Theoretical Approach Towards Rational Design and Characterization of Benzo[1,2-b:5-B’]dithiophene (BDT)-Based (A-D-A) Small Molecules of Relevance for High Performance Solar Cells

Benzo[1,2-b:5-B’]dithiophene (BDT)–based small molecules with acceptor-donor-acceptor (A-D-A) structure were designed based on the experimental system BDTT-S-TR (1) for use as potential donor materials for organic photovoltaic (OPV) devices. Their geometry structures, electronic properties and other key parameters related to OPVs such as absorption spectra, energetic driving forces L L E − ∆ , power conversion efficiencies (PCEs) and intramolecular charge transfer properties have been investigated by means of density functional theory (DFT) and time dependent density functional theory (TDDFT) methods. These have been exploited as donor materials for a heterojunction with [6,6] phenyl-C71-butyric acid methyl ester (PC70BM) as acceptor material. Based on Marks model, an excellent agreement between the experimental and predicted PCE was obtained for the reported system 1/PC70BM and a significant improvement in PCEs of BHJ devices based on 2-4/PC70BM was manifested. The charge transfer rates of the interfacial charge transfer int er CT k − and recombination int er CR k − in 1-4/PC70BM heterojunctions have been calculated using Marcus-Levich-Jortner rate equation. The calculations show that the ratios / int int er CT er CR k k − − for the 2-4/PC70BM heterojunctions are ~10 4 times higher than that of the 1/PC70BM. From these predictions, we reached our purpose to provide rational design of three novel molecules that will be more promising candidates for high-efficiency SMs OPVs materials.

L L E − ∆ , power conversion efficiencies (PCEs) and intramolecular charge transfer properties have been investigated by means of density functional theory (DFT) and time dependent density functional theory (TDDFT) methods. These have been exploited as donor materials for a heterojunction with [6,6] phenyl-C 71 -butyric acid methyl ester (PC 70 BM) as acceptor material. Based on Marks model, an excellent agreement between the experimental and predicted PCE was obtained for the reported system 1/PC 70  for the 2-4/PC 70 BM heterojunctions are ~10 4 times higher than that of the 1/PC 70 BM. From these predictions, we reached our purpose to provide rational design of three novel molecules that will be more promising candidates for high-efficiency SMs OPVs materials.

Introduction
Organic photovoltaic cells (OPVs) have recently brought considerable attention to their potential to become an economically viable source of affordable, clean, and renewable energy. In the quest to improve the performance of polymer solar cells (PSCs), the distinction of the critical factors limiting their power conversion efficiency (PCE) with a view to rationalizing the relationship between the structures of the active layers, their morphology, and the electronic processes taking place at their interface is required. Following the groundbreaking work of Tang et al. [1], it is very well believed that the presence of a donor/ acceptor (D/A) interface in PSCs can significantly impact the dynamics of the charge carriers and facilitate the dissociation mechanism of excitons and most of the OPVs till date are fabricated with such a design. Bulk-heterojunction (BHJ) PSCs, where typically a conjugated polymer or a small molecule (SM) as an electron donor (D) is blended with fullerene derivative as an electron acceptor (A) into a favorable nanoscale phase-separated morphology, is the most prominent and successful PSCs device at present [2][3][4]. In principle process, the photo-generated excitons formed at the D/A interface dissociate into bound electron-hole pairs forming charge transfer, which drift to be collected at separate electrodes to generate current. Cooperatively, these processes including the critical parameters to impact the performance of OPV calibrate the PCE of BHJ device [5][6][7][8][9][10].
