Hot Charge-Transfer States Determine Exciton Dissociation in the

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Hot Charge-Transfer States Determine Exciton Dissociation in the DTDCTB/C Complex for Organic Solar Cells: A Theoretical Insight 60

Xingxing Shen, Guangchao Han, Di Fan, Yujun Xie, and Yuanping Yi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp512574d • Publication Date (Web): 05 May 2015 Downloaded from http://pubs.acs.org on May 9, 2015

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The Journal of Physical Chemistry

Hot Charge-Transfer States Determine Exciton Dissociation in the DTDCTB/C60 Complex for Organic Solar Cells: A Theoretical Insight Xingxing Shen,1,2 Guangchao Han,1,2 Di Fan,1 Yujun Xie,1 Yuanping Yi1,*

1

Beijing National Laboratory for Molecular Sciences, CAS Key Laboratory of Organic Solids,

Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China 2

University of Chinese Academy Sciences, Beijing 100049, China

1

ACS Paragon Plus Environment


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ABSTRACT

To understand charge-transfer (CT) processes at the donor/acceptor interface of DTDCTB/fullerene solar cells, we have investigated the electronic couplings and the rates for exciton-dissociation and charge-recombination processes based on two representative intermolecular geometries of the DTDCTB/C60 complex by means of quantum-chemical calculations. Consistent with the experimental measurements of the time scale of over sub-ns or even ns for charge recombination (CR), the calculated CR rates are lower than 1010 s-1 and in most cases, below 109 s-1. The calculated rates for exciton dissociation into the CT ground state are mostly lower than 1010 s-1, which is however, in sharp contrast with the ultrafast charge separation (~100 fs) observed experimentally. Interestingly, our calculations point out that excitons are able to dissociate into a higher-energy excited CT state much faster, with the rates being as large as about 1012 and 1014 s-1 in all cases for excitons based on C60 and DTDCTB, respectively. Thus, exciton dissociation in the DTDCTB/C60 complex is determined by the hot CT states. As the excess energy of the excited CT state can facilitate the geminate electron and hole to further separate at the donor/acceptor interface, our theoretical results suggest that the high performance of the DTDCTB/fullerene-based solar cell can be mainly attributed to the fact that excitons dissociate via the hot CT states to effectively form mobile charge carriers.

2


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1. Introduction In recent several decades, organic solar cells (OSCs) have attracted much attention because of their advantages of low cost, light weight, mechanical flexibility, large-area capability, and easy processing.1-4 The power conversion efficiency (PCE) of OSCs is determined by several processes, including exciton generation, diffusion, and exciton dissociation (ED) at the donor/acceptor (D/A) interface, charge carrier migration and collection at the electrodes.5-6 In order to achieve high PCE, many strategies have been made, such as designing new donor and acceptor materials and device structures, and optimizing morphology.7-13 At present, although polymer/small molecule based bulk heterojunction (BHJ) OSCs have achieved large success, 14-17 the mechanism of charge generation has not been well understood including the effects of excess energy,18-19 charge delocalization,20 and “hot” exciton.21-22 The ED process at the D/A interface is one of the key factors to achieve high PCE for OSCs. 23-24

The interface geometries affect the energies of excited states and interfacial charge-transfer

(CT) states and electronic couplings, which are very crucial for separating bound exciton into free charge carriers.25-27 Several theoretical researches have investigated the impact of interfacial geometries on the ED and charge-recombination (CR) processes. For instance, the CR process is more limited in perpendicular configurations with respect to parallel configurations for the pentacene/C60 complex.28 For Rubrene/TCNQ system, the crystal orientation in bilayer system exhibits lower geminate recombination due to higher D-A separation than the cofacial orientation in bulk system.29 At the P3HT/PCBM interface, the flat-lying orientation of PCBM (side alkyl chain of PCBM is parallel to the backbone of P3HT) is more beneficial to both ED and CT 3



