Theoretical Studies of Photophysical Properties of D−π−A−π−D-Type Diketopyrrolopyrrole-Based Molecules for Organic Light-Emitting Diodes and Organic Solar Cells

A series of D–π–A diketopyrrolopyrrole(DPP)-based small molecules were designed for organic light-emitting diode(OLEDs) and organic solar cell(OSCs) applications. Applying the PBE0/6-31G(d,p) method, the ground state geometry and relevant electronic properties were investigated. The first excited singlet state geometry and the absorption and fluorescent spectra were simulated at the TD-PBE0/6-31G(d,p) level. The calculated results revealed that the photophysical properties were affected through the introduction of different end groups. Furthermore, the electronic transitions corresponding to absorption and emission exhibited an intramolecular charge transfer feature. Our results suggest that the designed molecules acted not only as luminescent for OLEDs, but also as donor materials in OSCs. Moreover, they can also be used as potential electron transfer materials for OLEDs and OSCs.


Introduction
Organic semiconductors have attracted considerable interest in recent years due to their advantages over their inorganic counterparts, such as low-cost, lightweight, and flexible electronic devices [1][2][3][4][5].
In particular, small-molecule-based organic semiconductors are expected to open new possibilities in terms of optoelectronic applications in organic electronic devices including organic light-emitting diodes (OLEDs), organic solar cells (OSCs), and field effect transistors (FETs). Small-molecule-based organic semiconductors exhibit strong absorption and emission, high fluorescence quantum yields, and good charge carrier mobility [6]. Nevertheless, the lower efficiency of OLEDs and OSCs has seriously restricted their commercialization. The development of new small molecular materials with highly desirable properties remains a major challenge. Therefore, it is critically important to design and synthesize efficient multifunctional materials. These materials can serve as efficient light emitters in OLEDs, donor material for OSCs, and, simultaneously, charge transport materials [7,8]. In order to achieve high performance and enhance the power conversion efficiency (PCE) of OSCs, the frontier molecular orbitals (FMOs) energy levels of donors should match the typical acceptors. A deep HOMO (highest occupied molecular orbital) energy provides a high open circuit voltage (V oc ). A relatively high LUMO (lowest unoccupied molecular orbital) energy ensures efficient charge separation. [9,10] Additionally, a lower HOMO-LUMO gap (E g )and strong absorption are required for effective harvesting of the solar photons. High charge-carrier mobility is also demanded for fast charge-carrier transport to maximize the short-circuit current (J sc ). Furthermore, another key

