Introduction

Recently used energy sources worldwide include petroleum, crude oil, water, and coal, although these have highly hazardous impacts on all over the world environment. Moreover, because of the over usage, these energy sources are rapidly diminishing with each passing day [1]. Therefore, it is required to shift toward sustainable energy sources that are environmentally friendly. Wind power, biomass, hydro power, and solar are some of the substitute renewable energy sources and are environment friendly as well [2]. Among different renewable energy sources, solar energy is the best appealing because it is ecologically safe, limitless, free of carbon, and can be converted into electrical power using photovoltaic devices [3]. Various technologies are being used based on this principle; among these, the most dominant one is the organic photovoltaics (OPVs) because of their economic aspect, adaptability, and semi-transparency [4,5,6,7,8,9,10].

Varieties of solar cells are organic solar cells (OSC), amorphous silicon solar cells, dye-sensitized solar cells, hybrid inorganic–organic solar cells, and perovskite solar cells, etc. [11]. In many solar cells, silicon-based inorganic materials are being used owing to the extreme stability and high power conversion efficiency (PCE) of them, but they have some drawbacks as well such as high cost and having compact structure [10, 12,13,14]. Recently, OSCs have gained much attention because of their esthetic properties like easy fabrication process, semi-transparency, flexibility, cost-effectiveness, tunable energy levels along with increased PCE up to 18% [15,16,17]. Different strategies have been adopted to manufacture high-efficiency OSCs such as by using p–n junction-based material to design the OSCs [18]. These single-layered organic solar cells have been reported for higher (15%) [19] efficiency. Second is by using a donor–acceptor amalgamated layer, and the third strategy is the bulk heterojunction organic solar cells. Mainly, they are made of conjugated polymers and fullerene equivalents and due to their lightweight and less cost, they offer a crucial revelation for tackling the global power crisis [20]. However, because of the reduced band gaps and poor absorption in visible range, the non-fullerene alternatives are leading for the previous few decades [21,22,23,24]. Non-fullerene acceptors (NFAs) are currently a prominent focus of research in bulk-heterojunction organic solar cell development. Fullerene is derived from another type of acceptor-molecule that was employed as the primary acceptor material in bulk heterojunction organic photovoltaic cells. NFA-based OSCs have higher thermal and photochemical stability, as well as longer device lifetimes [25]. Low voltage loss of NFAs and tunable optoelectronic properties along with great synthetic flexibility and full spectral coverage meet the need of power shortage and enable to attain power conversion efficiency (PCE) up to 17% [24, 26,27,28,29,30,31,32].

Moreover, the problem with OSCs is the lower efficiency of OSCs than other inorganic material–based solar devices. The reason for this is the very large band gap of organic semi-conductors as compared to the inorganic semiconductors [33]. Due to this reason, metal halide perovskites have now turned out to be the point of enormous interests in photovoltaics [34,35,36,37] because of their low cost, high exciton diffusion, strong light absorption properties, and high charge mobility [38,39,40]. Although perovskite solar cells (PSCs) have exhibited PCE of over 20% [41], the major problem for marketing of perovskite solar cell is the deficient stability caused by commonly employed hole-transport materials (HTMs) alongside dopants as these dopants are costly and allow moisture and ion diffusion which cause the degradation of stability. Consequently, the fabrication of dopant-free HTMs is required. Until recently, many advances have been made in cross-linked, polymer and smaller molecules involved in HTMs. So, this current research aims to select suitable organic materials having usage as HTMs in perovskite solar cells and donating materials for proficient organic solar cell.

In our current study, by the end-capped engineering of PF [34], five small donor molecules namely PF1, PF2, PF3, PF4, and PF5 have been considered. The structural modification has been made by one-sided substitution of methoxy groups of PF with diverse acceptor moieties. All the planned molecules consist of PF as donating group and thiophene bridged end-capped acceptor groups namely (2-methylenemalononitrile) PF1, (methyl 2-cyanoacrylate) PF2, (3-methyl-5-methylene-2-thioxothiazolidin-4-one) PF3, (2-(3-methyl-5-methylene-4-oxothiazolidin-2- ylidene) malononitrile) PF4, and (4-(5-methylthiophen-2-yl) benzo[c] [1, 2, 5] thiadiazol) PF5. Our current study describes concepts for planning largely effective small molecules as donating materials for competent organic solar cells and HTMs for perovskite solar cells (PSCs).

