Letter Cite This: J. Phys. Chem. Lett. 2017, 8, 5171-5176
pubs.acs.org/JPCL
Charge-Transfer Dynamics in the Lowest Excited State of a Pentacene−Fullerene Complex: Implications for Organic Solar Cells Saju Joseph,†,§,# Mahesh Kumar Ravva,†,# and Jean-Luc Bredas*,†,‡ †
KAUST Solar Center, Physical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia ‡ School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States S Supporting Information *
ABSTRACT: We characterize the dynamic nature of the lowest excited state in a pentacene/C60 complex on the femtosecond time scale, via a combination of ab initio molecular dynamics and time-dependent density functional theory. We analyze the correlations between the molecular vibrations of the complex and the oscillations in the electron-transfer character of its lowest excited state, which point to vibration-induced coherences between the (pentacene-based) local-excitation (LE) state and the complex charge-transfer (CT) state. We discuss the implications of our results on this model system for the exciton-dissociation process in organic solar cells.
rganic solar cells based on π-conjugated systems have attracted a great deal of interest.1−5 The generation of excited states upon light absorption and the subsequent separation of the photogenerated charge pairs into free electrons and free holes represent the fundamental processes in solar-energy conversion systems. In organic solar cells, the process of charge generation involves photoinduced electron transfer between an electron-donor component and an electron-acceptor component to lead either directly to a charge-separated state or to an intermediate state, referred to as a charge-transfer (CT) state, which then evolves into a charge-separated state.4−6 The CT state is thus a key intermediate electronic state in the operation of organic photovoltaic device, as it plays a determining role not only in the exciton-dissociation mechanism but also in the chargerecombination mechanism.6 In a number of highly efficient systems, the photoinduced electron transfer between the electron-donor component and the electron-acceptor component in donor/acceptor blends has been reported to occur within less than a 100 fs time scale, both experimentally and theoretically.7−16 For instance, Lienau and co-workers used ultrafast spectroscopy and quantum dynamics simulations to describe a coherent ultrafast electron-transfer process from a poly-3-hexylthiophene (P3HT) donor to a fullerene acceptor. These authors also reported that the transferred charge oscillates between the electron-donor component and electron-acceptor component with a period on the order of 25 fs.15 Scholes and co-workers also probed the mechanism of ultrafast electron transfer in polymer−fullerene blends by performing two-dimensional electron spectroscopy
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© 2017 American Chemical Society
on P3HT/PCBM blends.17 Combining time-resolved femtosecond spectroscopy and first-principles quantum dynamics simulations, Rozzi et al. reported how the coherent motion of atoms governs the light-induced charge generation as well as charge separation at the fs time scale.18 These studies point to the role of vibronic couplings in the description of CT states. The combination of ab initio molecular dynamics (AIMD) simulations and density functional theory (DFT) calculations has emerged as a powerful tool to study systems that are relevant to organic solar cells. In this Letter, we apply such a methodology to a pentacene/C60 complex, which we have extensively considered over the past few years as a representative model system.19−21 (We stress that because we are interested in depicting the evolution between the donor S1 state and the CT state we do not consider the possible singlet fission of the pentacene S1 state.) Our goal is to probe at the femtosecond time scale the dynamics of the lowest CT state of the complex in order to gain better insight into the chargeseparation and charge-recombination mechanisms at donor− acceptor interfaces. AIMD simulations have been carried out on the lowest excited state of the pentacene/C60 complex, using the timedependent (TD)-DFT-based NEWTON-X package interfaced with the Gaussian 09 package.22,23 Snapshots extracted from MD trajectories are used to characterize the evolution of the nature of the lowest excited state; to do so, we use a long-range Received: August 4, 2017 Accepted: October 2, 2017 Published: October 2, 2017 5171
DOI: 10.1021/acs.jpclett.7b02049 J. Phys. Chem. Lett. 2017, 8, 5171−5176
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Figure 1. Four lowest excited states of the pentacene/C60 complex calculated at the tuned TD-ωB97XD/6-31g(d) (ω = 0.137 bohr−1) level of theory (ε = 1). The hole and electron wave functions of each excited state come from a NTO analysis (λ denotes the fraction of the hole−electron pair contribution to the given electronic transition). The amount of charge on C60 (from a Mulliken population analysis) is also presented.
