electron transfer in DMN[10nb]DCV
(Rc ) 9.5 Å) is always slower than that in DMN[10]DCV (Rc
) 13.4 Å), despite the lower barrier that could give it a rate
advantage of up to an order of magnitude. Clearly, in the
extended system, the higher barrier must be overcompensated
by a larger V, which undoubtedly can be attributed to the
presence of an all-trans TBI pathway in that extended system.
Whether in DMN[10nb]DCV the decrease of VTBI is partly
compensated by an eventual increase of VTSI cannot be deduced
with certainty from a qualitative inspection of the data, but this
will be discussed in more detail below. We do, however, note
already that the rate reduction is rather strongly solvent
dependent and is especially less pronounced in the polar
aromatic solvents ODCB and BzCN, although in such polar
solvents the barrier reduction gained by reducing the distance
from 13.4 to 9.54 Å must be relatively small (see Table 1).
In DMN[10cy]DCV, Rc is further reduced to 7.5 Å, and as
compared to DMN[10nb]DCV, a dramatic rate increase occurs
in all solvents, making electron transfer as fast as or in several
cases even much faster than that for DMN[10]DCV (see Figure
3A). There is no reason30 to assume that TBI in DMN[10cy]-
(30) Paddon-Row, M. N., unpublished calculations.
(31) Matyushov, D. V.; Ladanyi, B. M. J. Chem. Phys. 1998, 108, 6362.

SolVent-Mediated Intramolecular ET in U-Shaped Systems
J. Am. Chem. Soc., Vol. 122, No. 21, 2000 5079
parameters, such as the average ionic radius and the internal
reorganization energy. Therefore, the absolute value of “zero
barrier rates” (kopt) obtained even in the case of such relatively
small barriers as those present in our DMN/DCV systems must,
in our opinion, be taken with a grain of salt. Although we will
return to the question of how large the V values actually are in
our compounds, we therefore now only assume that in each
solvent used the weaknesses inherent to the barrier corrections
made apply equally to at least the three very closely related
DMN/DCV systems. If so, the ratio of the “zero barrier rates”
obtained for the three DMN/DCV systems in each solvent carries
information about the eventual changes in the relative V2 values
as a function of solvent (note that an additional correction for
the change of the reorganization energies as required by eq 1 is
too small to be relevant within this context and has therefore
been omitted). The outcome of this operation is extremely
revealing, as shown in Figure 3B.
Again taking DMN[10]DCV as a reference, the strong
relative rate enhancement shown by DMN[10cy]DCV in the
low-polarity solvents benzene and TIPB as compared to that in
medium-polarity solvents is now less extreme and should thus,
to a large extent, be attributed to the increased importance of
barrier-induced retardation for DMN[10]DCV at low polarity.32
However, a clear solvent dependence of the rate ratio remains,
and the ratio still reaches its highest values in both low-polarity
and especially in high-polarity aromatic solvents as well as in
acetonitrile, thus suggesting a significant increase of V2 for
DMN[10cy]DCV in these solvents. Interestingly, the “zero
barrier” ratio exceeds unity only in ODCB (ratio ) 1.32) and
is significantly below unity in most other solvents. This implies
that in most solvents, even at the short distance of Rc ) 7.5 Å
in DMN[10cy]DCV, the loss of TBI as compared to that in
DMN[10]DCV (Rc ) 13.4 Å) is not fully compensated by the
gain in TSI!
The comparison of “zero barrier rates” for DMN[10nb]DCV
with DMN[10]DCV yields similar but less pronounced effects
for the polar aromatic solvents ODCB and BzCN, but much
less pronounced indications for a significant enhancement of
the relative V2 in ACN or in low-polarity aromatic solvents are
found.
Clearly, DMN[10]DCV is a rather poor reference for DMAN-
[10cy]DCV, and less value should therefore be attributed to
the absolute position of the data points plotted in Figure 3B for
the ratio of the kopt values of these two compounds. In fact, the
barrier correction to be applied to the ratio of the experimental
rate of DMAN[10cy]DCV over that of DMN[10]DCV ranges
from 1 order of magnitude in high- and medium-polarity
solvents up to almost 2 orders of magnitude in nonpolar solvents.
Nevertheless, the results obtained indicate that, for this system,
ODCB, BzCN, and ACN behave similarly and, just as for
DMN[10cy]DCV, enhance the V2 for the bent system relative
to that of the extended system as compared to the situation in
the medium-polarity solvents.
