Introduction

Chalcogen-containing heterocycles are considered as potential candidates for enhancing the photovoltaic properties of organic solar cells. Highly efficient devices with high power conversion efficiency expressed strong backbone having non-covalent bonding which leads to a long and strong charge transfer route in these photovoltaic devices.

Nowadays, the field of organic solar cells (OSCs) has recognized a rapid considerable thanks to their higher PCEs. In organic solar cells, the large charge transfer behavior and incorporation of some inorganic counterparts significantly enhance the PCE [1,2,3]. Non-fullerene acceptor molecules are considered pivotal candidates for organic solar cells (OSCs) and tremendous research has been carried out on the development of non-fullerene acceptor molecules for OSC applications [4,5,6]. Non-fullerene acceptor molecules disclosed several advantages such as rapid chemical modifications, easy synthesis, low toxicity rate, high tunability, and low-cost development [7,8,9,10].

In recent years, the advancement in NFAs materials has gained significant attention. Recently, a very famous molecule Y6 had been synthesized and has shown high power conversion efficiency with different donor polymers [11]. Y6 has A′-DAD-A′ configuration, A′ were the end-capped acceptor molecules, and the core was a fused ring of benzothiadiazole molecule. The donor bridge was thienophene [3,2-b] thiophene group that was flanked with acceptor moieties [11, 12]. This combination provided the perfect backbone for important charge transfer within the whole molecule.

Recently, Chai and his co-workers have taken Y6 molecule and modified the donor groups with different chalcogen-containing heterocycles [13]. They used different units such as thienophene [3,2-b] furan ring, thienophene [3,2-b] thiophene, and thienophene [3,2-b] selenophene as donor units. Selenopheno [3,2-b] thiophene in these molecules act as donor unit and disclosed low bandgap, high red-shifting in absorption spectrum along with best PCE. It is believed that end-capped acceptor modifications have been proved as a unique and perfect strategy for enhancing the PCE of non-fullerene OSCs. In the past, different reports on end-capped engineering suggested that this strategy not only enhanced the PCE but also optimized the structures with a narrow bandgap. Therefore, motivated by these previous reports, our research group decided to perform end-capped modifications of recently synthesized selenopheno [3,2-b] thiophene containing BPS-4F (R) [13] molecule with novel end-capped units. After modifications, we have disposed of nine new novel fullerene-free acceptor molecules (SN1-SN9) having selenopheno [3,2-b] thiophene as donor unit.

Herein, we efficiently designed the new series of half-moon-shaped molecules (SN1-SN9) and studied their structural and physio-chemical relationship along with optoelectronic properties by using DFT and TD-DFT approaches. Various symmetrical characteristics such as the alignments of FMOs, excitation energies, the density of states (DOS), absorption spectrum, transition density matrix (TDM), and binding energies of (SN1-SN9) materials have been explored. Furthermore, Voc, reorganizational energies of electron and holes, and bandgap of the designed molecules (SN1-SN9) were studied extensively in comparison with reference (R). Moreover, complex studies of SN2/PTB7-Th and SN2/SZ5 are discussed as well. Results of these parameters proved that end-capped engineering is an interesting strategy for enhancing the photovoltaic properties of non-fullerene acceptor molecules. Therefore, we suggested a new type of half-moon-shaped acceptor molecules for future OSCs processing with high PCE.

Computational procedure

DFT and TD-DFT approaches have been employed on reference and designed molecules. The chemistry of molecules can be found in supporting information. A Gaussian 16 is used along with GAUSS VIEW 6.0 suit of a program for all of the characterizations. Firstly, the geometrical optimization of R was studied with four various functionals such as B3LYP [14], ωB97XD [15], MPW1PW91 [16], and CAM-B3LYP [17] at 6-31G(d,p) [18,19,20,21] level of DFT. Then, maximum absorption was determined using the above functionals at 6-31G(d,p) basis set by using organic solvent through conductor-like polarizable continuum model (CPCM). From experimental [13] and TD-DFT-based calculations of absorption maxima, it was found that B3LYP/6-31G(d,p) is the reliable method to reproduce the experimental datum.