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processes compared with the upright-standing one (side alkyl chain of PCBM is perpendicular to the backbone of P3HT).30 Besides tuning interface geometries, exploiting high-energy excitons is another key factor to create free charge carriers. In general, a high exciton state of active molecules will relax to the lowest singlet excited state (S1) before evolving into CT states.31 However, some experimental results have shown that high exciton states could dissociate before relaxation due to the delocalization of excited states.32-34 In addition, some experiments have found that high-energy CT states (hot CT exciton) could dissociate to form free charge carriers within several hundreds of femtoseconds before decaying into the lowest CT (CT0) state.35-37 At the same time, the photocurrent could be enhanced after re-excitation of the CT0 exciton.38 Thus, these experimental evidences suggest that hot excitons have significant positive effects on the generation of free charge carriers and photocurrent. Recently, as one kind of vacuum-deposited small-molecule OSCs, the DTDCTB/fullerene heterojunctions have been intensively studied and achieved a relatively high PCE.39-42 The spectroscopic measurements by transient absorption and time-resolved photoluminescence have shown that charge separation occurs (~100 fs) much faster than CR (over sub-ns or ns time scale) in the DTDCTB/fullerene films and that a lifetime of 33 ps is found for the donor exciton.43 The results imply that the ultrafast charge separation is critical to achieve the high device performance. In this work, aiming to understand the exciton-dissociation mechanism in the DTDCTB/fullerene heterojunction-based solar cells, we investigate the charge-transfer processes 4


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in the DTDCTB/C60 complex. By means of quantum-chemical methods, we have calculated the electronic couplings and the rates for ED and CR processes based on two representative intermolecular configurations. In particular, we will unravel the dominant role of hot CT states in the ED process.

2. Methodology 2.1 Model Interface Geometries The geometry optimizations for the ground and charged states of isolated DTDCTB and C60 molecules were performed by density functional theory (DFT) and the excited-state geometries were optimized by time-dependent DFT (TDDFT). In order to consider different interface geometries in OPV devices, we construct two representative DTDCTB/C60 intermolecular configurations (I and II) by placing the acceptor C60 to be near to the electron-donating or electron-withdrawing moieties of the donor DTDCTB (see Figure S1). The initial geometrical structures of DTDCTB and C60 in the complex are adopted from the ground-state geometries of the isolated molecules. For configuration I, the C60 molecule is situated between the two phenyl groups (close to the electron-donating units of DTDCTB), and appears to be perpendicular to the backbone of DTDCTB. For configuration II, C60 is placed on the top of malononitrile unit (close to the electron-withdrawing units of DTDCTB), forming a parallel intermolecular configuration. These two intermolecular configurations were then optimized by DFT and DFT-D (DFT including the D3 version of Grimme’s dispersion).44 All these calculations were carried out using the B3LYP functional and 6-31G(d) basis set with the Gaussian-09 package.45 5



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2.2 Reorganization energies The reorganization energies for the charge-transfer processes of the donor-acceptor complexes were obtained approximately as the sum of relaxation energies of individual donor and acceptor molecules upon charging or discharging. The respective relaxation energies of donor and acceptor were computed through adiabatic potential energy calculations. The potential energy calculations in gas phase were performed on isolated molecules by TDDFT or DFT. Furthermore, since the DTDCTB molecule is relatively flexible, to include the steric effect in the condensed state, the corresponding potential energies of DTDCTB in solid state were evaluated by a hybrid quantum mechanics/molecular mechanics (QM/MM)46 approach, as implemented in the Gaussian-09 package. The initial cluster geometry was constructed as a 3×3×3 supercell of the crystal structure (see Figure S2), where the central QM molecule is fully surrounded by 107 MM DTDCTB molecules. Calculations of the potential energy surface of the ground, excited, and charged states were performed with the QM part treated by DFT and TDDFT at the B3LYP/6-31G(d) level while the surrounding molecules treated with the UFF force field. During optimizations of the geometries, the atomic positions for both QM and MM molecules are active. At this stage, we notice that, instead of some DTDCTB molecules, C60 molecules will appear at the donor/acceptor interfaces in practice. The different influence induced by replacing C60 with DTDCTB for the surrounding molecules is omitted here. 2.3 Electronic Couplings Based on the two representative DTDCTB/C60 intermolecular configurations as constructed above, the electronic couplings (Vab) between the local excited and CT states were computed by a 6


