*3.4. Energetics of Isolated FDs*

The computed HOMO energy of PCBM and P3HT are similar to experimental value while the LUMO values are overestimated by the chosen method which is accepted by the community [35]. According to McCormik et al. [35], B3LYP functional is sufficient to approximate HOMO energy of conjugated polymers while LUMO is not well approximated. Due to the overestimation of LUMO energy, the computed energy for HOMO-LUMO gap (Egap) is very high with B3LYP functional. To tradeoff between LUMO energy and Egap, we choose PBE functional for the ground state calculation. The computed value of the HLg for the gas phase isolated PCBM is 2.82 eV but González et al. reported 1.48 eV (PBE-D3/TZP) [31] and by Thompson et al. it amounts to 1.4 eV [36] whereas Cook et al. reported experimental value for pure PCBM films to be 1.8 eV [34]. The computed energy gap for the

isolated P3HT-8mer is 1.54 eV which is in good agreement with the reported results 1.31 eV [31] and 1.49 eV [37], whereas the experimental value for pure P3HT films is 1.9 eV [34]. Computed energetics of P3HT, PCBM and four FDs are compiled in Figure 5.

**Figure 4.** Structure of designed fullerene-derivatives (FDs) as lead acceptor molecule for polymer solar cells (PSCs).

**Figure 5.** Computed energy diagram of the four FDs along with [6,6]-phenyl-C61-butyricacidmethylester (PCBM) and P3HT. All the values obtained with the use of PBE/6-31G(d,p) level of theory in the gas phase.

We also compute the different driving forces for the exciton binding, dissociation, charge-transfer, and open-circuit voltage (VOC) for FDs which affect the smooth flow of exciton in the donor/acceptor blends. The following definition used to compute driving forces in terms of energy [38]:

$$
\Delta E\_1 = E\_{Donor}^{LLIMO} - E\_{Acceptor}^{LLIMO} \tag{2}
$$

$$
\Delta E\_2 = E\_{Acceptor}^{LILMO} - E\_{Donor}^{HOMO} = V\_{OC} \tag{3}
$$

$$
\Delta E\_3 = E\_{Domr}^{HOMO} - E\_{Acceptor}^{HOMO} \tag{4}
$$

The difference between the LUMO levels of donor and acceptor, ΔE1, is responsible for the charge dissociation of the excitons in polymer donor to overcome the excitations binding energy. The typical exciton binding energy is ca. 0.3–0.5 eV, if it is too large then the exciton charge separation will require more energy and lowers VOC. The value of ΔE2 determines the VOC which can be increased by up-shifted LUMO energy level of acceptors and thus higher efficiency of PSCs. ΔE3, the difference between the HOMO levels of donor and acceptor, affects the dissociation of electron-hole pairs in the donor/acceptor interface. If the HOMO levels of acceptor are too high, ΔE3 will be too small which hinders the dissociation of electron-hole pairs at interface in some extent [38]. So, it is necessary to maintain effective ΔE3 to maintain a smooth dissociation. But ΔE3 is not the sole factor which affects the efficiency of PSCs. Balancing between all the related factors (Table 3), FD4 will be efficient acceptor as it has the lower exciton binding energy and higher VOC with least ΔE3 value.

**Table 3.** Electronic energy level differences of P3HT and fullerene-derivatives (FDs) including [6,6]-phenyl-C61-butyricacidmethylester (PCBM).

