Fullerene derivatives have been shown to play a role in many applications. Consequently, both structural and vibrational properties of C60 and C80 fullerenes and their epoxides are studied by the quantum mechanical semi-empirical PM3 method. Results indicate a similarity between the structures of fullerenes as compared with their epoxides on the one hand and the studied dimers on the other hand. The final heat of formation is higher in the case of C80 and its epoxide as compared with that of C60. Results show that the calculated C60 spectra are higher than the experimental spectra, according to both anharmonicity effects and electron correlation.