*3.5. UV-Vis Absorption Spectra of Isolated FDs*

The Figure 6 shows the simulated absorption spectrum of the different PCBM, four designed FDs and P3HT. The spectrum of PCBM reproduces the qualitatively main features of reported experimental results [34,39], such as, it shows a strong optical absorption predominantly in the UV region, with very weak absorption (f = 0.0021) in the visible region (from 450 nm to 700 nm, see the inset in Figure 6). However, the spectrum of P3HT oligomer (Figure 6, Bottom) showing two strong absorption peaks at 241.20 nm (f = 0.3423) and 381 nm (f = 2.4886) with one shoulder at 307 nm (f = 0.4027), which represents a HOMO − LUMO + 6, HOMO − LUMO and HOMO − 1 − LUMO + 1 transition, respectively. As a reference, for pure P3HT films two maxima absorption peaks and one shoulder at 493 nm, 517 nm, and 572 nm, respectively have experimentally been reported, also attributed to the π-π\* transitions [40–42]. Our simulated absorption of P3HT oligomer shows a small blue shift compare to experimental one.

Also, PCBM has weak absorption in visible region which is one of the factors that can be tuned to get better efficiency from PSCs [43]. If one examines the absorption strength of FDs, it is obvious that except FD4 and FD7 all of them having very weak absorption in the visible region. C70 derivatives FD7 is showing a red shift extends up to 600 nm with large oscillator strength [43]. From this aspect our designed FD4 and FD7 will be the most efficient acceptor in conjunction with donor P3HT.

**Figure 6.** Simulated absorption spectra of PCBM, four FDs [Top] and P3HT [Bottom] with the use of TD/CAM-B3LYP/6-311G(d,p) level of theory in chlorobenzene solvent. Inset Top: Magnified PCBM absorption spectrum.

## **4. Conclusions**

In silico modeling followed by designing and optoelectronic properties evaluation of future lead FDs as acceptor for PSCs had been performed. The QSPR model led us to development of 10 novel FDs as acceptor including seven C60 and three C70. Based on the predicted PCE, optoelectronic properties of four FDs were evaluated by DFT and TDDFT. PBE/6-31G(d,p) and CAM-B3LYP/6-311G(d,p) level of theory were employed for gas phase DFT and solvent phase TDDFT computations. Frontier orbital energies and UV-Vis absorption spectra of the isolated P3HT oligomer, PCBM and FDs were analyzed to estimate the optoelectronic properties of four FDs as acceptor in future PSCs. Exciton binding energy plays the pivot role at interface when excitons diffuse and dissociate in to electrons on LUMO level of the acceptor. The big off-set of LUMO energy levels will hinders this process. FD4 is the best C60-derivatives candidates for PSCs as it has the lowest exciton binding energy, up-shifted LUMO energy level that assist to increase VOC and strong absorption in the UV region. In case of C70-derivatives, FD7 is a potential candidate for future PSCs due to its strong absorption in UV-Vis region and lower exciton binding energy with higher VOC. By trading off the computed optoelectronic properties, our analysis supports our QSPR model which predict highest PCE values for FD4.

The rational molecular modeling, designing, and prediction followed by quantum study offers valued reasoning for the synthesis of lead FDs with higher power conversion efficiency. The structural analysis concluded the following points:


**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/12/14/2282/s1, Table S1: Fullerene derivatives with their experimental and predicted % PCE, Table S2: Computed value of modeled descriptors for each FDs along with their predicted % PCE and mean normalized distance value.

**Author Contributions:** S.K., J.K.R., and J.L. conceived and designed the experiments; S.K. and J.K.R. performed the experiments; S.K., J.K.R., and J.L. analyzed the data; S.K. and J.K.R. contributed analysis tools; S.K., J.K.R., and J.L. wrote the paper.

**Funding:** Authors thankful to the Department of Energy (grant number: DE-SC0018322) and the NSF EPSCoR (grant number: OIA-1757220) for financial support.

**Acknowledgments:** Authors want to acknowledge the Extreme Science and Engineering Discovery Environment (XSEDE) by National Science Foundation grant number OCI-1053575 and XSEDE award allocation number DMR110088 and DMR110013P for providing state-of-the-art high-performance computing facilities for supporting this research.

**Conflicts of Interest:** The authors declare no conflict of interest.