Great progress has been achieved in both donor and acceptor materials development and device optimization, witnessed by the dramatic increase in devices PCEs from less than 2% before 2008 to over than 10% in recent years [11][12][13][14][15]. In this regard, fullerene and their derivatives have been extensively used as acceptor materials within BHJ devices because of their important electronic properties such as small reorganization energy, high electron mobility and affinity [16][17][18]. Nowadays π-conjugated small molecules (SMs) have attracted considerable research interest for OPVs, due to their great advantages over their polymers and copolymers counterparts, including low cost manufacturing, flexibility, light weight, and well-defined molecular structure [19][20][21][22]. Recently, record-high OPV efficiencies have been obtained by innovations of SMs donor materials. Among several designed SMs for solution processed solar cells, benzo[1,2-b:5-B'] dithiophene (BDT)-based SMs have been emerging as an attractive building block for donor molecules in OPVs. The BDT unit with a structural symmetry and rigid fused aromatic system can promote electron delocalization and cofacial π-π stacking in the solid state, leading to highly ordered systems and thus high charge carrier mobilities. Today's PCEs near 10% were demonstrated in OPVs using BDT-based solution processed SMs [23,24]. It deserves to mention here that high performance OPVs have also been designed using BDT containing polymers [24][25][26][27][28]. Lately, Li et al. [14] reported a linear acceptor-donor-acceptor (A-D-A) structured SM (BDTT-S-TR) with alkylthio-thienyl-substitued BDT (BDTT-S) as the core donor unit (D) and terthiophene end-capped with electron-withdrawing rhodanine (TR) as acceptor units (A). The synthesized molecule BDTT-S-TR (1) shows high solution processability, crystalline structure, broad absorption spectrum, good hole transport ability, and low-lying HOMO energy level [14,[29][30][31]. The optimized OPV device based on BDTT-S-TR/PC 70 BM ( [6,6] phenyl-C 71 -butyric acid methyl ester) (1/ PC 70 BM (Figure 1b)) exhibit high PCE of 9.2% [14].
Herein, taking (1) as a reference, we have designed SM 2 through keeping the BDTT-S as the core donor unit and varying the number of nitrogen atoms in the end-capped group of the acceptor units ( Figure  1). Previous studies have demonstrated that the crystalline character of BDT based D-A copolymers and SMs can be adjusted by increasing the number of nitrogen atoms in the acceptor unit [32,33]. Benefited from the good properties of SM 2, we have subsequently designed SMs 3 and 4 by retaining the core acceptor unit of 2 and modifying the core donor BDTT-S by substituting some carbon atoms by nitrogen atoms. Here, the introduction of nitrogen atoms in the donor unit is aimed to tuning the energy levels and thus lowering energy-gaps and broadening absorption spectra, which is expected to enhance the shortcircuit current (J SC ) and the open-circuit voltage (V OC ). Based on SM 4, we have designed the SM 5 by fluorination of the thiophene ring in the acceptor units. The geometric structures, electronic properties and other factors related to OPVs such as absorption spectra, driving forces ΔE L-L , PCEs and intramolecular charge transfer properties of SMs 1-5 have been systematically evaluated using density functional theory (DFT) and time dependent density functional theory (TDDFT) methods. Furthermore, the charge transfer and charge recombination rates in BHJ OPVs based on 1-4/PC 70 BM have been predicted using Marcus Theory [34,35], which has been extensively used to probe the kinetic data for charge separation and recombination in D/A systems in OPVs.

Computational Details
The ground state of all investigated molecular systems in the current work such as SMs 1-5, PC 70 BM, and 1-4/PC 70 BM was investigated with DFT method. No initial symmetry constrains were applied. It is worthy to note that, to save the computational cost, we have replaced the alkyl-branched chain in designed SMs 1-5 with methyl groups, since it is proved that they possess no significant influence on the electronic and optical properties of the host materials [36][37][38][39]. To verify the benchmark of energy levels in OPV, we tested the functionals B3LYP [40], B3PW91 [41] and PBE0 [42] with 6-31G(d) basis set to calculate the highest occupied molecular orbital (HOMO) energy level for the SM 1 as a reference. The results listed in Table S1 (ESI) indicate that while B3LYP overestimates the E HOMO , both B3PW91 and PBE0 predict E HOMO close to the experimental value (only 0.02 eV difference). Therefore, to substantiate the reliability of the computational methods B3PW91 and PBE0, we need to examine the excited state of SM 1. Thus, based on DFT calculations (B3PW91 or PBE0), M06, M06X, CAM-B3LYP, WB97X(D), BHandHLYP as well as the ground state of nitrogen atoms in donor core. In addition, twist angles between the thiophene rings in the acceptor moieties are the largest for SM 1 (17°-24°); this is a consequence of the repulsion between the sulfur atom of the thiophene ring and the adjacent methylene promoting the rotation of the alkyl chain [52]. The twist angles of SMs 2-4 are smaller than that of 1 (6°-20°). This difference, although quite small, might due to the intramolecular H … O attractive interactions in the end-capped groups in SMs 2-4, which are verified by the short distance between H and O atoms (~2.03 Å). However, SM 5 possesses a quasi-planar backbone conformation, with all thiophene rings coplanar to each other. Consistent with other reports [53], we believe that the origin of this planarization could be the intramolecular S … F attractive interaction, as the sulfur atom and the fluorine atom are in close proximity (~2.86 Å). As a consequence, it is reasonable to declare that SMs 2-5 exhibit a more linear structure as compared to that of SM 1, suggesting that the novel designed SMs have good planarity beneficial for providing high charge carrier mobilities [54].
