Studies of New 2,7‐Carbazole (CB) Based Donor‐Acceptor‐Donor (D‐A‐D) Monomers as Possible Electron Donors in Polymer Solar Cells by DFT and TD‐DFT Methods

Abstract The new donor‐acceptor‐donor (D‐A‐D) monomers have been studied using density functional theory (DFT) and time‐dependent density functional theory (TD‐DFT) methods to evaluate the optoelectronic and electronic properties for bulk heterojunction (BHJ) organic solar cells. The TD‐DFT method is combined with a hybrid exchange‐correlation functional using the B3LYP method in conjunction with a polarizable continuum model (PCM) and a 6–311G basis set to predict the excitation energies and absorption spectra of all monomers. The predicted bandgap (Eg) of the monomers decreasing in the following order D1<D2<D3<D4<D5<D6<D7<D9<D8. Furthermore, open‐circuit voltage (VOC) estimates for monomers with [6,6]‐phenyl‐C71‐butyric acid methyl ester (PC71BM) acceptor. The VOC of the studied monomers ranges from 0.976 to 1.398 eV in the gas and from 1.109 to 1.470 eV in the solvent phase with PC71BM acceptor, which is sufficient for efficient electron injection into the acceptor‘s LUMO. The results show that theoretically, a maximum energy conversion efficiency of roughly 5 % for D8 and 5.8 5 % for D7.


Introduction
All the world's energy demands can be provided by solar cells.
With new materials like semiconducting conjugated polymers in bulk heterojunction (BHJ) [1][2][3] solar systems, manufacturing costs could be drastically lowered. Organic solar cells (OSCs) based on bulk heterojunction (BHJ) technology combine donor polymers with acceptor fullerene derivatives. Despite their many advantages over silicon solar cells (cheap cost, lightweight, ease of manufacture, transparency & flexibility), these cells have received substantial attention from the physical, chemical, and scientific areas. [4,5] However, their broad bandgaps have hindered 3-hexylthiophene (P3HT) and poly[2-methoxy-5-(3',7'-dimethyloctyloxy)-p phenylenevinylene] (MDMOPPV's) capabilities (E g ). Thus recent investigations have looked into polymer architectures as a viable rival. [6,7] Internal molecular charge transfer (ICT) from an electron-rich unit to an electrondeficient moiety has been frequently employed for conjugated polymers for many years. [8][9][10] For the first time in history, new polymers can capture solar spectrum based on internal charge transfer (ICT). Low-performance solar cells have been made by Krebs [11,12] and Reynolds. [13,14] The power conversion efficiency (PCE) of polyfluorene derivatives ranges from 2.0 to 4.2 %. [15,16] However, the low carrier mobility of these polymers has an adverse effect on device performance. Furthermore, the PCE values of benzothiadiazole and cyclopentadithiophene copolymers were quite interesting. [17,18] As a result, it is possible to manufacture ICT polymers with low bandgap (E g ) and high carrier mobility. [19] Additionally, poly(2,7-carbazole) molecules can be used in BHJ solar cells. Poly(2,7-carbazole)s and poly(2,7-fluorene)s can be easily modulated in terms of their physical properties. [20,21] Carbazole units, which are electron-rich compounds, can be used to make ICT polymers. [22][23][24] It is also worth noting that poly(9-vinylcarbazole) (PVK) is one of the most extensively utilized photoconductive polymers nowadays. Polycarbazole materials with low solar cell efficiency were developed by K. Mullen in a preliminary study (0.6-0.8 %). [25] These polymers were poorly soluble and had little order. In recent studies, researchers have discovered a new polycarbazole derivative (PCDTBT), [26] containing a secondary alkyl chain on the carbazole unit's nitrogen atom that has a good PCE (3.6 %). It is possible to improve the electrical characteristics of polymeric materials.
The efficiency of BHJ solar cells can be estimated using various models. [27] When it comes to air stability, the first thing a polymer needs is a low HOMO energy level (approximately -5.27 % of SCE or 0.57 V). [28] It also assures that the completed gadget has a high open circuit potential (V OC ). A polymer's LUMO energy level must be at least 0.2-0.3 eV more elevated than the acceptor's - [6,6]-phenyl-C 61 -butyric acid methyl ester (PCBM). [29,30] LUMO energy level is necessary for efficient electron transfer between the polymer and acceptor. A donor LUMO energy level of approximately 3.75-4.0 eV is considered ideal. A bandgap of between 1.2 and 1.9 eV is desirable, taking into account the solar spectrum and the open circuit potential of the solar cell. As a result, À 5.2 to À 5.8 eV should be the ideal range for polymer HOMO energy. It must also reduce the LUMO energy level of PCDTBT (À 3.60 eV) while retaining the HOMO energy level to increase a polymeric cell's performance (i. e., À 5.45 eV).
We used these data and theoretical models for solar cell devices to explore alternating polymeric architectures to discover the optimum poly(2,7-carbazole) derivatives. [31,32] The HOMO and LUMO energy levels were calculated using quantum mechanics to evaluate their performance. Small organic molecule PCE improvements were made possible by the success of donor-acceptor copolymers, in which electron-rich and electron-deficient moieties were attached to one other. These structural frameworks have been constructed as well as oligomers and oligomer patterns. [33] It is possible to modify the characteristics of these polymers as organic semiconductors by changing the donor and acceptor units. D-A-D is a critical component for charge separation and molecular architecture governing charge transfer. Its bandgap (E g ) is lowered, its charge change is significant, and its visible light absorption is enhanced due to the high overlap of D and A molecular orbitals. Therefore, one of the criteria for developing a high photocurrent was synthesizing donor and acceptor materials with complementary absorption properties. The study's uniqueness is generated from these preliminary findings and theoretical models by using innovative donor-acceptordonor monomers as a 2,7-carbazole donor and benzothiazole derivatives as acceptors.

