Design of Acceptors with Suitable Frontier Molecular Orbitals to Match Donors via Substitutions on Perylene Diimide for Organic Solar Cells

A series of perylene diimide (PDI) derivatives have been investigated at the CAM-B3LYP/6-31G(d) and the TD-B3LYP/6-31+G(d,p) levels to design solar cell acceptors with high performance in areas such as suitable frontier molecular orbital (FMO) energies to match oligo(thienylenevinylene) derivatives and improved charge transfer properties. The calculated results reveal that the substituents slightly affect the distribution patterns of FMOs for PDI-BI. The electron withdrawing group substituents decrease the FMO energies of PDI-BI, and the electron donating group substituents slightly affect the FMO energies of PDI-BI. The di-electron withdrawing group substituents can tune the FMOs of PDI-BI to be more suitable for the oligo(thienylenevinylene) derivatives. The electron withdrawing group substituents result in red shifts of absorption spectra and electron donating group substituents result in blue shifts for PDI-BI. The –CN substituent can improve the electron transport properties of PDI-BI. The –CH3 group in different positions slightly affects the electron transport properties of PDI-BI.


Introduction
Organic solar cells (OSCs) with high power conversion efficiencies (PCEs) exceeding 10% have been fabricated [1]. Among them, organic small molecules as solar cell materials based on π-conjugate polymers are attractive because of their rapid energy payback time [2], low cost, flexibility, light weight, solution-based processing, and the capability to fabricate flexible large-area devices [3]. The PCEs of the OSCs have exceeded 11% when the conventional fullerene as the acceptors [4,5]. However, the fullerene and its derivative acceptors have several limitations, such as costly production, fixed band alignment, and limited optical absorption, which significantly prevent the development of new donor materials. Thus, developing and investigating novel acceptors has become a focus around the world. Up to now, many small molecule acceptors have been reported, such as 9,9 1 -bifluorenylidene [6,7], dicyan substituted quinacridone [8], diketopyrrolopyrrole derivatives [9,10], vinazene [11,12], fluoranthene-fused imide [13,14], naphthalene diimides [15,16], electron-deficient pentacenes [17], and perylene diimides (PDIs) [18][19][20][21]. Among the small molecule acceptors, PDI and its derivatives have attracted much attention in the past decade due to their superior optical Table 1. Chemical structure of PDI-BI derivatives (Rn are -H except for mentioned in the Table). superior optical and electric properties-for example, excellent chemical, photochemical, and thermal stabilities [22], high absorption (450 and 650 nm) [23], promising electron mobility [24][25][26], and excellent electron affinity [27]. Yao et al. obtained solar cells with 4.34% efficiency on the basis of PDI [21]. Nguyen et al. prepared the PDI bulk heterojunction solar cell [1]. Shin et al. obtained OSCs with a power conversion efficiency of 0.18% under AM 1.5 using PDI derivatives as acceptors [28]. Zhang et al. [29,30] and Tang et al. [31] deigned a series of PDI derivatives and calculated their properties. Won Suk Shin et al. prepared some PDI derivatives, and molecule PDI-BI had suitable properties as a solar cell acceptor [28]. In this manuscript, in order to improve the performance of PDI-BI, we have designed various PDI-BI derivatives (Table 1), which have different functional groups, to find the most promising acceptors with suitable frontier molecular orbital energies (FMOs) to match the OSC donor oligo(thienylenevinylene) derivatives (X1 and X2, Figure 1) with favourable properties designated by Yong et al. [32]. Generally, the higher the lowest unoccupied molecular orbital (LUMO) of the acceptor, the larger the open circuit voltage (Voc), because the difference in energy between the highest occupied molecular orbital (HOMO) energy of the donor and LUMO of the acceptor is in direct proportion to the Voc. In addition, to ensure separation of charge, the differences between the LUMO energies of the donor and the acceptor should be greater than 0.30 eV [33]. Considering the fact that the substituent groups affect the molecular properties significantly, we designed two kinds of molecules (PDI-BI-1-26) to study the push (-CH3) and pull (-CN and -NO2) substituent groups effects. The density function theory (DFT) [34] has been used for evaluating a variety of ground state properties of these molecules, such as FMO, including HOMO and LUMO energies, and the HOMO-LUMO gaps (Eg). The optical properties (absorption spectra) of the designed molecules have been predicted by the time dependent DFT [35][36][37] approach (TD-DFT). The reorganization energy (λ) was also calculated. Additionally, we discussed the correlation between structures and properties of these molecules.

Frontier Molecular Orbitals
The electronic and optical properties of molecules are related to the values of FMOs and Eg. Thus, in order to gain insight into the influence of the optical and electronic properties, the distribution patterns of the FMOs for the designed molecules are studied, and the electronic density contours of the designed molecules in ground states are shown in Figure 2. The evaluations of HOMO and LUMO energies (EHOMO and ELOMO) for designed molecules are plotted in Figure 3 and listed in Table 2.