It is well known that the performance in BHJ solar cells is closely affected by the frontier molecular orbitals (FMOs) (HOMO and LUMO (lowest unoccupied molecular orbital)) since they are involved in the generation of exciton, charge transfer, dissociation and exciton recombination. Thus, in order to gain insight into the charge separation ability in D/A interface, the HOMO and LUMO energy levels of SMs 1-5 and PC 70 BM were calculated and the results are summarized in Table 1. The experimental HOMO and LUMO energy levels of SM 1, obtained by cyclic voltammetry (CV) experiment, are -5.18 eV and -3.25 eV, respectively [14]. The calculated HOMO and LUMO energies of SM 1 (-5.16 eV and -3.18 eV, respectively) are very close to the experimental values, proving that DFT/B3PW91/6-31G(d) appears as suited method to study molecular electronic structures. It is worth mentioning that, for SMs 1-5 and PC 70 BM, the HOMO energies were evaluated at the B3PW91/6-31G(d), and in order to produce more accurate LUMO energies for these systems, we have adopted an indirect method of calculation by appending the HOMO energy to that of the first singlet excitation simulated using TDDFT. The reliability of this computational method has been successfully confirmed by Musgrave et al. [55] and by Nelson et al. [56].
Comparing 1 and designed SMs 2-5, it is clear that the substitution of end-capping groups (in 2-5), the introduction of nitrogen atoms (in [3][4][5], and finally the introduction of electron-withdrawing fluorine (in 5) stabilized significantly the HOMO energies by about 0.06 to 0.30 eV. This result denotes that the HOMO energy levels of the designed SMs 2-5, having more coplanar configuration across the backbone than 1, are very close to the HOMO energy of an ideal polymer (~-5.4 eV), providing them with good long-term stability in air and their BHJ photovoltaic devices with high V OC [32,57]. However, the LUMO energy levels of the molecules 2-5 are between -3.40 eV and -3.57 eV, lower by about 0.26 to 0.39 eV than that of 1. Note that SMs 1-5 are calculated to have energetically destabilized LUMO's compared to that functional (B3PW91 or PBE0) with 6-31G(d) basis set were utilized to simulate the absorption spectra of SM 1 using TDDFT calculations. Chloroform was employed as solvent in the TDDFT calculations, within the polarizable continuum model (PCM) [43,44]. The calculated and experimental data are collected in Tables S2 and S3 (ESI). The results show that, whatever SM 1 is optimized with B3PW91 or PBE0, the WB97X(D) functional gives a maximum absorption wavelength in good accordance with the experimental value. However, the difference between the WB97X(D) simulated maximum absorption wavelength and experimental values is only 2 nm when the structure is optimized with B3PW91 functional in its ground state. Consequently, based on the B3PW91/6-31G (d) optimized geometries in chloroform solution, the absorption spectra and excited-state energies of the SMs 1-5 were examined by TDDFT/ WB97X(D)/6-31G(d) method.
