Theoretical Investigation of Charge-Transfer Processes at Pentacene

Sep 22, 2014 - excitons, which may further undergo CS at the interface. In this work, we study charge- transfer processes at the pentacene−C60 inter...
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Theoretical Investigation of Charge-Transfer Processes at Pentacene−C60 Interface: The Importance of Triplet Charge Separation and Marcus Electron Transfer Theory Bo-Chao Lin,† Brian T. Koo,‡ Paulette Clancy,*,‡ and Chao-Ping Hsu*,† †

Institute of Chemistry, Academia Sinica, 128 Section 2 Academia Road, Nankang, Taipei 11529, Taiwan School of Chemical and Biomolecular Engineering, Cornell University, 120 Olin Hall, Ithaca, New York 14853, United States

‡

ABSTRACT: Photovoltaic devices have great potential in harvesting solar energy. In organic solar cells, the role of the donor−acceptor heterojunction is critically important; here optical excitation leads to charge separation (CS) and subsequently photocurrent generation. Charge recombination (CR) may also happen, which reduces the overall efficiency of the device. After light absorption, the singlet excitation of a pentacene can achieve CS at the interface, or it may also undergo singlet fission and produce two triplet excitons, which may further undergo CS at the interface. In this work, we study chargetransfer processes at the pentacene−C60 interface, including CS rates in both singlet and triplet surfaces, and the CR rate back to the ground state. We first constructed two different pentacene−C60 interfacial structures by force field optimization. With pentacene−C60 molecular pairs derived from the structures, we calculate the electronic couplings of CS and CR reactions. We found that the electron-transfer couplings have a systematic preference on the configurations. Both singlet and triplet CS coupling prefer to take place in the “head-on” configurations, where the C60 is located at the top of the pentacene, whereas CR coupling prefers the “inserted” configuration, where the pentacene is located between two C60 and is slightly lifted from the layer. In estimating the electron-transfer rates, we found that the interfacial energy shift has a determining effect. When an interfacial energy derived from experimental results is included, we found that the calculated triplet CS rate can reach 1013 s−1, while the singlet CS rate is only ∼105 s−1. The CR rate was calculated to be 1011 s−1 for a singlet ion pair. Our results indicate that triplet CS is fast. Because triplet CS can proceed after singlet fission, with its immediate recombination being spin-forbidden, it is important to photovoltaic performance in the pentacene−C60 system.

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INTRODUCTION Organic photovoltaic (OPV) devices have shown potential as a new source of renewable energy, offering the advantage of lowcost manufacturing.1−3 However, to improve the power conversion efficiency of OPV, the open-current voltage4,5 and the short-circuit current need to be increased; thus issues of charge separation and recombination are paramount.3,6−9 OPV systems are typically composed of two types of materials, one p-type and the other n-type, forming a donor−acceptor heterojunction at which charge separation is intended to occur. In operation, at least one of the donor and acceptor molecules absorbs sunlight and creates electronically excited molecules, called excitons. When an exciton migrates to a heterojunction, where the n- and p-type materials are in contact, charge separation (CS) may take place, and the charges may be harvested through migration separately to their respective electrodes. There is also a chance that the charge may recombine (charge recombination, CR), causing the performance of the device to be reduced. Hence, both CS and CR processes are important to the performance of the short-circuit current and eventually the overall efficiency of the device. Pentacene and C60 are archetypal donor and acceptor materials, respectively, due to their high mobilities for both charge and exciton.10 Accordingly, heterojunction devices © XXXX American Chemical Society

formed with pentacene and C60 have received a lot of attention.11−13 In such OPV devices, both pentacene and C60 are capable of absorbing visible light. When the excitons diffuse to the interface, electron transfer from pentacene to C60 takes place, and then C60 and pentacene transport the electrons and holes to their respective electrodes. There are several possible charge-transfer processes at the pentacene−C60 interface, as sketched in Figure 1. The electronic processes taking place at the pentacene−C60 interface have been studied by femtosecond spectroscopy experiments.14−16 It has been reported that an ultrafast 1013 s−1, barrierless singlet fission takes place in the pentacene film first,14,15,17 followed by electron transfer from the triplet excited state in pentacene to the C60, taking place within 10−11 s.16 In the triplet CS state, the corresponding CR to the singlet ground state is spin-forbidden. Thus, compared with its singlet counterpart, the separated charges in triplet states can exist with a considerably longer lifetime and thus have a larger chance to be harvested as photocurrent.18 To investigate the electronic processes at the pentacene−C60 interface, the interfacial configuration plays an important role because it determines the intermolecular forces between Received: August 8, 2014 Revised: September 21, 2014

