Fundamentally Different Distance Dependences of Electron-Transfer Rates for Low and High Driving Forces

Article abstract of DOI:10.1021/acs.inorgchem.8b02973

The distance dependences of electron-transfer rates (k_ET) in three homologous series of donor-bridge-acceptor compounds with reaction free energies (ΔGET0) of ca. -1.2, -1.6, and -2.0 eV for thermal charge recombination after initial photoinduced charge separation were studied by transient absorption spectroscopy. In the series with low driving force, the distance dependence is normal and k_ET decreases upon donor-acceptor distance (r_DA) elongation. In the two series with higher driving forces, k_ET increases with increasing distance over a certain range. This counterintuitive behavior can be explained by a weakly distance-dependent electronic donor-acceptor coupling (H_DA) in combination with an increasing reorganization energy (λ). Our study shows that highly exergonic electron transfers can have distance dependences that differ drastically from those of the more commonly investigated weakly exergonic reactions.

Full text of DOI:10.1021/acs.inorgchem.8b02973

Article
pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Fundamentally Different Distance Dependences of Electron-Transfer
Rates for Low and High Driving Forces
Svenja Neumann and Oliver S. Wenger*
Department of Chemistry, University of Basel, St. Johanns-Ring 19, 4056 Basel, Switzerland
S
* Supporting Information
ABSTRACT: The distance dependences of electron-transfer
rates (kET) in three homologous series of donor−bridge−
acceptor compounds with reaction free energies (ΔG0ET) of ca.
−1.2, −1.6, and −2.0 eV for thermal charge recombination
after initial photoinduced charge separation were studied by
transient absorption spectroscopy. In the series with low
driving force, the distance dependence is normal and kET
decreases upon donor−acceptor distance (rDA) elongation. In
the two series with higher driving forces, kET increases with
increasing distance over a certain range. This counterintuitive
behavior can be explained by a weakly distance-dependent
electronic donor−acceptor coupling (HDA) in combination
with an increasing reorganization energy (λ). Our study shows that highly exergonic electron transfers can have distance
dependences that differ drastically from those of the more commonly investigated weakly exergonic reactions.
Excitation of the metal photosensitizers in these compounds
induces rapid (≤10 ns) charge separation leading to a radical
pair state that subsequently undergoes thermal charge
recombination between reduced acceptor and oxidized
donor. The driving force for that recombination process
(−ΔG0CR) varies from ca. 1.2 eV (TAA-phn-Ru-phn-NDI series)
to ca. 1.6 eV (TAA-phn-Ru-phn-AQ) and ca. 2.0 eV (TPA-phn-
Ir-phn-AQ). The key finding is that for the triads with −ΔGC0 R
≈ 1.2 eV, the distance dependence of the electron-transfer rate
for charge recombination (kCR) is normal (i.e., kCR decreases
with increasing distance), whereas in the two other triad series,
INTRODUCTION
■
Numerous prior studies investigated the distance dependence
of electron-transfer rates (kET) and the role of the intervening
medium between the donor and the acceptor.1 Rigid rod-like
donor−bridge−acceptor compounds,2−13 properly folded
proteins, or DNA equipped with suitable photosensitizers are
particularly useful for investigations in which the donor−
acceptor distance (rDA) must be kept constant on the timescale
of an electron-transfer event.1,14−17 Saturated hydrocarbon
bridges or protein backbone typically enable long-range
electron transfer via tunneling,18,19 whereas conjugated bridges
or DNA can give rise to hopping.20−27 Though the distance
dependences of kET are markedly different for these two
mechanisms, both usually lead to a decrease of kET with
increasing distance. Experimental studies that reported on an
increase of kET at greater rDA are extremely rare.28−30 To
complement such distance-dependence studies, other inves-
tigations focused on the dependence of kET on reaction free
energy (ΔG0ET),31−35 and the dependence of kET on ΔGE0T at
fixed rDA is now reasonably well understood. However, we are
unaware of prior systematic studies of the distance dependence
of kET as a function of ΔG0ET. Against the background of our
recent finding that kET can increase with increasing distance in
donor−photosensitizer−acceptor triads,36,37 and given the
theoretical prediction of such counterintuitive effects,38,39 we
explored the distance dependence of kET in the three series of
triads shown in Scheme 1. These triads contain either a
relatively strong triarylamine (TAA) donor with methoxy
substituents or a weaker triphenylamine (TPA) donor with
chloro substituents. As acceptors, a naphthalene diimide
(NDI) unit or an anthraquinone (AQ) moiety was employed.