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diabatic-state approach,47

Vab = ΨaLE HΨbCT

(1)

where ΨaLE denotes the wavefunction of the ground or local excited state, and ΨbCT represents the wavefunction of the CT state. They are constructed as spin-adapted antisymmetrized products of the isolated donor and acceptor wavefunctions, ΨijLE(S,M) =

C SSMM S M ΨiD(S i ,M i )Ψ jA(S j ,M j ) ∑ M M i i j

(2)

j

i j

Ψ kmCT (S ,M ) =

+

−

C SSMM S M Ψ kD (S k ,M k )Ψ mA (S m ,M m ) ∑ M M k

k

k m

(3)

m

m

here, S and M denote the total spin and spin projection of the donor-acceptor complex, respectively; ΨiD/A represents the ith excited state of the donor or acceptor with spin Si and spin projection Mi; Ψ kD

+

/A −

represents the oxidized state of donor or the reduced state of acceptor.

SM The C S i M i S j M j terms are the Clebsch-Gordan coefficients that ensure the linear combination of

the products of the isolated wavefunctions to be the eigenfunction of the total spin. The isolated excited and charged states for donor and acceptor were obtained using the intermediate neglect of differential overlap (INDO) Hamiltonian48 coupled to a single configuration interaction (SCI) scheme. All the π-orbitals were considered in the active space. The coulomb repulsion term was described by the Mataga-Nishimoto potential.49-50 Because the local excited states and CT states of C60 are orbitally degenerate, we calculate the effective electronic couplings (Veff) as follows:28 2 Veff =

1

gI

(ΨaI HΨbF ) ∑ ab

2

(4)

where ߖ௔ூ and ߖ௕ி correspond to the many folds of the initial and final diabatic states, 7



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respectively; ga is the multiplicity of the initial diabatic state. 2.4 Electron-transfer Rates The semi-classical model of Marcus electron-transfer theory was exploited to estimate the rates of ED and CR processes,51 k ab = V ab2

π exp[ −(∆G + λ )2 / 4λk BT ] λk BTh 2

(5)

Here, the electronic coupling between the initial and final states Vab, reorganization energy λ, and Gibbs free energy of electron-transfer reaction ∆G are the three key parameters. kB and ħ denote the Boltzmann and the reduced Planck constant, respectively. Temperature T is set to 298.15 K in our calculations. Here, our goal is to make a qualitative comparison between different rates for the ED and CR processes. As discussed in the latter, the studied system is in the normal or near-inverted region of the Marcus charge transfer, thus the comparison should be reliable. Nevertheless, it is necessary to note that an accurate charge-transfer rate can be achieved by means of a more complex full quantum approach that will take account of the nuclear tunneling effects.52-56

3. Results and Discussion 3.1 DTDCTB/C60 Interfacial Geometries: the Role of Dispersion Interaction The DFT-D and DFT-optimized DTDCTB/C60 intermolecular geometries are shown in Figure 1 and Figure S3, respectively. Both the DFT and DFT-D interfacial geometries exhibit obvious difference from the initial complex geometries. The changes for the DFT geometries lie 8


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mainly in the orientations of C60 relative to DTDCTB; however, the intramolecular structures of DTDCTB are almost unaffected. In contrast, both the C60 orientations and the molecular geometries of DTDCTB are modified for the DFT-D interfacial geometries due to the additional dispersion interaction between DTDCTB and C60. In configuration I, while the DTDCTB backbone keeps a coplanar structure, one of the phenyl groups rotates to be perpendicular to the backbone. More interestingly, in configuration II, C60 moves from the malononitrile to benzothiadiazole unit and the DTDCTB backbone makes a significant bend around C60, differing much from the DFT structure. In addition, the shortest intermolecular distances for the DFT-D geometries are 3.2 and 3.1 Å in configurations I and II, respectively, which are substantially smaller than the corresponding DFT estimates of 4.1 and 3.7 Å. Therefore, dispersion interactions play a critical role in determination of the DTDCTB/C60 complex geometries. It should be noticed that the bending structure of DTDCTB could get more planar in configuration II when more DTDCTB molecules are added. However, the intermolecular distance and relative positions between DTDCTB and C60 would not be modified too much and thus none of essential changes can be expected for electronic couplings. In the following, we will concentrate our results and discussion on the DFT-D intermolecular geometries.

