Energy spectrum and optical absorption spectrum of exohedral fullerene С$_{50}$Cl$_{10}$ within the Hubbard model

Energy spectra of fullerene С$_{50}$ and exohedral fullerene С$_{50}$Cl$_{10}$ with the D$_{5\mathrm{h}}$ symmetry groups have been obtained within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecules С$_{50}$ and С$_{50}$Cl$_{10}$ have been determined. On the basis of the energy spectrum of exohedral fullerene С$_{50}$Cl$_{10}$ is given an interpretation of experimentally observed optical absorption bands molecule С$_{50}$Cl$_{10}$.