k
CR increases with increasing donor−acceptor separation. This
shows that highly exergonic electron transfers can have
distance dependences that differ fundamentally from those of
the more frequently investigated weakly exergonic reactions.
RESULTS AND DISCUSSION
■
The molecular triads were synthesized and characterized as
described in the Supporting Information. Cyclic voltammetry
was used to determine the redox potentials of the individual
components of all triads (Supporting Information, page S35),
leading to the −ΔG0CR values in Scheme 1. When exciting a 20
μM CH3CN solution of TAA-ph1-Ru-ph1-NDI at 532 nm with
laser pulses of ∼10 ns duration, the transient absorption
spectrum recorded immediately afterward (Figure 1a) shows
the spectroscopic signatures of the anticipated charge-
separated state, as confirmed by the chemical oxidation and
reduction UV−vis difference spectra for TAA+ (Figure 1b) and
Received: October 19, 2018
© XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.8b02973
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Inorganic Chemistry
Article
Scheme 1. Structures of Molecular Triads and Driving
Forces for Charge Recombination (−ΔG0CR) between
Oxidized Donors and Reduced Acceptors
Figure 1. (a) Transient UV−vis absorption spectrum of 20 μM TAA-
ph1-Ru-ph1-NDI in de-aerated CH3CN at 20 °C. The sample was
excited at 532 nm with laser pulses of ca. 10 ns duration, detection
occurred by integration over a period of 200 ns immediately
afterward. (b) UV−vis difference spectrum resulting from chemical
oxidation of the TAA unit in TAA-ph1-Ru-ph1-NDI with Cu(ClO4)2
in CH3CN. (c) UV−vis difference spectrum resulting from chemical
one-electron reduction of the NDI unit in TAA-ph1-Ru-ph1-NDI with
sodium in tetrahydrofuran. (d) Temporal evolution of the transient
absorption signals for TAA-ph1-Ru-ph1-NDI (n = 1) and TAA-ph2-
Ru-ph2-NDI (n = 2) monitoring the NDI− band at 475 nm. (e)
Analogous to (d) but monitoring the TAA+ band at 770 nm.
NDI− (Figure 1c). After selective excitation of the Ru(II)
sensitizer at 532 nm, MLCT-quenching by NDI followed by
3
subsequent electron transfer from TAA to Ru(III) is mainly
responsible for the rapid (≤10 ns) formation of the observable
TAA+/NDI− photoproduct (Supporting Information, page
S41). This is also the case for the longer congener TAA-ph2-
Ru-ph2-NDI (Supporting Information, page S41). Conse-
quently, when monitoring the temporal evolution of the TAA+
and NDI− signals at the relevant wavelengths (Figure 1d/e and
Supporting Information, page S46), one observes instant
decays because of thermal charge recombination via intra-
molecular electron transfer (Supporting Information, page
S47). On the basis of kinetic measurements at 475, 607, and
770 nm, rate constants (kCR) of (4.8 0.5) × 106 s−1 and (1.3
0.1) × 105 s−1 were determined for TAA-ph1-Ru-ph1-NDI
and TAA-ph2-Ru-ph2-NDI in de-aerated CH3CN at 20 °C
(Table 1). Thus, a decrease of kCR is observed when elongating
rDA from 21.7 to 30.2 Å (red squares in Figure 2), as
commonly expected. rDA corresponds to the centroid-to-
centroid distances between donors and acceptors of our triads.