Frontier Molecular Orbitals
To gain insight into the influence of the FMO energies on the optical and electronic properties, we examined the HOMO and LUMO contour plots of the designed molecules, as shown in Figure 1. On the basis of Mulliken population analysis, we also investigated the distribution patterns of FMOs using percentage contributions from DPP, π-bridge(BB), and end group(EG) moieties by means of partial density of states (PDOS) (see Table 1). The E HOMO , E LUMO , and E g of 1-8 are plotted in Figure 2. Obviously, the FMOs exhibited π-orbital and strong delocalization features for 1-8, as shown in Figure 2. It was quite obvious that, comparing the contributions of DPP, BB, and EG fragments to the LUMOs with HOMOs, the DPP fragment contributions to LUMOs were smaller than those to HOMOs for 1-4 and 6-8, respectively. In contrast, the contribution of DPP fragment to LUMO was larger than that to HOMO for 5.For the contributions of BB fragments, the contributions to LUMOs were larger than those to HOMOs for 1-5, 7, and 8, respectively. The contribution to LUMO was smaller than that to HOMO for 6. For EG fragments, the contributions to LUMOs were larger those to HOMOs for 2, 3, and 6 respectively. However, the contributions to LUMOs were smaller than those to HOMOs for 1, 4, 5, 7, and 8, respectively.  Inspection of the results displayed in Table 1 revealed clearly that the excitation of the electron from the HOMOs to LUMOs led the electronic density to flow mainly from the DPP and AR fragments to CB fragments for 1, 4, 7 and 8.For 2, 3, and 6, the electronic densities mainly flowed from DPP fragments to AR and CB fragments. However, the electronic density mainly flowed from the AR fragments to DPP and CB fragment for 5. This suggests that the different AR groups had obvious effects on the distribution of FMOs for the designed compounds. The percentages of charge transfer from DPP and AR fragments to CB fragments were 9.3%, 11.2%, 7.8%, and 10.1%for 1, 4, 7, and 8, respectively. For 2, 3, and 6, the percentages of charge transfer from DPP fragments to AR and CB fragments were 41.4%, 15.3%, and 35.6%, respectively. The percentage of charge transfer from AR to DPP and BB fragment for 5 was 35.6%. Therefore, the order of the electron-donor ability of end groups for the studied compounds was benzo[c]thiophene (5) > thieno [3,2- (6). These results revealed that the DPP and AR fragments served as donors and CB fragments served as acceptors for 1, 4, 7, and 8. The DPP fragments served as donors and the AR and CB fragments served as acceptors for 2, 3, and 6. For 5, the DPP and CB fragments served as acceptors and AR fragment served as donors. Clearly, the vertical S 0 →S 1 transitions for the current system possessed an intramolecular charge transfer (ICT) nature. The end groups affected the distributions of FMOs for the D-π-A-π-D molecules. From the results displayed in Figure 2, it can be seen that the trends of E HOMO and E LUMO were 7 > 1 > 5 > 3 > 6 > 8 > 4 > 2 and 1 > 7 > 3 > 4 > 5 > 8 > 2 > 6, respectively. This suggests that molecules 2-6 and 8 were able to decrease the E HOMO and E LUMO compared with molecule 1. However, molecule 7 could increase/decrease the E HOMO /E LUMO compared with that of molecule 1. Furthermore, the predicted E g sequence was 4 > 1 > 3 > 7 > 8 > 2 > 5 > 6. Obviously, molecules 2, 3, and 5-8 could narrow, whereas molecule 4 could decrease the E g compared with that of molecule 1. Obviously, the introduction of benzo[c] [1,2,5] (7), and thieno[3,2-b]thiophene (8) end groups led to narrower E g values compared to molecules with a butoxybenzene (1)end group. However, the introduction of a naphthalene (4) end group decreased the E g compared with that of molecule 1. This implied that the introduction of different AR fragments (donor groups) to the DPP led to the change of the E HOMO , E LUMO , and E g values for its derivatives. These results indicated that these D-π-A molecules can lower the band gap and extend the absorption spectrum towards longer wavelengths. The absorption and fluorescence spectra can be tuned by donor groups. Consequently, the designed molecules except for 4 may possess longer absorption and fluorescence wavelengths compared with those of molecule 1. Therefore, it can be concluded that the E HOMO , E LUMO , and E g of the designed D-π-A-π-D molecules can be tuned via different end groups.

Match between Donor and Acceptor Material
It is worth noting that the match between donor and acceptor is crucial for OSC devices. Namely, donor materials should possess suitable FMO energy levels. Firstly, with the aim of efficient electron transfer, the E LUMO of the donor should be higher than that of the acceptor. Additionally, the ∆E L-L should be larger than the binding energy (0.2−1.0 eV) [40,41], and should reach at least 0.3 eV. Secondly, in order to improve the performance of OSCs, donor materials should exhibit higher J sc and V oc values and efficient charge transfer. Therefore, lower E g s are required for ensuring the successful harvesting of sunlight and to enhance the J sc . A large difference between the E HOMO of the donor and the E LUMO of the acceptor is favorable for enhancing the V oc and efficient exciton dissociation [42][43][44][45].
We took PC 61 BM, bisPC 61 BM, and PC 71 BM as acceptors for the current system (see Figure 2). We calculated the ∆E L-L of 1-8 (see Table 2). As visualized in Figure 2, the E LUMO s of 1-8 were positioned above those of PC 61 BM, bisPC 61 BM, and PC 71 BM, respectively. When PC 61 BM, bisPC 61 BM, and PC 71 BM were taken as acceptors, the predicted ∆E L-L of 1-8 was 0.428-0.968, 0.321-0.861, and 0.396-0.963 eV, respectively. Obviously, they are all exceeded 0.3 eV. As a consequence, the electron transfer to acceptors was efficient for these molecules. On the other hand, the E HOMO of the designed molecules was lower by 1.916, 2.023, and 1.9481 eV than the E LUMO of PC 61 BM, bisPC 61 BM, and PC 71 BM, respectively. With the above considerations, the designed molecules possess suitable FMO energies to match those of the three typical fullerene acceptors. Therefore, the FMOs of these molecules can be tuned via planar electron-rich aromatic end groups to match PC 61 BM, bisPC 61 BM, and PC 71 BM acceptors.