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imental results. In the work, we focus on the charge-transfer properties that result from a consideration of the nonideal configurations that are generated by a large-scale molecular mechanics simulation, in which the upright configurations are found in equilibrated pentacene−C60 interfaces.25 When two different materials are in contact, the difference in their Fermi energy induces a charge redistribution until a new equilibrium is established. This effect may lead to a final realignment of Fermi energy levels, and the exact redistribution will depend on the intrinsic electronic properties of the components at the interface. It is also dependent on the detailed arrangement of the molecules at the contact layer.29 The effects of interfacial polarization at the pentacene−C60 heterojunction have been investigated experimentally and theoretically30−33 The ionization potential (IP) for pentacene with one molecular layer thickness covering the C60 surface has been measured to be 0.5 eV higher than the corresponding bulk value;30 the corresponding energy shift for pentacene is less, measured to be 0.1 eV. Therefore, for the pentacene−C60 interface, these experimental measurements allow us to determine the energy levels at the interface. In this work, we study electron-transfer processes, particularly CS and CR, in the pentacene−C60 interface. In contrast with earlier similar studies, we include interfacial effects on the energies of the two materials derived from experiments30 and explore the charge-transfer properties that result from the nature of the interfacial configuration.20,21 We characterize the triplet CS process that starts from a triplet excited pentacene molecule and results in an ion pair. The singlet CS process is also considered to offer a theoretical limit on its plausibility. Because direct CR from a triplet ion pair is spin-forbidden, we only consider the CR rate from the singlet charge-transfer (CT) state. The electronic couplings are obtained from ab initio calculations, which also allows us to study the preference of CR and CS in different configurations in terms of molecular orbital interaction. Finally, we compare our calculated CT rates with that found in experiments.15

Figure 1. Electronic processes at the pentacene−C60 heterojunction. (a) Absorption of a photon and formation of a singlet exciton (b) singlet fission (SF), leading to two triplet excitons, (c) charge separation on the triplet surface (3CS), (d) charge separation on the singlet surface (1CS), (e) electron and hole pair recombine to form 1 CS (1CR), and finally (f) electron and hole dissociation. In the present work, charge-transfer processes (c−e) are studied.

pentacene and C60. Alternatively, one could say that the interfacial structure is the net result of the weak van der Waals forces between the components. It is well known that different experimental processing conditions may result in structurally different thin-film phases.19−24 Depending on the nature of the underlying substrate, temperature, and the thickness of the pentacene film, pentacene molecules may either stand up or lie down on a surface (as depicted in Figure 2).20,22,23 In the early

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Figure 2. Schematic representation for the upright and lying-down configuration for a pentacene−C60 interface.

METHODS Pentacene−C60 Interface. To mimic the pentacene−C60 interfacial structure observed experimentally,20 we combine the [001] lattice plane of the “thin-film” phase pentacene crystal grown on an organic substrate21 and the [111] lattice plane of the C60 crystal.34 The angle between the (110) axis of C60 crystal and the π-stacking direction of the pentacene crystal was reported to be ∼20°. We have scanned for the lowest energy configuration for this pentacene−C60 interface and found that it occurs at an angle of 21° between the two axes, which is very similar to experimental results. The scan was performed by bringing together rigid layers of pentacene and C60 with a number of different displacements and rotations that cover all possible contacts. We use the optimized structure and add one more layer of C60 and two more layers of pentacene to the outer layers of C60 and pentacene, respectively, for further energy optimization using the Allinger et al. MM3 force field. Except for pentacene molecules in the bottom layer, all other molecules were energy-optimized without any constraints. At the interface, there are 326 pentacene molecules and 80 C60 molecules. From this, we derived 571 pentacene−C 60 contacting configurations, selected by the nearest distances between C atoms under 3.9 Å, which is the sum of two van der Waals radii plus 0.5 Å.