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Figure 1. The DFT-D optimized intermolecular geometries for configurations I and II of the DTDCTB/C60 complex. 3.2 Electronic Couplings For ED processes, we have calculated the electronic couplings of the local S1 state on DTDCTB (VS1D) and C60 (VS1A) with the ground CT state (CT0), as well as the couplings involving four higher-energy excited CT states, namely CT1A, CT2A, CT3A, and CT1D, which are originated from the lowest excited charged states on either C60 or DTDCTB. In general, the excited CT states are assumed to relax to CT0 prior to decay into the ground state. Hence, the electronic coupling for CR processes (VCR) is limited to between CT0 and the ground state. The calculated electronic couplings are shown in Figure 2 along with the interfacial energy alignments. As expected, the electronic couplings are much dependent on the interface geometries. Generally, because of much closer intermolecular packing, configuration II exhibits stronger electronic couplings as well as a lower total energy with respect to configuration I. For configuration I, VS1D and VS1A with CT0 are only 5 and 6 meV, respectively, smaller than VCR (9 10


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meV). For configuration II, VCR can be as strong as 23 meV, which is somewhat larger than VS1A (19 meV), but substantially smaller than VS1D (75 meV) with CT0. Interestingly, significant electronic couplings are found for exciton dissociation into the higher-energy excited CT states. For instance, VS1D involving CT1A in both configuration I (5 meV) and configuration II (72 meV) are comparable to the corresponding couplings with CT0. In addition, for configuration I, VS1D [VS1A] involving the CT2A, CT3A, and CT1D states are 3, 4, and 7 meV [0, 1, and 11 meV], respectively; the corresponding values for configuration II can be as large as 27, 34, and 53 meV for VS1D and 1, 5, and 36 meV for VS1A, respectively.

2.5

I 2.0 Energy (eV)

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V (CT0; CT1A;CT2A;CT3A;CT1D)

S ⊗S 1D

0A

S ⊗S

1.5

0D

1A

CT1D CT 3A

5; 5; 3; 4; 7

CT

2A

6; 2; 0; 1;11

CT

II

V (CT0; CT1A;CT1D;CT2A;CT3A)

S ⊗S 1D

0A

S ⊗S 0D

1A

CT

3A

75;72;53;27;34

CT 2A CT 1D

19; 5;36; 1; 5 CT

1A

1A

1.0

CT

CT

0

0.5 0.0

0

9

23

S ⊗S 0D

S ⊗S

0A

0D

0A

Figure 2. Electronic couplings (meV) for exciton dissociation from the DTDCTB and C60 based S1 states to the excited and ground CT states and for charge recombination from the ground CT state to the ground state, and the energy alignments between the local and CT states for configurations I and II of the DTDCTB/C60 complex.

3.3 Gibbs free energies As seen from equation 5, Gibbs free energy ∆G is one of the key parameters to determine the charge-transfer rates. If we ignore the entropy contribution, ∆G is estimated as the energy 11



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difference between the initial and final diabatic states of the complex. That is to say, ∆G is equal to the energy difference between the CT states and the local excited states for ED processes and between the ground state and the CT0 state for CR processes. The energy of the diabatic state can be approximate to the sum of the total energies of the isolated states of DTDCTB and C60 and the Coulomb energy between DTDCTB and C60. Since the Coulomb energies of the neutral diabatic local states can be neglected, using the total energy of the ground state as reference, the energies for local excited states of the DTDCTB/C60 complex are estimated as the excitation energies of the isolated DTDCTB and C60; while the energies for CT states must consider the Coulomb energies,28, 57

E CT = IP + EA + E Coul

(6)

where IP is the ionization potential of DTDCTB; EA is the electron affinity of C60; and ECoul is the Coulomb energy between the DTDCTB cation and C60 anion,