Absorption and Fluorescent Properties
Tables 3 and 4 collect the predicted properties of the absorption and fluorescence spectra of the designed molecules, respectively. The simulated absorption and fluorescence spectra of 1-8 are shown in Figures 3 and 4. For the absorption spectra, clearly, they were mainly derived from HOMO → LUMO transitions with 71% contributions for 1-8. The longest wavelengths of absorption (λ abs ) of molecules 2, 3, and 5-8 showed bathochromic shifts 43.4, 5.4, 52.1, 93.7, 29, and 36.1 nm, respectively, whereas molecule 4 exhibited a hypsochromic shift of 2.3 nm compared with molecule 1. At the same time, the λ abs was in the order of 6 > 5 > 2 > 8> 7 >3 > 1 > 4, which was in excellent agreement with the corresponding reverse order of E g values. Moreover, it was noted that molecules 6-8 had larger f value than that of 1, while the while the corresponding f values of 2-5 were slightly less than that of 1, respectively. Generally, a larger f value corresponds to a larger experimental absorption coefficient or stronger fluorescence intensity. This suggests that molecules 2, 3, and 5-8 were able to increase the λ abs values compared with molecule 1. On the other hand, molecule 4 did not significantly affect the λ abs compared with molecule 1. Therefore, the designed molecules can be used as donor materials for OSC applications.   The longest wavelengths of fluorescence (λ flu ) of 1-8 mainly originated from the LUMO → HOMO excitations, as shown in Table 4. Similar to those absorption spectra, the λ flu of molecules 2, 3, and 5-8 showed bathochromic shifts 62.3, 6.8, 119.9, 51.5, 22, and 37.9 nm compared with molecule 1, respectively. In contrast, molecule 4 exhibited a hypsochromic shift of 5.3 nm compared with that of 1. The λ flu values were in the sequence 5 > 2 > 6 > 8 > 7 > 3 > 1 > 4. Furthermore, the f values of 2-5 were slightly less than that of 1 and the corresponding values of molecules 6-8 were larger than that of molecules 1, respectively. Therefore, the designed molecules had high fluorescent intensity. As a consequence, they can be used as luminescent materials for OLEDs, particularly for 6-8. The results displayed in Tables 2 and 3 revealed that the absorption and fluorescence spectra of the designed molecules could be affected significantly by end groups. The designed molecules exhibited larger absorption coefficient and stronger fluorescence intensity. It suggests that these molecules could serve not only as luminescent for OLEDs, but also as donor materials in OSCs.

Reorganization Energies and Stabilities
The predicted λ e and λ h values of 1-8 are listed in Table 5. It was quite clear that the λ h values of 1-8 were larger than those of λ e , respectively. This suggested that rates of electron transfer may have been higher than rates of hole transfer for 1-8. Interestingly, molecule 1 possessed both the largest λ e and λ h values, indicating that the introduction of different end groups could lower the λ e and λ h for the designed molecules. Furthermore, molecules 5 and 6 exhibited the smallest λ h and λ e , respectively. From these results, it can be seen that the introduction of different end groups was favorable for hole and electron transfer. They may act as electron transport materials in OLEDs and OSCs. Usually, the stability of materials can be predicted by means of the η value. As shown in Table 5, the η value of molecule 4 was larger than the value of molecule 1. However, as expected, molecules 2, 3, and 5-8 possessed slightly smaller than that of molecule 1. Compared with molecule 1, the stabilities of 2, 3 and 5-8 decreased slightly because of their steric hindrances. This suggested that the end groups had a little effect on the stability of molecules.
Another way to evaluate the stability of material is to analyze their electrostatic surface potentials. Therefore, the electrostatic surface potentials of the designed molecules were calculated and are plotted in Figure 5. The high negative charges of 1-8 resided at the two oxygen atoms of DPP moieties, as visualized in Figure 5. The reason for this may be the presence lone pairs on oxygen atoms. In contrast, partial positive charges were found on the aromatic end groups. It was observed that molecules 1-8 had similar positive and negative potential distributions, implying that they possessed the same magnitude of photostability. Apparently, these results also revealed that the introduction of different end groups lightly affected on the stability of the molecules.