Figure 4. 3D model of a benzene molecule in the “jaws” of DMN-
[10cy]DCV.
benzene disappear at Rc ) 9.54 Å for DMN[10nb]DCV, but
especially also ACN seems to be much less effective in
promoting TSI at the latter distance in comparison to the polar
aromatic solvents. It is important to note that earlier results
obtained by Zimmt et al. for DMAN/acceptor pairs appear to
show this trend too. Thus, in a system with Rc ) 10 Å, the
value of V for ACN was concluded18 to be only 14% of that in
PhCN, but in a system with Rc ) 7.1 Å it was found20 to be
33%. Also for the Rc ) 7.5 Å DMAN[10cy]DCV system we
study here, acetonitrile appears to be “above average” in
supporting TSI across such a small cleft.
In this relation, it should be realized that the distance
dependence of TSI can, in principle,2 be highly discontinuous
and solvent structure dependent. Taking a van der Waals
thickness of T ) 3.5 Å for a typical π-system, the Rc ) 7.5 Å
cleft in DMN[10cy]DCV allows a rather tight fit of a single
aromatic solvent molecule in that cleft (see Figure 4). For the
9.54 Å cleft in DMN[10nb]DCV, this fit would be very loose
for one solvent molecule and extremely tight for two. The small
number of solvent molecules interposed between D and A makes
the decrease of TSI with distance, in principle, highly discon-
tinuous with local maxima at distances that allow tight fit of
one, two, three, etc. solvent molecules.
A crude prediction of the degree of discontinuity can be
achieved by a simple superexchange pathway analysis.3,33,34 In
this model, the cleft is filled with the maximum number of
solvent molecules that can be fitted in (N), leaving a total free
space F ) Rc - T(N + 1), where the van der Waals thickness
of D, A, and each of the solvent molecules is set at T.
If the fit is tight (F ) 0), the superexchange via the stack of
N solvent molecules may be written as VTSI ) V0(V0/∆E)N,
where V0 stands for the resonance integral between nearest
neighbors (assuming an equal value for solvent/solvent, D/sol-
vent, and A/solvent contacts), while ∆E is the energy gap
between the transition state for electron transfer from D to A
and a virtual state in which charge is on one of the solvent
There seems to be little doubt that the rate ratio modulations
observed in Figure 3B must be attributed to a significant value
and solvent dependence of VTSI in the bent systems. Logically,
this effect is more pronounced at Rc ) 7.5 Å than at Rc) 9.54
Å, but it also appears that this increase in distance reduces the
number of solvents capable of producing significantly enhanced
TSI. Thus, not only the indications that for DMN[10cy]-
DCV, at Rc ) 7.5 Å, TSI is slightly enhanced in TIPB and in
(32) We are very grateful to one of the reviewers who pointed out how
strongly “contaminated” by barrier effects the ratio of the uncorrected rate
constants (Figure 3A) becomes at low polarity.
(33) McConnell, H. M. J. Chem. Phys. 1961, 35, 508.
(34) Balzani, V.; Scandola, F. Supramolecular Photochemistry; Ellis
Horwood: New York, 1991.

5080 J. Am. Chem. Soc., Vol. 122, No. 21, 2000
Lokan et al.
directly related to the ionization potential of the donor and the
electron affinity of the solvent. The UB3LYP-calculated36
ionization potential (IP ) 7.24 eV) of DMN[2] differs little
from that reported18 for DMAN (IP ) 7.4 eV), which should
make DMN- and DMAN-based systems equally sensitive to the
effects of TSI. The electron affinities of the solvents employed
vary widely (e.g., EA ) -1.12 eV for benzene,37 -0.8 eV for
BzCN,18 and -2.8 eV for ACN18). ∆E decreases with increasing
solvent electron affinity, and as a result, solvents with high
electron affinity are expected to provide more efficient TSI.
Therefore, the apparently strong VTSI contribution in elec-
tronegatively substituted aromatic solvents such as BzCN as
compared to that in benzene by itself comes as no surprise.
