The energy spectrum and optical properties of fullerene С$_{36}$ within the Hubbard model

The anticommutator Green's functions and the energy spectra of fullerene С$_{36}$ and endohedral fullerene La@C$_{36}$, with both of them belonging to the D$_{6h}$ symmetry group, are obtained analytically within the Hubbard model in the mean-field approximation. Using group-theory methods, their energy states are classified and allowed transitions in the energy spectra of the С$_{36}$ and La@C$_{36}$ molecules, both belonging to the D$_{6h}$ symmetry group, are determined.