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What Makes Fullerene Acceptors Special as Electron
Acceptors in Organic Solar Cells and How to Replace Them
Tao Liu and Alessandro Troisi*
Many things have changed since the first report of a bulk heterojuction organic solar cell[1] initiated a long series of improvements in materials and device fabrication[2] that lead to power
conversion efficiencies not far from the commercialization
threshold. One thing did not change though: the vast majority
of bulk heterojunction solar cells still use a fullerene derivative
as electron acceptor, just as the original report did.[2a,3] In this
letter we propose that there is one, so far underappreciated,
property of fullerene derivatives which makes them particularly suitable for promoting charge separation at the interface,
namely the existence of low lying (0.2–0.4 eV) excited states in
their anions. We show that these states are responsible of a tenfold increase of the charge separation rate while they do not
affect the charge recombination rate. This observation is used
to design a new class of “fullerene mimics” that are much more
similar to fullerene derivatives than the alternative electron
acceptors currently under consideration.
The conventional justifications of the advantages of fullerene
derivatives as electron acceptor are convincing but do not
explain the lack of a large number of alternatives. Certainly,
the ability to easily accept electron can be matched by alternative compounds with similarly high electron affinity[4] and the
reasonably good electron mobility[5] is not without matches.[6]
Another excellent characteristic of fullerene derivatives is that a
favorable nanoscale morphology, where the donor and acceptor
domains are of a size similar to the exciton diffusion length,
can be obtained through suitable processing additives.[7] Probably also the ability to support electron transport in 3 dimensions (more than 2 or 1 as most molecules or polymers) may
help the properties of fullerene derivatives. Guided by the principles above a large number of synthetic groups are designing
alternative electron acceptor materials (both polymeric and
molecular) trying to increase the pool of acceptors.[4,8] Going
beyond fullerene derivatives will increase immediately the possible blends that can be considered and pave the way to address
some of the limitations of the fullerene derivatives, e.g. the very
limited light adsorption[9] and the very high cost of the most
efficient derivatives.[3b]
An ideal introduction to our result is provided by the classical work of Closs and Miller[10] who verified the counterintuitive prediction by Marcus[11] that, by increasing the exoergonicity
–ΔGCT of a charge transfer reaction beyond a threshold
Dr. T. Liu, Prof. A. Troisi
Department of Chemistry and Centre
of Scientific Computing
University of Warwick
E-mail: [email protected]
DOI: 10.1002/adma.201203486
1038
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(corresponding to the reorganization energy λ), the charge
transfer rate kCT decreases as –ΔGCT increases (this is the socalled Marcus inverted region). Before Miller’s experiment and
for many years after Marcus prediction the decrease of the rate
with increase of –ΔGCT was not observed because, if the donoracceptor pair is not designed accurately, the electron can be
transferred to a higher excited state of the acceptor. As illustrated in Figure 1, if the electron can be transferred to a higher
electronic charge transfer state, the Marcus inverted region is
not observed. Because of the very small reorganization energy
in organic photovoltaic interfaces the formation of the charge
transfer state from the excitation residing on the donor is in the
inverted region[12] and the presence of low lying excited states
of the acceptor’s anion increases the rate of the charge transfer
(CT) process.
The monoanions of C60 derivatives are certainly expected to
have very low lying excited states. The LUMOs of C60 are, in
fact, triply degenerate belonging to the T1u irreducible representation. In actual bulk heterojunction solar cells the C60 soluble derivative [60]PCBM is the most commonly used acceptor
followed by the C70 analogous [70]PCBM. The derivatization
will lift the degeneracy without altering much the nature of
the orbitals so that the optical transition between anion states
occupying one of the three different orbitals is expected to be
extremely weak. We have carried out straightforward quantum
chemical calculations on [60]PCBM− to verify these statements,
extending the calculations also on [70]PCBM− to confirm that
similar properties are shared by the larger derivative.
The geometries of [60]PCBM and [70]PCBM neutral and
anion were fully optimized at the B3LYP/(U)B3LYP/6-31G(d)
level and the excitation energies of the anion were also calculated at the same level using a TDDFT approach and the optimized anion geometries. The spin contamination for the anion
calculation was small (<S2> is 0.76). A diagram of the orbital
energies for the neutral [60]PCBM and [70]PCBM is given in
Figure 2B. LUMO+1 and LUMO+2 are only 0.07 and 0.15 eV
higher than LUMO for [60]PCBM and 0.06 and 0.28 eV higher
than LUMO for [70]PCBM.
To verify more rigorously that fullerene derivatives can accept
electrons in one of their excited states, it is necessary to compute the excitation energies of the anion which are reported
in a diagram in Figure 2C. The first and second lowest excitation energies of [60]PCBM− are at 0.21 and 0.43 eV and they
are dominated respectively by the LUMO→LUMO+1 and the
LUMO→LUMO+2 transition (using the orbital nomenclature
of the neutral molecule). Both these transitions are predicted
to be essentially forbidden with oscillator strengths below 10−3.
