The roles of singlet fission in the triplet generation of silicon phthalocyanine (SiPc), a compound analogous to the IRDye700DX photosensitizer used in near-infrared photoimmunotherapy, are investigated by considering the energetical relation between the excitations of this compound. These excitations are obtained through spin-flip long-range corrected time-dependent density functional theory calculations. To initiate singlet fission, chromophores must meet two conditions: (1) near-degenerate low-lying singlet and quintet (triplet-triplet) excitations with a considerable energy gap of the lowest singlet and triplet excited states and (2) moderate π-stacking energy of chromophores, which is higher than but not far from the solvation energy, to facilitate the dissociation and generation of triplet-state chromophores. The present calculations demonstrate that SiPc satisfies both of these conditions after the formation of π-stacking irrespective of the presence of an axial ligand(s), suggesting that singlet fission plays a crucial role in the triplet generation process, although intersystem crossing occurs simultaneously at a very slow rate.