E Coul =

∑d

− ∈DTDCTB + ,a ∈C 60

qd q a 4πεεr da 0

(7)

here, qd and qa denote the partial charges (obtained via an INDO Mulliken population analysis) on atoms d and a belonging to the DTDCTB cation and C60 anion, respectively; and rda is the distance between atoms d and a. ε0 and ε are dielectric constants of the vacuum and medium (here, we set it to be an average value of 4.0), respectively. Our calculations reveal the same Coulomb energies for CT0 and the excited CT states (CT1A, CT2A, CT3A, and CT1D), which are estimated to be -0.38 and -0.46 eV for configurations I and II, respectively. The first excitation energies and ionization energies for isolated DTDCTB and C60 are 12


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collected in Table 1. By analyzing the experimental UV-vis absorption spectra, the first excitation energy of DTDCTB is determined to be 1.87 eV in CH2Cl2 solution, and is red-shifted to 1.81 eV in solid-state film.41 Compared to the experimental measurements, the S1 energy is somewhat overestimated by vertical TDDFT (1.96 eV) and INDO/SCI (2.07 eV) calculations while substantially underestimated by adiabatic TDDFT calculations (1.51 eV). Since the S1 energy for C60 has been discussed in our previous works,28, 57 we just listed the values in Table 1 for simplicity. The value in solid state is measured to be 1.70 eV.59 The IP of DTDCTB is determined to be 5.3 eV in thin film from the onset in the ultraviolet photoelectron spectroscopy (UPS) spectra.60 Both DFT and INDO calculations in gas phase overestimate the IP value due to lack of polarization effect. The EA of C60 has been quite ambiguous despite of much effort devoted in experiment and theory.61-62 In recent, the EA of C60 is precisely measured to be about -4.0 eV in solid state by employing a new low-energy inverse photoemission spectroscopy (IPES) that can avoid damage of organic samples and has a higher energy resolution.63 In addition, according to the improved fitting relationship between the open-circuit voltages (VOC) and the energy differences between the solid-state donor IP and acceptor EA, as suggested by Yoshida recently, the predicted VOC (ca. 0.81) for DTDCTB/C60 solar cells is in good agreement with the experimental measurements (0.8 eV). This indicates that these ionization energies measured by UPS and IPES should be reliable for estimation of the CT energy. According to equation 6, the CT0 energy is computed to be 0.92 and 0.84 eV for configurations I and II, respectively. The energy for the excited CT states can be obtained by further adding the excitation energy of relevant isolated excited charged states. As a result, the 13



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CT1A energy is estimated to be 1.52 eV for configuration I and 1.44 eV for configuration II, which is lower than the S1 energies of DTDCTB and C60. However, the CT1D, CT2A, and CT3A states are lying at least 0.1 eV above the S1 states of DTDCTB and C60; thus, these excited CT states will not be considered in ED processes. Since organic solar cells are fabricated in the form of thin films, ∆G for ED and CR processes can be obtained using the energies of the local S1 and CT states, as measured by experiments in the solid state. For configuration I, the ∆G for electron transfer from the S1 states on DTDCTB and C60 to CT0 are estimated to be -0.89 and -0.78 eV, and the ∆G to CT1A are -0.29 and -0.18 eV, respectively. The absolute values of the corresponding ∆G are 0.08 eV larger for configuration II. The ∆G for CR processes from CT0 to the ground state are just the opposite values of CT0 energies, -0.92 and -0.84 eV for configurations I and II, respectively.

Table 1. The first singlet excitation and ionization energies (in eV) for DTDCTB and C60 calculated in gas phase; the experimental values are also provided for comparison. DTDCTB S1

IP

S1

EA

Vertical

1.96

6.33

2.10

-1.99

Adiabatic

1.51

6.27

1.85

-2.06

INDO

Vertical

2.07

6.32

2.24

-1.47

Exp.

In solution

1.87a

―

1.94c

-2.68e

In film

1.81a

5.30b

1.70d

-4.0f, g

DFT

a

C60

Ref. 41. b Ref.60. c Ref.58. d Ref.59. e Ref.61. f Ref. 62. g Ref. 63.