Computational Calculation Details
Carbazoles, 2,7-carbazoles, were employed in this work as donors (D) and acceptors (A1-A9) (Scheme 1). We have created small-molecule organic photovoltaic (OPV) donors of the D-A-D type. There are many D and A unit combinations that it would be impossible to develop small molecule OPV donors without first running them via pre-synthesis simulated screenings. We have clearly defined molecular orbital (MO) energy levels, bandgap (E g ), UV/Vis absorption spectra, and PCEs of different D-A-D polymer donors using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations at the B3LYP/6-311G level. [34][35][36][37][38] The 6-311G basis set was used for all computations. The Gaussian 09 package [39] was used to calculate the density (DFT) and time-dependent (TD-DFT) functional [40] in gas and chlorobenzene solvents. TD-DFT/B3LYP Scheme 1. Donor-Acceptor-Donor (D-A-D) monomers in the present study. method was employed to predict the vertical excitation energy and electronic absorption spectra of studied monomers. This approach, which has been around for more than two decades, is one of the most effective ways to deal with bulk solvent effects in ground and excited states. This work used the Polarizable Continuum Model (PCM) [41] model to compute the excitation energy. Using TD-DFT computations for DFT optimized geometries, oscillator strengths and excited-state energy were studied. The total density states (TDOS) were visualized using the GaussSum program. [42] Results and Discussion

