Rational Design and Characterization of Symmetry-Breaking Organic Semiconductors in Polymer Solar Cells: A Theory Insight of the Asymmetric Advantage

Asymmetric molecule strategy is considered an effective method to achieve high power conversion efficiency (PCE) of polymer solar cells (PSCs). In this paper, nine oligomers are designed by combining three new electron-deficient units (unitA)—n1, n2, and n3—and three electron-donating units (unitD)—D, E, and F—with their π-conjugation area extended. The relationships between symmetric/asymmetric molecule structure and the performance of the oligomers are investigated using the density functional theory (DFT) and time-dependent density functional theory (TD–DFT) calculations. The results indicate that asymmetry molecule PEn2 has the minimum dihedral angle in the angle between two planes of unitD and unitA among all the molecules, which exhibited the advantages of asymmetric structures in molecular stacking. The relationship of the values of ionization potentials (IP) and electron affinities (EA) along with the unitD/unitA π-extend are revealed. The calculated reorganization energy results also demonstrate that the asymmetric molecules PDn2 and PEn2 could better charge the extraction of the PSCs than other molecules for their lower reorganization energy of 0.180 eV and 0.181 eV, respectively.


Introduction
Polymer solar cells (PSCs) have attracted wide attention for their low-cost, lightweight, flexible, and roll-to-roll fabricating characters [1][2][3][4][5][6][7], and could be one promising candidate for next generation renewable energy techniques [8,9]. Generally, a classical bulkheterojunction (BHJ) PSC device is based on the active layer blended with the electron donor and electron acceptor materials [10][11][12]. The power conversion efficiency (PCE) of the PSCs has been further improved by many new organic semiconductors that have been well-designed and synthesized during the past decades [13][14][15][16][17][18]. For electron donor materials, the representative donor-acceptor (D-A) polymers, such as PM6 [19], PBDT-C [15], and D18 [20], have shown excellent performance. To date, the PCE is over 18% [20]. The D-A structure played a key role to improve device properties since their suitable bandgaps and energy levels can be easily tuned [21][22][23]. In addition, a strong intramolecular charge transfer (ICT) can form between donor and acceptor units, which leads to the expansion of the absorption spectrum and an increase in the absorption coefficient [24]. To obtain more Materials 2021, 14, x FOR PEER REVIEW 3 of 14

Computational Methods
The molecular structure at the ground state and the molecular electrostatic potential (ESP) of all the monomers, as shown in Figure 1, were optimized in the gas phase under

Computational Methods
The molecular structure at the ground state and the molecular electrostatic potential (ESP) of all the monomers, as shown in Figure 1, were optimized in the gas phase under

Computational Methods
The molecular structure at the ground state and the molecular electrostatic potential (ESP) of all the monomers, as shown in Figure 1, were optimized in the gas phase under the B3LYP-(D3)BJ/6-311G(d) level [44][45][46]. The nine oligomers, as shown in Figure 2, were optimized in chloroform using the conductor-like polarizable continuum model (CPCM) [47], under the B3LYP-(D3)BJ/6-311G(d) level. The electronic absorption spectra and other excited-state properties of the oligomers were calculated using the time-dependent density functional theory (TD-DFT) under the CAM-B3LYP/6-311G(d) [42,48] level, employing chloroform (CPCM) as a solvent. All the alkyl side chains were replaced by methyl groups. All the calculations were performed by Gaussian 09 package [49]. Furthermore, the absorption spectra and electron transitions were analyzed by Multiwfn 3.7 [50,51].