The first transition with appreciable oscillator strength (f =
0.0254) occurs at 1.27 eV and corresponds to the well-known
spectroscopic signature of the C60 anion between 950 and
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Energy
D*A
D+A−
Ea
ΔGCT
D*A
D+(A−)*
D+A−
Eex
Reaction coordinate
Figure 1. The top panel shows the standard Marcus schematics for the
potential energy curves involved in the photoinduced electron transfer in
a donor(D)-acceptor(A) pair following the excitation of the donor. In the
inverted region (represented) an increase of –ΔGCT causes an increase
of the activation energy Ea and a decrease of the rate. The bottom panel
shows that, if there are energetically close excited charge transfer state,
for example an excited state of the anion-acceptor (D+(A−)∗), the rate of
the charge transfer is enhanced. This is the hypothesis considered in this
work for fullerene based acceptors.
1010 nm,[13] confirming the reasonable quality of the computational method.
The pattern is not too dissimilar for the [70]PCBM− anion,
whose lowest three excitations (at 0.27, 0.37, 0.79 eV and oscillator strength below 10−3) have similar transition properties as
the lowest two of [60]PCBM−, indicating a possibly even better
ability of C70 derivatives to act as electron acceptors.
The next step is to evaluate the effect of these excited states
on the rate of formation of the charge transfer state. We have
recently studied a minimal model of the P3HT/[60]PCBM interface consisting only of a single acceptor molecule and short hexamer chain of P3HT with hexyl chains substituted by methyl
(P3MT).[11] Considering the very weak coupling between donor
and acceptor the most suitable theoretical framework for the
study of the electron transfer reaction is given by non-adiabatic
reaction rate theory. In particular, considering that nuclear reorganization following charge transfer involves intra-molecular
high frequency modes, the most appropriate rate expression is
given by Marcus-Levich-Jorner theory more than the simpler
Marcus formula discussed in the introduction:[14]
Adv. Mater. 2013, 25, 1038–1041
Figure 2. (A) The optimized geometries of [60]PCBM and [70]PCBM
anions. (B) Diagram of the frontier orbital energies of neutral [60]PCBM
and [70]PCBM. (C) The excitation energies of [60]PCBM− and [70]PCBM−
calculated using TDDFT/B3LYP/6-31G∗.
kC T =
1
Sv
2π
|V | 2 √
e −S
v!
4 π λ e xt K B T v
( λ e xt + v ω + GC T )2
exp −
4 λ e x t KB T
(1)
Where V is the electronic coupling between the initial and final
states, λext is the external reorganization energy, S is the effective
Huang–Rhys factor, ω is frequency of one effective mode that
incorporates in an average way the effect of all quantum modes,
䉭GCT is the Gibbs free energy for the electron transfer reaction
and KBT the thermal energy.
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If, instead of having only a single accessible charge transfer
state, there are three (as in [60]PCBM), the total rate of charge
transfer will be simply the sum of the charge transfer rates
toward each of the final states. The three states differ only for
the occupation of the extra electron that will be in one of the
orbitals with characteristics very similar to the three degenerate
orbitals of C60. For this reason both the reorganization energy
(internal and external) and the coupling between donor and
acceptor are expected to be very similar for the charge transfer
between initial and final states (for the coupling this was explicitly verified in ref. [12]). To an excellent degree of accuracy the
charge transfer rate toward the ground, first and second excited
state can be obtained by substituting in Equation (1) three different values of the free energy changes.
To provide a quantitative estimate we use the parameters VCT = 13.6 meV, λext = 0.11 eV, S = 1.37, បω = 0.186 eV
determined in ref. [12], where we also discuss the inaccuracy
intrinsic in them and the effect on the rate calculations. It
should be noted that changing these parameters within a plausible range consistent with the data available in literature will
not change the main finding of this paper. The rate k1 for the
charge transfer toward the ground state of the CT state was
computed using 䉭GCT =–0.969 eV,[12] while for the calculation
of the rate k2 and k3 this parameter was increased by 0.21 and
0.43 eV (the excitation energies of [60]PCBM anion) respectively. kCT increases as 䉭GCT becomes less negative (as we
are in the Marcus inverted region) and the computed charge
transfer rates are k1 = 1.50 × 1011 s−1, k2 = 6.68 × 1011 s−1, and
k3 = 1.97 × 1012 s−1. The total kCT, the sum of these three rates,
is 2.79 × 1012 s−1 in much better agreement with the experimentally available data of kCT > 4 × 1011 s−1.[15] Importantly, the total
rate is 18 times larger than k1 indicating that the effect is not
simply due to a greater density of states in the acceptor (which
would cause just a 3 fold increase) but also to the energy off-set
of the accepting states (see also SI).