However, the finding that at short range, i.e., at the Rc ) 7.5 Å
distance available in DMN[10cy]DCV as well as in DMAN-
[10cy]DCV also in ACN, where ∆E should be 2 eV larger than
that in BzCN and 1.68 eV larger than that in benzene, VTSI seems
to be important is surprising and clearly cannot be accounted
for on the basis of ACN’s electron affinity alone. Another aspect
of solvent-mediated electron transfer in U-shaped systems may
deserve attention in this connection. In fact, the situation where
one or a few solvent molecules are intercalated between D and
A, as modeled in Figure 4, should be considered as a distinct
thermodynamic entity which is in equilibrium with an entity
(or entities) lacking tightly intercalated solvent and in which
electron transfer is thus probably much slower. The rate of
electron transfer observed under fast solvent-exchange condi-
tions is then a weighted average of that occurring in molecules
possessing “solvent-filled” cavities and those having “solvent-
free” cavities. This complication, if present, would have a
number of interesting and far-reaching consequences, such as
the following: (i) the overall rate would not be a direct measure
of the solvent participation but rather the product of that
participation and the affinity of the solvent to occupy the cleft;
(ii) the temperature dependence of electron transfer would
contain a contribution20 of the change in the equilibrium constant
between the filled and empty states, which can, in principle,
give rise to an apparent (negative) activation energy of electron
transfer that is, in fact, due to a change in electronic coupling
Figure 5. Distance dependence of VTSI (in units V0) as predicted by
eq 3 for a molecular “thickness” T ) 3.5 Å and assuming that the
maximum number of molecules (N) is inserted between D and A. The
curves drawn were calculated for a ratio V0/∆E ) 0.05 (dotted line),
0.1 (dashed line), and 0.2 (solid line).
molecules. It is assumed that this gap is the same for each
solvent molecule in the cleft.
If the fit is not tight, the free spaces reduce the interaction
between successive components. For this, an empirical through-
space distance dependence is assumed with a high damping
factor γF. In an earlier parametrization for electron pathway
analysis in proteins, a value γF ) 1.7 Å-1 was proposed,35 which
implies a decrease of electron-transfer rates through space with
a damping factor of 2γF ) 3.4 Å-1. Ab initio MO calculations1
indicate that a smaller value for γF of 1.4 Å-1 is more
appropriate. The expression for VTSI then becomes
VTSI ) V0(V0/∆E)N [exp(-1.4F)]
) V0(V0/∆E)N [exp{-1.4(Rc - T(N + 1)] (3)
It is important to note that, within this approximation, the
distance dependence of VTSI predicted by eq 3 is independent
of how the total free space F is divided along the DSNA array.
Thus, solvent motions that do not change F should not influence
the distance dependence of VTSI, even though the absolute value
of VTSI is certainly strongly dependent on the orientation of the
solvent molecules relative to D and A and to each other3,19
because this influences V0. In Figure 5, the dependence of VTSI
(in units of V0) on Rc predicted by eq 3 is plotted for T ) 3.5
Å and for the values of the ratio V0/∆E ) 0.05, 0.1, and 0.2. In
the simple model underlying eq 3, it is then found (see Figure
5) that local maxima in coupling should result at Rc values that
allow a tight fit of a whole number of solvent molecules, while
beyond each of these Rc values the coupling drops steeply.
Although the steep steps predicted will certainly be smoothed
by solvent motions that modulate the total free space F, a rather
strong discontinuity is expected to remain for small numbers
of N under the constraint of well-defined cleft sizes in U-shaped
D-bridge-A molecules.
V
TSI; (iii) under conditions of slow solvent exchange electron
transfer can no longer be described by a single exponential and
may even be limited by the rate at which a solvent molecule
enters the cleft.
These aspects are presently under active investigation, but
with respect to the unexpected efficiency of acetonitrile in
mediating TSI across short distances, we already note that the
small size, polar nature, and strongly solvating properties of
this solvent have recently been found to allow it to enter quite
effectively a narrow, π-system lined cavity.38 Also, the rates of
photoinduced ET in a tetrad, in which the terminal chro-
mophores are separated by less than 7 Å, have been reported17
to be the same in both benzonitrile and acetonitrile, and in view
of the very long TBI pathway there is no doubt that, in that
tetrad, ET should occur by a dominant TSI mechanism.
(36) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;
Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G.
A.; Montgomery, J. A.; Raghavachari, K.; Al-Latham, M. A.; Zakrzewski,
V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.;
Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.;
Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.;
Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-
Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94 (Revision B); Gaussian
Inc.: Pittsburgh, PA, 1994.