the large increase in the dispersion interactions between the πelectron clouds of the two molecules in the case of the face-on configuration.26 (ii) Also because of these favorable dispersion interactions, the pentacene backbone somewhat deforms to wrap slightly around the fullerene cage. In the face-on pentacene/C60 complex, the geometrical changes and intermolecular interactions between pentacene and C60 result in a ∼150 meV increase in the IP with respect to that of pentacene itself and a ∼200 meV decrease in the EA with respect to that of C60 (see Table S1); these results bring, to a first approximation, a ∼350 meV increase in the (pentacene/C60) HOMO−LUMO gap. The four lowest excited states of the pentacene/C60 complex at the ω-tuned TDωB97XD/6-31g(d) level of theory (ε = 1) are depicted in Figure 1 along with the hole and electron wave functions obtained from a NTO analysis. The two lowest excited states in the pentacene/C60 complex (ε = 1) can be characterized as CT states, while the third and fourth excited states are states with a hybrid character between a local-excitation (LE) state on pentacene and a CT excitation. On the basis of a simple Mulliken charge population analysis, C60 gains an excess (negative) charge of −0.9 |e| in the S1 (CT) state of the complex; the calculated excess charge densities in states S2, S3, and S4 are −0.87, −0.42, and −0.46 |e|, respectively (Figure 1). Importantly, for the “isolated” complex (ε = 1), the total energy difference between the S1 and S4 states is only on the order of 150 meV. This actually makes the isolated complex particularly interesting as it can be taken as representative of donor−acceptor systems with a small energetic difference between the LE state of the light-harvesting species and the interfacial CT state, which is a most sought-after characteristic in order to minimize the energy (and voltage) losses in the course of the charge-separation process. We will thus mainly discuss this case in the remainder of the work. We now turn to the dynamics and focus on the lowest excited state of the complex, which we analyze over a time scale of 100 fs; this is sufficient to track several periods of oscillation for the high-frequency modes (such as C−C bond-stretching or ring-breathing modes) that are known to couple strongly with electronic excitations in π-conjugated systems. We initiated the
corrected density functional that minimizes the electron selfinteraction error and provides a sound description of the localization/delocalization nature of the wave functions in extended π-conjugated systems.24 The starting geometry for the AIMD simulations is set as the ground-state geometry optimized at the DFT-ωB97XD/6-31G(d) level of theory (with the range-separation parameter ω optimized a using nonempirical tuning procedure,24 ω = 0.137 bohr−1). Dynamics are run at the TD-ωB97XD/6-31G(d) level using a microcanonical ensemble, with a time step for integration of the classical equations of one fs. The initial geometry and velocity conditions are generated by Wigner sampling, and seven trajectories in the S1 state are propagated for 100 fs (we note that the complex remains bound over the course of the dynamics). The nature of the excited state at each time step is investigated using a Natural Transition Orbital (NTO) analysis at the TD-ωB97XD/6-31G(d) level.25 The calculations are carried out both for the isolated complex (ε = 1) and in an implicit dielectric medium (with ε set equal to 3.5, which is a typical value for organic conjugated materials) using the conductor-like self-consistent reaction field (SCRF) method at the ωB97X-D/6-31G(d) level (the range-separation parameter ω decreases to 0.021 bohr−1 when optimized in the presence of the ε = 3.5 polarizable continuum model); the comparison of the ε = 1 and ε = 3.5 results allows us to analyze the impact of the solid-state environment on the energy of the lowest CT states. The large computational requirements of such an AIMD approach are what explains the limitations of the system to a single pentacene−fullerene complex, which does not allow us to take disorder effects into account. We first discuss the static picture. The optimized geometries of pentacene, C60, and the pentacene/C60 complex are illustrated in Figure S1, and the calculated ionization potentials (IPs) and electron affinities (EAs) are compared in Table S1. Very good agreement is found with earlier theoretical and experimental results. There are two notable aspects regarding the geometry of the pentacene/C60 complex: (i) Edge-on configurations (where the fullerene sits on the periphery of the pentacene backbone) are not stable and evolve to the most stable face-on configuration, shown in Figure S1. The reason is 5172
DOI: 10.1021/acs.jpclett.7b02049 J. Phys. Chem. Lett. 2017, 8, 5171−5176
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Figure 2. Calculated Mulliken charge population on C60 in the pentacene/C60 complex as a function of time for a representative trajectory (Traj-3) at the tuned TD-ωB97XD/6-31G(d) (ω = 0.137 bohr−1) level of theory.
