Theoretical design and characterization of new terpolymer donors based on PTB7Ir for high-efficiency triplet-material-based organic photovoltaics

Abstract

In the current work, eleven terpolymer donors with different electron-withdrawing groups were designed and investigated based on the reported PTB7Ir to screen outstanding donors for triplet-material-based organic photovoltaics (T-OPVs). Geometry structures, frontier molecular orbital energy levels, energy driving forces (ΔE_L–L), absorption spectra, energy differences between S₁ and T₁ states (ΔE_ST), and driving forces of the triplet charge recombination (−ΔG_CRT) of PTB7Ir and designed 1–11 systems were evaluated by DFT and TD-DFT methods to estimate the light absorption abilities and the charge transfer dynamics. The results show that designed 5, 8, 10 and 11 possess larger spin–orbit couplings (SOC) affinity and smaller ΔE_ST and −ΔG_CRT values, which could effectively suppress the triplet charge recombination process at the donor/acceptor interface. Excitingly, the designed terpolymer 10 presents enhanced light absorption, revealing that it will be a promising donor candidate for high-performance T-OPV devices. Moreover, the results can provide theoretical guidelines to predict new terpolymer donors of T-OPVs.

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1. Introduction

Organic photovoltaics (OPVs) have achieved impressive advances in their low-cost fabrication, large-area production, and flexible device structure.^1–5 To date, favorable power conversion efficiencies (PCEs) of over 18% have been obtained,^6–9 which make the industrialization possible. The exploration of high-efficiency photovoltaic materials in OPVs has been regarded as one of the significant challenges for improving the PCE.

In OPV devices, excitons are photogenerated in donor (D) and/or acceptor (A) species and dissociated at D/A interfaces. This process leads to either direct long-range charge separation or generation of interfacial singlet charge transfer (¹CT) states followed by vibrational relaxation to the lowest ¹CT (¹CT₁) states. Then the interfacial ¹CT₁ states dissociate into free charge carriers, but also can occur geminate charge recombination (CR) which competes with exciton dissociation.¹⁰ In order to achieve a high-efficiency solar cell device, it is necessary to restrain geminate CR processes. One effective way is to promote the generation of triplet charge transfer (³CT) states. On one hand, triplet excitons can provide sufficient time for the CT state to dissociate the bound charge pair rather than recombination, because their radiative decay is dipole forbidden which will lead to longer lifetimes.^11,12 On the other hand, it is found that the charge transfer from the lowest charge transfer triplet (³CT₁) to triplet excited (T₁) states, i.e., the charge recombination to triplet (CRT), can be prevented when the energy level of ³CT state is lower than that of T₁ state of donor materials.^13,14 The state diagram of various photophysical processes is shown in Fig. 1.

Fig. 1 State diagram of various photophysical processes in the case of “donor” excitation for T-OPVs. Charge transfer (CT) and charge separated (CS) state energies are shown in relation to the first singlet excited state (S₁), the first triplet excited state (T₁) and ground state (S₀). Excitons are photogenerated in donors and dissociated at D/A interfaces, when CT energy below the T₁ state, photoexcited excitons go through a fast intersystem crossing (ISC) from S₁ to T₁ states at a rate k_ISC (green dotted arrow), then the ³CT states are formed from the T₁ at a rate k_CTT (red arrow), and finally separated into free charges at a rate k_CS (purple arrow); also, one possibility even in the triplet system, ¹CT excitons may generate from S₁ without going through T₁ at a rate k_CT (red dotted arrow). In addition, when CT energy above the T₁ state, the ¹CT states are formed directly from S₁ (red dotted arrow), yielding the ISC from ¹CT to ³CT, and thus the ³CT state separated into free charges. It's worth noting that there can occur the triplet charge recombination (CRT) from ³CT to T₁ at a rate k_CRT (blue arrow). ΔG_CT, ΔG_CR and −ΔG_CRT refer to the driving forces of CT, CR and CRT, respectively.

