Theoretical design and characterization of pyridalthiadiazole-based chromophores with fast charge transfer at donor/acceptor interface toward small molecule organic photovoltaics

Abstract

A class of D₁–A–D₂–A–D₁-type small molecule (SM) donors (2–5) was engineered via modifying or replacing the core donor moiety in three building blocks based on the reported DTS(PTTh₂)₂ (1) to screen suitable donor materials for organic photovoltaics (OPV). Density functional theory calculation was performed to investigate the electronic structures, open circuit voltage (V_oc) and key parameters closely relevant to the short-circuit current density (J_sc), including (i) absorption spectrum, (ii) electron–hole coherence, (iii) energy driving force, (iv) charge transfer dynamics, and (v) carrier transport efficiency. The results manifest that the designed 2–5 show good performance with large V_oc, stable charge transfer and effective charge transport. Surprisingly, the ratios k_inter-CT/k_inter-CR of 2/PCBM, 3/PCBM, and 5/PCBM heterojunctions present over 10⁴ times higher than that of 1/PCBM. Our conclusions indicate that designed PT-based SMs can better the performance of OPVs, which will provide theoretical guideline for the design and synthesis of new organic SM donors.

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1. Introduction

Organic photovoltaic (OPV) devices have received tremendous interest in the field of the research on bulk heterojunction (BHJ) OPVs comprised of π-conjugated small molecules (SMs) and attention in academic and community due to their potential advantages of low cost manufacturing, flexibility, light-weight, and ease of processing.^1–3 During the past years, there is emerging fullerene derivatives with the aim to design novel SM donor materials and herein to enhance the power conversion efficiency (PCE).^4–12 The achievement (i.e., the improvement of PCE) could be reached through molecular structure modification on donor materials. Currently, Yang and coworkers successfully designed and synthesized thiophene-substituted benzodithiophene (BDT)-based two-dimensional conjugated SM donor material SMPV1. The single junction solar cell device based on the blending of SMPV1 and [6,6]-phenyl-C₇₁-butyric acid methyl ester (PC₇₁BM) exhibits an impressive PCE up to 8.1%. Meanwhile the optimized tandem solar cell can achieve a PCE of 10.1%, which is the highest PCE reported to date for solution-processed SM OPVs.¹³ Although the PCEs of SM OPVs came up with that of triple-junction polymer solar cells (11.5%),¹⁴ they still lagged behind efficiency of inorganic solar cells (25% for Si-based cell).^15,16 Obviously, the exploration of novel SM donor materials is identified as one of the significant strategies to improve the performance of SM OPVs.

It is widely known that the performance of OPVs is mainly dominated by PCE, which is determined by open circuit voltage (V_oc), short-circuit current density (J_sc) and fill factor (FF). To increase the SM solar cell efficiency, the main design strategies of donor materials are employed generally, such as optimizing highest occupied and lowest unoccupied molecular orbitals energy levels (HOMO and LUMO) and energy-gap (E_g) values to increase V_oc and J_sc,^17,18 and increasing planarity of chemical structure and interchain π–π stacking for improving charge carrier mobility of donor material to maintain stable charge separation at donor/acceptor interface and efficient charge transfer in donor, thus enlarging J_sc and FF.^19,20 Meanwhile, energy offset associated with driving charge separation is a critical consideration of the efficiency of charge generation, and thereby photocurrent generation. Thereby, the driving force ΔE_L–L should be discussed in depth to analyze whether the charge separation of devices could be drove and stabilized.^17,20 Furthermore, the intermolecular charge transfer (inter-CT, namely exciton dissociation) and intermolecular charge recombination (inter-CR) between D and A as two pivotal interfacial processes need to be considered due to their strong influences on the whole device efficiency. Recent years, many groups devote major efforts to developing theoretical methods,^2,21–26 and afterwards fast inter-CT and slow inter-CR mechanisms were widely used as a strategy for screening excellent donor or acceptor materials.^27–29 For example, Bredas and co-workers explained that lower performance observed experimentally for the α-sexithienyl/perylenetetracarboxy-diimide (PDI) solar cell than that of α-sexithienyl/C₆₀ solar cell, which is derived from the faster inter-CR process.²⁷ Li and co-workers designed a series of dithienogermolodithiophene (DTTG)-based polymers with senior charge transfer efficiency in active layer, which were considered as promising polymer materials for high-performance OPV devices.