Electron and hole reorganizational energies are sub-categorized into internal and external reorganizational energies. The internal reorganizational energy is associated with the internal changes of geometries and the effect of different internal factors that influence the internal geometries of molecules. At the same time, external reorganizational energies are associated with the polarization in the external environment. In this discussion, we have ignored the external reorganizational energy as it has a negligible contribution. For calculating internal and external reorganizational energy energies of the considered molecules, we have used the following equations [22,23,24].:

$${\lambda }_{e}=\left[{E}_{0}^{-}-{E}^{-}\right]+[{E}_{-}^{0}-{E}_{0}]$$
(1)
$${\lambda }_{h}=\left[{E}_{0}^{+}-{E}_{+}\right]+[{E}_{0}^{+}-{E}_{0}]$$
(2)

Hence, the cationic and anionic energies of neutral material optimization are \({E}_{0}^{+}\) and \({E}_{0}^{-}\), respectively. \({E}_{-}\) and \({E}_{+}\) are anionic and cationic energies of cation and anion geometries optimization, respectively. \({E}_{-}^{0}\) and \({E}_{+}^{0}\) define the energies of the neutral molecules optimized at anionic and cationic states. E0 is the neutral molecule energy at the ground state geometry. For the calculation of binding energy, different parameters like the first principle excitation energy (which comes from excitation energy calculation of a molecule in an excited state by employing the TD-DFT approach) and energy band gaps are considered. The following equation is proved to calculate calculating the binding energy:

$${E}_{b}={E}_{g}-{E}_{\mathrm{opt}}$$
(3)

where Eb corresponds to binding energy, Eg is the bandgap, and Eopt is the first principle excitation energy. Generally, the lower Eb value of a molecule allows an important charge transfer and thus high PCE.

Result and discussion

Basic optimization

Figure 1 shows the designed structures of (SN1-SN9) materials after modifying R as SM-NFAs for OSCs. Initially, the optimization of R was carried out at B3LYP, ωB97XD, CAM-B3LYP, and MPW1PW91 at 6-31G(d,p) basis set. Subsequently, the maximum absorption of R was obtained in chloroform solvent at the above-cited functionals and basis set. The absorption maxima of R was at 760 nm, 842 nm, 701 nm, and 811 nm at B3LYP/6-31G(d,p), ωB97XD/6-31 g(d,p), CAM-B3LYP/6-31G(d,p), and MPW1PW91/6-31G(d,p), respectively, as shown in Fig. 2. The experimental absorption maxima of R is obtained at 749 nm [13]. From these values, it is evident that the B3LYP/6-31G(d,p) level of theory revealed the best agreement with experimental data; therefore, this basis set and method have been used for further calculations.

Fig. 1
figure 1

Schematic molecular designing (SN1-SN9) and R materials

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Fig. 2
figure 2

Absorption maxima values of reference molecule (R) with four different functionals at 6-31G(d,p) level of DFT in chloroform solvent

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Frontier molecular orbital analysis

Based on molecular orbital theory (MOT), the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are considered as valance and conduction bands, respectively. Both orbitals are also known as frontier molecular orbitals (FMOs) [25,26,27,28]. The occurrence of FMOs is of crucial importance regarding charge transfer efficiency. The occurrence of FMOs is also a decisive factor for determining the charge transfer extent as it is directly linked with the performances of the materials. The energy difference between these molecular orbitals is described as the HOMO–LUMO energy gap (Eg). The Eg plays a significant role in deciding the charge transfer rate and also helps in estimating the PCE of a molecule for OSC [18, 22, 29,30,31,32,33,34,35,36,37]. A molecule that exhibits a narrow bandgap will lead to an important charge transfer rate. The optimized structures of designed (SN1-SN9) and R are shown in Fig. S1.

The alignment of FMOs of designed (SN1-SN9) and R are displayed in Fig. 3. The calculated HOMO energies of R and SN1-SN9 are given in Table 1. The deigned molecules (SN1-SN9) exhibit stabilized HOMO and LUMO orbitals which leads to reducing the bandgap energies. The bandgap is also another important tool that disclosed the OSC performance. Molecules with narrow band gaps are considered rich in charge carrier transfer. The HOMO and LUMO energy levels along with the bandgap values are tabulated in Table 1.