The relevance of higher energy charge transfer states transcends the agreement between experiment and computations,
always affected by the quality of the model and the ever changing
state of the art of electronic structure calculations. There is no
doubt that low lying excited state of the fullerene anion exist and
these will always increase the total rate of charge transfer when
the potential energy curves can be represented as the bottom
panel of Figure 1 (this qualitative behavior is also not affected by
the possible inaccuracies of Equation (1)). It should be remarked
that this paper does not clarify the actual mechanism of free
charge generation in fullerene solar cells, but the essential idea
that the excited states of the anion are important for the charge
separation can be combined with other ideas put forward to
explain free charge generation, such as long range exciton dissociation[16] or interface dipole effects.[17] The key consequence
of our observation, however, is that an acceptor not designed on
purpose to have low lying excited states in the anionic form will
not match the electron accepting properties of fullerenes.[18]
It is relatively easy to design molecules that have quasi
degenerate LUMOs and possess low lying excited states (in the
0.1–0.4 eV range) when they are negatively charged. As illustrated in Figure 3 it is sufficient to connect two (or more) identical conjugated molecules through a small saturated bridge
that breaks the conjugation (so that the electronic structure of
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Figure 3. Two identical conjugated fragments connected by a methylene
form compounds with low lying excited state as anion. Five examples
are considered here. For compound b, R′ = H, for compound b′, R′ =
−OC6H5.
the overall system is not completely altered) such as a methylene unit. If the bridge is too long the conjugated fragments
would behave as independent molecules or non-bonded dimers
(see SI for the relevant data), with the lower excited states of
the anion energetically too close (<0.1 eV) to the ground state.
The compounds (a-d) chosen to illustrate this idea in Figure 3
have been selected to be potential replacements of [60]PCBM
in a bulk heterojunction solar cell with P3HT but, of course,
if one is able to go beyond fullerene derivatives in this type of
cells, it will be possible to consider completely different donor/
acceptor pairs.
The data in Figure 4 confirm that compounds a-d have quasi
degenerate LUMOs in an energy window comparable to that of
[60]PCBM and also possess low lying excited states when in the
mono-anion form. The most striking result however is that the
molecules currently considered to substitute fullerene derivative
do not have this latter property. We have considered all nonpolymeric compounds listed in Tables 1 and 2 of ref. [4] where the
performance of a number of alternative acceptors blended with
P3HT was summarized. They are labeled as 10a, 48a, 53a, 57,
73b as in ref. [4] and the corresponding computed data are also
reported in Figure 4. Obviously, the currently investigated alternatives to fullerene derivatives are not in general good fullerene
mimics as they lack one of the key characteristics of fullerenes,
i.e. the availability of additional electron accepting states at low
energy. The difference between the two groups is much larger
than any possible inaccuracy of the method[19] (which however
compares well with the experimentally available data on fullerene
and di-arylmethane anions[20]) or environmental effects. Of
course, we cannot make very specific claims on the ability of
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Acknowledgements
-2.0
-2.5
This work was supported by ERC (project MIMESIS), EPSRC and the
Leverhulme Trust.
Received: August 21, 2012
Revised: September 24, 2012
Published online: November 27, 2012
-3.0
-3.5
-4.0
2.0
1.5
1.0
0.5
existing
acceptors
a
b
b'
c
d
0.0
10a
48a
52a
57
73b
[60]PCBM
Excitation Energy / eV
-1.5
new proposed
acceptors
Figure 4. Virtual orbital energy (top) and excitation energy of the anion
(bottom) for the reference [60]PCBM, the five new proposed electron
acceptors and five alternative acceptors from a review paper.[4] Only [60]
PCBM and the new proposed acceptors have low lying excited state when
negatively charged.
compounds (a)-(d) to replace [60]PCBM because the efficient
charge separation is only one of the requirements for good
solar cells[21] but we can more confidently state that fullerene
substitutes should be sought from compounds with electronic
structure more similar to compounds (a)-(d). Very interestingly,
linked dimers of perylene-bisimides have been recently synthesized and evidence of low lying anionic state has been presented
for these compounds.[22] The data in Figure 4 also suggest that
charge separation dynamics in PCBM containing blend should
not be directly compared with the same process for acceptor
without low lying excited states of the anion.
In summary, we observed that the availability of electron
accepting states in fullerene derivatives improves the efficiency
of the charge separation process and we illustrated that current
synthetic efforts to find alternatives to fullerene acceptors typically lead to compounds that do not have this desirable property, unless accidentally. On the other hand, we show that a new
class of molecular acceptors with this necessary electronic characteristic can be easily designed providing one route (clearly not
the only one) for replacing fullerene derivatives in solar cells.
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
Adv. Mater. 2013, 25, 1038–1041
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