Generally, in the design of efficient materials, donor/acceptor structures were utilized to fine-tune the HOMO/LUMO energy levels and energy-gaps, and to enhance the intermolecular interaction and order-arrangement and thus improve the PCE significantly.^30,31 However, the absorption spectra of the traditional donor molecules, such as D–A or D–A–D structure, are not broad enough to cover the ultraviolet-visible (UV-vis) regions. The absorption spectrum is a critical consideration for the improvement of the J_sc as mentioned above. Lately, Bazan and co-workers reported a representative D₁–A–D₂–A–D₁-type SM donor material DTS(PTTh₂)₂ (1) that utilized dithienosilole (DTS) as the core donor unit (D₂), pyridalthiadiazole (PT) as acceptor units (A), and hexyl-substituted bithiophene as end-cap units (D₁). It deserves to be mentioned that this SM material shows strong intramolecular charge transfer character, strong and broad absorption spectrum and good hole transport ability (see Fig. 1(a) for its molecular structure).^6,32–35 And the optimized devices based on 1/PC₇₁BM and 1/PCBM([6,6]-phenyl-C₆₁-butyric acid methyl ester) both exhibit high PCEs of 6.7% (ref. 36) and 5.7%,³⁷ respectively. Herein, taking 1 as a reference, we have designed SMs 2–5 through modifying and replacing the election-withdrawing groups of core donor unit D₂ and retaining PT as electron with-drawing acceptor groups A and hexyl-substituted bithiophene as end-cap units D₁. The core donor units of 2–5 are thiophene analogue cyclopentadithiophene³⁸ (CPTz, D₂ for 2), cyclopenta[2,1-b:3,4-b′]dithiophen-4-one³⁹ (CDT, D₂ for 3), 4,4-ethylenedioxy-4H-cyclopenta[2,1-b:3,4-b′]dithiophene⁴⁰ (ethylenedioxy-CDT, D₂ for 4), and cyanomethylene cyclopenta-dithiophene⁴¹ (cyanomethylene-CPDT, D₂ for 5), respectively (Fig. 1(a)). Here, the introductions of nitrogen, carbon, oxygen, vinyl group and cyano groups are aimed at tuning the energy levels and energy-gaps and also broadening absorption spectra in near infrared range as much as possible, importantly, to improve parameters of V_oc and J_sc. We investigated electronic and optical properties of these SM systems with the aim of predicting more promising donor candidates for OPV devices and providing an in-depth theoretical simulation of SM donor materials. For this purpose, the electronic structures, V_oc, and some parameters related to J_sc, such as absorption spectrum, intramolecular transferred charge value and electron–hole coherence during donor and acceptor fragments were systematically calculated by density functional theory (DFT) and time-dependent density functional theory (TD-DFT) methods. Especially, we discussed energy driving forces (ΔE_L–L), the dynamics of inter-CT and inter-CR at donor/acceptor interface, and hopping rates (k_hopping) of face-to-face π stacked dimer models referred to J_sc of these systems, in order to perform a further analysis on charge transfer properties at donor/acceptor interfaces for efficient charge separation and photocurrent generation in OPVs. The results demonstrate that, compared to unsubstituted 1, the designed 2–4 could show more optimal combinations of D–A materials with improving performance. It is our expectation that this work may provide series of promising PT-based SM donor material candidates for high photovoltaic performance OPV devices.

Fig. 1 Molecular structures of investigated 1 and engineered 2–5 (a), and the starting interface geometry of the 1/PCBM complex (b).

2. Computational methods

2.1 Models

In most cases, to save the computational cost, all alkyl-branched chains (R₁ and R₂, shown in Fig. 1(a)) were truncated to methyl groups, since the alkyl-branched chain is proved to have almost no significant influence on the electronic structures and optical properties of materials.^{2,12,21,41,42} The ground-state geometries of 1–5 SM systems and PCBM were optimized in the vacuum and dichloromethane solution at the PBE0/6-31G(d) level which has been confirmed that can give a good evaluation on the geometrical and electronic structures of thiophene derivatives.^12,43–45 As for the absorption, based on the optimized geometries in dichloromethane solution, BP86, B3LYP, B3P86, PBE0, M06, M062X, BH and HLYP, and CAM-B3LYP with 6-31G(d) basis set were utilized to simulate the absorption spectra of 1 in the TD-DFT calculations. During the TD-DFT calculations, we took into consideration the effect of the solvent (chloroform) within polarizable continuum model (PCM) in a linear response (LR) and nonequilibrium regime.^12,46 The functional effects and the experimental data are listed in Table S1 and plotted in Fig. S1 in ESI.† The results show that the BH and HLYP functional gives a maximum absorption wavelength of 634 nm, in good accordance with the experimental value at 655 nm. Thus, absorption spectra of 1–5 were simulated by TD-PCM-BH and HLYP/6-31G(d) method. The transition density matrix (TDM) maps, which were used to investigate electron–hole correlation of charge transfer based on electronic transition, were depicted from Multiwfn 3.2.^47,48 Additionally, geometry optimizations of the parallel conformation of the stacked dimers 1–5 were performed at the B3LYP-D3(BJ)/6-31G(d) level. Note that B3LYP-D3(BJ) with BJ-damping is a functional considering dispersion correction.⁴⁹