Fig. 3
figure 3

HOMO and LUMO distribution of the studied molecules

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Table 1 HOMO, LUMO, and bandgap energies of the studied molecules
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Designed molecules expressed narrow band gaps compared to R which indicated that our designed half-moon-shaped molecules are appropriate for NFA-based OSCs. Despite this, we realize that SN2 has the lowest bandgap value (Eg = 2.82 eV) because of the presence of incorporated 3-(dicyanomethylene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile end-capped moiety. The second and third lowest band gap values are noted for SN8 and SN1 which is probably generated from the effect of 2-(2-methylene-3-oxo-2, 3-dihydro-1H-inden-1-ylidene) malononitrile combined with 1,1,1-trichloroethane and 2-(5,6-dichloro-2-methylene-1-oxo-1H-inden-3(2H)-ylidene) malononitrile end-capped acceptor moieties, respectively. The energy band gap of SN7 suggested that the addition of three fluorine atoms significantly causes the reduction of the bandgap energy. Similarly, the obtained band gap value of SN5 demonstrated that the incorporation of additional functional groups as end-capped units may decrease the band gap value. Molecules SN6 and SN3 displayed approximately similar bandgap values which might be due to the efficient 2-(2-methylene-3-oxo-2, 3-dihydro-1H-inden-1-ylidene) malononitrile with methyl acetate and methyl 6-cyano-3 (dicyanomethlene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5-carboxylate acceptor moieties. Molecule SN9 also exhibited a narrow bandgap (Eg = 2.98 eV) compared to R which could be explained by the addition of Si metal in the acceptor unit. As revealed, the designed molecules exhibited a narrow bandgap compared to R which is surely generated from the extra-functional addition within the acceptor moiety. The decreasing trend of the bandgap values is as follows: R > SN4 > SN9 > SN3 > SN6 > SN5 > SN7 > SN1 > SN8 > SN2. A narrow energy band gap allows easy transfer of charge from lower level to higher level orbital. The designed molecules exhibited a narrow band gap (2.82 to 2.98 eV) as compared to the reference molecule (3.05 eV). Similarly, designed molecules also exhibited red-shift in the absorption spectrum (761 to 778 nm) as compared to the reference molecule (760 nm). Further, designed molecules also expressed good values of excitation energy (1.60 to 1.89 eV). Among all designed molecules, SN2 expressed the narrowest band gap with high red-shifting. Moreover, it also expressed excellent excitation energy which suggested that SN2 show easy excitation in the excited state, thus enhancing the efficiency of the molecule for solar cell applications. From the preceding discussion and based on the bandgap order, we can conclude that the designed molecules (especially SN2) are suitable NFAs for OSCs.

Density of states analysis

The DOS analysis is a useful tool to determine the HOMO and LUMO positions within a molecule which in return measures the performance of a solar cell. DOS analysis is also of quite an important to explore the nature of different units of a molecule, i.e., the donor and acceptor part. Therefore, we have considered the DOS analysis to get in-depth information of designed (SN1-SN9) and R molecules and also to point out the position of stable HOMO and LUMO orbitals [38, 39]. DOS plots are illustrated in Fig. 4. In our case, the central unit of the studied molecules is an acceptor represented with A and attached to two donor units (D). The donor units are flanked with two efficient acceptor units (A′). Hence, in this way, a perfect A′-DAD-A′ backbone is formed for high charge transfer.

Fig. 4
figure 4

DOS plots of R and SN1-SN9 molecules

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From Fig. 4, we can see the HOMO density distributed over the donor unit which suggested the strong electron-donating nature of selenopheno [3,2-b] thiophene units. However, the LUMO orbital density is dispersed over the central acceptor core unit and slightly over the end-capped acceptor units which indicated the electron-accepting nature of strong acceptor molecules. The distribution behavior of FMOs remains the same in all the studied molecules which indicated the efficient design of the new nine half-moon-shaped acceptor molecules (SN1-SN9). From DOS plots, we can determine that our designed (SN1-SN9) materials are suitable to be used as acceptors for OSCs.