Molecule Design
We generally design molecules with large conjugated polycyclic aromatic units for D-A alternative oligomers, which could effectively increase the coplanarity and π-electron delocalization, and could thus benefit for the light absorption and charge transportation [52]. As revealed in previous research [52,53], the unit A blocks based on benzothiadiazole demonstrated excellent performance in organic electronics. In this work, we designed three benzothiadiazole-based moieties with the expansion of the conjugation area n1, n2, and n3, as shown in Figure 1. In addition, the phenyl substituted the benzo(1,2-b:4,5-b')dithiophene (BDTP)-based two-dimensional (2D) electron-donating moieties have an advantage in the solubility, optical, and electrical properties [54]. Three electron-donating moieties based on BDTP (D, E, and F) were designed with gradual π-extend. n2 and E are asymmetric units. We further obtained PDn1, PDn2, PDn3, PEn1, PEn2, PEn3, PFn1, PFn2, and PFn3 by combining nine oligomers. As shown in Figure 2, the unit A conjugated area extended of the oligomers for each line from left to right, and the unit D conjugated area extended of the oligomers for each column from top to bottom. The nine molecules are evidently periodic variational in structure, and PDn2, PEn1, PEn2, PEn3, and PFn2 are asymmetric structures. In what follows, we will discuss the relationship between the structure and properties of these ideal molecules.

Geometric Optimization and Electronic Structure
The optimized geometry at the ground state of the unit D and unit A moieties exhibited good planarity, as shown in Supplementary Materials Figure S1. The calculated frontier molecular orbits (FMOs) of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) energy levels are shown in Supplementary Materials Figure S2. To deeply understand the charge distribution of the structures of the unit D and unit A moieties, the ESP was calculated and plotted, as shown in Figure 3. The blue and red color represent the high and low potential, respectively, which means the absence and abundance of electrons in this area, respectively. Intermediary transition colors depict the neutral electrostatic potentials. The results indicate that the conjugated thiophenes regions are highly electron-rich. Most of its positive regions are mainly localized at the hydrogen atoms in the non-conjugated methyl groups. The location of the electron-rich sulfur atoms is also evident, and they appear yellowish around these regions. For the moieties n1, n2, and n3, the N atoms connected directly to the S atoms, which attract considerable electron density. The electronegativity difference of atoms led to a redistribution of charge.  As shown in Figure 4, the ground state geometry of oligomers was optimized. The dihedral angles (θ) between the two moieties of PDn1, PDn2, and PDn3 are 7.66°, 9.15°, and 24.25°, respectively. The θ of PFn1, PFn2, PFn3 are 18.45°, 19.93°, and 20.21°, respectively. The θ increased with the π-extended among the PDn and PFn series oligomers; it is very likely that the expansion of the conjugate area leads to the enhanced rigidity. This phenomenon also appeared among PEn1 and PEn3, as 10.11° and 20.31° respectively. The size of the conjugation region also significantly affected the molecular planarity. However, the θ (PEn2) was only 6.50°; it was compounded by two asymmetric units (E and n2). The PEn2 with the minimum dihedral angles will be beneficial for intermolecular π-π stacking, which may produce good molecular stacking morphology among the BHJ PSCs [55].  