The donor/PCBM interface models were placed together at 3.5 Å distance. The benzene cycle of PCBM is oriented parallel to PT acceptor moiety (Style 1, shown in Fig. 1(b)), which has been proved a preferred donor/acceptor arrangement and the resulting intermolecular interaction may act as the key factor in dominating the performance of OPV materials.⁵⁰ Meanwhile, we also simulate donor/PCBM interface models, where PCBMs are docked with the D₂ donor moieties of the donors (Style 2) to give a comparison with Style 1 and ensure the rigor of the calculation. The ground-state geometries of 1–5/PCBM were optimized at the B3LYP/6-31G(d) level which has been demonstrated to provide a reasonable simulation of the heterojunction model by Troisi and co-workers.² In addition, it is widely accepted that the CAM-B3LYP functional as a long-range-corrected functional can correctly describe the inter-CT excitations of blends.^25,26,51 Thus, the excited-state energies were calculated at the TD-CAM-B3LYP method with 6-31G(d) basis set. The charge density difference (CDD) maps employed to explore inter-CT excited states were obtained by using Multiwfn 3.2.^47,48 All the above calculations were carried out by the aid of Gaussian 09 software package.⁵²

2.2 Marcus rate expression

In order to evaluate inter-CT and inter-CR rates (k_inter-CT and k_inter-CR) of the interface models under investigation, we employed the Marcus semi-classical model.^53,54 This formalism has already been explained in great detail elsewhere and applied several times within the rates of nonadiabatic electron transfer in OPVs,^2,21–24 which is expressed as:where λ represents the reorganization energy, V_DA represents the electronic coupling between D and A, ΔG is the Gibbs free energy change of the reaction, h is the Planck constant, k_B is the Boltzmann constant, and T is the temperature, which is defined as 300 K in our calculations. The total reorganization energy λ includes internal reorganization energy (λ_int) and external reorganization energy (λ_ext), where the former is due to the rearrangement of the nuclear positions of D and A molecules upon intermolecular charge transfer, and the latter is due to electronic and nuclear polarization from the surrounding medium. The computational details of the total reorganization energy, the electronic coupling, and the Gibbs free energy change have been presented in our previous work,²⁹ and corresponding computations are given in Section S.1 of the ESI (S3).†

As for the hopping rate k_hopping between two adjacent molecules in the self-exchange electronic transfer reaction, it also can be expressed by Marcus semi-classical model.^53,54 The total reorganization energy λ′ includes internal reorganization energy (λ^′_int) and external reorganization energy (λ^′_ext). The former originates from the geometry relaxation when an electron is removed or added from a molecule, and the latter is derived from the solvent polarization effects in the surrounding medium, which is usually neglected due to the weak polarization in the medium of organic solids.⁵⁵ Herein, we only concentrate on λ^′_int, which can be estimated by the eqn (S2) in ESI.† The electronic couplings V_DD of designed face-to-face π stacked 1–5 dimers were evaluated by the site-energy corrected method^45,56–58 at the PW91/TZP level in ADF software.^59–61 The Gibbs free energy change is zero in the self-exchange electronic transfer reaction.⁶²

3. Results and discussions

3.1 Electronic structure and open circuit voltages

3.1.1 Frontier molecular orbitals. It has been highly proved that the V_oc of device, the charge separation ability in donor/acceptor interface, and the absorption of the solar photons in OPV are closely influenced by the frontier molecular orbital (FMO) energy levels.^19,63 Therefore, choosing an efficient calculation method to match the experimental measurement on HOMO energy level is a high priority. The experimental HOMO energy level of 1 has been measured by the cyclic voltammetry (CV) experiment in dichloromethane solution, showing an energy level value of −5.20 eV.³⁶ We obtained the ground-state geometries and FMO energy levels of all the investigated SMs in both the vacuum and dichloromethane solvent by PBE0/6-31G(d) method which is proved to provide the satisfactory estimate on geometrical and electronic structures of thiophene derivatives.^12,43–45 All the FMO energy levels of investigated SMs and PCBM are displayed in Fig. S2† and Table 1. It is seen from Table 1 and Fig. S2† that FMO energy levels of all the investigated SMs in both the vacuum and dichloromethane solvent exhibit the same tendency. However, the calculated HOMO energy level in the dichloromethane solvent (−5.23 eV) gives a closer value to experimental value than that in the vacuum. Thus, subsequent simulations of SMs are all based on ground-state geometries and FMO energy levels in the dichloromethane solution. The HOMO energy level and energy-gap (HOMO–LUMO) values of 1–5 systems are found to be in the order of 4 > 1 > 5 > 3 > 2 and 1 > 2 > 3 = 4 > 5, respectively, implying that the introductions of nitrogen, carbonyl group, and vinyl group contribute to the lower HOMO values and the reduced energy-gaps. The same as calculation in prior work,^64–66 the HOMO energy level of PCBM was simulated at the PBE0/6-31G(d) level in the dichloromethane solution, and considering the importance of giving a more accurate LUMO energy for PCBM, an indirect calculation method was adopted, namely, the LUMO energy level was derived by adding the energy-gap (the first singlet excited energy using TD-DFT based on ground-state geometry in the dichloromethane solution) to the HOMO level. Here, we discussed the FMO energy levels in depth to analyze the major parameters related to the performance of OPVs, such as V_oc, absorption spectrum, and energy driving force ΔE_L–L.