Photovoltaic characteristics

The excitation energy, oscillating strength, absorption behavior (absorption spectrum), and related molecular orbitals assignments are considered the key features of a molecule. The photovoltaic properties of a molecule are very important for explaining the quality of a solar cell. Commonly, molecules that exhibit red-shifting in absorption spectrum are considered highly efficient molecules in terms of PCE. The absorption spectrum red shiftcate along with the absorption high intensity leads to a higher charge transformation from HOMO to LUMO and the possibility of enhancing the PCE of a solar cell. Therefore, the photovoltaic characteristics of the desi (SN1-SN9) and R design carried out in chloroform solvent. The calculated photovoltaic parameters are shown in Table 2.

Table 2 Experimental and theoretical absorption maxima, oscillating strength, excitation energy values, and major molecular orbital assignments of R and SN1-SN9 in chloroform solution
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In Table 2, we realized that the absorption of R is 760.98 nm (based on DFT) and 749 nm (based on experimental). The λmax values of the designed molecules are found at 762.83 nm (SN1), 778.21 nm (SN2), 765.19 nm (SN3), 761.96 nm (SN4), 766.71 nm (SN5), 769.11 nm (SN6), 770.01 nm (SN7), 776.92 nm (SN8), and 762.45 nm (SN9). From these results, it is evident that the designed (SN1-SN9) materials are highly red-shifted in absorption spectra compared to R. The highest red-shifting was detected for SN2 (λmax = 778.21 nm) generated from the efficient 3-(dicyanomethylene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile end-capped acceptor unit. While the second and third highest red-shifting absorption is attributed to SN8 (λmax = 776.92 nm) and SN7 (λmax = 770.01 nm) which is probably originating from the addition of trichloro and tri-fluoro groups in end-capped acceptor moiety. SN5 (λmax = 766.71 nm) and SN3 (λmax = 765.19 nm) exhibited approximately similar absorption maxima which is explained by the presence of 2-(2-methylene-3-oxo-2, 3-dihydro-1H-inden-1-ylidene) malononitrile acetate and methyl 6-cyano-3 (dicyanomethlene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5-carboxylate end-capped acceptor groups, respectively. SN4 and SN1 also expressed close values of absorption maxima and a red-shifting compared to R. From the obtained results, it is concluded that SN1-SN9 is better than R in terms of red-shifting absorption. Thus, the designed half-moon-shaped materials are promising runners for efficient OSC devices.

Moreover, excitation energy could help in determining the photovoltaic performances of OSCs [40]. In general, lower reorganizational energies lead to a high PCE [41]. Likewise, low values of Ex also help to determine the extent of charge transformation originating from excited HOMO to LUMO [42,43,44,45,46,47]. Thus, materials that exhibit low excitation energies are considered as the most suitable molecules for high-performance photovoltaic devices [48]. Herein, we performed an excitation energy analysis that is shown in Table 2. Reference molecule (R) expressed an excitation energy value of 1.89 eV, while for the designed molecules, it is observed as SN1 (Ex = 1.77 eV), SN2 (Ex = 1.60 eV), SN3 (Ex = 1.82 eV), SN4 (Ex = 1.88 eV), SN5 (Ex = 1.89 eV), SN6 (Ex = 1.72 eV), SN7 (Ex = 1.85 eV), SN8 (Ex = 1.79 eV), and SN9 (Ex = 1.77 eV). Compared to R, it is revealed that SN1-SN9 exhibited low excitation energies indicating the formation of highly efficient OSCs. The decreasing trend of the excitation energy is as follows: R = SN5 > SN4 > SN7 > SN3 > SN8 > SN1 = SN9 > SN6 > SN2. Further, major molecular orbitals assignments are calculated. These outcomes showed that the designed (SN1-SN9) materials have the maximum charge density transition ability from HOMO to LUMO. The simulated absorption spectra are depicted in Fig. 5 which are recorded in chloroform solvent.