Computational Methods
All the calculations were carried out using the Gaussian 09 suite of programs [46]. The DFT was employed to perform the geometry optimization and frequency calculations of the molecules in ground states (S 0 ). The frequency analysis characterized that the optimized structures are true minima. The equilibrium geometries of the molecules in the first excited singlet state (S 1 ) were optimized by mean of TD-DFT method. On the basis of the optimized structures in S 0 and S 1 , the absorption and fluorescent spectra were simulated by TD-DFT method, respectively. With the aim of choosing a choose reasonable method, different functionals were taken to optimize the geometry of 1 in S 0 and S 1 . These functionals contained, for example, B3LYP [47], PBE0 [48], CAM-B3LYP [49], M062X [50], MPW1PW91 [51], and ωB97XD [52]. Under the optimized structures in S 0 and S 1 , the absorption and fluorescent spectra of molecule 1 were predicted using the TD-DFT method. The λ abs and λ flu values are plotted in Figure 6. The tested results revealed that the λ abs and λ flu (478.2 and 565.6 nm) using the PBE0 (583 nm) method were well able to reproduce the experimental results (494 and 562 nm) [39], and the deviations were 15.8 and 3.6 nm, respectively. The Stokes shift was 87.4 nm, which was comparable to the experimental 68 nm. As a consequence, the PBE0 method was the best choice with which to investigate our system. The PBE0 method was also used to optimize the acceptors PC 61 BM, bisPC 61 BM, and PC 71 BM. The 6-31G (d,p) basis set was used for all calculations. It is commonly known that reorganization energy (λ) is a key parameter for charge transfer rates [53,54]. Lower electron (λ e ) and hole (λ h ) reorganization energies are beneficial for the higher electron and hole transfer rates, respectively. In this work, we only considered the internal λ, ignoring any environmental relaxation and changes. The λ e and λ h values were predicted at the PBE0/6-31G (d,p) level on the basis of the single-point energy. The λ e and λ h values were evaluated via the following equations [55]: where E ± 0 is the energy of cation/anion structure based on the optimized neutral structure. Conversely, E 0 ± represents the energy of the neutral structure based on optimized cation/anion structure. Similarly, E ± ± is the energy of cation/anion structure based on the optimized cation/anion structure, while E 0 0 is the energy of the neutral molecule at ground state.
It was critically important to evaluate the stability of the material in OSC and OLED devices. The absolute hardness (η) of materials can be used as useful criterion with which to investigate the stability of the material. The η values can be predicted using the following equation [56,57]: where µ and N are the chemical potential and total electron number, respectively. AIP and AEA correspond to the adiabatic ionization potential and adiabatic electron affinity, respectively. The AIP is the energy difference between the cation radical and its neutral species, while the AEA represents the energy difference between the neutral and its anion radical molecules. The PBE0/6-31G (d,p) method was applied to calculate the AIP and AEA values of the molecules. The electrostatic surface potentials can also be used to estimate the stability properties of molecules [58][59][60]. Therefore, we calculated the electrostatic surface potentials of molecules at the PBE0/6-31G (d,p) level.

Conclusions
Several D-π-A-type DPP-based small molecules were designed for OLED and OSC applications. Their photophysical and charge transfer properties were investigated using DFT and TD-DFT computational approaches. The calculated results revealed that the photophysical properties were affected through the introduction of different end groups. Furthermore, the electronic transitions corresponding to absorption and emission exhibited an intramolecular charge transfer feature. Additionally, the designed molecules possessed suitable FMO energies to match those of three typical fullerene acceptors, PC 61 BM, bisPC 61 BM, and PC 71 BM. It was disclosed that the designed molecules acted not only as luminescent for OLEDs, but also as donor materials in OSCs. Moreover, they could also be used as potential electron transfer materials for OLEDs and OSCs.
Author Contributions: R.J. conceived and designed the calculations; X.Z. contributed to the performance and analysis of the frontier molecular orbitals and absorption and fluorescent spectra; W.X. performed the reorganization energies and transport properties; X.Z. helped with results interpretation. R.J. wrote the paper. All authors have read and agreed to the published version of the manuscript.
Funding: Financial supports from the NSFC (No. 21563002) are gratefully acknowledged.

Conflicts of Interest:
The authors declare that they have no conflict of interest.