Electronic Properties
DFT/B3LYP and a 6-311G basis set have been used to optimize all of the studied donors (D-A-D) monomers, and the optimized geometries are shown in Figure 1. It's vital to note that theoretical components are essential in investigating organic solar cells, which we use as an example of their electrical applications. To determine whether or not photovoltaic devices work, the HOMO and LUMO energy levels of the donor and acceptor components must be considered. As illustrated in the experiment, an empirical formula may be used to determine HOMO and LUMO energies by changing voltage as they occur in an electrochemical cycle. For the HOMO and LUMOS, however, DFT is theoretically possible. Furthermore, when calculating HOMO and LUMO energy levels in a thin film, DFT does not consider the effects of solid-state packing, which can impact the energy levels of molecules. Therefore, it is possible to gather information about similar oligomers or polymers by comparing the anticipated energy levels, even if they are inaccurate.
For frontier molecular orbitals (FMO), orbitals for the nine monomers are shown in the solvent phases in Figure 2. The FMO distribution of all nine monomers is nearly identical. While all HOMOs exhibit typical aromatic features with electron delocalization over the entire conjugated molecule, they are concentrated at the donor parts and conjugated spacers, whereas LUMOs focus on the acceptor moieties (A). Anti-bonding properties exist in the HOMO between successive subunits. While all oligomers have a bonding character between the two adjacent pieces, the LUMO of all oligomers corresponds to the π* electronic transition in the lowestlying singlet states. Photo excited electrons can be more  easily injected into a semiconductor's LUMO if transferred from a donor moiety into an acceptor moiety during excitation (PC71BM). All compounds contribute significantly to LUMOs, resulting in solid electronic coupling with PC71BM surface upon photo excitation electrons, thus improving electron injection efficiency and, as a result, increasing the short-circuit current density (J sc ) by increasing the shortcircuit current density.
For nine monomers (D1-D9), B3LYP/6-31G predicted the HOMO, LUMO, and band gaps using the B3LYP/6-311G level in Table 1. For D1, these are the HOMO/LUMO energies: À 5.3726/À 2.4354 eV; for D2, these are À 5.3527/À 2.7491 eV; for D3, these are À 5.2765/À 2.6762 eV; and for D4, these are À 5.5570/À 3.1491 eV. For D9, the energy gap is À 5.4996/ À 3.4038 eV, with equivalent energy gaps of 2.9372 eV for D1, 2.6036 eV for D2, 2.6003 eV for D3, 2.4079 eV for D4, 2.2980 eV for D5, 2.2934 eV for D6, 2.2096 eV for D7, and 2.096 eV for D8. Table 1 shows the HOMO-LUMO energy gaps (E g ) for studied D-A-D monomers. Every donor has a lower bandgap (E g ) value except for the D8 and D9 monomers. In both gas and solvent phases, the predicted bandgap (E g ) of the monomers decreasing in the following order D1 < D2 < D3 < D4 < D5 < D6 < D7 < D9 < D8. Intramolecular charge transfer strongly influences the absorption spectra of D8 and D9, which is linked to the impact of the electron-donor unit, which is particularly potent in these two monomers. This means that the acceptor unit's inductive effects considerably impact the band gaps of the molecules formed. Figure 3 shows the FMO energy levels and energy gaps of the all monomers model. HOMO energy levels of the D1-D9 monomers in the gas and solvent phases are shown in Table 1, indicating that these systems may be stable in the air with BHJSC and PC71BM.
In addition, their results showed that sulfur, nitrogen, and oxygen groups could help close energy gaps. SCP acceptor unit's more substantial electron-donor capabilities should be

Photovoltaic Properties
There are several essential parameters, including the shortcircuit current density (J SC ), the open-circuit voltage (V OC ), the fill factor (FF), and the incident photon-to-current efficiency that can be used to compare and quantify solar cell performance (P inc ). Therefore, Equation (1) was used to calculate the power conversion efficiency (PCE).
A device's form and charge carriers' lifetime and mobility affect the flow of this fluid when no voltage is provided. [43] Assuming the photo charge loss is taken into account, one may calculate the maximal open-circuit voltage (V OC ) by subtracting the donor's HOMO (conjugated molecule) from the acceptor's LUMO (conjugated molecule). The V OC was found to have a low dependence on the electrodes' work functions.
Therefore, the open-circuit voltage Voc of the BHJ solar cell was calculated using the following formula: [44,45] (2) This equation has two components: the elementary charge and the empirical component. For the PC71BM, Scharber et al. [45] used Equation (2), using the PC71BM LUMO energy of 4.3 eV. Another reason for high solar cell efficiency is due to the low LUMO of conjugated molecules and high LUMO of the electron acceptor (PC71BM), which raises the value of V OC . [46,47] To provide efficient electron injection into the acceptor's LUMO, the predicted open-circuit voltage V OC of the examined molecules ranges from 0.976 eV in the gas and from 1.109 to 1.470 eV for PC71BM. While this discrepancy is more than 0 eV, Table 2 demonstrates that the differences in LUMO energy levels between the newly produced donors (D1-D9) and the acceptor of PC71BM are more significant than this value   (Figure 4). D8 and D7 polymer solar cells (PSCs) theoretically have a maximum energy conversion efficiency of about 5 % and 5.8 %, respectively. [48,49] Optical Properties The TD-DFT/B3LYP/ 6-31G level was used to calculate electronic properties and absorption spectra in the gas and chlorobenzene solvent phases. The calculated absorption wavelengths (λ max ), oscillator strengths (ƒ) and vertical excitation energies (E) for gaseous phase and solvent (chloroform) were carried out and listed in Tables In gas-phase and chloroform solution, the  transition from HOMO to LUMO is the most likely transition from the ground state to an excited state, and this electronic absorption corresponds to the transition from the molecular orbital HOMO to the LUMO excited state and is a π* transition. Figures 5 and 6 show that all molecules in the visible region (abs > 700 nm) have only one band ( Figure 5&6), suggesting that the solar cells linked with D7 and D8 may be able to harvest more light at longer wavelengths, benefiting the photo- Table 4. Computed maximum absorption wavelength (λ max ), excitation energies (Ex), oscillator strengths (f os ), major molecular orbital assignments and configuration interaction (C.I) of designed D-A-D monomers in chlorobenzene solvent at the TD-DFT/B3LYP/6-311 G level of theory.  to-electric conversion efficiency. As a result, the acceptors can fine-tune the transition at the lowest point.