stages of deposition of pentacene thin films on the [111] lattice plane of a C60 crystal, pentacene molecules initially lie flat on the C60 surface; then, as deposition continues, a well-ordered upright morphology is observed.20 Molecular dynamics (MD) simulations have also observed a similar transformation to take place at roughly 0.6 molecular-layer (ML) coverage of pentacene.25−27 With abundant experimental data available, the pentacene− C60 heterojunction is an ideal system to test different approaches to the theoretical modeling of charge transport. Charge-transfer characteristics in artificially constructed, ideal “lying down” and “standing-up” configurations have been reported in a previous work.28 The authors of ref 28 found, not surprisingly, that the strength of the electronic couplings for both the CS and the CR reactions is sensitive to the precise pentacene−C60 configuration. With Marcus theory and a free energy derived from bulk values plus the Coulomb interaction, they concluded that the singlet CS is very fast (on the order of 1013 s−1). However, the intermolecular electronic coupling is highly dependent on the relative positions of the two molecules, and thus results derived from ideal, artificial structures may not be applicable for understanding experB

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For comparison, we also constructed a second, periodic C60− pentacene interface by choosing supercell dimensions that minimized the lattice mismatch between the [001] pentacene and [111] fullerene surfaces. Our trial and error approach used the thin-film phase unit cell containing two pentacene molecules, as estimated from grazing incidence X-ray diffraction data of pentacene on silicon oxide35 (a = 6.0 Å, b = 7.6 Å, c = 15.6 Å, α = 81.3°, β = 86.6°, γ = 89.8°) and a 4-fullerene orthorhombic unit cell (a = 9.7 Å, b = 16.8 Å, c = 15.8 Å, α = 90.0°, β = 90.0°, γ = 90.0°). The result of matching the pentacene and fullerene layers at the interface gave a pentacene supercell with dimensions (a = 77.5 Å, b = 83.6 Å, γ = 89.8°) containing 286 pentacene per layer and a fullerene supercell with dimensions (a = 77.6 Å, b = 84.0 Å, γ = 90.0°) containing 80 fullerene per layer. Our C60−pentacene interface was similarly constructed with three pentacene layers and two fullerene overlayers. The farthest pentacene layer from the interface was frozen to add rigidity to the structure. The interface was minimized with the limited memory Broyden− Fletcher−Goldfarb−Shanno Quasi-Newton algorithm36 with an energy gradient convergence criterion of 0.01 RMS, and the atomic interactions were modeled in the Tinker MD program37 with the MM3 force field,38−40 which is tuned to fit crystal parameters for hydrocarbon materials. After minimization, we harvested 519 pairs of contacting pentacene−C60 configurations. Calculating the Charge Transfer Rates. The rate of electron transfer can be described by the Marcus rate theory41 k if =

2π ℏ

⎡ (ΔG + λ)2 ⎤ |V |2 exp⎢ − ⎥ 4λkBT ⎦ ⎣ 4πλkBT

molecules were used as a source charge for the ICA model. We note that if we calculate the same pentacene−C60 pairs without ICA solvent effects, the excitation energies of the CT states can be higher than 3.5 eV, and some of the CT states are mixed with local excitations (LEs), arising from artifacts of CIS. The ICA solvent model was used to remove the erroneous LE components in the CT state and to improve the computational quality, without increasing the computational cost.45,49 To calculate the electronic couplings for the CS and the CR reactions, we employ the fragment charge difference (FCD) scheme.50 FCD calculates the electronic coupling, V, between two adiabatic states based on a two-state model. In FCD, the donor and acceptor space are defined, and the charge difference operator Δq is defined as Δqij =

∫r∈D dr ρij (r) − ∫r∈A dr ρij (r)

(2)

where ρij(r) is the one-particle density matrix. For two CIS eigenstates |i⟩ and |f⟩, the coupling is then given by V=