The 1-4/PC 70 BM interfaces were simulated using the optimized geometries of the SMs 1-4 and PC 70 BM. Each SM is placed in the vicinity of PC 70 BM at a distance of 3.5 Å with the fullerene anchored with the electron accepting moiety of the SM and the benzene cycle is oriented parallel to the donor core. This specific donor/fullerene arrangement has been verified, using NMR analyses, as the preferred arrangement for the highest performing BHJ OPV materials [45]. The ground state geometries of 1-4/PC 70 BM were simulated at the B3LYP/6-31G (d) level which has been proved to be a very powerful method to simulate the polymer/fullerene heterojunctions [39]. Based on the B3LYP/6-31G (d) optimized geometries, absorption spectra and excited-state energies were evaluated at the TDDFT/CAM-B3LYP/6-31G (d) method. It is well accepted that this long-range-correlated functional is a reliable functional for describing the intermolecular charge transfer (inter-CT) excitations in the D/A heterojunctions model [46][47][48]. The inter-CT excited states of the 1-4/PC 70 BM interfaces were examined via the charge density difference (CDD) maps as implemented in Multiwfn 3.3 [49,50]. All the above mentioned quantum chemical calculations were carried out using Gaussian 09, revision A.02 [51].

A-D-A small molecules: Geometric and electronic structures
As above mentioned, the ground state molecular geometries of SMs 1-5 were optimized at the B3PW91/6-31G(d) level with no symmetry constraints. The optimized structures with the torsion angles along the conjugated backbones are plotted in Figure S1 (ESI).
All the optimized structures show twist angles between A and D moieties close proximity to 21° due to the existence of the alkyl chain in the thiophene of the acceptor core, as confirmed in our previous work [52]. It can be seen from the side view, that SM 1 deviate more from the coplanar architecture compared to the designed SMs 2-5. The dihedral angle between the methyl-thienyl group and the BDT is ~56° for SMs 1-3, larger than 19° for SMs 4 and 5. This difference is the result of the limiting steric interactions provoked by the introduction of PC 70 BM, which can positively impact the electrons transfer between the studied SMs and the electron-transport material (PC 70 BM).
The distribution patterns of the FMOs for SMs 1-5 are carried out at B3PW91/6-31G(d) level and the electronic density contours are shown in Figure 2. For all molecules, the electronic cloud distributions of HOMO's show typical feature with electron delocalization on the thiophene rings of the acceptor units and the core donor BDTT-S, and partially on the end-capping groups. The orbitals in the LUMO's are mainly located on the electron-deficient units and partially on the donor core BDTT-S for SMs 1-3. For 4 and 5, the LUMO's also reside at the side chains (alkylthio-thienyl groups) on the donor unit. These results display that the introduction of nitrogen atoms in positions Y ( Figure 1) has a slight impact on the LUMO distribution of 4 and 5. Interestingly, the larger extent of orbital delocalization of 4 and 5 can be understood geometrically, since they are the most planar i.e. the most conjugated ( Figure 2).

A-D-A small molecules: Lowest excitation energies and intramolecular charge transfer
The ability to effectively absorb sunlight is a critical parameter for BHJSCs performance. Since it is the main light absorber in BHJSCs, the overall aim of donor materials design is to increase and optimize their absorption coverage to maximize J SC . From this point of view, Figure 3 shows the absorption spectra of SMs 1-5 simulated at TDDFT/ WB97X(D)/6-31G(d) level of theory. Additionally, the dominant excited states vertical transition energies reported from the absorption maximum of SMs 1-5, their corresponding oscillator strengths, dominant excitation characters, and charge difference density (CDD) maps are shown in Table 2.