Table 1 FMO energy level values (eV) of 1–5 and PCBM at the PBE0/6-31G(d) level in the vacuum and dichloromethane solvent with the experimental HOMO energy level of 1, open circuit voltages V_oc (V), and energetic driving forces ΔE_L–L (eV) for 1–5 systems

	In the vacuum		In the dichloromethane solvent			Exp.^a	Voc (exp.)	ΔEL–L
	HOMO	LUMO	HOMO	LUMO	Eg	HOMO
a Ref. 36.
1	−5.07	−3.01	−5.23	−3.13	2.10	−5.20	0.77 (0.78)	0.83
2	−5.20	−3.13	−5.34	−3.27	2.07		0.88	0.69
3	−5.24	−3.20	−5.33	−3.28	2.05		0.87	0.68
4	−5.06	−3.05	−5.22	−3.17	2.05		0.76	0.79
5	−5.18	−3.18	−5.28	−3.25	2.03		0.82	0.71
PCBM	−5.87	−3.87	−5.95	−3.96

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The FMO sketches of the SMs at the PBE0/6-31G(d) level in the dichloromethane solvent are depicted in Fig. 2. As shown that similar distributions of the FMOs are presented for all investigated SMs. The electronic cloud distributions of HOMOs are delocalized on the thiophene and pyridine rings of the whole molecules. The orbitals in the LUMOs are mainly localized on the core thiophene rings and two PT units, and partially on the hexyl-substituted bithiophene end-caps. For 3 and 5, the LUMOs also reside at the core electron-drawing groups of D₂, i.e., the oxygen atom in 3 and the cyano group in 5. These results manifest that the introduction of electron-withdrawing group has a slight influence on the distribution patterns of FMOs.

Fig. 2 The FMOs of SMs 1–5 at the PBE0/6-31G(d) level in the dichloromethane solvent.

3.1.2 Open circuit voltages. As mentioned in Section 1, a significant parameter to evaluate the performance of OPVs is the V_oc. We note that V_oc is limited to the material and environmental parameters such as semiconductor energy levels, work functions of the electrodes, light intensity, solar cell and light-source temperatures, charge-carrier recombination, and external fluorescence efficiency.^67,68 However, lots of theoretical and experimental researches^67–73 support the view that energy-gap between the acceptor LUMO and donor HOMO gives the dominant contribution to V_oc for BHJ OPVs. In the meanwhile, V^max_oc of SM donor–acceptor systems could be described by:⁷⁴

V^max_oc = (|E_IP(D) − E_EA(A)|−E_B)/e (2)

here e is the elementary charge, E_IP(D) and E_EA(A) are the ionization potential of the donor and electron affinity of the acceptor, respectively. These quantities are normally estimated from the energies of HOMO and LUMO energy levels of the donor and acceptor, respectively. E_B corresponds to the exciton binding energy (bound electron–hole pair) following charge transfer, which is generally estimated in the range of 0.1 to 1 eV. As a result, here, we have assumed an estimated value of 0.5 eV for the exciton binding energy.⁷⁴ The results summarized in Table 1 suggest that, the estimated V_oc of 1 (0.77 V) is in agreement with that obtained at the optimized annealing temperature of 100 °C (0.78 V). The open circuit voltages of five systems are found to be in the order of 2 > 3 > 5 > 1 > 4, implying that the designed materials 2, 3 and 5 could possess higher V_oc than that of 1, while 4 could have slightly lower V_oc than that of 1. As a result, 2, 3 and 5 could become potential candidates in high-performance OPVs due to their high open circuit voltages.

