A series of complexes based on the structure of an H2O2-responsive Ir(III) phenylpyridine(ppy)-containing complex were designed. The effect of changing the conjugation in the ppy ligands as well as of replacing the Ir(III) metal centre with the isoelectronic Os(II) were evaluated by means of DFT and its time-dependent formulation. The computational exploration of the photophysical properties of all the designed complexes suggest that the character of the low-lying singlet state represent the main factor affecting the region of absorption. In particular, for some of the Ir(III)-based complexes the change of the band character from mixed MLCT/LLCT to almost exclusively LLCT is essential for red-shifting the maximum absorption wavelength together with the destabilization of HOMO thus reducing the HOMO-LUMO energy gap; similarly, the replacement of Ir(III) with Os(II) converts the character of the band to mainly MLCT. The computed spin–orbit coupling constants and the triplet states’ energy confirm that all the designed complexes could, in principle, be able to generate the cytotoxic singlet oxygen under one-photon excitation by energy transfer from the triplet state of the photosensitizer to molecular oxygen, while the production of other types of ROS is precluded, similarly to the reference complex.