Computational details

All the calculations are done using Gaussian 09 program, and Gauss view program is used to visualize the results [42]. Density functional theory (DFT) was used for structural optimization of reference and performed using B3LYP [43], CAM B3LYP [44], MPW1PW91, and ωB97XD [45] levels of theory and 631G (d,p) basis set. For investigating the absorption profile of reference molecules, TD-DFT calculations were achieved at same B3LYP, CAM B3LYP, MPW1PW91, ωB97XD levels and 6–31G (d,p) basis set. The absorption maximum of reference molecule is then compared to the experimental value and among four methods, MPW1PW91/6–31G (d,p) level of theory has manifested the nearest value with the experimental value. Hence, the absorption profile of all architecture molecules has been investigated in both the gaseous and solvent (chlorobenzene) medium employing MPW1PW91/6–31G (d,p) level of theory.

The frontier molecular orbital analysis, TDM and DOS analysis, dipole moment (µ), reorganization energies (RE), and charge transfer study of the model and all freshly prepared compounds are performed at MPW1PW91/6-31G (d,p) functional. The TDM and DOS are obtained using Multiwfn 3.7 software and PyMolyze 1.1 software packages, correspondingly [46, 47]. Optimized cationic and anionic structures were obtained by employing MPW1PW91/6-31G (d,p) for the calculation of reorganization energy (RE), for electron (λe), and hole (λh) using Eqs. (1) (2) [48].

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

E0 is the single point energy of neutral molecule optimized at ground level. \({E}_{0}^{-}\), \({E}_{0}^{+}\) are ground-state energies of anions and cations obtained from neutral molecule, and \({E}_{+}^{0}\), \({E}_{-}^{0}\) represent energy values of cation and anion calculated from cationic and anionic optimized structures.

Results and discussions

Initially, the reference molecule is optimized at four different DFT methods B3LYP, CAM B3LYP, MPW1PW91, ωB97XD levels and 6–31G (d,p) basis set. The value of absorption maximum for reference molecule PF is calculated at four distinctive levels of theory. The experimental value of λmax (336 nm) is found in agreement with the MPW1PW91/6-31G (d,p) functional. Hence, all the calculations herein are performed by employing MPW1PW91 DFT method and 6-31G (d,p) basis set. The chemical structures of all currently investigated molecules are shown in Scheme 1.

Scheme 1
scheme 1

Chemical structures of PF and architecture molecules (PF1-PF5)

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Frontier molecular orbital analysis

The optimized geometries of all the designed molecules along with reference molecule have been shown in Figure S1 (Supporting Information).

FMO (frontier molecular orbital) analysis is a technique that estimates the electron charge density distribution around the highest molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Moreover, the electronic properties of a system are investigated by performing FMO analysis. The FMOs of planned molecules and the reference PF molecule have been presented in Fig. 1. From Fig. 1, it is observed that the HOMO and LUMO of the reference molecule are scattered on half portion of the donor part while in our designed molecules, the HOMO is spread on half of the donor section and LUMO lies on the entire acceptor fragment as shown. The substitution of acceptor end groups has influenced the charge density distribution, and hence, charge transfer occurs from the donor fragment to acceptor end moieties. The charge density is distributed on the acceptor segment in all planned molecules. The HOMO energy values for all designed molecules are discovered as PF (− 4.71 eV) > PF5 (− 4.78 eV) > PF2 (− 4.83 eV) > PF3 (− 4.86 eV) > PF4 (− 4.87 eV) > PF1 (− 4.94 eV), and the LUMO values reported are PF (− 0.66 eV) > PF5 (− 2.51 eV) > PF2 (− 2.61 eV) > PF3 (− 2.67 eV) > PF4 (− 2.97 eV) > PF1 (− 2.99 eV). The HOMO − LUMO band gap energies explored are PF (4.05 eV) > PF5 (2.27 eV) > PF3 (2.24 eV) > PF2 (2.22 eV) > PF1 (1.95 eV) > PF4 (1.9 eV). Among all the planned molecules, PF4 has reported the lowest band gap owing to the presence of Cyano (CN) containing (2-methylene malononitrile) acceptor unit that is responsible for the auspicious charge transmission from HOMO to LUMO.

Fig. 1
figure 1

FMOs of reference and all architecture molecules

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From these interpretations, we can conclude that all our designed molecules possess excellent charge transfer properties due to the strong electron-pulling substituents.