In order to get more ³CT states, triplet materials containing heavy metal complexes are adopted as source of ³CT by some research groups, and leading to the increased charge-transfer efficiency and improved photovoltaic performance.^{11,12,15–20} Notably, Huang and co-workers reported a series of Ir-embedded PTB7Ir polymers (see in Fig. 2), in which various low concentrations of (dfppy)₂Ir(dbm) (0–5 mol%) were introduced into the backbone of PTB7 (polythieno[3,4-b]-thiophene-co-benzodithiophene), and the improved PCEs have been achieved owing to the participation of triplet effects. Compared to PTB7, the PCEs of the devices based on PTB7Ir1 (containing 1 mol% Ir concentration) were all enhanced over 30%.¹² In addition, they introduced a low concentration of Pt/Ir complexes into the PTB7-Th polymer backbone (it is made by grafting the 2-ethylhexyl-thienyl group into the benzodithiophene unit of PTB7) by a similar approach, achieving the increases of PCEs from 7.92% to 8.45% and 9.19%, respectively.^19,20 However, so far, there are no explicit design strategies of terpolymer donors containing heavy metal complexes of triplet material-based OPVs (T-OPVs), because it is difficult to build a direct relationship between photoelectric conversion efficiency and molecular structure of the donor or D/A complex. Previously, we explored why PTB7Ir/PC₇₁BM device exhibits the enhanced PCE (8.71%) compared with 6.64% of PTB7/PC₇₁BM device, and discussed how to prevent the CRT process at D/A interface for T-OPVs.²¹ The results indicate that the improved PCE of the PTB7Ir/PC₇₁BM device is mainly ascribed to the increasing exciton diffusion length of triplet excitons. Besides, the proper increase of angle and number of torsional angles between electron donating and withdrawing units of terpolymer donors can prevent the CRT process and further improve photovoltaic performance.

Fig. 2 Molecular structures of PTB7Ir and 1–11. Among, the defined electron-withdrawing group contains π-bridge, x represents the various ratio of (dfppy)₂Ir(dbm) complex, and n represents the number of repeating units.

Herein, in the basis of PTB7Ir, we designed eleven terpolymers 1–11 through modifying and replacing the electron-withdrawing acceptor groups of PTB7Ir. All repeated units of PTB7Ir and terpolymers 1–11 are shown in Fig. 2. The introductions of thiophene π-bridge, fluorinated thiophene π-bridge, benzothiadiazole (BT) group and fluorinated benzothiadiazole (FBT and DFBT) group are aimed at tuning the energy levels and energy-gaps of S₁, T₁ and CT₁ states to improve the short-circuit current density (J_sc). For example, (i) reducing the S₁ energy level to broaden absorption spectra in near infrared range; (ii) reducing the energy difference between S₁ and T₁ states to promote intersystem crossing (ISC) process of excitons from singlet to triplet; and (iii) tuning ³CT₁ energy level lower than T₁ energy level to decrease values of driving force for the CRT (−ΔG_CRT) as well as prevent CRT process. By density functional theory (DFT) and time-dependent DFT (TD-DFT) methods, we systematically investigated geometry structures, frontier molecular orbital (FMO) energy levels, energy driving forces (ΔE_L–L), absorption spectra, energy differences between S₁ and T₁ states (ΔE_ST), and −ΔG_CRT of PTB7Ir/PC₇₁BM and 1–11/PC₇₁BM systems, to perform a further analysis on charge transfer properties for efficient charge separation and photocurrent generation in T-OPVs. We expect that this work may serve as a theoretical guideline for the design and synthesis of high-performance T-OPV terpolymer donors.