We now return to the question of what determines the
efficiency of a particular type of solvent molecule in mediating
electron transfer in terms of the ∆E term from the simple
superexchange model above (eq 3) that takes into account the
energy gap between the transition state for charge separation
and a state in which the negative charge is on the solvent and
the positive charge on the donor (D+/S-/A). The energy required
to put an electron from the donor on a solvent molecule is
(37) Balaji, V.; Ng, L.; Jordan, K. D.; Paddon-Row, M. N.; Patney, H.
K. J. Am. Chem. Soc. 1987, 109, 6957.
(35) Betts, J. N.; Beratan, D. N.; Onuchic, J. N. J. Am. Chem. Soc. 1992,
114, 4043.
(38) Kla¨rner, F. G.; Burkert, U.; Kamieth, M.; Boese, R.; Benet-Buchholz,
J. Chem. Eur. J. 1999, 5, 1701.

SolVent-Mediated Intramolecular ET in U-Shaped Systems
J. Am. Chem. Soc., Vol. 122, No. 21, 2000 5081
Finally, we return briefly to the question of what the actual
value of V is in our compounds. While we think that the
variations in V2 are reasonably well reflected by the plots
provided in Figure 3B, we are, for reasons amply outlined above,
hesitant to put too much value on the absolute values of V that
can, in principle, be calculated readily from the data in Table 1
via application of eq 1. Nevertheless, it seems important to point
out that, for DMN[10]DCV, a value of V ) 17.6 cm-1 has been
reported39 that was determined not from kinetic data but
independently from the radiative transition probability of the
very weak charge-transfer fluorescence it displays in DBE. This
V, therefore, should be related to the electronic coupling of the
charge-separated state with the ground state rather than with
the locally excited state. Nevertheless, it appears quite comfort-
ing to find that from the data in Table 1 and application of eq
1, a value V ) 21 cm-1 in DBE is derived.
ficient descriptor to estimate the electronic interaction involved
in the actual electron-transfer process.
Experimental Section
Syntheses. The synthesis of DMN[10]DCV has been described
earlier.24 DMN[10nb]DCV, DMN[10cy]DCV, and DMAN[10cy]DCV
were synthesized as described in the Supporting Information.
Charge separation rates were determined by time-resolved fluo-
rescence spectroscopy employing time-correlated single-photon counting
as described previously.24 An excitation wavelength of 322 nm was
employed for the DMN systems and 339 nm for the DMAN systems,
and the decay of the DMN or DMAN fluorescence was detected at
three wavelengths around the maximum. For the model system DMN-
[2], the (monoexponential) decay time (τref) was determined in each
solvent and varies between 5.9 ns in benzene and 7.5 ns in acetonitrile.43
For the model DMAN[2], the fluorescence lifetime appears more
variable, i.e.: benzene, 22 ns; DBE, 15.6 ns; DEE, 13.1 ns; EtAc, 18.5
ns; THF, 21.8 ns; ODCB, 16.4 ns; BzCN, 23 ns; PhCN, 22.3 ns; and
ACN, 20.7 ns. This is a serious problem because the experimental rate
of charge separation is calculated from kexp ) 1/τ - 1/τref, and the rate
in DMAN[10cy]DCV is so low (see Table 1) that the actual value of
Concluding Remarks
The three DMN-bridge-DCV molecules depicted in Figures
1 and 2 have allowed us to investigate the possible role of
through-solvent interaction (TSI)-mediated electron transfer over
a wider solvent polarity range than that accessible for similar
systems in which the strong DMN donor is substituted by the
much weaker DMAN donor, such as in DMAN[10cy]DCV.
Especially at the 7.5 Å distance present in DMN[10cy]DCV,
through-solvent interaction is detectable for some polar as well
as nonpolar solvents. Although a simple superexchange model
predicts that the solvent electron affinity should be a decisive
factor, acetonitrile, which has a very negative electron affinity
(EA ) -2.8 eV), appears to mediate TSI more effectively than,
e.g., benzene (EA ) -1.12 eV) across a 7.5 Å distance. At the
longer distance of 9.54 Å found in DMN[10nb]DCV, however,
acetonitrile largely loses its ability to mediate TSI, while in
electronegatively substituted aromatic solvents TSI is still
apparent. The “bite size” of the D-bridge-A system thus
appears to have an effect on the relative efficiency of solvent
molecules in mediating TSI across short ranges corresponding
to one or two solvent molecule diameters, but it cannot yet be
established whether this is the result of differences in the
orientation of the various solvent molecules in the cleft between
D and A or whether different affinities for residing in that cleft
also play a role.