Fig. 5
figure 5

Calculated absorption spectra of all studied molecules in chloroform solvent

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Reorganizational energy

The electron and hole mobility decide the overall performance of an OSC as it is inversely related to the reorganizational energy of the hole and electron of a material [49]. Usually, the lower reorganizational energies of hole and electron are considered for higher mobilities of hole and electrons, respectively. To sum up, the reorganizational energies of molecules play a major role in measuring OSC performances. Therefore, the reorganizational energies of hole and electron of all studied (SN1-SN9) molecules.

The electron reorganizational energy of R is 0.0097, while for the designed (SN1-SN9) molecules, the reorganizational energy of electron is of 0.0083 (SN1), 0.0061 (SN2), 0.0083 (SN3), 0.0091 (SN4), 0.0077 (SN5), 0.0086 (SN6), 0.0081 (SN7), 0.0088 (SN8), and 0.0090 (SN9). It is found that SN1-SN9 has exhibited lower reorganizational energies of electrons in contrast to R, which suggested that the new half-moon-shaped fullerene-free acceptor molecules are potential candidates for highly efficient OSCs. The lowest reorganizational energy of electron was found for SN2 that is certainly originating from the efficient end-capped acceptor unit effect. Hence, we demonstrated that the end-capped acceptor modification disposes of a reliable tool for enhancing the performance of OSCs, while second and third lowest values of electron reorganizational energy were observed for SN5 and SN7 originating from the effect of 2-(2-methylene-3-oxo-2, 3-dihydro-1H-inden-1-ylidene) malononitrile acetate and 2-(2-methylene-3-oxo-2, 3-dihydro-1H-inden-1-ylidene) malononitrile combined with 1,1,1-trifluoroethane end-capped acceptor units. SN3 and SN1 disclosed similar values of electron reorganizational energies. Similarly, SN9 and SN4 expressed approximately the same values of electron reorganizational energies. The decreasing order of electron reorganizational energies is as follows: R > SN4 > SN9 > SN8 > SN6 > SN1 = SN3 > SN7 > SN5 > SN2. Thus, it is concluded that all designed molecules exhibited high charge mobilities compared to R. Based on these results, we can deduce that the designed (SN1-SN9) materials are fine electron transport molecules for efficient OSCs devices.

The hole reorganization energies were also calculated with the same method. The hole reorganizational energy of R is found at 0.0113. The designed SN1-SN9 materials present reorganization energies of 0.0101, 0.0089, 0.0105, 0.0112, 0.0109, 0.0118, 0.0091, 0.0098, and 0.0106, individually. Hence, these (SN1-SN9) molecules displayed lower and corresponding reorganization energy of hole as of R. In Fig. 6, the highest hole mobility was obtained for SN2 followed by SN7 and SN8, respectively. So, from the proceeding discussion, Fig. 6 and Table 3, it is illustrated that the designed (SN1-SN9) molecules are suitable hole and electron transport materials for high-performance OSCs.

Fig. 6
figure 6

Reorganizational energy of hole and electron of all studied molecules

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Table 3 DFT-based computed electron and hole reorganization energy of SN1-SN9 molecules
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Transition density matrix

Transition density matrix (TDM) investigations are widely employed to elaborate electron, hole, and hole-electron pair positions [50,51,52,53,54]. Further, TDM analysis disposes of an efficient evaluation for an OSC performance. Location of electron and hole inside a molecule considered crucial regarding the charge transfer analysis. Otherwise, TDMs are a helpful tool to estimate the unveiled nature of different parts of a molecule. The TDM plots have been calculated. Hydrogen does not involve in the overall charge transformation as its effect is ignored.

In this report, we separated the investigated (SN1-SN9) molecules into three portions, a central core which is an acceptor in nature represented with C, a donor bridge represented with D, and a terminal acceptor represented with A (Fig. 7). This molecular dissociation helps the readers to better understand the TDM plots. As shown in Fig. 7, it is indicated that electron density is located over the acceptor diagonal. The electronic density is also present at the center and terminal acceptors. Hence, it is deduced that the donor bridge donates electron density and also facilitates the energy transfer from the core to the donor to the terminal acceptor end. We discovered that electronic coherence is existing in all designed (SN1-SN9) molecules indicating that the end-capped modification represents a key approach for improving SCs parameters. The existence of electronic density in all designed (SN1-SN9) materials also proposed efficient end-capped modifications in these molecules. Therefore, after TDM analysis we can suggest that the designed (SN1-SN9) materials are promising candidates for efficient OSCs.

