Energy spectrum and optical properties of fullerene C$_{50}$(D$_{5h})$ within the Hubbard model

The energy spectra of C$_{50}$ fullerene and molecule C$_{50}$Cl$_{10}$ of symmetry group D$_{5h}$ were obtained within the Hubbard model in the mean-field approximation. Using group theory methods, the classification of energy states was carried out, and the allowed transitions in the energy spectra of C$_{50}$ and C$_{50}$Cl$_{10}$ molecules of symmetry group D$_{5h}$ were determined. On the basis of this spectrum, an interpretation of experimentally observed optical absorption bands of molecule C$_{50}$Cl$_{10}$ is proposed.