Figure 3. Time-dependent evolution of the energies of the LUMO, LUMO+1, LUMO+2, and LUMO+3 levels in the pentacene/C60 complex, as determined at the tuned ωB97XD/6-31G(d) (ω = 0.137 bohr−1) level of theory for the Traj-3 trajectory.
lowest excited state has a hybrid LE−CT character. These results, on the one hand, underline the fs scale of the electron transfer between donor and acceptor, which is consistent with ultrafast spectroscopy data,14,17 and, on the other hand, point to charge oscillations occurring with periods of some 20−25 fs, which is also in line with previous dynamics studies.15,27 Very similar observations can be made in the case of the other six trajectories (see Figure S3). An extensive depiction of the geometry evolutions occurring in the course of the dynamics for ε = 1 is given in Figures S4− S9 (see also the structural dynamics movie attached to the SI corresponding to the Traj-3 trajectory). Since the basis for the rich physics of extended π-conjugated systems is the intimate connection between geometric structure and electronic structure (i.e., strong electron−vibration couplings),28,29 the dynamical geometry fluctuations do deeply impact the electronic properties. We note that while there occur significant modifications in C−C and C−H bond lengths as well as in bond and dihedral angles in the course of the 100 fs simulations, the intermolecular distance between pentacene and C60 hardly evolves over such a period of time (by less than 0.1 Å; see Figure S4), as expected from the much lower frequency of these intermolecular displacements. The excitedstate C−C stretching/ring-breathing periods in the pentacene
nonadiabatic ab initio dynamics of the pentacene/C60 complex by populating its lowest excited (S1) state, initially at the optimal ground-state geometry. The time evolutions of the S0 and S1 potential energy surfaces for seven trajectories are given in Figure S2. While the structural fluctuations have a considerable impact on the individual ground-state and excited-state energies, the energy difference between the S1 and S0 states is found to have a much smoother evolution, within a ∼500 meV range. A useful descriptor of the dynamics in the S1 state is the amount of excess charge on the fullerene molecule, whose evolution is depicted in Figure 2 from charge density analysis for a representative trajectory (Traj-3 in Figure S2; the molecular vibrations in the course of that trajectory are illustrated in a movie attached to the SI)). We note that in the course of the whole dynamics the hole wave function in the S1 state remains localized on the pentacene molecule. In contrast, the electron wave function does strongly fluctuate between C60 and pentacene. While the electron starts on C60 (with S1 having initially the CT character of the “static” S1 state), it jumps onto pentacene after some 18−20 fs (S1 then corresponds to a LE on pentacene) before going back into C60 (see the movies of the electron and hole dynamics in the S1 state in the SI). It takes some 2−3 fs to complete a jump, in the middle of which the 5173
DOI: 10.1021/acs.jpclett.7b02049 J. Phys. Chem. Lett. 2017, 8, 5171−5176
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Figure 4. Statistical distribution of the S1 state energies computed at the tuned TD-ωB97XD/6-31G(d) level from the snapshots of the AIMD trajectories for (a) ε = 1 (tuned ω = 0.137 bohr−1) and (b) ε = 3.5 (tuned ω = 0.021 bohr−1).
To summarize, we have presented a combined electronicstructure and AIMD investigation of the lowest excited state in a pentacene/C60 complex, which can be taken as a model system for the donor−acceptor interface in organic solar cells. The results underline that the molecular vibrations, in particular, the C−C bond-stretching and ring-breathing modes, lead to major oscillations of the energy levels. These vibronic couplings in turn influence the nature of the lowest excited state of the complex, activating transitions between a CT-type state and a LE-type state, via very short-lived hybrid LE−CT states. Also, the dynamics in the pentacene/C60 complex results in a distribution of the lowest excited-state energies over several tenths of an eV. These results have important implications regarding organic solar cells: (i) If we consider the initial photogeneration of an exciton on, say, the electron-donor component (here, pentacene), the fluctuations in the electronic levels of the donor and acceptor components lead to mixing of the LE and CT states, which can be viewed as vibration-induced coherences that could trigger an ultrafast excitondissociation process. (ii) Given the size limitations of our model system (imposed by the computational requirements of the AIMD simulations), it will be important to keep investigating whether this mixing of quantum states indeed leads to longer-range coherences facilitating the charge-separation process at actual donor−acceptor interfaces.14,15,17,18,33,34 (iii) The dynamics of the CT states, which leads to a distribution in CT state energies, can be viewed as playing a dual role as, on the low-energy side, it can negatively impact the device VOC but, on the high-energy side, it can help in overcoming the barrier to charge separation.