2. Computational details

It has been reported that alkyl-branched chains possess little influence on the electronic structures and photoelectric properties of materials.^22–24 Therefore, for all investigated polymers, the branched ethylhexyl side chains were substitute by methyl groups and the ends of oligomers were capped by hydrogen atoms to save computational cost. All of the calculations were performed by using Gaussian 09 software.²⁵ Ir atom and non-metal atoms were described by LANL2DZ basis set and 6-31G(d) basis set, respectively.

In our previous research,²¹ it is confirmed that when PTB7Ir molecule contain one metal complex and three organic building blocks (x = 0.25), the calculated HOMO energy level by PBE0 functional show good accordance with the measured experimentally (the calculated HOMO level is −5.16 eV and experimental values are in the range of −5.14 to −5.22 eV).¹² Additionally, the B3LYP functional was proved to be an effective method to evaluate the absorption spectrum and the S₁ vertical excitation energies of PTB7Ir molecule, because the maximum absorption wavelength value of PTB7Ir molecule calculated by TD-B3LYP//PBE0 functional (672 nm) is closer to the experimental data (678 nm).²¹ Meanwhile the effect of solvent (o-dichlorobenzene (DCB)) within polarizable continuum model (PCM) was considered in TD-DFT calculations. Also, the HOMO–LUMO energy gap of PTB7Ir was estimated as S₁ vertical excitation energy, and the LUMO energy level was derived by adding the band-gap to HOMO level. The result from this method agreed well with the experimental LUMO level (the calculated LUMO energy level is −3.29 eV, electronic energy level is −2.70 eV, and experimental values are −3.02 to −3.13 eV).¹² Thus, in this work, the above calculated methods were employed to investigate the geometries, FMO energy levels and photoexcitation properties of all terpolymer molecules. The calculation details are listed as follows: (i) ground-state geometries and HOMO energy levels are simulated by PBE0 functional; (ii) the absorption spectra, S₁ and T₁ vertical excitation energies are evaluated at the TD-PCM-B3LYP//PBE0 level in DCB solution; and (iii) the LUMO energy levels are obtained by adding S₁ vertical excitation energies to the HOMO energy levels.

Our previous results indicated that when PC₇₁BM is docked with the centre of polymer donor, the interfacial arrangement is preferable for PTB7Ir/PC₇₁BM complex, since the lowest energies occur at the configuration.²¹ Therefore, in current work, for each D/PC₇₁BM interface model, the starting configuration is designated that benzene cycle of PC₇₁BM is oriented parallel to the thiophene (for PTB7Ir, 1 and 2 molecules) or benzene (for 3–11 molecules) cycles of acceptor units which are closer to the (dfppy)₂Ir(dbm) complexes, which has been proved to be a preferred interfacial arrangement in our previous research. The initial distances between terpolymer donors and PC₇₁BM were fixed at 3.5 Å. To save the computational cost, we demonstrated a comparative analysis of intermolecular charge transfer properties of PTB7Ir/PC₇₁BM based on the ground-state geometries calculated by PBE0 and PBE0-D2 functionals, respectively (see Section SI of the ESI†). Note that PBE0-D2 is a functional considering dispersion correction, which presents the high computational cost. The results indicate that the two interface configurations of PTB7Ir/PC₇₁BM exhibit similar equilibrium geometries and intermolecular charge transfer behaviors. Therefore, ground-state geometries of D/PC₇₁BM complexes can be performed by PBE0 functional instead of PBE0-D2 functional with dispersion correction. Excited state properties were performed at the long-range-corrected CAM-B3LYP^26,27 levels. It has been confirmed that CAM-B3LYP functional is suitable for the description of CT excited state properties of interfacial systems.^28–30 The charge density difference (CDD) maps were simulated using Multiwfn 3.3.8 code^31,32 to visualize CT excited states.^33,34

