In order to clarify whether C-36 has a fullerene structure with D-6h symmetry, B3LYP calculations were performed for hydrogenated species of the putative [36-D-6h]fullerene (C36Hn; n = 1, 2, 4, and 6) as well as mono- and dianions of C36H6. Contrary to the experimental results, it appears that the hydrogenated [36-D-6h]fullerene no longer has a diradical character corroborating the high reactivity. If the long-lived C36H6 is derived from [36-D-6d]fullerene, the first electron affinity is predicted to be 0.60 eV, lower than that of intact C-36, 2.5 eV, and, furthermore, the C-13-NMR spectrum for C36H6 would show a signal in the extremely low field region.