3.2 Parameters related to short-circuit current density

3.2.1 Absorption spectra. Photovoltaic energy conversion needs to collect sunlight as much as possible.^75–77 From this regard, the absorption spectra of the donor materials should provide a good match with the solar spectrum to increase the J_sc. Therefore, the photoexcitation properties were discussed to better understand the physical processes involved in the photocurrent generation. The excited-state vertical transition energies, corresponding oscillator strengths and the major configurations of 1–5 calculated at the TD-PCM-BH and HLYP/6-31G(d) level are all listed in Table 2, and the simulated absorption spectra involved are gathered in Fig. 3. The longest wavelength of absorption spectra are in the order of 5 > 3 > 4 > 2 > 1, which is in line with the opposite sequence of their corresponding E_g values based on FMO energy levels from Table 1. As seen from Fig. 3, for investigated systems 1–5, the maximum absorption peaks with the largest oscillator strength come from S₀ → S₁, which correspond to the transition from HOMO (H) to LUMO (L) (Table 2). Fortunately, compared with 1, the designed 2–5 have similar or slightly broadened and red-shifted absorption in low-energy region. This indicates that the introduction of electron-withdrawing groups into D₂ brings about red-shifted absorption, in particular the introduction of carbonyl and cyanomethylene groups. In addition, for 1–5, the strong absorption peaks in high-energy region appear at ∼340 nm are mainly created by the transitions of S₀ → S₇, S₀ → S₆, S₀ → S₉, S₀ → S₇, and S₀ → S₈, respectively. For 1, 3 and 4, the transitions of strong absorption peak in high-energy region correspond to H-1 → L + 4 and H → L + 3. For 2, the high-energy absorption peak in the visible light region majorly is ascribed to H-1 → L + 3 and H → L + 2 transitions. And high-energy absorption peak in 5 is deemed to the electronic transitions of H-1 → L + 3, H-1 → L + 4, and H → L + 3. Consequently, the analysis of optical and electronic properties implies that the designed 2–5 will possess similar to 1 or better performance for OPV devices, as a result of their similar broad and red-shifted absorption in the visible and near-infrared (NIR) regions of the solar spectrum. Besides optical absorption, intra and intermolecular charge transfer properties are also discussed in depth to assess the J_sc.

Table 2 Calculated excitation energies E, oscillator strengths f and major configurations of 1–5 at TD-CPCM-BH and HLYP/6-31G(d) level

		E/eV (nm)	f	Configurations^a
a H denotes HOMO and L denotes LUMO.
1	S1	1.95 (634)	2.0816	H → L (85%)
	S7	3.65 (340)	0.7356	H-1 → L + 4 (25%)
				H → L + 3 (43%)
2	S1	1.93 (643)	2.5007	H → L (95%)
	S6	3.67 (338)	0.6564	H-1 → L + 3 (19%)
				H → L + 2 (61%)
3	S1	1.90 (656)	1.8710	H → L (80%)
	S9	3.69 (336)	0.8399	H-1 → L + 4 (35%)
				H → L + 3 (54%)
4	S1	1.91 (649)	2.2816	H → L (85%)
	S7	3.65 (340)	0.5991	H-1 → L + 4 (25%)
				H → L + 3 (44%)
5	S1	1.87 (665)	1.9185	H → L (83%)
	S8	3.66 (338)	0.8458	H-1 → L + 3 (17%)
				H-1 → L + 4 (18%)
				H → L + 3 (45%)

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Fig. 3 Simulated absorption spectra and corresponding oscillator strengths of 1–5 at the TD-PCM-BH and HLYP/6-31G(d) level. The value of the full width at half maximum is 0.66667 eV.

3.2.2 Intramolecular charge transfer. Intramolecular charge transfer is normally utilized to evaluate the ability of the exciton dissociation into free charges. Effective exciton separation of donor materials can lead to the increase of photogenerated charge carriers, and thus improve J_sc and FF.^19,78 In this contribution, the intramolecular charge transfers upon electronic transitions in 1–5 are visualized by TDM map. It is now readily accepted that TDM map can be employed to probe the possibility of the exciton escaped from the Coulomb attraction.^12,21,79

The contour plots of TDM for the major excited states of systems 1–5 are plotted in Fig. 4 and S3,† where electron–hole coherences can be visualized directly. As revealed by Fig. 4, electron–hole coherences of the lowest excited states in 1–5 mainly concentrate on the diagonal box (D₂–D₂, A–A) and off-diagonal box (D₁–A, D₂–A) for photoexcitation. And the electron–hole coherences localized at the D₂–D₂ and A–A (along the diagonal element) demonstrate the π → π* transitions on the D₂ and A. Furthermore, the coefficients of D–A correlation are in the order of 1, 2 > 4 > 5 > 3. Consequently, the couplings of electron and hole in systems 3 and 5 may be very weak, indicating that the exciton dissociation is easier than those of 1, 2 and 4. Likewise, the extent of charge transfer of 4 may be stronger than those of 1 and 2, and 2 has the similar extent of charge transfer to 1. Additionally, other intramolecular charge transfer characters involved major excited states of all systems are shown in Fig. S3.† It shows that the electron–hole coherence between D and A fragments in 2 is slightly stronger than those in 1 and 3–5. However, these results illustrate that the exciton in all systems may be easily dissociated owing to their weak electron–hole correlation coefficients, especially in 3 and 5 which includes charge transfer from D₂ to carbonyl (for 3) or cyanomethylene (for 5) groups (see Fig. 2). It is therefore fortunate that designed SMs 3–5 could effectively improve the J_sc since the exciton can efficiently escape from the Coulomb attraction.