As shown in Figure 4, the ground state geometry of oligomers was optimized. The dihedral angles (θ) between the two moieties of PDn1, PDn2, and PDn3 are 7.66 • , 9.15 • , and 24.25 • , respectively. The θ of PFn1, PFn2, PFn3 are 18.45 • , 19.93 • , and 20.21 • , respectively. The θ increased with the π-extended among the PDn and PFn series oligomers; it is very likely that the expansion of the conjugate area leads to the enhanced rigidity. This phenomenon also appeared among PEn1 and PEn3, as 10.11 • and 20.31 • respectively. The size of the conjugation region also significantly affected the molecular planarity. However, the θ (PEn2) was only 6.50 • ; it was compounded by two asymmetric units (E and n2). The PEn2 with the minimum dihedral angles will be beneficial for intermolecular π-π stacking, which may produce good molecular stacking morphology among the BHJ PSCs [55].  As shown in Figure 4, the ground state geometry of oligomers was optimized. The dihedral angles (θ) between the two moieties of PDn1, PDn2, and PDn3 are 7.66°, 9.15°, and 24.25°, respectively. The θ of PFn1, PFn2, PFn3 are 18.45°, 19.93°, and 20.21°, respectively. The θ increased with the π-extended among the PDn and PFn series oligomers; it is very likely that the expansion of the conjugate area leads to the enhanced rigidity. This phenomenon also appeared among PEn1 and PEn3, as 10.11° and 20.31° respectively. The size of the conjugation region also significantly affected the molecular planarity. However, the θ (PEn2) was only 6.50°; it was compounded by two asymmetric units (E and n2). The PEn2 with the minimum dihedral angles will be beneficial for intermolecular π-π stacking, which may produce good molecular stacking morphology among the BHJ PSCs [55].  The values of HOMO and LUMO energy levels, and the energy difference (∆H-L) between HOMO and LUMO values of the studied oligomers in solvent phases were also calculated and are presented in Table 1 and Figure 5. The HOMO increased, but LUMO declined with the moieties in the π-π conjugation region that extended gradually, which resulted in the decreased ∆H-L values. It means the π-extended strategy could effectively lower the LUMO and improve the HOMO simultaneously. The π-extended strategy could be applied to regulate the molecular energy level. Figure 5 distinctly shows the electron cloud density transition from HOMO to LUMO, which could be attributed to the ICT from donor unit to acceptor unit and the π-π* transition of the oligomers. It also indicates their good charge transfer capacity to a certain extent. The values of HOMO and LUMO energy levels, and the energy difference (ΔH-L) between HOMO and LUMO values of the studied oligomers in solvent phases were also calculated and are presented in Table 1 and Figure 5. The HOMO increased, but LUMO declined with the moieties in the π-π conjugation region that extended gradually, which resulted in the decreased ΔH-L values. It means the π-extended strategy could effectively lower the LUMO and improve the HOMO simultaneously. The π-extended strategy could be applied to regulate the molecular energy level. Figure 5 distinctly shows the electron cloud density transition from HOMO to LUMO, which could be attributed to the ICT from donor unit to acceptor unit and the π-π* transition of the oligomers. It also indicates their good charge transfer capacity to a certain extent.
The PCE of the PSCs can be calculated by Equation (1) [56]: where JSC, VOC, FF, and Pin are short-circuited current density, open-circuit voltage, fill factor, and incident light intensity, respectively. The illustration of the working mechanism of the D/A blend and the device structure are displayed in Figure 6. The voltage is proportional to PCE and a higher VOC would be of benefit to achieve a high PCE, which could be estimated by Equation (2) [56]: where D HOMO