However, the new TAA-phn-Ru-phn-NDI data are in clear
contrast to the results previously obtained for the TAA-phn-Ru-
phn-AQ series of triads (Scheme 1, middle), in which the
elongation from n = 1 to n = 2 caused an increase of kCR by
roughly a factor of 8 (blue circles in Figure 2).36,37 In this triad
series where AQ instead of NDI is the terminal acceptor,
−ΔG0CR is considerably higher (ca. 1.6 eV, Scheme 1), and an
activation barrier (ΔG‡CR) of ca. 43 meV made electron transfer
in the compound with n = 1 relatively slow, whereas in the
triad with n = 2, it was activationless. Given the relatively
strongly exergonic nature of charge recombination in that
series and the expected increase of the (outer-sphere)
reorganization energy (λ) with increasing distance,40,41 these
observations were attributed to a changeover from the inverted
regime (−ΔG0CR > λ for n = 1) to the activationless point
(−ΔGC0 R = λ for n = 2).36,37 This raised the question whether
in a compound series with even more negative ΔG0CR, an even
stronger increase of kCR with increasing distance could become
observable because the reaction could be more deeply inverted
in the shortest compound. This question can now be addressed
with the TPA-phn-Ir-phn-AQ series for which ΔG0CR = ca. −2.0
eV (Scheme 1 bottom, Supporting Information, page S38).
The envisioned formation of a charge-separated state storing
2.0 eV necessitated the use of a cyclometalated Ir(III)
3
sensitizer with a photoactive MLCT state at higher energy
than that of Ru(bpy)32+. In combination with a chloro-
substituted TPA donor and an AQ acceptor, a highly energetic
charge-separated state comprising TPA+ and AQ− is indeed
formed within 10 ns in both TPA-ph1-Ir-ph1-AQ and TPA-ph2-
Ir-ph2-AQ after excitation at 450/420 nm (Supporting
Information, page S43). When monitoring the transient
absorption decays at the wavelengths diagnostic for TPA+
and AQ− (Supporting Information, page S46), this radical ion
pair is found to collapse with rate constants of (1.0 0.1) ×
106 s−1 in the compound with n = 1 and (1.2 0.1) × 107 s−1
in the triad with n = 2 (Table 1). Evidently, electron transfer
accelerates with increasing distance (green triangles in Figure
B
DOI: 10.1021/acs.inorgchem.8b02973
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Article
Table 1. Electron-Transfer Parameters for the Four New Triads: Donor−Acceptor Distance (rDA), Rate Constant for Thermal
Charge Recombination (kCR), (Negative) Reaction Free Energy (ΔG0CR), Activation Free Energy (ΔG‡CR), Reorganization
Energy (λ), and Electronic Donor−Acceptor Coupling (HDA
)
compound
r
DA/Å
k
CR/s−1
−ΔG0CR/eV
ΔG‡cr/meV
λ/eV
H
DA/cm−1
TAA-ph1-Ru-ph1-NDI
TAA-ph2-Ru-ph2-NDI
TPA-ph1-Ir-ph1-AQ
TPA-ph2-Ir-ph2-AQ
21.7
30.2
22.0
30.6
(4.8 0.5) × 106
(1.3 0.1) × 105
(1.0 0.1) × 106
(1.2 0.1) × 107
1.27 0.05
1.23 0.05
1.99 0.05
1.96 0.05
0
1.27 0.05
1.82 0.35
1.37 0.36
1.96 0.05
0.13 0.02
0.09 0.02
0.35 0.06
0.22 0.04
47
69
0
6
5
increase of the distance-dependent outer-sphere reorganization
energy (λ0),41 and such models cannot be expected to give an
accurate quantitative description of our triads. All our
compounds include a cationic photosensitizer, and the
reorganization of counteranions in the course of intramolecular
electron transfer is likely to play a non-negligible role, yet is not
included in such models. Moreover, the experimental
uncertainties in λ are up to nearly 0.4 eV (Table 1) for
reasons discussed in the Supporting Information on page S51.