To achieve the PSCs with enhanced performance, comparison of energy levels of perovskite and HTMs is a crucial factor [49]. The HOMO–LUMO energy level diagram of planned molecules and perovskite has been shown in Fig. 2. The determined HOMO levels for PF, PF1-PF5 HTMs are − 4.71, − 4.94, − 4.83, − 4.86, − 4.87, and − 4.78 eV, correspondingly. These values are considerably larger than the HOMO of perovskite (− 5.43 eV) that suggest higher hole-extraction [49], and the LUMO values for PF, PF1-PF5 HTMs (− 0.66, − 2.99, − 2.61, − 2.62, − 2.97, and − 2.51 eV) are sufficiently higher than the LUMO value of perovskite (− 3.92 eV). Consequently, the transfer of undesired electrons from perovskite to counter electrode will be suppressed, and therefore, the charge recombination reduces [50]. These results demonstrate that these PF-based molecules are efficient for using as HTMs for high-performance PSCs.

Fig. 2
figure 2

Energy level diagram of PF-PF5 HTMs and perovskite

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TDM and exciton binding energy (Eb)

The utmost influential technique for evaluation of electronic excitation processes including diffusion, creation, recombination, and separation of charges is transition density matrix (TDM) analysis [51]. TDM analysis aims to validate the quantum geometry of compounds when excitation occurs. This analysis reveals the relationship between donor and acceptor groups in excited state [52]. TDM represents the density of electronic distribution in a molecule along with the transitory location of holes and electrons in the compound during excitation [53]. TDM analysis of the PF molecule and newly designed compounds (PF1-PF5) has been computed at 6-31G (d,p) using selected functional hybrid of DFT and is presented in Fig. 3 as two-dimensional colored plot using Multiwfn 3.6 software package. The reference molecule was sectioned apart as donor and acceptor regions labeled by D and A respectively. The designed molecules have been divided into four parts as donor, acceptor-1, acceptor-2, and spacer regions designated by D, A1, A2, and S respectively as shown in Fig. 3. As presented in TDM graphs, the standard straight x-axis and left upright y-axis exhibit the numbering of all the atoms present in the molecule excluding hydrogen atoms, as hydrogen atoms have been ignored by default during numbering of atoms because of their insignificant influence in the electronic excitations. On the other hand, the right y-axis is presenting the increasing electronic charge density from blue to red color in upper course. In the reference (PF) molecule, charge consistency is constantly confined in the donor region. While in the designed molecules (PF1-PF4), more charge consistency is seen in acceptor and spacer regions.

Fig. 3
figure 3

TDM plots for reference PF and designed molecules

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Another parameter exciton (electron–hole pair) binding energy that determines the photophysical and opto-electronic properties of devised compounds is defined as the amount of energy to estimate the exciton dissociation potential [54]. Binding energy and columbic interaction are in direct relation with each other. The lesser will be the binding energy, the lower is the columbic interaction that results in higher power conversion efficiency by escalating the charge dissociation rate. The binding energies calculated using Eq. 3 [55] for all designed molecules in gaseous and solvent both (chlorobenzene) media have been reported in Tables 1, 2 and 3.

Table 1 Contribution of acceptor and donor in raising the HOMO and LUMO of model PF and designed (PF1-PF5) molecules
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Table 2 Calculated λmax, transition energy (ΔE) oscillator strength (f0) and C.I. (%) in gaseous medium
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Table 3 Calculated λmax, transition energy (ΔE) oscillator strength (f0), and C.I (%) in solvent (chlorobenzene) medium
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$${E}_{b}={E}_{g}-{E}_{x}$$
(3)

In Eq. 3, Eg symbolizes the band gap energy, and Ex is the transition energy of first excited state.

DOS analysis

The density of states (DOS) investigation provides a map for charge transfer and determines the electronic charge distribution on HOMO and LUMO. The plotted DOS diagrams for reference and all architecture compounds are displayed in Fig. 4. It comprises a horizontal axis expressing energy in eV (electron volts) and a perpendicular axis for relative intensity. The negative values on plane x-axis represent conduction band HOMO, and the valence band LUMO is expressed by right positive values on the x-axis of the DOS plots, and the region indicated by dotted lines indicates the band gap energy (Eg) value of molecules. It explains the contribution of different fragments, i.e., acceptor, donor, and spacer represented by A1, A2, D, and S in raising the HOMO and LUMO of a molecule in the excited state. The DOS analysis was performed for all molecules by using the selected DFT functional and basis set. The contribution of all fragments in raising the HOMO and LUMO of all molecules is summarized in Table 1.