The results reveal that, for all molecules, the maximum absorption peaks with the largest oscillator strength originate from 0 1 S S → , which is principally attributed to the transition of electrons from HOMO to LUMO. It was found that, in low-energy region, the absorption spectra of the designed 2-5 are slightly red-shifted in comparison with 1. The redshift in optical absorption for the designed 2-5 is due mainly to the substitution of end-capped groups, in particular, the introduction of more nitrogen and oxygen functional groups in molecular chain. The maximum absorption wavelengths are in the order of 4>2>3>5>1. This trend is governed by the geometric and electronic properties of the designed molecules; indeed, it is well known that optical absorption is sensible to the conformational planarity and electronic conjugation [58,59]. Compared to 1-3, 4 has the most red-shifted absorption, which is related to the more coplanar nature of the molecular structure. However, despite it is more planar than 4, the maximum absorption of the fluorinated straight molecular chain (5) is slightly blue shifted in comparison with 2-4. The same effect has been reported by Martin et al. [53] for fluorinated thiophene-based polymers. High-energy absorption peaks of 1-5 appear at ~297, 303, 305, 308, and 304 nm, respectively, generated by the transitions of Intramolecular charge transfer (intra-CT) in 1-5 was visualized by CDD maps as shown in Table 2 to analyze the charge transfer properties in the major excited states 0 1 S S → . It is found that the maximum absorption bands in all systems are originated from an intra-CT between BDT unit of the core donor and the thiophene rings of the acceptor units. It can be seen that the contribution of BDT unit in electron transition increase in 4 and 5 since they are the most planar and then the most conjugated.
Therefore, the analysis of electronic and optical properties reveal that the designed SMs 2-5 possess broad and strong absorption, suitable FMO energy levels and high air-stability. The HOMO/LUMO overlap and the strong absorption of 2-5 are related to their geometries, since they are more planar and hence more conjugated than 1. This would be helpful for enhancing their performances as excellent donor materials for OPVs, since the introduction of planar molecule with more extended π-conjugation can maximize the charge carrier mobility [60,61].

OPVs performance prediction: Marks model
In the effort to direct scientists to design new materials and device structures, several empirical and theoretical models that describe limits to photovoltaic energy conversion in OSCs have been developed. Particularly, attention was paid to the absorption spectrum, the FMOs energy levels of donor and acceptor materials to estimate the opencircuit voltage V OC , and the driving force ( L L E − ∆ ) for efficient charge transfer.
Recently, in 2009, Marks et al. [62] advanced a practical efficiency limit of OPVs, where the J-V curve is assumed to be described by the classical diode model including series and parallel resistances. In their work, they treat the OPV efficiency as a function of LUMO offset ( L L E − ∆ ) by applying similar empirical estimate of the V OC as Scharber et al. [63]. Indeed, they suggest that the V OC is expressed in terms of the optical gap E g and the LUMO offset: where e is the elementary charge, and 0.3 V is an empirical value for efficient charge separation [63,64]. Based on this assumption about the V OC , a practical efficiency limit of ~14% is predicted for systems where the charge generation process occurs efficiently at  [62][63][64]. On the basis of these results, we deduce that the introduction of the endcapped group and nitrogen atoms allows for the tuning of FMOs of SMs 2-4 and make them more appropriate to serve as BHJSCs donors with PC 70 BM as an acceptor material. Nevertheless, the L L E − ∆ = 0.26 eV of SM 5 is lower than 0.30 eV, which denotes that the heterojunction based on 5/PC 70 BM has the poor capacity of electron transfer from donor material (5) to acceptor material (PC 70 BM). Therefore, molecule 5 will be not mentioned in the next section (Figure 4).
The predictions (using the calculated values of Table 1) using Marks model display that the predicted PCE (~9.3%), corresponding to L L E − ∆ = 0.65 eV, of 1 is in excellent agreement with the experimental value (9.2%, calculated with an experimental data FF=70.5% and V OC =0.97 V [14]). Interestingly, this result reveals that Marks model is a powerful tool to provide OPVs performance. Thus, we employed Marks model to predict the PCEs of three OPVs made by SMs 2, 3 and 4 with PC 70 BM. The predicted values are found to be ~12.5%, ~13.3%, and ~14.3%, respectively. From this prediction, we reached our purpose to provide substantiation for the rational design of three novel molecules that will be more promising candidates for high-efficiency SMs OPVs materials. Even though, to further justify the high performance of the designed SMs 2-4, we have investigated the charge transfer process from donor to acceptor materials in the systems 1/PC 70

Interfacial electron transfer: Marcus Theory
One of the major challenges in designing OPVs devices is achieving maximum charge transfer at the D/A interface, consequently increasing exciton dissociation and decreasing non radiative recombination [65,66]. Here we focus on the intermolecular charge transfer (inter-CT) excited states, because they are the excited states that present the ability of charge transfer from ground to excited states with the holes are localized on both donor and acceptor and the electrons are concentrated only on the acceptor.  Tables S4-S7. It is found that for each system, there is only one strong absorption peak in the low-energy region with the largest oscillator strength; S 3 for 1/PC 70 BM and S 2 for 2/PC 70 BM, 3/PC 70 BM and 4/PC 70 BM. Charge density difference (CDD) maps in Figure 5 reveal that these peaks correspond to local excited (LE) transitions where electron and holes are concentrated on 1-4 similar to S 1 excited states of 1-4 plotted in Table 2.