3. Results and discussions

3.1 3D geometries

All molecular geometries were optimized at the PBE0 level as the above methods. The computed twist angles between each building blocks of PTB7Ir and 1–11 are plotted in Fig. 3 and S3 in ESI.† As seen from Fig. 3, twist angles between donor (benzothiadiazole, BDT) and acceptor (fluorinated benzothiadiazole, F-TT) units of PTB7Ir are in the range from 15° to 32°. Compared with PTB7Ir, the designed 1 and 2 show planar molecular structures due to the introductions of thiophene and fluorinated thiophene π-bridges. In particular, for 2 (see Fig. S3†), the twist angles between organic building blocks are all in close to 0° because of intramolecular F⋯S attractive interactions. And the distances between F and S atoms are approximately 2.92 Å, which are shorter than the sum of F and S van der Waals radii (3.27 Å proposed by Bondi and 3.19 Å proposed by Pauling). The planar molecular structures in the conjugated backbone increase more efficient π delocalization along the polymer chain, which will favor π-stacking and charge-transport properties. Compared to PTB7Ir, the designed 3, 6 and 9 also present increasing planarity due to the attractive interactions between N atom from benzothiadiazole and H atom from BDT, respectively. Obviously, 6 and 9 show perfect planar constructions, and the optimized twist angles between BDT and acceptor units (FBT for 6 and DFBT for 9) are also about 0°, which is attributed to N⋯H and F⋯S attractive interactions. In addition, compare with PTB7Ir, 4, 5, 7, 8, 10 and 11 adopt more twisted conformation, which may decrease the conjugation extent of polymers and increase the energy levels of S₁ and T₁ states. When T₁ energy above the CT₁ state, the CRT at D/A interface will be prevented to improve photovoltaic performance. However, note that the less planarity will cause the limited π-stacking interactions and lead to the undesirable charge transport and collection. Specifically, 4 present decreasing planarity in comparison with that of 3, which is because the repulsive interactions between H atom from thiophene π-bridge (or BDT) unit and S atom from BDT (or thiophene π-bridge) unit. Similarly, the planarity of 7 and 10 is lower than those of 6 and 9, respectively, because of the introduction of thiophene π-bridge. Unexpectedly, for 5, 8 and 11, the significant repulsive interactions, between F atom from fluorinated thiophene π-bridge and N atom from benzothiadiazole, lead to twist angles of ∼40° in the polymer backbone. As a result, the designed 1–3, 6 and 9 could display better charge transport and collection owing to their improved planarity, meanwhile, 4, 7 and 10 may suppress the CRT at the interface and enhance photovoltaic performance due to the proper torsional angles.

Fig. 3 Schematic illustration of twist angles between donor and acceptor moieties of PTB7Ir, 1 and 3–5. The green dotted boxes represent the highlights.

3.2 FMO energy levels

It is well known that FMO energy levels can dominate the photon absorption and charge separation abilities of OPVs.^35,36 The FMO energy levels of all terpolymers are listed in Fig. 4, which are obtained according to the description of calculation details in Section 2. Also, the HOMO energy levels (E_HOMO) calculated at the B3LYP/6-31G(d) (LANL2DZ for Ir atom) level are displayed in Table S2 in ESI.† Additionally, the FMO energy levels of the acceptor PC₇₁BM measured in experiment are also depicted in Fig. 4.^37,38 Seen from Fig. 4, the energy-gap (HOMO–LUMO) values of 5, 8 and 11 are larger than that of PTB7Ir, indicating that they may exhibit blue-shifted absorptions in comparison with PTB7Ir. This is because the significant twist angles in polymer backbones decrease the effective conjugation lengths.

Fig. 4 Calculated FMO energy levels and S₁ vertical excitation energies (E_g) of PTB7Ir and 1–11 (the pink color represents the experimental value of PTB7Ir), along with the FMO energy level of PC₇₁BM measured in experiment.

The energetic driving force ΔE_L–L, defined by the difference between LUMO levels of donor and acceptor, is an important factor to evaluate charge separation ability at D/A interface.^28,39 The charge separation of polymers will occur when ΔE_L–L > 0.3 eV which is the estimated value of empirical exciton binding energy for polymers.^37,40 As seen from Fig. 4, the calculated ΔE_L–L values of all systems are larger than 0.3 eV, revealing the efficient charge separation at D/A interface.