(Ef − E i)|Δqif | (Δqii − Δqff )2 + 4Δqif2

(3)

where Ei (Ef) is the energy of the initial (final) state, the Δqii (Δqff) is the donor−acceptor charge difference in the state |i⟩ (| f⟩), and the Δqif is the corresponding quantity derived from transition density ρif(r). Because of the high symmetry of C60, there exist three degenerate lowest unoccupied molecular orbitals (LUMOs) with t1u symmetry. Under the perturbation of a nearby pentacene, these MOs are still very close in energy, and thus three quasi-degenerate CT states in each pentacene−C60 pair exist. For the triplet CS (3CS) reaction, the initial state is the lowest triplet excited state, where the pentacene is in its triplet state, and the final state is one of the three quasi-degenerated triplet CT (3CT) states. We also test for the singlet CS (1CS), which starts from the lowest singlet excited state of pentacene, and ends at one of the three quasi-degenerated singlet CT states. The singlet CR (1CR) reaction starts with one of the three quasi-degenerated singlet CT states and ends with the ground state. All of the quantum chemistry calculations were performed using a developmental version of the Q-Chem program package.51 For CS, we estimate the free-energy (ΔGCS) as the energy gap between the energy of the excitation of pentacene (ET1 or ES1) and the interfacial CT state (ECT)

(1)

where V is the electronic coupling between the initial and final states, λ is the reorganization energy, and ΔG is the change of free energy for the ET. Because both pentacene and C60 are molecules with rigid π-conjugated structure, their inner reorganization energies are expected to be small.42−44 Using density functional theory (DFT) calculations, the inner reorganization energies of the pentacene cation and C60 anion have been reported as 9344 and 132 meV,43 respectively. In a photovoltaic device, the charged molecules are embedded in a nonpolar solid environment, and thus the outer reorganization is expected to be small as well. The outer reorganization energy of the pentacene cation was measured to be 97 (gas phase), and 109 meV (in a pentacene thin film).42 In the present work, we employ a value of 0.3 eV for the total reorganization energy for both CS and CR processes. To calculate the electronic couplings, V, for the CS and CR reactions, we first calculate the singlet and triplet excited states for all 1090 pentacene−C60 pairs by the single-excitation configuration interaction calculation (CIS) with DZ* basis set, with all molecular orbitals included in the excitation. In our previous studies, CIS often yield satisfactory results for electronic coupling.45−47 The self-interaction error in most exchange-correlation functionals of DFT leads to large errors in time-dependent DFT (TDDFT) for states with charge-transfer characters.48 The excited states are obtained using the image charge approximation (ICA) approximation49 to mimic the modest dielectric solvation effect of the environment. The dielectric constant was set to 4, and the radius of the cavity was measured from the center-of-nuclear-charge to the furthest atom, plus 1.5 Å to account for a general van der Waals radius. The electrostatic potential fitting (ESP) charges of the

ΔGCS(T ) = ECT − E T1

(4)

ΔGCS(S) = ECT − ES1

(5)

where values of ET1 and ES1 for pentacene are taken from experiment, being 0.8652 and 1.85 eV,17 respectively. For CR, we estimate the free energy (ΔGCR) as the energy difference between ECT and the ground state (EG) ΔGCR = EG − ECT = −ECT

(6)

where the energy of the ground state is the zero reference. The energy of the CT state at the interface, ECT, was estimated as the energy difference between the IP of the donor and the electron affinity (EA) of the acceptor, plus the interfacial effect, and the Coulomb interaction between the two charged C

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We name the first structure as the “aligned” structure and the other as the “rotated” one. The rotated structure was obtained by a conformation search following results from LEEM experiments.20 As seen in Figure 3a,b, in both structures, after the force-field optimization, the layered conformations are maintained accompanied by small local deformations in the topmost pentacene molecular layers nearest the interface. Pentacene molecules located between two or three C60 molecules tend to shift up and fill small spaces at the interface to form a dense packing. As a result, wavy pentacene layers are formed in both structures. Pentacene located at the crest of this “wave” is inserted into the C60 layer, and pentacene located at the trough of the wave “pokes” the C60 molecules by the C−H bonds. Obviously, the nature or character of these two ways in which pentacene and C60 contact one another is different. We qualitatively assigned the former configuration as the “inserted” form and the latter by the “head-on” form. Illustrations of these two types of the pentacene−C60 configuration are included at the right-hand side in Figure 4a.

species.28,53 In the present work, an additional term Eint is added to the interfacial effects on the CT state energy ECT = IP(D) − EA(A) + E int + ECoul(D+ − A−)

(7)