Frontier Molecular Orbitals
The electronic and optical properties of molecules are related to the values of FMOs and E g . Thus, in order to gain insight into the influence of the optical and electronic properties, the distribution patterns of the FMOs for the designed molecules are studied, and the electronic density contours of the designed molecules in ground states are shown in Figure 2. The evaluations of HOMO and LUMO energies (E HOMO and E LOMO ) for designed molecules are plotted in Figure 3 and listed in Table 2.

Frontier Molecular Orbitals
The electronic and optical properties of molecules are related to the values of FMOs and Eg. Thus, in order to gain insight into the influence of the optical and electronic properties, the distribution patterns of the FMOs for the designed molecules are studied, and the electronic density contours of the designed molecules in ground states are shown in Figure 2. The evaluations of HOMO and LUMO energies (EHOMO and ELOMO) for designed molecules are plotted in Figure 3 and listed in Table 2.     The black is PDI-BI, the blue means mono-pull substituent, the purple represents di-pull substituent, and the olive is mono-push substituent.     The black is PDI-BI, the blue means mono-pull substituent, the purple represents di-pull substituent, and the olive is mono-push substituent.  From Figure 2, one can see that the FMOs are spread over the entire molecule for the designed molecules. This indicates that there is great spatial overlap between the HOMO and LUMO, and the transition from HOMO to LUMO may lead to strong optical adsorption. As shown in Figure 3 and Table 2 Figure 4. The molecules PDI-BI-1, PDI-BI-13, and PDI-BI-19 are the representatives of the different kinds of substituent molecules, respectively. As shown in Figure 4, one can see that the LUMO energies of PDI-BI-13 are lower (0.32 and 0.30 eV) than those of X1 and X2, which indicates that PDI-BI-13 is suitable for the FMOs of X1 and X2, respectively. That is to say, molecules PDI-BI-14, PDI-BI-15, PDI-BI-16, and PDI-BI-17 are also suitable for the FMOs of X1 and X2, respectively. This reveals that the di-CN, di-NO 2 , or -CN and -NO 2 groups substituents can decrease the FMOs of PDI-BI. Thus, proper substitutions can tune the FMOs of PDI-BI to be more suitable to X1 and X2. Moreover, we calculated the triplet energies of X1, X2, and PDI-BI-13. The calculated results show that the triplet energies are higher than the corresponding singlet energies for X1, X2, and PDI-BI-13, respectively. This indicates that there may be no triplet loss when X1, X2, and PDI-BI-13 are used as the candidates for OSCs devices [38][39][40]. and PDI-BI-13, respectively. This indicates that there may be no triplet loss when X1, X2, and PDI-BI-13 are used as the candidates for OSCs devices [38][39][40].

Absorption Spectra
The longest and the shortest wavelengths of the absorption spectra (λmax and λmin) and adsorption region (R) of the designed molecules are listed in Table 2. The simulated adsorption spectra, plotted using GaussSum 1.0 [41], are shown in Figure 5. The first 20 excited states were considered.

Absorption Spectra
The longest and the shortest wavelengths of the absorption spectra (λ max and λ min ) and adsorption region (R) of the designed molecules are listed in Table 2. The simulated adsorption spectra, plotted using GaussSum 1.0 [41], are shown in Figure 5. The first 20 excited states were considered. and PDI-BI-13, respectively. This indicates that there may be no triplet loss when X1, X2, and PDI-BI-13 are used as the candidates for OSCs devices [38][39][40].

Absorption Spectra
The longest and the shortest wavelengths of the absorption spectra (λmax and λmin) and adsorption region (R) of the designed molecules are listed in Table 2. The simulated adsorption spectra, plotted using GaussSum 1.0 [41], are shown in Figure 5. The first 20 excited states were considered.   The calculated absorption spectra of PDI-BI and its derivatives (value of full width at half maximum is 3000 cm −1 ). Figure 5. The calculated absorption spectra of PDI-BI and its derivatives (value of full width at half maximum is 3000 cm´1). Table 2 and Figure 5, the -CN group in different positions could increase the λ abs-max and λ abs-min values of PDI-BI, respectively, except the -CN group in 4-position could decrease the λ abs-max value of PDI-BI slightly. The -CN group in the 5, 6, 7, or 8-position can increase the R values of PDI-BI, and the R value increase is larger than the other positions when the -CN group in the 6-position. For -NO 2 substituent molecules, the λ abs-max values are, in increasing order, PDI-BI-11 < PDI-BI-12 < PDI-BI < PDI-BI-9 < PDI-BI-10, the λ abs-min values are, in decreasing order, PDI-BI-10 > PDI-BI-11 « PDI-BI-12 > PDI-BI-9 > PDI-BI, and the R values are in the order PDI-BI-11 < PDI-BI-12 < PDI-BI-9 < PDI-BI-10 < PDI-BI. This shows that the -NO 2 group in 2-position could produce a larger increase of λ abs-max and λ abs-min values than the other positions for PDI-BI, and the -NO 2 group in 3-position could produce a larger decrease of the R value than the other positions for PDI-BI. For di-substituent molecules, the substituent groups could increase the λ abs-max and λ abs-min values of PDI-BI, respectively, except the di-NO 2 groups in 3 and 6-position decrease the λ abs-max value of PDI-BI, obviously. The di-substituents could decrease the R values of PDI-BI, respectively, except the di-CN groups in 3 and 6-position increase the R value of PDI-BI significantly. The -CH 3 groups in different positions affect the λ abs-max , λ abs-min , and R values of PDI-BI slightly. These results reveal that the mono-pull group can increase the λ abs-max , λ abs-min , and R values of PDI-BI, and the push group affects the λ abs-max , λ abs-min , and R values of PDI-BI slightly. Among these molecules, PDI-BI-14 has the largest λ abs-max value and PDI-BI-6 has the largest R value, which indicates that it could be a good candidate for the solar cell acceptor.