3.3 Photon absorption

It is acknowledged that absorption spectra of donors need match the solar spectrum to ensure the efficient photovoltaic conversion, which will increase the J_sc and thus improve the PCE.^41–43 The absorption spectra of PTB7Ir and 1–11 are shown in Fig. 5. Vertical excitation energies, oscillator strengths and dominant configurations of S₁ states, and electronic density contours of FMOs are gathered in Tables S3† and 1, respectively. Seen from Fig. 5, the absorption range of all molecules cover the entire ultraviolet-visible, and the designed 3–11 display the similar peak shape and intensity in comparison with PTB7Ir. In addition, compared with PTB7Ir, the designed 5, 8 and 11 exhibit slightly blue-shifted absorption in low-energy region. This is because the introduction of fluorinated thiophene π-bridges brings about their large twist angles, which lead to poor conjugation along polymer backbones. Fortunately, other designed molecules have broadened and red-shifted absorption in the 400–1000 nm region. Table S3† illustrates that the maximum absorption peaks of all systems come from S₀ → S₁, corresponding to the transition from HOMO (H) to LUMO (L). The orbitals in HOMOs are mainly delocalized on the organic building blocks of polymers. Also, for PTB7Ir, the distribution of LUMO is localized on all organic building blocks (Table 1). For designed 3, 6 and 9, LUMO orbitals are mainly localized the middle three BDT units and three organic acceptor units. For other designed molecules, LUMO orbitals are localized the second and third BDT units from right, π-bridges, and organic acceptor units. The results indeed show that the designed 1–3, 4, 6, 7, 9 and 10 will present enhanced light absorption owing to their broad and red-shifted absorption in the visible and near-infrared regions of the solar spectrum.

Fig. 5 Simulated absorption spectra and oscillator strengths of PTB7Ir and 1–11 at the TD-PCM-B3LYP/6-31G(d) (LANL2DZ for Ir atom) level. The dotted line is the experimental absorption spectrum of PTB7Ir. Gaussian function was chosen as the broadening function with the value of the full width at half maximum set at 0.66667 eV, which is considered as an average width for the absorption band observed in the UV-vis region.⁴⁴

Table 1 Calculated electronic density contours of FMOs for PTB7Ir and 1–11 at the TD-PCM-B3LYP/6-31G(d) (LANL2DZ for Ir atom) level. The orbitals are plotted at a contour value of 0.01 a.u

Molecule	HOMO	LUMO
PTB7Ir
1
2
3
4
5
6
7
8
9
10
11

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3.4 Energy difference between S₁ and T₁ states