At an interface, the IP(D) and the EA(A) may be shifted from their bulk values due to the effects of polarization and chargeredistribution in the interface. For the pentacene−C60 interface, the change of pentacene IP and C60 IP energy levels has been measured as +0.5 and +0.1 eV, respectively.30 Accounting for both changes and assuming that EA is shifted accordingly in C60, we use a value of 0.4 eV for Eint in eq 7. The Coulomb energy was estimated according to the ESP charges54,55 of the donor cation and the acceptor anion as qiqj ECoul(D+ − A−) = ∑ ∑ εrij i ∈ D+ j ∈ A− (8) where ε is the dielectric constant, qi and qj are the fitting ESP charges for the donor cation and the acceptor anion, respectively, and rij is the distance between the atom i in the donor and the atom j in the acceptor. The dielectric constants for condensed phase pentacene and C60 are both small,28,32 and we use a value of 4 for both pentacene and C60 in this work. With eq 8, we calculate the Coulomb interaction energy for the charge-separated state for each pentacene−C60 pair. Values for ECoul are between −0.26 and −0.34 eV for both structures. The ranges of the ECT now becomes 0.76−0.84 eV.

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RESULTS AND DISCUSSION Details of the Pentacene−C60 Interfacial Configurations. The two different optimized pentacene−C60 interfaces are shown in two viewing angles in Figure 3a−d. The two

Figure 3. Two pentacene−C60 interface models employed in the present work. The aligned structures are shown in (a) and (c), while (b) and (d) show the rotated structure. Views (a) and (b) are taken from the side, whereas (c) and (d) show views from the top. Figure 4. Spatial distribution of C60 relative to pentacene. (a) For each pentacene−CC60 configuration, the pentacene is superimposed onto a reference frame and the relative position of the C60 center is represented by a small gray sphere. Shown are results for the aligned structure (b and c), and the rotated structure (d and e). Two different views, from the +y-axis (b and d) and the +z-axis (c and e) are shown for each case.

interfaces can be distinguished according to the orientation of the pentacene layer. As seen in Figure 3a,c, the (110) axes of the C60 and the π-stacking lattice axis are aligned. In the second structure, shown in Figure 3b,d, the lattice of the pentacene layer was rotated by 21°. We depict the direction of the πstacking in the pentacene layer with red arrows in Figure 3c,d. D

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Figure 5. Calculated electronic couplings for the aligned (a−c) and rotated (d−f) structures for 1CR (a and d), 1CS (b and e), and 3CS (c and f) processes as a function of the shortest intermolecular C−C distance. The largest coupling in each distance is picked (filled circles) and fit for exponential decay rates (1.3 to 1.5 Å−1).

Figure 6. Spatial distribution of ET couplings for the aligned (a−c) and rotated (d−f) structures for 1CR (a and d), 1CS (b and e), and 3CS (c and f) processes. The diameters of the circles are proportional to the square values of the coupling. The spatial axes are in units of angstroms. The units for the coupling are millielectronvolts.

property, we need a simplified representation. In this case, we can expect that the intermolecular configuration is important to the CT property. Therefore, we overlap the pentacene−C60 bimolecular configurations to the same pentacene structure and use a small dot to represent the center of C60. The result is

To investigate CT at the interface, we analyzed the two interfaces and obtained 519 and 571 pentacene−C60 configurations from the aligned and the rotated structures, respectively. To systematically represent hundreds of pentacene−C60 configurations and the correlation with the CT E

