Electronic and vibrational properties of the C₆₀ molecule

We have studied the electronic and vibrational properties of the C₆₀ molecule by means of simplified models where only a few parameters are adjusted to experimental data. For the electronic part we use an independent electron model with a central Morse potential corrected by splitting the spherical degeneracy by properly including the icosahedral symmetry given rise to the LUMO and HOMO states. The vibrational spectra is obtained by solving the corresponding secular equation using a Born-Mayer type potential with two parameters adjusted to Raman and IR spectra. The results of our model are compared with some of the best ab initio calculations, phenomenological models and experimental data. We found in general a good agreement for the vibrational spectrum particularly for the high frequency part. Since in our model contains only two parameters we are not able to reproduce accurately the whole spectra. The main contribution of this model is its simplicity to extract most of the gross features of the C₆₀ molecule without cumbersome computation.