14


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3.4 Reorganization energies The reorganization energy (λ) consists of internal or intramolecular (λint) and external or intermolecular (λext) contributions (λ=λint+λext); the former is originated from the change in the geometry of the individual molecules and the latter in the electronic and nuclear polarization of the surrounding medium upon electron transfer. λint can be calculated from the adiabatic potential surfaces of the involved molecular states of individual donor and acceptor molecules. For exciton dissociation from the LE state on donor [acceptor] to the CT state, λint is evaluated as the sum of the relaxation energies in the positively charged state of donor from the excited-state [ground-state] to cationic geometry and in the negatively charged state of acceptor from the ground-state [excited-state] geometry to the anionic geometry. For charge recombination from the CT state to the ground state, λint corresponds to the total relaxation energies in the ground states of donor and acceptor from their ionic geometries to their neutral geometries. Here, we have calculated the relaxation energies for ED and CR processes in DTDCTB. The corresponding values in C60 are adopted from our previous work.57 All the relaxation energies are listed in Table 2. We can find that, the relaxation energies of DTDCTB involving the ground state are very similar in gas phase, 0.064 and 0.065 eV for ED and CR, respectively. The relaxation energy from the S1 state to cationic state for the isolated DTDCTB molecule is very large, reaching 0.67 eV. Such large relaxation energy is attributed to the significant change in the geometry from the S1 state to the cationic state, as illustrated in Figure S4. In the S1 state, the plane composed of the electron-donating N atom and its two bonding C atoms in the phenyl groups is almost 15



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perpendicular to the thiophene unit. In contrast, this structure is altered to be coplanar in the cationic state. In fact, such big geometrical rotation can be largely constrained in solid state. As a result, the relaxation energy from the S1 state to the cationic state by the QM/MM method is reduced to 0.134 eV. On the contrary, the relaxation energies involving the ground state for DTDCTB are slightly increased in the condensed state, 0.098 and 0.071 eV for ED and CR, respectively. Considering the rigid structure of C60, its molecular relaxation energies in solid state should be unchanged with respect to those in gas phase. Also, the relaxation energy involving the first excited and ground states of C60 anion can be very similar. Using the relevant relaxation energies of DTDCTB and C60, the internal reorganization energies in solid state are thus estimated to be 0.203 and 0.194 eV for ED processes involving the S1 states on DTDCTB and C60, and 0.137 eV for CR process, respectively. At present, accurate evaluation of the external reorganization energy represents a challenge. Although some computational methodologies based on QM/MM,64 polarizable force field,65 and classical dielectric continuum model,66-67 have been applied, these calculations have their limitations and the accuracy could vary much. Here, for the sake of generality, the external reorganization energy is taken as an adjustable parameter and set to be in a relative wide range of 0.06~0.20 eV, similar to that estimated for an oligothiophene/PCBM system.68-69

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Table 2. The internal relaxation energies (in eV) of DTDCTB and C60 for exciton-dissociation and charge-recombination processes. DTDCTB

Molecular state

a

C60a

Molecular state

In gas phase

In solid state

S0→cation

0.064

0.098

S0→anion

0.069

S1→cation

0.670

0.134

S1→anion

0.096

cation→S0

0.065

0.071

anion→S0

0.066

In gas phase

Ref. 57. The values in solid state can be regarded as the same to those in gas phase.

3.5 Exciton-dissociation and charge-recombination rates Now, we can calculate the ED (kED) and CR (kCR) rates as a function of the external reorganization energies by means of Marcus electron-transfer theory. The results are shown in Figure 3. Here, both the ED and CR processes are regarded as exothermic reactions (∆G < 0). According to equation 5, when ∆G + λ < 0, the rates will increase with λ and take the maximum value when the sum of ∆G and λ approaches zero, then the rates will decrease gradually when further increasing λ. For the ED process from the S1 states of DTDCTB and C60 to CT0 and the CR process from CT0 to the ground state, the absolute value of ∆G is the same order of magnitude as while relatively larger than λ by 0.8 eV. Consequently, these ED and CR rates are increased with λext for both configurations I and II. On the contrary, because λ is slightly smaller than or very close to the absolute ∆G, the ED rate from the S1 state on DTDCTB or C60 to CT1A keeps constant or is just slightly decreased with λext. By and large, all the ED and CR processes are mostly in the normal or near-inverted regime, therefore it seems to be reliable for us to qualitatively compare these rates by means of the semiclassical Marcus electron-transfer model. 17