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shown in Figure 4. Interestingly, in this representation, the rotated structure is more regular than the aligned structure, as seen in Figure 4e. This result indicates the pentacene−C60 stacking in the rotated structure is restricted, and some pentacene−C60 configurations may be found more frequently than others. On the contrary, for the aligned structure, the C60 are randomly distributed over the space surrounding the pentacene, as shown in Figure 4c. Electronic Couplings for CS and CR Reactions. The electronic couplings for the pentacene−C60 pairs are calculated with the FCD method. The results are shown in Figure 5 with respect to intermolecular C−C distance. Because of the symmetry of C60, there exists a set of triple degenerate lowest unoccupied molecular orbitals (LUMOs). Therefore, there are three quasi-degenerate CS states for each pentacene−C60 pair in both singlet and triplet states, each with a different coupling value. For each pentacene−C60 configuration, there are three electronic coupling values for the triplet CS, singlet CS, and singlet CR processes. The maximum triplet CS couplings of the aligned and the rotated structures are 48.2 and 42.1 meV, respectively. For singlet CS, they are 69.0 and 45.5 meV, and for singlet CR, they are 59.5 and 64.6 meV. It is seen that there is no obvious preference in the coupling factor among the CS and CR processes. In Figure 5, it can be seen that the largest coupling in each distance decays exponentially. The slope of the linear outer “envelope” in the data lies between 1.3 and 1.5 Å−1, which is very similar to typical distance dependence in electron transfer coupling.46,56 It can also be seen that at the shortest intermolecular distance the coupling strength can still be varied by more than an order of magnitude. The smaller coupling values below the exponential decay reflects the effects of different orientations in different pairs. To see the distribution of coupling strength across different positions, in Figure 6, we use the radii of circles to represent the size of the coupling for the corresponding C60 molecules using the representation and coordinate as defined in Figure 4c. In Figure 6b,c,e,f, it can be seen that the large CS couplings are concentrated at the center, indicating that head-on contact between pentacene and C60 leads to a good CS rate. Large CR couplings are found at the outer regions, as seen in Figure 6a,d, where the C60 are located away from the top of pentacene, or, as indicated in Figure 4a, the pentacenes are in the “inserted” configurations. We can see that the distribution of large couplings is very similar in both aligned and rotated structures. To see the determining factors behind the coupling values, we include the frontier MOs of pentacene in Figure 7. If all inactive MOs were frozen, that is, those with their electron occupancy unchanged in ET, then the ET coupling is approximately the off-diagonal Fock matrix element for the two active MOs involved.57 The ET coupling value is thus highly dependent on the spatial overlap for these active MOs. For the CR process, an electron in the LUMO of C60 moves back to the HOMO of pentacene. For CS, the electron transfer takes place from the LUMO of pentacene to the LUMO of the C60 if we assume that the excitation of pentacene is essentially an excitation to the LUMO and the next lowest unoccupied MO (LUMO+1). When viewed from the short edge of the pentacene, there are two nodal planes for HOMO but only one nodal plane for LUMO, as seen in Figure 7. Therefore, the couplings involving the HOMO of pentacene are easily canceled at this region and, as a result, at the “head-on” configuration, the CR coupling values are likely be small. A

Figure 7. (a) Frontier MOs for pentacene and C60 involved in both CS and CR processes. (b) Good overlap is seen between the LUMO of pentacene and the LUMO of C60 (left) but not for the case with pentacene’s HOMO and C60’s LUMO (right). The MOs are derived from calculations with isolated pentacene and C60. The contour surface values are 0.01 au and 0.004 au for panels a and b, respectively.

similar cancellation effect is smaller for the LUMO of pentacene, and thus CS coupling is not canceled as much. Therefore, the spatial distribution of coupling strengths seen in Figure 6 is consistent with the spatial overlap of the MO involved between pentacene and C60. Good photovoltaic devices should have fast CS and slow CR. Our result indicates the pentacene−C60 interface can be improved if the “inserted” configuration is avoided. A similar approach is applicable for other systems. A system with good spacial overlap between the LUMOs of the two molecules but with a poor interaction between the HOMO of p-type and LUMO of the n-type molecules is desirable. Electron Transfer Rates. The triplet CS (3CS), singlet CS 1 ( CS), and singlet CR (1CR) rates of all pentacene−C60 configurations were calculated. The distribution of these rates, together with their reaction free-energy change, slightly modified by the intermolecular Coulomb interaction in the CT state, are included in Figure 8. The maximum reaction rates are also listed in Table 1 because the ultrafast experimental measurements likely capture the fast reacting portion in the ensemble. It can be seen that the triplet CS (3CS) rate is near the activationless region, with its maximum value on the order of 1013 s−1. Our sampling covers a range of over four orders of magnitude, which covers the experimentally reported CS rate 1011 s−1.15 This ultrafast portion of 3CS rate is comparable to the observed rate for singlet fission ((100 fs)−1). Therefore, the fast 3CS process provides a good efficiency in draining the triplet excited pentacene, and it will contribute to a good yield in harvesting electrons. To examine the roles of other electron transfer processes, in Figure 8 and Table 1, we also include calculated rates for the relevant photovoltaic processes, singlet CS and CR, and triplet CS (3CS). It is seen that the estimated rates of singlet CS are very low, 105 s−1, many orders of magnitude slower than triplet CS and the singlet fission rates. According to this result, even when both processes are available, a singlet excitation would be F

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Figure 9. Overall kinetics after a photo excitation in a pentacene−C60 interface.