The key point from this analysis of reorganization energies is
that λ0 shows the qualitatively expected increase upon distance
elongation, but simple models are unable to provide a
quantitative description of the observable effect, and large
experimental uncertainties make application of more sophis-
ticated models not worthwhile. The prior use of a model taking
electron−vibrational coupling44 into account did not lead to a
significant improvement.37
Figure 2. Distance dependence of kCR in the three triad series from
The temperature-dependent measurements of kCR further-
more give access to estimates of the electronic donor−acceptor
couplings (HDA, Supporting Information, page S52), and we
find values on the order of 0.1−0.4 cm−1 (Table 1). Depending
on donor−acceptor distances and the type of molecular bridge,
values in the range of 102 to 10−1 cm−1 are not
uncommon.45−47 The decrease in HDA upon distance
elongation from n = 1 to n = 2 is relatively modest and
would translate to distance decay constants (β) of ca. 0.1 Å−1,
which is considerably lower than what is typically expected for
oligo-p-phenylene bridges (β = 0.4−0.8 Å−1).28,47−50 However,
β is not a bridge-specific parameter but instead depends on the
entire combination of donor, bridge, and acceptor.51−53
Moreover, our estimate for β can only be based on two data
points, and it is possible that there are nonexponential
contributions to the distance-dependent electronic coupling.54
Evidently, our bridges all contain a bipyridine ligand and as
such do not constitute a homologous series of identical
elements, which is a key assumption of many models treating
the distance dependence of kET.55,56 As noted earlier,57 the
distance decay constants below 0.2 Å−1 are likely to be an
indication of a more complex situation, which may involve
conformational variability and which could signal the onset of
multistep hopping rather than tunneling. On the other hand,
our earlier investigations of oligo-p-xylenes demonstrated that
the electronic structure of this particular bridge type is
significantly less length dependent than that of oligo-p-
phenylenes,48,49,58 making a distance-dependent changeover
from tunneling to hopping, as reported previously for
unsubstituted p-phenylene bridges,28 less likely in our systems.
Using the parameters in Table 1, Marcus parabola showing
kCR as a function of reaction free energy (ΔG0CR) at fixed rDA
can be calculated (Figure 3). Upon distance elongation, the
parabolas undergo the expected bottom rightward shift
because of the decrease of HDA and the increase of λ with
increasing distance (Table 1).42 The driving force is essentially
Scheme 1.
2), contrasting the behavior found for the TAA-phn-Ru-phn-
NDI series (red squares in Figure 2) but in line with the TAA-
phn-Ru-phn-AQ triads (blue circles in Figure 2). In the TPA-
phn-Ir-phn-AQ series where charge recombination is more
exergonic (ΔG0CR = −2.0 eV), kCR increases by a factor of 12
between n = 1 and n = 2, compared to a factor of 8 for the
TAA-phn-Ru-phn-AQ triads (ΔG0CR = −1.6 eV). Thus, the
anticipated enhancement of the rate acceleration upon further
increase of the driving force (−ΔG0CR) is indeed observable but
it is modest. By measuring the charge recombination kinetics
as a function of temperature (Supporting Information, page
S49), an activation energy of 69 meV is found for TPA-ph1-Ir-
ph1-AQ, whereas the charge recombination turns out to be
activationless in TPA-ph2-Ir-ph2-AQ (Table 1, Supporting
Information, page S49). Thus, in TPA-ph1-Ir-ph1-AQ, electron
transfer occurs in the more deeply inverted regime than in the
previously investigated TAA-ph1-Ru-ph1-AQ triad (ΔG‡CR = 43
meV),36,37 as anticipated. The driving force is essentially
temperature independent in the relevant regime (Supporting
Information, page S39).