Fig. 4 Simulated transition density matrix (TDM) associated with the lowest excited states of 1–5 (the hydrogen atoms of all systems are omitted), and the color bars are given on the right.

3.2.3 Driving forces. The photoinduced charge separation at the donor/acceptor interface is significant to give the photogenerated positive and negative charges sufficient lifetime to be collected by two electrodes. Nevertheless, driving and stabilizing this charge separation need energy losses.^20,25 Here, Fullerene derivative PCBM is employed as the electron acceptor material because of its stability, its generous capacity to accept electrons, the relatively cheap price and commercial availability.⁸⁰ In principle, the driving force ΔE_L–L based upon electronic orbital energies is considered as the energy difference between LUMOs of donor and acceptor. It is widely reported that driving force ΔE_L–L > E_B is required to ensure quantitative charge separation at the donor/acceptor interface.^17,18 The energy offset, overcoming the binding energy of the excitons generated in organic semiconductor films, is estimated at 0.5 eV for SM donors, which arises from experimental evidence.⁷⁴ According to the FMO energy levels in Table 1 and Fig. S2,† the obtained energetic driving forces are collected in Table 1. The ΔE_L–L values for 2–5 are 0.69, 0.68, 0.79, and 0.71 eV, respectively, which are all larger than 0.5 eV, demonstrating favorable electron transfer from donor to acceptor materials.

3.2.4 Intermolecular charge transfer and recombination. We note that the exciton at donor/acceptor heterojunction can dissociate into hole and electron, and electron will transfer from donor to acceptor materials in the organic layer with rate k_inter-CT. Alternatively, the positive and negative charge carriers can recombine with rate k_inter-CR, which competes with the exciton dissociation. Thereby, maximizing the charge transfer process at donor/acceptor interface, i.e., increasing k_inter-CT and decreasing k_inter-CR, is commendable for excellent PCE of organic solar cell devices. Here, we utilize the CDD map to find inter-CT excited states, which is normally used to evaluate the ability of the charge transfer from ground state to excited states. The excited state, where hole is localized on donor and acceptor, and electron is only localized on acceptor, is identified as the inter-CT excited state.^21,29 The transition energies, oscillator strengths and respective CDD maps of inter-CT excited state for all the investigated Style 1 heterojunctions are detailed in Fig. 5. From the CDD maps depicted in Fig. 5, we also infer that the inter-CT excited states S₁₇ and S₁₈ are degenerate in energy for 2/PCBM. Likewise, the inter-CT excited states S₁₄ and S₁₅ for 4/PCBM, and S₁₅ and S₁₇ for 5/PCBM are also degenerate excited states, respectively. We shall stress that we only considered the inter-CT excited states characterized by partial charge transfer from donor to acceptor. The pure intermolecular charge separate excited state is ignored in current work, which is regarded as the fully charge separation state, corresponding to hole and electron localized on donor and acceptor, respectively. Of cause, the change of excited state character, from one type to another, depends on the presence of charge carrier nearby.⁸¹ This dynamic process would be not considered here.

Fig. 5 Charge density difference maps, excitation energies E (eV(nm)), corresponding oscillator strengths f, and electronic coupling V_DA (eV) of inter-CT excited states for 1–5/PCBM heterojunctions of Style 1 at the TD-CAM-B3LYP/6-31G(d)//B3LYP/6-31G(d) level, where the violet and turquoise colors stand for the increase and decrease in electron density, respectively.