E and
A LUMO E represent the energy level of HOMO (donor) and LUMO (acceptor), respectively. The value of 0.5 V is the non-fullerene PSCs empirical factor of efficient charge separation [57]. In this paper, a well-known NAFs ITIC was selected [57] and   The PCE of the PSCs can be calculated by Equation (1) [56]: where J SC , V OC , FF, and P in are short-circuited current density, open-circuit voltage, fill factor, and incident light intensity, respectively. The illustration of the working mechanism of the D/A blend and the device structure are displayed in Figure 6. The voltage is proportional to PCE and a higher V OC would be of benefit to achieve a high PCE, which could be estimated by Equation (2) [56]: where E D HOMO and E A LUMO represent the energy level of HOMO (donor) and LUMO (acceptor), respectively. The value of 0.5 V is the non-fullerene PSCs empirical factor of efficient charge separation [57]. In this paper, a well-known NAFs ITIC was selected [57] and calculated under the B3LYP-D3(BJ)/6-311G(d) level. The calculated energy levels of ITIC  Figure S3. The calculated V OC are summarized in Table 1.

Spectral Properties
For organic semiconductor materials in PSCs, the sunlight absorbance and absorption spectrum of molecules play a vital role in the photoelectric conversion process. To deeply investigate the optical properties of these molecules, the light absorption spectra were simulated, as shown in Figure 7. All the nine spectra also expend two main absorption areas located at ~300 nm (peak 1) and 400~460 nm (peak 2). As an instance of PDn1, PDn2, and PDn3, peak 2 redshifts move from 410.4 nm to 439 nm, but peak 1 shifts slightly. Compared with PDn1, PDn2, and PDn3, the peak 2 redshift is mainly attributed to the π-extended unitA. According to molecular orbital theory, the π-π conjugation extended region could increase the energy of π orbital, but lower the π* and lower the energy gap (Eg), which correspond well to where f is the oscillator strength of the donor molecule. The higher f of the transition suggests a larger absorption coefficient [59]. The results of the calculations indicate that, with the increase in the conjugation region, the LHE increased, and PFn3 has the maximum LHE 0.975. Other crucial spectroscopic parameters, such as the vertical excitation energies and compositions of vertical transitions in terms of molecular orbital, were carried out through TD-DFT calculations. The corresponding results were extracted and are summarized in Table 2.

Spectral Properties
For organic semiconductor materials in PSCs, the sunlight absorbance and absorption spectrum of molecules play a vital role in the photoelectric conversion process. To deeply investigate the optical properties of these molecules, the light absorption spectra were simulated, as shown in Figure 7. All the nine spectra also expend two main absorption areas located at~300 nm (peak 1) and 400~460 nm (peak 2). As an instance of PDn1, PDn2, and PDn3, peak 2 redshifts move from 410.4 nm to 439 nm, but peak 1 shifts slightly. Compared with PDn1, PDn2, and PDn3, the peak 2 redshift is mainly attributed to the π-extended unit A . According to molecular orbital theory, the π-π conjugation extended region could increase the energy of π orbital, but lower the π* and lower the energy gap (E g ), which correspond well to where f is the oscillator strength of the donor molecule. The higher f of the transition suggests a larger absorption coefficient [59]. The results of the calculations indicate that, with the increase in the conjugation region, the LHE increased, and PFn3 has the maximum LHE 0.975. Other crucial spectroscopic parameters, such as the vertical excitation energies and compositions of vertical transitions in terms of molecular orbital, were carried out through TD-DFT calculations. The corresponding results were extracted and are summarized in Table 2.
According to the PSCs photoelectric conversion mechanism, the excitons were generated by donor materials after absorbing light, then diffused to the D/A interface and, lastly, split into electrons and holes. Nevertheless, the excitons were bounded by the Coulomb attraction and would not directly split into free charges. Generally, the Coulomb attraction is defined as exciton binding energy (E b ). The E b could be estimated by Equation (4) [60]: (4) In addition, the amount of excitons that arrive at the D/A interface is determined by the exciton diffusion length (L D ). Generally, a long exciton lifetime τ (ns) corresponds to a long L D of the material in a solid film. In this paper, τ could be evaluated by the Einstein spontaneous emission relationship [61]: where in E if is the excitation energy in cm −1 . Based on Equation (5), a lower f and E if will lead to a larger τ. The calculated τ results are summarized in Table 2; PDn2 had the longest τ = 2.56 ns. This means that the excitons produced by PDn2 have a higher probability of arriving at the D/A interface under the circumstance of neglecting other factors, which would be of benefit to achieve a high PCE.  According to the PSCs photoelectric conversion mechanism, the excitons were generated by donor materials after absorbing light, then diffused to the D/A interface and,

Ionization Potential (IP) and Electron Affinity (EA)
The holes/electrons transport barriers of the active layer in the PSCs can be determined by the vertical ionization potentials (IP) and electron affinities (EA) of the molecule, which is an important reference for molecular design. Ordinarily, a small IP could lower the hole injection barrier, and a larger EA makes the electron injection easier [62]. The IP and EA of the molecules could be calculated by Equations (6) and (7): The calculated IP/EA valances result of the nine molecules indicated close relations with their unit D /unit A conjugate area sizes. For instance, the IP valances of PDn1, PEn1, and PFn1 are 5.56 eV, 5.42 eV, and 5.44 eV, respectively, while the EA valances are almost unchanged with the π-extended of the unit D . This indicates that the IP valances are in intimate connection with the unit D . PEn1 is an asymmetric molecule for their block with asymmetry unit D . Meanwhile, compared with PDn1, PDn2, and PDn3, the EA valances increased with the π-extended of the unit A . The results suggested the IP and EA values could be regulated by changing the magnitude of the conjugate region. It could be a useful way to design PSCs donor materials.

