The low-lying charge-transfer (CT) excited-state plays an unprecedented role in promoting charge separation processes in organic photovoltaic (OPV) materials typically made of electron donor and acceptor building blocks. A Zn–porphyrin donor non-covalently bound to a fullerene derivative PCBM ([6,6]-phenyl-C₆₁-butyric acid methyl ester) acceptor displays low-lying CT excited states close to the donor absorbing state, and this unique donor–acceptor (D–A) complex is considered to be a potential candidate material for harvesting solar energy. Chemical tuning is expected to alter the CT energetics and their nature as well, which may affect the charge-separation efficiency. In this study, we computationally explore the possibility of tailoring the CT excited states of this novel composite by molecular-scale means via selective pyrrole ring hydrogenation of the Zn–porphyrin macrocycle donor using dispersion-corrected density functional theory (DFT) and time-dependent DFT methods employing an optimally tuned range-separated hybrid functional. Three representative donors are considered: Zn–porphyrin (no pyrrole ring hydrogenation), Zn–chlorin (one hydrogenated pyrrole ring) and Zn–bacteriochlorin (two hydrogenated diagonal pyrrole rings) that differ by the degree of pyrrole ring hydrogenation. Predictions are thoroughly compared to available theoretical and experimental data. Our results suggest that all three D–A complexes are energetically stable and show slightly increasing binding affinity with the extent of ring hydrogenation. This is ascribed to only a slight increase in the ground-state CT and significant van der Waals dispersion interactions. On the other hand, all three D–A complexes exhibit considerably tuned low-lying donor-localized π–π* absorbing and donor-to-acceptor CT states in their excited electronic states, which strongly affect the CT rates calculated in polar solvent. Among the three complexes studied, the one with the Zn–chlorin donor blended with the PCBM acceptor reveals energetics (such as driving force, reorganization energy and electronic coupling) strongly favouring the forward CT process with significantly reduced backward CT, and therefore, it turns out to be the best performer. This study sheds light on the fundamentals of molecular-scale engineering of excited-state properties in novel D–A complexes, which strongly affects the CT rates in polar solvent, and, thereby, opens up possible synthetic routes for tailoring and optimizing the performance level of OPV devices.