Table 3 summarizes that the computed k_inter-CT, k_inter-CR and k_inter-CT/k_inter-CR with the Marcus rate parameters, including reorganization energy λ, electronic coupling V_DA, and Gibbs free energy change ΔG of all donor/acceptor heterojunctions of Style 1. From Table 3, there are the same λ values for all heterojunctions when rounded down to two decimal places, suggesting that this factor will not cause difference in k_inter-CT and k_inter-CR in current work. Note that the increasing V_DA values of designed systems may realize an increment in the k_inter-CT and k_inter-CR, since the rate constant is proportional to the square of the electronic coupling matrix element. The V_DA values of the involved inter-CT excited states in 1–5/PCBM are gathered in Fig. 5. For degenerate inter-CT excited states, the assessment of total electronic coupling V_DA, which can obtained from the summation of V_DA values of the involved inter-CT excited states. The results suggest that V_DA values of all systems 2–5/PCBM are obviously larger than that of the experimental system 1/PCBM, which may increase final Marcus rates. It is widely accepted that both the inter-CT and inter-CR dynamics are considered as exothermal reactions, i.e., ΔG < 0. Thus, from the Marcus formula (eqn (1)), the electron transfer rate will decrease with the increasing of the absolute value of ΔG when |ΔG| is larger than λ. As a result, an excellent donor material would employ large |ΔG_inter-CR| and small |ΔG_inter-CT| for effective exciton dissociation and weak charge recombination. For 1–5/PCBM, the values of |ΔG_inter-CR| are in the order 3 > 2 > 5 > 1 > 4, and the values of |ΔG_inter-CT| are in the sequence 3 < 5 < 2 < 4 < 1. Consequently, the orders of k_inter-CR and k_inter-CT are 3 < 2 < 5 < 1 < 4 and 3 > 5 > 2 > 4 > 1, respectively. The results reveal that electron transfer rate is greatly influenced by Gibbs free energy change, because it exponentially decreases with |ΔG| base on the eqn (1). Surprisingly, for the 2/PCBM, 3/PCBM, and 5/PCBM, the ratios of k_inter-CT/k_inter-CR exhibit obvious increases, which are over 10⁴ times higher than that of 1/PCBM. Besides, the ratio of k_inter-CT/k_inter-CR of 4/PCBM is slightly larger than that of 1/PCBM. In addition, the inter-molecular charge transfer dynamics of all systems of Style 2 are also provided in Fig. S4 and Table S2 in ESI.† The results reveal that the values of k_inter-CT/k_inter-CR of 1/PCBM, 2/PCBM and 5/PCBM complexes are the same compared with those of Style 1, except for 3/PCBM and 4/PCBM, which have no inter-CT states in the first 20 excited states. This reinforces the face that all engineered systems may have much stronger effective exciton dissociation into the separated free charge carriers, and thus present higher J_sc and PCE than that based on the reported 1/PCBM, especially 2/PCBM, 3/PCBM, and 5/PCBM.

Table 3 Computed internal reorganization energy λ_int (eV), total reorganization energy λ (eV), Gibbs free energy change ΔG (eV), rates of charge recombination k_inter-CR (s⁻¹) and charge transfer k_inter-CT (s⁻¹), and k_inter-CT/k_inter-CR of 1–5/PCBM heterojunctions of Style 1

	λint	λ	ΔGinter-CR	ΔGinter-CT	kinter-CR	kinter-CT	kinter-CT/kinter-CR
1/PCBM	0.27	0.38	−1.20	−0.86	1.50 × 10^7	1.15 × 10^12	7.67 × 10^4
2/PCBM	0.27	0.38	−1.33	−0.74	9.01 × 10^5	3.14 × 10^14	3.49 × 10^8
3/PCBM	0.27	0.38	−1.37	−0.67	2.70 × 10^5	2.16 × 10^15	8.00 × 10^9
4/PCBM	0.27	0.38	−1.19	−0.82	8.04 × 10^8	1.04 × 10^14	1.29 × 10^5
5/PCBM	0.27	0.38	−1.31	−0.69	2.57 × 10^6	8.07 × 10^14	3.14 × 10^8

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3.2.5 Hopping rates and transport properties. After the dissociation of excitons at the donor/acceptor heterojunction interface, the separated electrons and holes will transport along conjugated SMs and acceptor interpenetrating network toward the ITO anode and metal cathode, then producing photocurrent.¹⁹ Therefore, on the premise of the same acceptor PCBM, high hole mobility of the SM donor is necessary to enhance the charge transport efficiency (to increase J_sc) of the devices.

We know the planar conjugated backbone structures are superior, leading to tightly-packed stacking arrangements which can contribute to providing large charge carrier mobilities via strong intra and intermolecular electronic couplings and minimal reorganization energies.⁶³ All the optimized structures plotted in Fig. 6 reveal that the computed energy-minimized twist angles between the planes of A and D₂ moieties in all systems are in close proximity to 0° due to the intramolecular N⋯S attractive interaction, which are verified by the short distance (∼2.90 Å) between N and S atoms. They are significantly shorter than the sum of N and S van der Waals radii (3.35 Å). Meanwhile, twist angles of thiophene and A of 2–5 (≈1°–3°) are slightly smaller than that of 1 (≈5°), however, all of them closely follow planar structures because of intramolecular H⋯N attractive interaction. In addition, twist angles of thiophene and thiophene are close to 10° owing to S⋯H attractive interaction. Thus, it is reasonable to assert that these molecules will exhibit the similar rigid-planarity and π–π stacking.

Fig. 6 Optimized geometries for 1–5 calculated at the PBE0/6-31G(d) level in the dichloromethane solvent with the twist angles between donor and acceptor units.