In T-OPVs, photoconversion channel that we are mainly concerned about is the CRT process, which can be estimated from the state diagram with measured/calculated relative energetic positions of S₁ and T₁ on the donor material and the CT₁ at the D/A interface.^13,45 Therefore, our discussion focuses on energy levels of S₁, T₁ and CT₁ rather than higher excited states. When −ΔG_CRT < 0, the ³CT excitons from T₁ or/and ¹CT from S₁ excitons would diffuse toward D/A interface to dissociate into separated charges.²¹ Therefore, the ISC process from S₁ to T₁ need to be promoted to obtain more long-lived ³CT excitons. It is widely accepted that a large spin–orbit coupling (SOC) and a small energy difference between S₁ and T₁ states (ΔE_ST) will lead to a fast ISC process. However, the SOC calculation of large systems is a difficult challenge need to be overcome. Fortunately, Brédas and co-workers have reported that the SOC matrix element can be qualitatively evaluated by estimating the changes in π-conjugation of either hole or electron wave functions between the singlet and triplet excited states, which is in accord with El-Sayed rule.⁴⁶ Therefore, the natural transition orbital (NTO) analyses for S₁ and T₁ were performed to examine the nature of the excited states and qualitatively evaluated SOC. Taking the NTOs of PTB7Ir and 4 molecules as examples (see Fig. 6), for PTB7Ir molecule, an obvious local excitation (LE) within the middle three BDT and F-TT units appears in both S₁ and T₁ states, which will lead to a small SOC; for 4 molecule, besides the LE character within organic acceptor units, a clear CT character from middle two BDT donor units to organic acceptor units also occurs in the S₁ state because of the spatial separation of LUMO wave function, while only LE character appears in the T₁ state, consequently, 4 molecule will exhibit a lager SOC value than PTB7Ir due to the change in π-conjugation between S₁ and T₁ states. Turning to 1–3, 6, and 9, a predominant LE character are presented in S₁ and T₁ states (see Fig. S4†). For 5, 7, 8, 10 and 11, the LE and CT characters are both observed in S₁ states in addition to a LE character for their T₁ states. As a result, designed 4, 5, 7, 8, 10 and 11 may give the lager SOC values than others. Note that, Ir metal centers of the designed terpolymers are not involved at both S₁ and T₁ states, indicating that the SOC mainly comes from the organic parts of terpolymer systems.

Fig. 6 Hole–electron pairs of NTOs in S₁ and T₁ states of PTB7Ir and 4.

Additionally, the energy difference between S₁ and T₁ states (ΔE_ST) values were calculated to evaluate ISC process of all systems from S₁ to T₁ states. The calculated ΔE_ST values are summarized in Table 2, respectively. It shows that ΔE_ST values of all designed molecules are smaller than that of PTB7Ir. Obviously, the ΔE_ST of 5 and 8–11 are below the value of 0.5 eV, indicating that their ISC process could be promoted to form more long-lived ³CT exciton. Unfortunately, the ΔE_ST values of all systems are still quite large, which will be further reduced in future. Consequently, designed 5, 8, 10 and 11 exhibit larger SOC affinity and smaller ΔE_ST values than those of PTB7Ir, which will promote their ISC process from S₁ to T₁ states and the formation of ³CT exciton.

Table 2 Calculated energy level values of S₁, T₁ and ΔE_ST for PTB7Ir and 1–11 systems

	PTB7Ir	1	2	3	4	5	6	7	8	9	10	11
S1/eV	1.87	1.76	1.70	1.77	1.69	1.96	1.75	1.70	1.92	1.77	1.72	1.95
T1/eV	1.28	1.19	1.15	1.23	1.16	1.50	1.25	1.20	1.48	1.28	1.24	1.53
ΔEST1/eV	0.59	0.57	0.55	0.54	0.53	0.46	0.50	0.50	0.44	0.49	0.48	0.42

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3.5 Intermolecular charge transfer