Fig. 4
figure 4

DOS plots for PF and all designed molecules

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It can be seen from the tabulated data that in raising the HOMO of all the investigated molecules, the major contributor is acceptor and spacer along with a minor role of donor fragment, while in the formation of LUMO, donor fragment is contributing majorly with a small participation of acceptor and spacer fragments as illustrated in Table 1.

Dipole moment (µ)

Dipole moment determines the polarity and dissolution of molecule in organic solvent [56,57,58,59]. The dipole moment expresses the polarity of molecules, it has a direct relation with the dissolution rate, and the greater the dipole moment, the greater will be the dissolution of molecule in polar solvent [60]. All the architecture molecules have reported the highest degree of dipole moment than the reference molecule in excited state. This upsurge in dipole moment proves the factor that all molecules are placed in a manner to lower the charge recombination and escalate the fill factor. The reported dipole moment in chlorobenzene for all architecture molecules ranges in 1.6845–19.4845 D. Among all the reported molecules, PF1 has explored the maximum dipole moment owing to its greater solubility in chlorobenzene and the polar regions’ presence in the structure, reducing the charge recombination and making multilayer fabrication easy. The dipole moment of devised molecules in gaseous state lies in the range 1.5046–16.4192 D. The graphical view of dipole moment has been shown in Fig. 5.

Fig. 5
figure 5

Graphical presentation of dipole moment (µ) in ground state, excited state, and difference between them

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Absorption analysis

Absorption of light and harvesting are two core parameters that have gained interests of researchers in production of solar energy. The UV–Visible spectra must be evaluated because they provide an understanding about the charge transfer analysis and electronic excitations [54, 61, 62]. The evaluated absorption spectra of all architecture molecules in gaseous and solvent medium are displayed in Fig. 6 and their excited state energies are shown in Fig. 7. In the current research, the absorption spectra of all designed molecules have been simulated via TD-DFT calculations in IEFPCM model, and the outcomes are tabulated in Tables 2 and 3 respectively.

Fig. 6
figure 6

UV–Visible spectra of investigated molecules in gaseous and solvent (chlorobenzene) medium

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Fig. 7
figure 7

Pictorial view of excitation energy in ground and excited state

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The absorption analysis demonstrates that all the architecture molecules have reported a greater value of λmax in comparison to the model molecule PF. The absorption maxima have an inverse relation with the band gap value. A lesser band gap value causes the higher λmax value and vice versa. And hence, all the investigated molecules have reported higher λmax values. C.I. is the percentage of excitation from HOMO to LUMO. The molecules with lower C.I have less charge dissociation rate and vice versa. Among all our designed molecules, PF1, PF2, PF3, and PF4 have higher percentage of interactions between highest occupied molecular orbital and lowest unoccupied molecular orbital compared to reference molecule, which cause the dissociation of photons easier, and the PCE can be improved.

These results reveal that all the freshly planned molecules are accompanied by strong electron-extracting species. The absorption values for all molecules in gaseous state follows PF (339 nm) < PF2 (491 nm) < PF1 (511 nm) < PF3 (522 nm) < PF4 (545 nm) < PF5 (592 nm). And for the solvent medium, it follows PF (344 nm) < PF2 (529 nm) < PF1 (556 nm) < PF3 (558 nm) < PF4 (581 nm) < PF5 (614 nm).

MEP surfaces

Molecular electrostatic potential surface conveys a good concept about the charge transfer from donor to acceptor moieties. The molecular electrostatic potential (MEPs) of all the analyzed compounds demonstrate that the blue color is spread largely over the central part whereas the red color is existing on the end-capped acceptor areas. The oxygen atoms in molecules present on the terminals are highlighted with red color indicating the region of concentrated electronic charge. Similarly, the cyano (CN) groups are blue colored owing to the nitrogen atoms present on the terminals of the molecules that indicates the nucleophilic reaction site with strong electron cloud. The MEPs of the reference (PF) along with all newly designed molecules have been computed at the selected DFT functional MPW1PW91/6-31G (d,p) and are mapped with red and blue hues showing negative and strong positive-charge regions, respectively, as displayed in Fig. 8.

Fig. 8
figure 8

Colored maps of MEP for PF and designed molecules (PF1-PF5)

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RE

Reorganization energy (RE) is a significant factor which determines the charge transfer properties of a molecule by computing the charge transfer mobilities [48]. The RE plays a vital role in estimating the PCE of OSCs [63]. Reorganization energies are of two types, internal and external reorganization energy. We are only concerned with the internal reorganization energy due to the insignificant effect of external RE. The graphical representation of reorganization energies is shown in Fig. 9.