Fig. 7
figure 7

TDM plots of SN1-SN9 in S1 emission state

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Binding energy (Eb) is yet another method to demonstrate the potential of SC materials [55]. The low value of Eb also presents a higher current charge density in a molecule [56]. Therefore, the Eb analysis of SN1-SN9 has been performed and results are summarized in Table 4.

Table 4 HOMO–LUMO energy gap, first principle excitation energy (Eopt), and binding (Eb) energy values of SN1-SN9 expressed in eV
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As shown in Table 4, the R revealed Eb value of 1.16 eV, while SN1-SN9 expressed binding energy values of 1.13 eV (SN1), 0.92 eV (SN2), 1.14 eV (SN3), 1.11 eV (SN4), 0.96 eV (SN5), 1.07 eV (SN6), 1.08 eV (SN7), 1.09 eV (SN8), and 1.10 eV (SN9). The designed (SN1-SN9) materials displayed lower Eb, indicating their ability to dispose of a higher current density compared to R, while the lowest Eb is detected for SN2 and SN5 which could be originated from the addition of additional functional groups present over end-capped acceptors. As shown in Fig. 8, the designed (SN1-SN9) materials exhibited lower Eb values compared to R, whereas the decreasing trend of materials Eb is as follows: R > SN3 > SN1 > SN4 > SN9 > SN8 > SN7 > SN6 > SN5 > SN2. The recorded trend demonstrates that designed (SN1-SN9) materials, particularly SN2, could be a better material for OSC devices.

Fig. 8
figure 8

Binding energy, first principle excitation energy, and bandgap of R and SN1-SN9

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Open-circuit voltage (Voc)

The Voc of materials is another parameter to explore OSC performances. The Voc solar cell is measured at null voltage. The Voc is ascribed as the total current drawn by the device at null voltage [57]. It is a combination of two currents, i.e., photo-generated current and device saturated current. To measure Voc of any device, the following equation is employer [58]:

$$Voc=\frac{1}{e}\left({E}_{HOMO }^{D}- {E}_{LUMO }^{A}\right)-0.3$$
(4)

Here, e is the elementary charge, EHOMO is the HOMO orbital of the donor molecules which are PTB7-Th and SZ5 in this report, and ELUMO is the LUMO orbital of our studied molecules. PTB7-Th and SZ5 are commonly known as efficient donor polymers for OSCs. SZ5 was used in the experimental part as donor polymer; therefore, both donor polymers are considered for Voc analysis and charge transfer investigation (study of the complex).

The Voc calculations by using PTB7-Th and SZ5 (donor polymer) blended with R and designed SN1-SN9 materials are shown in Fig. 9. First, we discussed the PTB7-Th/acceptor molecules, where the designed (SN1-SN9) materials displayed high Voc values compared to R which indicates that our designed (SN1-SN9) materials are competent candidates for OSCs. While the R exhibits a Voc of 1.85 V, the Voc values of the investigated molecules are 2.00 V (SN1), 2.08 V (SN2), 1.94 V (SN3), 1.91 V (SN4), 1.96 V (SN5), 1.95 V (SN6), 1.97 V (SN7), 2.02 V (SN8), and 1.92 V (SN9). The highest Voc is found for SN2 which could be explained by the effect of 3-(dicyanomethylene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile end-capped group. Similarly, second and third highest Voc values are noted for SN8 and SN1 which is probably originating from the chloro groups in end-capped moieties. Molecules SN3, SN6, and SN5 exhibit close values of Voc which indicates that these (SN1-SN9) materials possess effective end-capped acceptor groups which help in improving the performances of materials.