Finally, it should be noted that ab initio MO calculations
on the charge-transfer-state geometry of several U-shaped
D-bridge-A systems closely related to those studied here have
revealed a strong tendency of such systems to undergo extensive
conformational changes driven by the electrostatic attraction of
the oppositely charged termini.40 While until now these calcula-
tions have been restricted to the gas phase, it is well known
from experiments on less rigidly bridged systems that such
“harpooning” phenomena41 also can be significant in low
dielectric constant solvents.42 Under such conditions, the ground-
state conformation and the transition state of electron transfer
may differ sufficiently to make the ground-state Rc an insuf-
τ
ref has a large influence. For the DMN/DCV bichromophores, the rates
are, on the other hand, so high that the precise value of τref plays little
role, i.e., kexp ) 1/τ - 1/τref ≈ 1/τ. It should be noted that, for the
bichromophores, the decay in general contains, in addition to a major
short component, a minor component with τ ≈ τref due to small
impurities that lack the DCV acceptor. This does not influence the
accuracy of the rate determination as long as the two components can
be separated reliably. For DMAN[10cy]DCV, this becomes quite
problematic in low-polarity media (where charge separation is, in fact,
calculated to be endergonic), and therefore no rate data in such media
are given in Table 1.
Molecular Geometries. The molecular geometries shown in Figures
2 and 4 were determined employing the Sybyl force field in MacS-
partan.44 In the case of DMN[10]DCV and DMN[10nb]DCV, X-ray
structural data are available for the precursor ketones (i.e., CdO instead
of CdC(CN)2)45,23 that fully substantiate the validity of this approach.
Thus, the X-ray structure of the ketone precursor to DMN[10nb]DCV
gives a value of 9.5 Å for the distance between the center of the
naphthalene unit and the carbonyl oxygen. Interestingly, this ketone
recrystallized with one molecule of CH2Cl2 in a 1:1 stoichiometry with
the CH2Cl2 molecule lying within the ketone’s molecular cavity.
Quantum Chemical Calculations. Vertical IPs were calculated as
the UB3LYP energy of the radical cation minus the B3LYP energy of
the neutral, and the vertical EAs as the B3LYP energy of the neutral
minus the UB3LYP energy of the radical anion. The 6-311G(d) and
6-311+G(d) basis sets were used for the IP and EA calculations,
respectively. Geometries employed were HF/3-21G-optimized structures
of the corresponding neutrals. All calculations were performed with
Gaussian 94 (Revision B).36
Acknowledgment. This research has been financially sup-
ported by the Council for Chemical Sciences of The Netherlands
Organization for Scientific Research (CW-NWO) and by the
Australian Research Council (ARC). The award of an ARC
Senior Research Fellowship to M.N.P.-R. is also gratefully
acknowledged.
Supporting Information Available: Full experimental
details for the synthesis of DMN[10cy]DCV ()25, DMN[10nb]-
DCV ()26), and DMAN[10cy]DCV ()31) (PDF). This mat-
erial is available free of charge via the Internet at http://pubs.
acs.org.
(39) Oevering, H.; Verhoeven, J. W.; Paddon-Row, M. N.; Warman, J.
M. Tetrahedron 1989, 45, 4751.
(40) Shephard, M. J.; Paddon-Row, M. N. J. Phys. Chem. A 1999, 103,
3347.
(41) Wegewijs, B.; Verhoeven, J. W. In Electron TransfersFrom Isolated
Molecules to Biomolecules, Part One; Jortner, J., Bixon, M., Eds.; Advances
in Chemical Physics 106; John Wiley & Sons: New York, 1999; pp 221-
264.
(42) Lauteslager, X. Y.; Bartels, M. J.; Piet, J. J.; Warman, J. M.;
Verhoeven, J. W.; Brouwer, A. M. Eur. J. Org. Chem. 1998, 2467, 7.
JA991895M
(43) Kroon, J.; Oliver, A. M.; Paddon-Row, M. N.; Verhoeven, J. W. J.
Am. Chem. Soc. 1990, 112, 4868.
(44) MacSpartan; Wavefunction, Inc.: Irvine, CA, 1996.
(45) Craig, D. C.; Paddon-Row, M. N. Aust. J. Chem. 1987, 40, 1951.