Quantum Chemical Parameters
Calculating chemical potential, electronegativity, and chemical hardness can be done using HOMO and LUMO energy values for monomers[Eq. (3)(4)(5)]: [50] Chemical potential Chemical hardness (4) Electronegativity (5) Electronic charge asymmetry is common in molecules that have a significant dipole moment. Due to the effect of an external electric field, they may be more sensitive to changes in their electronic structure and features. D8 and D9 monomers have a much higher dipole moment than the other monomers in Table 5, for example. In another way, we may say that some monomers are more reactive than others. Indeed, these monomers are more likely to liberate electrons from PCBM than other monomers.
In contrast to the nine monomers (D1, D2, D3, D4, D5, D6, D7, and D9), PCBM has the lowest chemical potential (= 4.9) (see Table 5). This indicates that electrons are more likely to escape from compound Pi, which has a high chemical potential than PC71BM, a slight chemical possibility. Consequently, PC71BM is an electron acceptor, whereas the other monomers studied are electron donors. Furthermore, according to electronegativity, PC71BM has a higher value than any other monomer (D1 through 9) in terms of electronegativity ( Table 5). As a result, electrons from other compounds can be attracted to the  PC71BM molecule. We also see that the PCBM compound has a high chemical hardness (η) value compared to other monomer donors; this shows that the PC71BM is challenging to release electrons from, whereas the other compounds are good candidates for providing electrons for the PC71BM (see Table 5).

Density of States (DOS)
A great way to demonstrate the importance of molecular orbitals in chemical bonding is to use DOS charts. The DOS plot data may be an overlapping population of molecular orbitals. DOS also shows the orbital group composition part of the molecular orbital. DOS graphs in gas and solvent phases are depicted in Figures 7 and 8. In the energy range from 7.0 to 13 eV, the probability of localized states forming increases dramatically. The graph shows the orbital properties of various energy levels. Orbital of carbon and 'essential orbital functions' in the frontier molecular orbital contribute fundamentally. It is possible to employ organic solar cells based on V OC values because electron injection into the acceptor's conduction band and subsequent regeneration are allowed in photovoltaic cells.

Conclusions
Density functional theory was used to study the properties of 2,7-carbazole donors and benzothiazole-based acceptors. Electrical and optical properties can be dramatically altered and improved by changing the chemical structure of pure materials. The following are some final thoughts: Band gaps in the solvent phase are expected to be in the range of 2.151-2.919 eV, according to DFT-B3LYP/6-31G calculations. The minuscule bandgap is due to increased electron displacement between the donor and acceptor spacers. Intramolecular charge transfer is significantly impacted by the lower E g of D7 and D8 monomers than other monomers. For PC71BM, the open-circuit voltage V OC ranges from 1.109 to 1.470 eV, suitable for efficient electron injection. All of the molecules studied can be used as BHJs since electron injection into the conduction band of PC71BM, and subsequent regeneration is possible in an organic sensitive solar cell. D7 can achieve a maximum power conversion efficiency of 5 %, and D8 can reach a maximum power conversion efficiency of 3 %. At least TD/B3LYP/6-31G TD-DFT calculations were used to predict the optical transitions; the starting vertical excitation energies (E) were varied in decreasing order for the gas phase: There is a redshift in the When it comes to solar cell photoelectric conversion efficiency, D7 and D8 may capture more light at longer wavelengths. As a result, the acceptors can fine-tune the transition at the lowest point.