Reorganization Energy
The charge transport property of material is important to design the acceptor for a solar cell device, and the reorganization energy plays a role in charge transport and charge separation. It is well-known that the lower the λ values, the better the charge transport property. Thus, we calculated the λ e and λ h values of PDI-BI and its derivatives. The calculated results are listed in Table 3. As shown in Table 3 [42], indicating that their electron transfer rates are higher than that of Alq3. The λ h values of molecules PDI-BI-1-26 are smaller than that of N,N 1 -diphenyl-N,N 1 -bis(3-methlphenyl)-(1,10-biphenyl)-4,40-diamine (TPD) (λ h = 0.290 eV), which is a typical hole transport material [43]. This implies that their hole transfer rates are higher than that of TPD. Among these molecules, PDI-BI-13 has the best electron transport property, and PDI-BI-21 has the best hole transport property.

Computational Methods
All the calculations were performed with the Gaussian 09 software [44]. Our previous work [31] suggested that the DFT method CAM-B3LYP with the 6-31G(d,p) basis set was reliable for optimization of PDI and its derivatives, and the TD-B3LYP/6-31+G(d,p) was reasonable for optical property simulation. Hence, the CAM-B3LYP/6-31G(d,p) method was employed to optimize all the geometry including neutral, cation, and anion PDI-BI-1-26 molecules. The absorption spectra of PDI-BI-1-26 molecules were predicted by the B3LYP/6-31+G(d,p) method. The PBE1PBE/6-31G(d) method was used to optimize the geometry of molecules X1 and X2 [32], and the HOMO and LUMO energies of molecules X1 and X2 were calculated at the CAM-B3LYP/6-31G(d,p) level on the basis of the single point energy. The B3LYP/6-31G(d,p) functional was successful in calculating the charge transport parameters [45]. Thus, we calculated the single point energy at the B3LYP/6-31G(d,p) level. The necessary parameters, such as single point energies of neutral, cation, and anion molecules in the ground state (S0), were recomputed for calculating the electronic properties of the molecules. The reorganization energy (λ) was predicted on the basis of the single point energy at the B3LYP/6-31G(d,p) level optimised neutral, cationic, and anionic geometries. Herein, the environmental relaxation and changes were ignored, and the reorganization energy of the isolated active organic π conjugated systems was the internal reorganization energy. As a result, Equations (1) and (2)

Conclusions
In the present work, we report a theoretical investigation predicting the substitution effects on optical and electronic properties for PDI-BI. The calculated results show that the substituents slightly affect the distribution patterns of FMOs for PDI-BI. The -CN and -NO 2 groups in different substituent positions can decrease the E HOMO , E LOMO , and E g of PDI-BI. The -CH 3 group in different substituent positions affects the E HOMO , E LOMO , and E g of PDI-BI slightly. The -CN group in different positions could increase the λ abs-max and λ abs-min values of PDI-BI, respectively, and the -CN group in the 5, 6, 7, or 8-position can increase the R values of PDI-BI. The -NO 2 group in 2-position could produce a larger increase in λ abs-max and λ abs-min values, and the -NO 2 group in 3-position could produce a larger decrease of the R value of PDI-BI. The -CH 3 groups in different positions slightly affect the λ abs-max , λ abs-min , and R values of PDI-BI. Among these molecules, PDI-BI-14 has the largest λ abs-max value and PDI-BI-6 has the largest R value. The -CN group in different positions can decrease the λ e values and increase the λ h values of PDI-BI. In the -NO 2 substituent molecules, the substituent groups can increase the λ e and λ h values of PDI-BI. The -CH 3 group in different positions slightly affects the λ e values, and decreases the λ h values of PDI-BI. PDI-BI-13 and PDI-BI-21 have the best electron and hole transport properties, respectively. On the basis of these results, we suggest that PDI-BI-13, PDI-BI-14, PDI-BI-15, PDI-BI-16, and PDI-BI-17 are suitable acceptors for X1 and X2. This study should be helpful in further theoretical investigations on such systems and also in the experimental study of solar cell acceptor materials.