The hopping rates k_hopping of 1–5 dimers referred to charge carrier mobilities were investigated to probe charge transport efficiency in depth, which have a positive correlation with charge carrier mobilities.⁴⁴ The molecular packings of dimers with the face-to-face π stacked formation were simulated at the B3LYP-D3(BJ)/6-31G(d) level in terms of intermolecular perpendicular distances of 7.3, 6.7, 5.1, 4.1, and 4.2 Å, respectively. These distances are all larger than the van der Waals distances between atoms in dimers. The optimized structures are shown in Fig. 7, the intermolecular perpendicular distances of all dimers present a good approximation to 3.2 Å after the geometry optimization. The calculated λ^′_int, V_DD, and k_hopping of the face-to-face π stacked hopping pathway of 1–5 dimers are summarized in Table 4. The results clearly illustrate that 1 and 3–5 possess the same λ^′_int values, which are slightly lower than that of 2. It is intriguing to see that the similar λ^′_int are presented for all systems. Thus, the normal-mode (NM) analysis, which includes the contributions from each vibrational mode, is provided further insight into the internal reorganization energy λ^′_int. We took 1 molecule as the example to visualize contributions of vibrational modes to reorganization energies. The diagram of reorganization energies of 1 into the contributions of each normal mode is exhibited in Fig. S5.†

Fig. 7 Dimer models of 1–5.

Table 4 Computed internal reorganization energies λ^′_int (eV), electronic couplings V_DD (eV), and hopping rates k_hopping (s⁻¹) of 1–5 dimers

	λ^′int	VDD	khopping
1	0.23	0.0079	2.36 × 10^11
2	0.25	0.1770	9.88 × 10^13
3	0.23	−0.0618	1.41 × 10^13
4	0.23	0.1908	1.40 × 10^14
5	0.23	−0.0576	1.25 × 10^13

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As seen from the Fig. S5,† there are two obvious vibrational contributions to the reorganization energy of 1. The contributions at 91 cm⁻¹ appeared in low frequency region mainly correspond the vibration of two PT and bithiophene end-cap units. Meanwhile, the contributions at high frequency (1398 cm⁻¹) are attributed to the C–C single and double bond stretching modes of the PT moieties. This result supports the view that, the core D₂ unit seldom contributes to the internal reorganization energy λ^′_int, and thus accounts for approximately equal λ^′_int values of all systems.

In addition, the order of V² is predicted in the decreasing sequence of 4 > 2 > 3 > 5 > 1, and their corresponding k_hopping values are in the same decreasing order. Consequently, k_hopping values of designed 2–5 exhibit more than two or three orders with respect to that of 1. It confirms that the OPV devices constructed from 2–5 and PCBM may have higher charge carrier mobilities and thus more effective charge transport after exciton dissociation into the fully separated positive and negative charges, and lead to higher J_sc than that based on 1/PCBM reported in experiments.

4. Conclusions

To summarize, in the present work, we systematically characterized a class of D₁–A–D₂–A–D₁-type SMs based on PT acceptor units and hexyl-substituted bithiophene end-cap donor units by means of DFT and TD-DFT methods. The results of our calculations suggest that designed 2–5 exhibit large V_oc values, red-shifted absorption spectra, weak electron–hole coherences, and ΔE_L–L values of them, which are overall enough to realize a desirable charge transfer from donor to acceptor and ensure the effective exciton splitting. Importantly, BHJ devices constructed by engineered molecules present fast interface charge transfer processes in the blends especially 2/PCBM, 3/PCBM, and 5/PCBM whose ratios of k_inter-CT/k_inter-CR are over 10⁴ times higher than that of 1/PCBM. This reveals that the heterojunctions based on designed systems may gain high J_sc and PCE due to the fast inter-CT and slow inter-CR processes. In addition, the k_hopping values of 2–5 present more than two or three orders in comparison with that of 1, which promote the effective charge transport as well as exciton dissociation, and thus improve the J_sc and PCE. In conclusion, our results imply that these engineered 2–5 SMs will replace 1 as promising candidates for high-performance PCBM-based BHJ OPVs. In addition, an effective way to predict conjugate SMs of OPVs is represented systematically. We hope it may be of service to experimentalists and theoreticians in developing novel high-performance and desirable SM donor materials.

Acknowledgements

The authors gratefully acknowledge financial support from National Natural Science Foundation of China (21131001, 21273030, 21203019 and 21203020), Specialized Research Fund for the Doctoral Program of Higher Education and Research Grants Council Earmarked Research Grants Joint Research Program (20120043140001) and the Science and Technology Development Planning of Jilin Province (201201071 and 201201067).

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Footnote

† Electronic supplementary information (ESI) available: Computational details of Marcus rate parameters and internal reorganization energy λ^′_int from normal mode. The table of functional test for optical absorption spectra by different functionals using 1 as a reference, inter-CT rates of Style 2. Plots of functional test for optical absorption spectra by different functionals of 1, FMO energy levels of 1–5 and PCBM, transition density matrix associated with the major excited states for 1–5, charge density difference maps and electronic couplings of inter-CT excited states of Style 2, and calculated reorganization energies versus the normal mode of 1. See DOI: 10.1039/c5ra00785b

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