and fullerene moieties are evaluated to be on the order of 23 fs, which is in good agreement with the results of recent investigations.15,18 To better comprehend the oscillations in the electron transfer between pentacene and fullerene, it is in fact useful to analyze the fluctuations in the molecular-orbital energies of the complex; see Figure 3 for the Traj-3 trajectory. We recently showed that the molecular vibrations in the PCBM (derivative of C60) lead to a Gaussian distribution of the LUMO level, with a standard deviation on the order of 0.075 eV.30 Here, for the “static” pentacene/C60 complex, the ωB97XD/6-31g(d) HOMO and LUMO+3 levels reside on pentacene while the LUMO, LUMO+1, and LUMO+2 levels are nearly degenerate and localized on the fullerene (they correspond to the triply degenerate C60 LUMO); the wave functions of these levels are shown in Figure S10. Figure 3 highlights that when the simulation reaches times around τ = 15−20, 40−50, and 60−80 fs, i.e., the times when the complex S1 state gains a LE character (in the Traj-3 trajectory), these are precisely the times when the (pentacene-based) LUMO+3 energy comes close (within less than 0.1 eV; see Figure 3) to the (fullerene-based) LUMO +2 energy. Interestingly, the transition between a LE and CT character of the S1 state goes through a hybrid LE−CT state. Such a hybrid LE−CT state has recently been reported in a polymer−fullerene solar-cell-active layer, where the energy difference between the polymer S1 state and the interfacial CT state is very small.31 We have also evaluated the statistical distributions of the CT state energies arising from the structural fluctuations of the pentacene/C60 complex in both ε = 1 and 3.5 environments; see Figure 4. For ε = 1, analyses of the hole−electron wave functions indicate that out of the 707 structures that we generated (7 trajectories over 100 fs with 1 fs steps) 386 structures (i.e., about 55% of the structures) have full CT character. The energies of these CT configurations have an average value of 1.81 eV with a standard deviation of 0.14 eV (overall, they distribute over a range going from 1.46 to 2.20 eV); see Figure 4a. Solid-state effects are expected to lower significantly the energies of CT states while hardly affecting the energies of LE states. Thus, when considering an implicit dielectric medium (ε = 3.5), the S1 state of the complex gets stabilized to an average energy of 1.03 eV (with a standard deviation of 0.11 eV; see Figure 4b), which matches the range of experimental estimates for CT state energies in pentacene/ C60 heterojunctions;32 in that instance, the S1 state maintains CT character throughout the trajectories.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b02049. Calculated ionization potentials (IPs) and electron affinities (EAs) of pentacene, C60, and pentacene/C60; time-dependent evolutions of the S0 and S1 state energies for seven AIMD trajectories; time-dependent evolutions of the excess charge on C60 for various AIMD trajectories; time-dependent evolutions of selected 5174
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pentacene C−C and C−H bond lengths and of the intermolecular distance between pentacene and C60 for Traj-3; and frontier molecular orbitals from HOMO−1 to LUMO+3 (PDF) Movie the hole wave function evolution for a representative AIMD trajectory (Traj-3) (AVI) Movie illustrating the electron wave function evolution for a representative AIMD trajectory (Traj-3) (AVI) Movie illustrating the vibrations for a representative AIMD trajectory (Traj-3) (AVI)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Mahesh Kumar Ravva: 0000-0001-9619-0176 Jean-Luc Bredas: 0000-0001-7278-4471 Present Address §
S.J.: International and Interuniversity Centre for Nanoscience and Nanotechnology (IIUCNN), Mahatma Gandhi University, Kottayam, Kerala 686560, India. Author Contributions #
S.J. and M.K.R. contributed equally.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Dr. Greg Scholes, Dr. Sean Ryno, and Dr. Simil Thomas for insightful discussions. This work has been supported by King Abdullah University of Science and Technology (KAUST), the KAUST Competitive Research Grant program, and the Office of Naval Research (Award No. N00014-17-1-2208). We acknowledge the IT Research Computing Team and Supercomputing Laboratory at KAUST for providing computational and storage resources.
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