It is insightful to compare all relevant electron-transfer
parameters in the two extreme cases of the newly investigated
TAA-phn-Ru-phn-NDI and TPA-phn-Ir-phn-AQ systems (Table
1). On the basis of the experimentally determined activation
energies, reorganization energies (λ) can be estimated
(Supporting Information, page S51), and they are found to
increase from 1.3−1.4 eV in the systems with n = 1 to 1.8−2.0
eV in the triads with n = 2 (Table 1). The dielectric continuum
model based on spherical donors and acceptors with radii of 4
Å predicts an increase in λ of ca. 0.3 eV for CH3CN
solvent,36,37,40−43 but the experimentally observed effect is
larger (0.5−0.6 eV). However, it has been noted earlier that
dielectric continuum models tend to underestimate the
C
DOI: 10.1021/acs.inorgchem.8b02973
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Article
energy conversion.42 In particular, the competition between
photoinduced charge separation and (undesired) thermal
charge recombination reactions in solar energy conversion
devices could crucially depend on the different distance
dependences of weakly and more strongly exergonic electron-
transfer reactions.
ASSOCIATED CONTENT
* Supporting Information
■
S
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.8b02973.
Figure 3. Plots of kCR vs ΔG0CR based on the parameters from Table 1.
(a) TAA-phn-Ru-phn-NDI systems with n = 1 (solid red) and n = 2
(dotted red). (b) TPA-phn-Ir-phn-AQ systems with n = 1 (solid
green) and n = 2 (dotted green). The dotted vertical lines mark the
relevant driving forces for charge recombination.
Synthetic protocols and characterization data, descrip-
tion of equipment and methods, supplementary electro-
chemical and spectroscopic data, and thermochemical
discussion (PDF)
constant in a given series of our triads, and this is represented
by dotted vertical lines in Figure 3. In the TAA-phn-Ru-phn-
NDI series where ΔG0CR is relatively low (−1.2 eV), this nicely
visualizes the changeover from activationless electron transfer
in the compound with n = 1 (red square at the top of the solid
red parabola, Figure 3a) to electron transfer in the normal
regime (red square in the left half of the dotted red parabola,
Figure 3a) in the triad with n = 2. By contrast, in the TPA-phn-
Ir-phn-AQ series, charge recombination in the compound with
n = 1 occurs in the inverted regime (green triangle in the right
half of the solid green parabola of Figure 3b), whereas in the
compound with n = 2, it takes place at the activationless point
(green triangle at the top of the dotted green parabola of
Figure 3b).
AUTHOR INFORMATION
Corresponding Author
*E-mail: oliver.wenger@unibas.ch.
■
ORCID
Oliver S. Wenger: 0000-0002-0739-0553
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Financial support from the Swiss National Science Foundation
through grant number 200021_178760 and from the Swiss
Nanoscience Institute (SNI project P1406) is gratefully
acknowledged.
CONCLUSIONS
■
In summary, our study shows that electron-transfer rates can
either increase or decrease with increasing donor−acceptor
distance, in clear contrast to the common belief that reaction
rates always get slower when the distance between individual
reactants increases.43 This counterintuitive behavior is readily
understandable in the framework of Marcus theory, as pointed
out in two early theory papers,38,39 yet this does not seem to be
nearly as widely known as the inverted driving force effect. The
present study is the first systematic investigation of the
distance dependence of kET as a function of driving force,
geared at testing these early theoretical predictions. The key
finding is that highly exergonic electron-transfer reactions can
indeed exhibit fundamentally different distance dependences
than the more commonly studied weakly exergonic reactions.
The semiclassical Marcus model used herein (and in the
early theoretical prediction)38 provides an adequate qualitative
description, but there is evidence from our investigations that
an accurate quantitative description will require more
sophisticated models.36 Specifically, the model used herein
yields relatively large increases of the outer-sphere reorganiza-
tion energy paired with rather shallow distance dependences of
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