Fig. 9
figure 9

Open-circuit voltage of a PTB7-Th/acceptors and b SZ5/acceptors

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In SZ5/Acceptor molecules, the Voc has been carried out at the same basis set. In these systems, the calculated Voc is found of 2.15 V (R), 2.30 V (SN1), 2.38 V (SN2), 2.24 V (SN3), 2.21 V (SN4), 2.26 V (SN5), 2.25 V (SN6), 2.27 V (SN7), 2.32 V (SN8), and 2.22 V (SN9). These materials displayed high values of Voc as compared to R which is the consequence of the adding of an extra-functional group within the end-capped acceptor units. The highest Voc is attributed to SN2 arising from the effect of 3-(dicyanomethylene)-2-methylene-1-oxo-2,3-dihydro-1H-indene-5,6-dicarbonitrile end-capped unit. Similarly, the second and third Voc values are assigned to SN8 and SN1 resulting from the presence of chloro group in the end-capped moiety. Molecules SN3, SN6, and SN5 exhibited close values of Voc indicating that these groups have effective end-capped acceptor units.

Based on these findings, it is evident that our designed half-moon-shaped (SN1-SN9) acceptor materials are potential runners for efficient OSC devices.

Molecular electrostatic potential analysis

We have also calculated molecular electrostatic potential (MEP) plots to estimate for designed (SN1-SN9) and R material, as illustrated in Fig. 10. The main determination of these calculations is to investigate the presence of various charge sites inside the materials. The investigations of MEP plots of SN1-SN9 and R were performed using an iso-surface value of 0.02e/Å3, respectively. The formed MEP plots showed colorful representation, where every color corresponds to some unique feature of the molecule. Hence, the positively charged moieties are accomplished to form the blue color representation, while the red color signifies the negative charge accumulation and the green color corresponds to neutral charge, i.e., the maximum possible potential area among the designed (SN1-SN9) materials and R.

Fig. 10
figure 10

MEP map of the studied molecules. The iso-surfaces value is 0.02e/Å3

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Interestingly, we revealed similar charged sites for SN1-SN9 and R. As it can be seen in Fig. 10, the investigated molecules exhibit quite similar clouds densities. It was observed that similar electronic charge density spreads over all the newly designed molecules (SN1-SN9) as well as R. These investigations revealed the efficiency of our molecular modeling strategy to tune the photophysical and optoelectronic characteristics of the materials. Hence, regarding the compatibility of these newly designed (SN1-SN9) materials for an efficient charge transformation reaction, we are looking forward to their synthesis in the future to fabricate highly efficient solar cell devices.

Conclusion

In conclusion, we have developed a theoretical investigation based on a series of non-fullerene-based molecular systems to understand their photovoltaic and optoelectronic characteristics. The geometrical parameters, the absorption maxima, the FMOs, and the electronic structures of these materials were successfully analyzed by using DFT and TD-DFT approaches with various methods and basis sets. Interestingly, we realized that HOMO–LUMO molecular energy orbitals exhibited a noteworthy correlation as compared with experimentally verified molecule R. The designed materials (SN1-SN9) exhibited narrower energy gaps compared to R. The DOS analysis explained the distribution patterns of HOMO–LUMO levels. The photophysical studies of SN1-SN9 and R revealed that all the newly constructed materials are extremely red-shifted as compared to R ensuring our effective molecular modeling approach. Moreover, all the designed materials (SN1-SN9) exhibited Ex and Eb, which is helpful to produce higher photocurrent density values. The lower reorganization energies of electrons and holes denote higher charge mobilities. Our designed (SN1-SN9) materials produced much lower values of electron mobility which corresponds towards higher electronic mobilities as compared to R. In addition, we have also calculated the Voc of SN1-SN9 and R by considering the well-known polymers donor PTB7-Th and SZ5. TDM and electron–hole overlapping analysis uncovered the hidden charging site of the molecules which may provide a helpful tool to realize the electronic transition behavior of SC materials. Regarding these theoretical studies, we can conclude that our designed materials have a great ability to produce better photovoltaic and optoelectronic characteristics compared to the reference R. Moreover, we highly recommend these designed materials (SN1 to SN9) to be synthesized for fabricating efficient OSC devices.