**1. Introduction**

Polymer solar cell (PSC) is a subject of discussion over the last decade due to its initial encouraging power conversion efficiency (PCE). Over time, organic dye-sensitized solar cells (DSSCs) and perovskite solar systems outperform the PSCs based on better and efficient PCE. Additionally, high cost and low-life time factors are other threats, which pose a great task for the researchers [1–4]. The PSC functions similarly to another kind of solar cell through the conversion of photons into an electrical current. The most common types of PSC are fullerene-based and non-fullerene based where they act as acceptor fragment and the role of polymer is a donor. Cuiet al. [2] experimentally showed that chlorinated non-fullerene acceptor-based PSC converts 16.5% of solar energy into an electrical current which is the highest reported PCE value for any non-fullerene PSCs till date. On the contrary, Meng et al. [4] reported 17.3% conversion employing tandem cell strategy using PTB7-Th:O6T-4F:PC71BM (PTB7-Th is poly[4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)benzo[1,2-b:4,5-b ]

dithiophene-co-3-fluorothieno[3,4-b]thiophene-2-carboxylate]; O6T-4F is carbon-oxygen-bridged i8 difluoro-substituted 1,1-dicyanomethylene-3-indanone; PC71BM is [6,6]-phenyl C71 butyric methyl ester) with an architecture of ITO/ZnO/PFN-Br/active-layer/M-PEDOT/Ag and ITO/ZnO/active-layer/MoO3/Ag where PC71BM acts as acceptor material under fullerene-based PSC. Fullerene derivative (FD) PC61BM conjugated with diverse polymers P3HT (poly(3-hexyl)thiophene), PTPTB (poly-Ndodecyl-2,5,-bis(2'-thienyl)pyrrole, 2,1,3-benzothiadiazole), PEOPT (poly(3-(4'-(1,4,7-trioxaoctyl) phenyl)thiophene), PFDTBT (poly{[2,7-(9-(20-ethylhexyl)-9-hexylfluorene])-alt-[5,50-(40,70-di-2 thienyl-20,10,30-benzothiadiazole)]}) showed PCE values range from 2.8 to 4.4 [5–8], 1.7–2.1 [9], 1.75 [9] 1.9 [9], respectively. Even, PCPDTBT (poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4 b ]dithiophene)-alt-4,7(2,1,3-benzothiadiazole)]) and PBDTP-DTBT (poly{4,8-bis(4-(2-ethylhexyl)- phenyl) benzo[1,2-b:4,5-b ]dithiophene-alt-[4,7-di(4-(2-ethylhexyl)-2- thienyl)-2,1,3-benzothiadiazole)-5, 5 -diyl]}) showed PCE of 3.2 [10] and 8.07 [11] with PC71BM, respectively. While, PCDTBT (poly[N-9 -heptadecanyl-2,7-carbazole-alt-5,5-(4 ,7 -di-2-thienyl-2 ,1 ,3 -benzothiadiazole)]) and PCPDTBT offers PCE of 6.1 [12] and 6.16 [13] with PC70BM, respectively.

The PCE value of existing PSCs is reasonable but not better than other commercial solar cell systems. Thus, improved and efficient PSCs are required by the implementation of rational designing of different fragments followed by optoelectronic properties evaluation to establish them as a future system. Based on the above discussion, it is quite clear that a good amount of simple and complex polymers has been examined, but the PCE value has not improved drastically. Therefore, we have aimed for novel modifications of FDs to improve the PCE of PSCs. Arbitrarily synthesizing various FDs is not a practical solution, as well as it is costly and time-consuming. Thus, considering experimental PCE data of existing FDs, in silico models can be prepared by quantitative structure-property relationship (QSPR) model [14]. Our group has proposed the first QSPR model followed by the virtual screening of FDs generating future lead acceptor fragment for PSC with PCE value of 12.11% [15]. Additionally, the QSPR technique was successfully employed in all steps from designing to prediction purpose for DSSCs by our group [16,17] and other researchers [18,19] with encouraging outcomes. Therefore, without any doubt, the QSPR modeling can be tactfully employed for designing better acceptor FDs for PSCs.

In continuation of our previous work [15], in the present study, we have prepared a QSPR model followed by implementation of the mechanistic interpretation and identified vital structural fragments obtained from the model to design new FDs as an acceptor for PSC. Previously we had used the QSPR model to screen 169 FDs to find the best FDs based on PCE value only without considering identified features from the model [15]. In the present study, designing will help us to consider the structural fragments more precisely and effectively. Ten FDs have been designed including seven C60 and three C70 FDs. The PCE of designed FDs are predicted employing the developed QSPR model prepared from 59 existing experimental PCE data of FDs. Top four lead acceptors (3 from C60 and 1 C70) are further employed for energetics study along with analysis of UV-Vis spectra of isolated dyes. The rational scheme from designing to the electrochemical analysis of FDs for PSCs offers a detailed idea of how one can implement a QSPR model to design various future solar cells, not confined to only PSCs pool of species.

#### **2. Materials and Methods**

#### *2.1. QSPR Modeling Study and Designing*

#### 2.1.1. Dataset

A series of 59 FDs consist of 52 C60 and 7 C70 derivatives as acceptor for PSCs with experimental PCE data were taken from our previous research [15] to generate a statistically acceptable and predictive QSPR model. The experimental data for all solar cells is measured according to bulk-heterojunction (BHJ) devices, where FD acts as the electron acceptor and Poly(3-hexylthiophene) (P3HT), a commonly used photovoltaic polymer as the donor material. The experimental data and chemical structures of FDs have been reported in Table S1 in the Supplementary material section.

## 2.1.2. Descriptors Calculation

Molecular structures of FDs had been drawn in GaussView 6.0 [20] and optimized by semi-empirical PM6 method using Gaussian 16 software [21]. The output structures were employed in MarvinView (ChemAxon) [22] software to calculate physicochemical and solvent accessible surface area descriptors. To compute Simplex Representation of Molecular Structure (SiRMS) [23,24] descriptors, QSAR4U software was applied which helps to identify and understand the major structural fragments responsible for higher PCE.
