One of the most important processes for photosensitisers is the intersystem crossing to the triplet state. We considered theoretically this process for the complex of fullerene C ₆₀ with the amino acid tryptophan (Trp) in comparison with pure fullerene C ₆₀ and C ₆₀ modified with trimalonic acid by use of density functional theory. Our comparative findings suggest that C ₆₀-Trp possesses high intersystem crossing rate to saturate T ₁ state. We suppose that C ₆₀-Trp could bind to DNA aptamer by CO-NH bonds creating novel conjugates with carriers for specific purposes on the cell surface without affecting the photosystem, which may allow it to efficiently generate reactive oxygen species.