From analysis of the CDD maps of electronic transitions, we have selected the inter-CT excited states for systems 1/PC 70 Where V DA , is the electronic coupling (charge transfer integral) between D and A molecules, λ, is the reorganization energy, G ∆ is the free energy change during electron transfer reaction, h is the Planck's constant, k B , is the Boltzmann constant and T is the temperature, (defined as 300 K in our calculations).
The electronic coupling between the two states S 0 and S n can be computed using the generalized Mulliken-Hush (GMH) formalism [67,68]: The reorganization energy λ includes the internal reorganization energy (λ int ) and external reorganization energy (λ ext ) [69,70]. The λ int arises from the change in the molecular geometry of donor (D) and acceptor (A) due to the gain or loss of electronic charge throughout electron transfer process. The λ int can be estimated with [71]: where E(A -) and E(A) are the energies of the neutral acceptor at the anionic geometry and optimal ground state geometry, respectively. E(D) and E(D) are the energies of the cationic electron donor at the neutral geometry and optimal cation geometry, respectively. The λ ext designates the variation in the surrounding medium due to the electronic and nuclear polarizations effects [71][72][73]. However, it is confirmed that it is not easy to estimate quantitatively the λ ext in solid state. For the heterojunction P3HT/PC 61 BM, the reorganization energy λ ext is 0.11 eV [39], so we admit a value of 0.11 eV for the λ ext in our calculations.
where, 0 0− ∆E is the lowest excited state energy of the donor and E b is the exciton binding energy. However, E b is defined as the energy difference between the electronic band-gap and the first singlet excitation energy [67,68,71,[74][75][76]: Based on equation (7), CT G ∆ can be expressed as:  However, we can notice that the performance of SM 1 remains acceptable (9.2%) despite its low int er CT k − compared to those of SMs 3 and 4, implying that the device performance is not only driven by the interfacial charge transfer rate. Indeed, to optimize the BHJ device efficiency, it is important to find an efficient D/A combination in terms of electronic energy level, optical absorption, exciton lifetime, charge carrier mobility, solubility and thickness of the active layer [64,77]. All these factors impact OPV device efficiency. In that context, Cui et al. [14] have found that SM 1 is a very attractive donor candidate for the fabrication of BHJ device with high PCE of 9.2% because of its good solution processability, crystalline structure, low lying HOMO energy, broad absorption profile and higher hole mobility.

Conclusions
To summarize, we have carried out DFT and TDDFT calculations on the geometric, electronic and photophysical properties of new designed (A-D-A) small molecules based on the experimental system BDTT-S-TR (1). Our simulated results reveal that the designed SMs 2-5 possess quasi-planar geometries, well-matched energy levels and broad absorption in the UV-visible range. From these molecules, the designed molecules 2-4 display suitable ~10 4 times higher than that of 1/PC 70 BM, which favors effective exciton dissociation and then an improvement in J SC . These results suggest that the designed small molecules 3 and 4 will be attractive candidates for high-efficiency SMs OPVs materials. Finaly, it is hoped that this computational study may stimulate experimentalists to synthesize and study these new small molecules; structural parameters, optical and photovoltaic properties were computed, which will facilitate future experimental work.