Reorganization Energy
The excitons generated by the donor materials diffused and arrived at D/A interface, which split into electrons and holes under the energy difference of the donor and acceptor. Then, the electron/hole was transmitted in the double continuous interpenetrating network active layer and collected by the corresponding electrode in the terminal. The charge transfer mechanism of the active layer is an incoherent hopping model, which could be described as electron/hole transport only between adjacent molecules. The charge transfer rate constants (k) can be calculated by Equation (8) [62], based on the semiclassical Marcus theory: The reorganization energy (λ) is closely connected with the mobilities of organic materials [63] so that the λ is significant to predict the charge extract property within PSC device. It is the sum of two energy terms, as shown in Figure 8, and λ 1 and λ 2 could be described as [62]: where E(M + ) and E(M) are the energy of neutral molecules at the cationic structure and neutral ground state, respectively. The E + (M) and E + (M + ) are the energy of the cation at the optimized structure of the neutral molecule and cation structure, respectively. The calculated λ results are summarized in Table 3; PFn1 has the maximum λ 0.531 eV, and PDn2 and PEn2 have the near minimum λ, 0.180 eV and 0.181 eV, respectively. According to Equation (8), the lower λ is, the higher k will be. It can be seen that, except PFn2, all the asymmetric molecules have a comparatively low λ [64][65][66][67]. This means that these asymmetric molecular skeletons in charge carrier transport have advantages in comparison with symmetry skeletons.
lated λ results are summarized in Table 3; PFn1 has the maximum λ 0.531 eV, and PDn2 and PEn2 have the near minimum λ, 0.180 eV and 0.181 eV, respectively. According to Equation (8), the lower λ is, the higher k will be. It can be seen that, except PFn2, all the asymmetric molecules have a comparatively low λ [64][65][66][67]. This means that these asymmetric molecular skeletons in charge carrier transport have advantages in comparison with symmetry skeletons.

Conclusions
In this work, three new electron-deficient units (n1, n2, and n3) and three electron-donating units (D, E, and F) were elaborately designed, and nine oligomers were obtained by combining different π-conjugation area unitA and unitD. The structure-performance rela-

Conclusions
In this work, three new electron-deficient units (n1, n2, and n3) and three electrondonating units (D, E, and F) were elaborately designed, and nine oligomers were obtained by combining different π-conjugation area unit A and unit D . The structure-performance relationships of the nine oligomers were systematically investigated by the quantum mechanical calculations. The nine symmetry or asymmetry molecule structures have been calculated at the B3LYP-D3(BJ)/6-311G(d) level and using chloroform as the solvent. The results of the DFT calculations indicate that asymmetry molecule PEn2 has the minimum dihedral angle among all the molecules, which points to the advantages in the molecular stacking of asymmetric structures. The energy level and E g also periodically changed along with the molecule structure periodic variation. The results of the TD-DFT calculations indicate that the spectral absorption region/peak could be regularly affected by changing the π-extended size. The size of the conjugate region of the unit D /unit A has close relation with IP/EA values. The calculated reorganization energy also demonstrated that asymmetric molecules PDn2 and PEn2 are more conducive to realize a higher PCE, because of their lower λ. The results certified that the asymmetric structure could be of benefit to the charge extraction within the PSCs device. There are still some limitations to accurately predict the real material properties in the application of the complex in real bulk-heterojunction solar cells, but our work has illustrated the advantages of asymmetric molecules, which also can be applied to molecule design.

Supplementary Materials:
The following are available online at https://www.mdpi.com/article/ 10.3390/ma14216723/s1: Figure S1: The side view of the optimized geometry of the monomers at ground state; Figure S2: The HOMO and LUMO orbital electron cloud distribution of the monomers; Figure S3: The optimized geometry at ground state and HOMO and LUMO orbital electron cloud distribution of the ITIC.