Prediction of the intensity and structure of spectra associated with the endohedral motions of metal-containing buckyballs

A theoretical simulation is presented of the absorption spectrum of a particle trapped within a spherical potential with a barrier to motion through the center of the potential. The system is investigated as a simple model for ionic endohedral metallofullerenes, such as Na+@C60−. The radial Schrödinger equation was solved using an inverted Morse potential from Ballester and Dunlap, which they obtained by spherically averaging an icosahedral potential calculated with density functional theory for a Na+ in a neutral C60. The resulting energies and wave functions were used to generate a spectrum which lies in the microwave and far infrared regions. The energy levels have been characterized using relations generally applied to diatomic molecules with parameters analogous to ωe, ωexe, Be, De, and αe. There is a high degree of mixing of vibration and rotation in this system. Transition matrix elements were computed for transitions in both the microwave and far infrared regions which suggest that the transitions would be quite intense. It is hoped that this investigation will encourage an experimental search for these spectra and provide a useful first step in guiding the interpretation of the far infrared and microwave spectra of metal-containing fullerenes.