A systematic first-principle study based on the density functional theory has been performed on the electronic structures and stabilities of fullerene C 68 and its derivatives C 68X 4 (X = H, F, Cl). By searching the 6332 classical and 43 nonclassical isomers of C 68, the ground state is found to be the classical isomer 6290 bearing C 2 symmetry. However, after attaching X atoms to the active sites of C 68, the heptagon-containing nonclassical derivatives C 68(c)-2 C 68H 4, C 68(c)-2 C 68F 4, and C 68(c)-3 C 68Cl 4 are predicted to be the most stable among all derivatives. The chemical deriving could affect the electronic structures distinctly, and enhance the stability of fullerene C 68. The Mulliken charge populations of the most stable C 68X 4 are calculated, showing that different X atoms added to C 68 will cause remarkably different charge populations. The IR, Raman, and NMR spectra of the most stable C 68X 4 are also calculated and presented to facilitate future experimental identification.