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Irrespective of interface geometries, the CR rates are much lower than the ED rates for both configurations I and II. Because of larger electronic couplings and more favorable driving forces, the CR rates in configuration II are about 2 orders of magnitude higher than those in configuration I at the same value of λext. In most cases, the CR rates are below 109 s-1 and the highest rate is no more than 1010 s-1, which is in good agreement with the experimental results that direct geminate charge recombination takes place over sub-ns and ns time scales. For electron transfer from the S1 state to the CT0 state, the rates in configurations I and II are similar for the C60-based excitons. They are lower than 1010 s-1 in most cases and below 1011 s-1 in the whole considered range of λext. The corresponding rates for the DTDCTB-based excitons are comparable to those for the C60-based excitons in configuration II, but at least one order of magnitude lower in configuration I. Obviously, these ED rates are in sharp contrast with the ultrafast charge separation (~100 fs) measured by transient absorption and time-resolved photoluminescence spectra.43 Interestingly, our calculations reveal that excitons can dissociate much more efficiently into a higher-energy excited CT state, CT1A. For configuration I, the rates for electron transfer to CT1A are mostly as large as 1011 and 1012 s-1 for excitons based on C60 and DTDCTB, respectively. For configuration II, the rates can reach 1012 for the C60-based excitons and even 1014 s-1 for the DTDCTB-based excitons. Thus, the excited CT states determine the time scale of exciton dissociation in the DTDCTB/C60 complex. As the excess energy of excited CT states would be beneficial to further separation of electron and hole at the donor/acceptor interface, our results suggest that the excited or hot CT states are crucial to achieve efficient photoinduced 18


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charge generation and high performance for the DTDCTB/fullerene solar cells. Also, as reported previously, interface geometry has an important impact on the charge-transfer processes in this kind of system.

14

10

I

II

-1

k (s )

10

10

S1D-CT1A 10

S1A-CT1A

6

S1D-CT0 S1A-CT0 10

CT0-S0

2

λext (

V e

0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

V e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


)

λext (

)

Figure 3. The rates of exciton dissociation from the S1 states on DTDCTB and C60 to the CT0 and CT1A states, and of charge recombination from the CT0 state to the ground state for configurations I and II of the DTDCTB/C60 complex.

4. Conclusion We have investigated the exciton-dissociation and charge-recombination processes through evaluation of the electronic couplings and the rates in two representative geometrical configurations of the DTDCTB/C60 complex for organic solar cells. The calculated results suggest that, the CR rates are mostly lower than 1010 s-1, which compare well with experiment. Moreover, the S1 excitons can dissociate into the CT1A state much faster than into the CT0 state. Especially for the excitons based on DTDCTB, the ED rates involving the CT1A state are several orders of magnitude higher than those involving the CT0 state and can be as large as 1014 s-1. Our 19



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results imply that the ultrafast charge separation is attributed to exciton dissociation into the CT1A state in the DTDCTB/fullerene solar cells and thus highlight the importance of hot CT states on the photoinduced charge generation and the eventual device performance for this type of system. Finally, we should stress that many and more complicated interface geometries can exist in the real heterojunction-based devices, as revealed by molecular dynamics simulations.70 For instance, the donor and/or fullerene molecules could crystallize to form aggregate structures, leading to delocalized excitons and/or charges.71 We are currently working along those lines.

ASSOCIATED CONTENT

Supporting information Initial and DFT-optimized interfacial geometries for configurations I and II of the DTDCTB/C60 complex, QM/MM model used for calculation of reorganization energy of DTDCTB in solid state, and DFT-optimized molecular geometries of the lowest singlet excited state and the cationic state of DTDCTB. This information is available free of charge via the Internet at http://pubs.acs.org/.

AUTHOR INFORMATION

Corresponding Authors

20


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*E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

This work has been supported by the National Natural Science Foundation of China (Grant No 91333117), the National Basic Research (973) Program of the Ministry of Science and Technology of China (Grant No 2014CB643506), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No XDB12020200).

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(57) Yi,

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Coropceanu,

V.;

Brédas,

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A comparative

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Hot Charge-Transfer States Determine Exciton Dissociation in the

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