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CONCLUSIONS With two different sets of pentacene−C60 interfacial structures, we analyzed the CT electronic couplings and corresponding rates for hundreds of different bimolecular configurations at the interface. We found that electron-transfer couplings have a systematic preference for a particular type of pentacene−C60 configuration: Couplings for CS are stronger for “head-on” configurations, while CR couplings prefer an “inserted” situation. Another important factor was the inclusion of the interfacial energy shift, and we found that this has a large determining effect in the electron-transfer rate. When an interfacial energy derived from experimental results is included, we found that the triplet CS rate is as high as 1013 s−1. The rates for singlet CS are much slower (105 s−1) due to the Marcus inverted effect. Singlet CR rates are faster than those of CS by a few orders of magnitude (1011 s−1), indicating that CS in a singlet surface is not likely to form and be maintained. Our result indicates that triplet CS is fast. Triplet CS follows fast singlet fission in pentacene15,16,58 and can proceed without immediate recombination. We believe that this finding is important as we try to understand photovoltaic processes in pentacene−C60 systems.

Figure 8. Calculated rates for the triplet CS (3CS, gray dots), singlet CS (1CS, yellow dots), and singlet CR (1CR, blue dots) reactions taking place in all of our pentacene−C60 configurations. The parabolic curve shows the CT rate estimated by the Marcus equation with λ = 0.3 eV, T = 300 K, and V = 40 meV.

Table 1. Maximum CT Rates Found in Pentacene−C60 Configurations full account for ΔGa

without Eintb

interface structure

aligned

rotated

aligned

rotated

k(3CS)c k(1CR) k(1CS)

1.7 × 1013 1.1 × 1011 4.4 × 105

1.3 × 1013 1.2 × 1011 2.2 × 105

4.7 × 108 4.1 × 103 1.4 × 1012

4.3 × 108 4.6 × 103 6.4 × 1011

a

Calculated using eqs 4−7. bCalculated using eqs 4−7 but without Eint. cIn all cases, the reorganization energy λ was set to 0.3 eV.

much more likely to proceed with singlet fission instead of CS. The singlet CR is found to be on the order of 1011 s−1. Therefore, the singlet channel for CS is unfavorable because it has a slow forward rate and a very fast rate for recombination back to the ground state. It is likely that the photoelectrons are mainly from singlet fission and subsequently triplet CS. On the other hand, the triplet CS is very fast (1013 s−1), and it is nearly activationless (Figure 8). This result suggests that the triplet excitons generated after singlet fission may contribute to CS effectively. Recent studies on singlet fission indicate that, when photoexcited, pentacene undergoes a fast singlet fission both in the solid as well as in solution.15,16,58 Therefore, CS may take place on triplet states. Our computational results indicate that the triplet-state CS is much faster than that in the singlet state, which may be the main contribution to the photovoltaic efficiency. The overall process and their corresponding rates, together with the singlet fission rates from experiments, is now included in Figure 9. As a final note, in estimating ΔG for the electron transfer, we have included interfacial effects by using the IP and EA values that are experimentally measured for pentacene and C60 at the interface. If we had ignored the interfacial effects and employed bulk values, −0.6 eV for the IP of pentacene and 0.9 eV for C60 EA, the ΔG value would have been 0.4 eV higher. In that case, for both structures, the maximum triplet CS rate would have dropped from 1013 to 108 s−1 (Table. 1), which is three orders of magnitude smaller than the experimental results, 2 × 1011 s−1.15 The interfacial energy shift is thus an important factor in the description of electron transfer events.

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AUTHOR INFORMATION

Corresponding Authors

*P.C.: E-mail: [email protected]; *C.-P.H.: E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS B.C.L. and C.P.H. thank the support from a research grant 1012628-M-001-003-MY4 from Ministry of Science and Technology, and the Nano program of Academia Sinica, Taiwan, ROC. B.T.K. and P.C. thank the U.S. National Science Foundation and NRI for financial support of this work through award number 1124754 in the Nanoelectronics Beyond 2020 program.

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