Fig. 9
figure 9

Graphical representation of reorganization energy (RE)

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The λe value for model molecule is 0.0115535 eV. The lower the value of λe value, the larger will be the charge transfer rate. Among all the investigated molecules, the lowermost value of λe has been showed by PF5. All other designed molecules (PF1-PF4) have also reported the lowest λe values than the model PF molecule owing to the strong electron-withdrawing groups. These results support the fact that end-capped acceptor modifications have a strong effect on the interior RE of a molecule. Furthermore, among all architecture molecules, the PF5 has the lowest value of hole reorganization energy (λh) which again expresses the high rate of charge transfer. The computed results of electron and hole reorganization energies have been displayed in Table 4.

Table 4 Anion and cation mobilities for PF and all freshly planned molecules
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V oc

Open circuit voltage is a factor that estimates the current of solar devices [64]. It is defined as the maximum amount of current that is taken out from a device. To find the best use of our investigated molecules as donor in organic solar cells, we have chosen PC16 BM acceptor for calculation of Voc. The HOMO value for PC16BM acceptor is − 6.1 eV and its LUMO value is − 3.7 eV. Voc is evaluated using Eq. 4 [65] and is graphically shown in Fig. 10. The Voc values computed for all the designed molecules have been presented in Table 5.

Fig. 10
figure 10

Graphical representation of open circuit voltage (Voc)

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Table 5 Calculated open circuit voltage Voc, normalized Voc, fill factor (FF), percentage FF (FF%), and PCE for reference and architecture molecules
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$$V_{oc}=\frac{\mathrm{ELUMO}\;\mathrm{of}\;\mathrm{acceptor}-\mathrm{EHOMO}\;\mathrm{of}\;\mathrm{donor}-0.3}e$$
(4)

FF and PCE

Fill factor (FF) is another parameter that determines the PCE of OSCs. The fill factor for designed molecules has been calculated using Eq. (5) [66]:

$$FF=\frac{\frac{e{V}_{oc}}{{K}_{B}T}-\mathrm{ln}(\frac{e{V}_{oc}}{{K}_{B}T}+0.72)}{\frac{e{V}_{oc}}{{K}_{B}T}+1}$$
(5)

The equation of FF has \(\frac{e{V}_{oc}}{{K}_{B}T} = V\mathrm{oc}\), a normalized open-circuit voltage in which e is the elementary charge fixed at 1 in the current study. Voc is voltage estimated by Eq. (4), KB is Boltzmann constant whose value is 8.61733034 × 10−5 electron volts/kelvin, and T is temperature whose value was fixed at 300 K [67, 68]. The computed FF results for all studied molecules are summarized in Table 5.

Power conversion efficiency investigation is a strategy that ensures the efficacy of solar cell materials for practical applications. The PCE computed for all molecules using Eq. (6), and the results are displayed in Table 5:

$$\mathrm{PCE }= \frac{{J}_{sc}{V}_{oc } FF}{{P}_{in}}$$
(6)

In the above equation, Jsc is the short circuit current and its value (21.5 mA/cm2) has been taken from reference paper [34]. This value has been assumed for all the designed molecules. The factor Pin is the power of the incoming rays whose value is fixed at 100 mW cm−2. Among all the investigated molecules, PF1 molecule has better PCE than all other designed molecules due to the significantly higher values of Voc, FF, and normalized Voc that relates directly with PCE.

Conclusion

In the current research, we aim for carbazole-based small molecules as donor materials for use in OSCs and as HTMs for efficient perovskite solar cells. All the calculations were performed at selected MPW1PW91/6–31G (d,p) DFT functional. The designed molecules (PF1-PF5) have reported impressive results. PF1-PF5 have explored lower band gap values (2.27–1.9 eV), alongside higher λmax values of (529–614 nm) in chlorobenzene solvent. All the reported molecules have manifested higher values of dipole moment ranging from 4.7190 to 19.4845 D in chlorobenzene showing their better solubility in organic solvent and least charge recombination. The smaller values of RE reported for all the designed molecules indicate high charge mobility rate of these molecules. The Voc calculated for all designed molecules when scaled with PC16BM acceptor are higher than the reference molecule. This suggests that all the newly designed molecules can achieve better performing efficiency. All the studied molecules have higher anticipated PCE values by scaling up with PCBM (7.04–9.29%) than the reference molecule PF (6.10%) suggesting that these molecules can be proved effective donor materials for future organic solar cells, and the HOMO LUMO energy level and reorganization energy values show that these designed PF-based molecules can be effective HTMs for use in upcoming elite PSCs.