3.5.1 Intermolecular charge transfer excited states. It is commonly accepted that the geometry of D/A interface plays an important role in the behavior of CT state.⁴⁷ To give a deep insight into the photovoltaic properties of all aforementioned terpolymers/A heterojunctions, the charge density difference (CDD) maps were calculated to investigate the charge transfer behaviors between the ground state and the lowest intermolecular CT excited state at D/A interface. The CDD maps of ¹CT₁ and ³CT₁ states are shown in Fig. 7 and 8, respectively. Note that the electrons of these CT excited states are mainly confined to acceptors.^22,30,48 As displayed in Fig. 7, the ¹CT₁ states of 1/PC₇₁BM, 6/PC₇₁BM and 10/PC₇₁BM heterojunctions include charge transfer from terpolymer backbones to PC₇₁BM. Differently, for other heterojunctions, the ¹CT₁ states involve PC₇₁BM-localized π–π* transition and electronic transitions from donors to PC₇₁BM. Moreover, for 5/PC₇₁BM, 8/PC₇₁BM and 11/PC₇₁BM heterojunctions, Ir complexes take part in the intermolecular charge transfer from terpolymer donors to PC₇₁BM, because their twist structures along polymer backbones increase donor–acceptor interactions via a decreasing in the distance between donor (mainly containing Ir complex and adjacent BDT unit) and acceptor. The increasing donor–acceptor interactions could enhance the electron–hole binding energy and result in a decrease in CT state energy.⁴⁹ Additionally, the Ir complex of 6/PC₇₁BM also involve the intermolecular charge transfer due to the short distance between Ir complex and acceptor. Likewise, the transition of ³CT₁ states for all heterojunctions are deemed to the charge transfer from donor polymers to PC₇₁BM (Fig. 8). For 3/PC₇₁BM, 5/PC₇₁BM, 8/PC₇₁BM, 9/PC₇₁BM and 11/PC₇₁BM, the ³CT₁ states contain the transition from Ir complexes to PC₇₁BM. The results illustrate that the increasing twist angles along terpolymer backbones can promote the intermolecular charge transfer process from metal complex to acceptor and reduce CT state energy in T-OPVs.

Fig. 7 CDD maps of ¹CT₁ excited states with isosurface value of 0.00002 a.u. for PTB7Ir/PC₇₁BM and 1–11/PC₇₁BM systems, where the violet and turquoise colors refer to the increase and decrease in electron density, respectively.

Fig. 8 CDD maps of ³CT₁ excited states with isosurface value of 0.00002 a.u. for PTB7Ir/PC₇₁BM and 1–11/PC₇₁BM systems, where the violet and turquoise colors refer to the increase and decrease in electron density, respectively.

3.5.2 Triplet charge recombination process. In T-OPVs, the charge recombination to triplet (CRT) process at the D/A interface needs to be suppressed to improve the efficiency of photocurrent generation. To illustrate the CRT process of all terpolymers, the driving force for the CRT (−ΔG_CRT) was characterized through the energetic difference (E_CT1 − E_T1) between CT₁ and T₁ states. Generally, ¹CT and ³CT states are degenerate in energy.^44,50,51 Herein, the E_CT1 energy value was employed to the description of ¹CT₁ and ³CT₁ energies. The energy of CT₁ state could be calculated through the equation E_CT1 = |E_IP(D) − E_EA(A)| + E_Coul,^13,52 in which E_IP(D) and E_EA(A) refer to the ionization potential of donor and the electron affinity of acceptor, which are estimated by the HOMO energy of donor and LUMO energy of acceptor, respectively.⁵³ E_Coul represents for the Coulomb interaction energy between the cation of donor and anion of accept, which is calculated using the formula E_Coul=(1/4πε₀ε_r)∑_i∈D+∑_j∈A−(q_iq_j/r_ij). Among, ε₀ and ε_r refer to dielectric constants in vacuum and medium (ε_r is set as 4.0, which refers to the experimental value reported for PTB7:PC₇₁BM system⁵⁴), respectively. q_i and q_j represent for charges of i and j atoms given by the natural population analysis charge distribution in this work, and r_ij is the distance between the two atoms.

The calculated energy level values of CT₁, E_Coul and −ΔG_CRT for all systems were summarized in Table 3, and energy diagrams of various states were presented in Fig. 9. As shown, the −ΔG_CRT values are found to be in the order of 4 > 3 > 9 > 6 > PTB7Ir > 1 = 7 > 2 > 10 > 5 > 8 > 11. The result indicates that, compared with PTB7Ir, designed 1, 2, 4, 5, 7, 8, 10 and 11 exhibit smaller −ΔG_CRT values due to the twist donor backbones. Especially, the −ΔG_CRT values of 5, 8, 10 and 11 are less than −0.1 eV, thus leading to the suppressed CRT process. Here, the value “−0.1 eV” is considered as the minimum −ΔG_CRT, which can give rise to the CRT process.⁴⁵ As a result, we infer that designed 10 will be a promising terpolymer donor for high-performance T-OPVs because of its broad and red-shifted absorption and suppressed CRT process at D/A interface.

Table 3 Calculated energy level values of E_Coul, E_CT1 and −ΔG_CRT for PTB7Ir and 1–11 systems

	PTB7Ir	1	2	3	4	5	6	7	8	9	10	11
ECoul/eV	−0.19	−0.09	−0.30	−0.15	−0.04	−0.43	−0.16	−0.19	−0.54	−0.18	−0.29	−0.69
ECT1/eV	1.22	1.12	1.05	1.28	1.25	1.17	1.27	1.13	1.08	1.32	1.07	0.97
−ΔGCRT/eV	−0.06	−0.07	−0.10	0.05	0.09	−0.33	0.02	−0.07	−0.40	0.04	−0.17	−0.56

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Fig. 9 Energy diagrams of the lowest singlet S₁, triplet T₁ and CT₁ charge transfer excited states relative to the ground states for the PTB7Ir/PC₇₁BM and 1–11/PC₇₁BM heterojunctions, respectively.

4. Conclusions

To summarize, motivated by the consideration of increasing the efficiency of photocurrent generation of T-OPVs, eleven terpolymer donors have been designed and characterized based on PTB7Ir using DFT and TD-DFT methods. Compared to reported PTB7Ir, the designed 3, 4, 6, 7, 9 and 10 present broader and red-shifted absorption in the low-energy region of the solar spectrum, which contribute to capture more photons to enhance the photocurrent. Moreover, designed 5, 8, 10 and 11 show larger SOC affinity and smaller ΔE_ST values than those of PTB7Ir, which will promote their ISC process from S₁ to T₁ states and the formation of ³CT exciton. Significantly, the −ΔG_CRT values of designed 5, 8, 10 and 11 are less than −0.1 eV, which can effectively suppress CRT process at the D/A interface. Consequently, the designed 10 possess enhanced light absorption, larger SOC affinity, smaller ΔE_ST and −ΔG_CRT values, which will be a promising candidate for terpolymer donors in high-performance T-OPVs. Meanwhile, the results manifest that the proper twist angles in terpolymer backbones could prevent the CRT process to achieve a balanced combination of charge separation, transport and collection, and further improve photovoltaic performance. Furthermore, an effective and integrated method to predict terpolymer donors embedded with metal complexes of T-OPVs is described systematically.

Author contributions

S. Li conceived the research and wrote the original draft. S. Li, Y. Chen, Z. Li, and J. Zhang performed the calculation. J. Chen, Y. Geng and Z. Su directed the research. All the authors contributed to the discussions, reviewing and editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors gratefully acknowledge financial support from Science and Technology Project of Jilin Education Department (JJKH20200239KJ), the Fundamental Research Funds for the Central Universities (2412018ZD006), Natural Science Foundation of Jilin Province (YDZJ202101ZYTS029) and Special Training Project for Outstanding Young Talents of Jilin City (20210103092).

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Footnote

† Electronic supplementary information (ESI) available: A comparative analysis of intermolecular charge transfer properties of PTB7Ir/PC₇₁BM based on the ground-state geometries calculated by PBE0 and PBE0-D2 functionals, respectively. The plots of schematic illustration of twist angles between donor and acceptor moieties of 2 and 6–11, and hole–electron pairs of NTOs in S₁ and T₁ states of 1–3 and 5–11. The tables of HOMO energy levels (E_HOMO) calculated using B3LYP functional, and the vertical excitation energies (E_g), oscillator strengths (f) and excitation characters of S₁ states calculated at the B3LYP/6-31G(d) (LANL2DZ for Ir atom) level in o-dichlorobenzene solvent for PTB7Ir and 1–11 molecules. Tables of coordinates of molecules. See DOI: 10.1039/d2ra00033d

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