Energy spectrum and optical absorption spectra of endohedral fullerenes Lu$_3$N@C$_{80}$ and Y$_3$N@C$_{80}$ within the Hubbard model

Anticommutator Green's functions and energy spectra of fullerene C$_{80}$, endohedral fullerenes Lu$_3$N@C$_{80}$ and Y$_3$N@C$_{80}$ with the $I_h$ symmetry groups have been obtained in an analytical form 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 C$_{80}$, Lu$_3$N@C$_{80}$ and Y$_3$N@C$_{80}$ have been determined. On the basis of these spectra, an interpretation of experimentally observed optical absorption bands endohedral fullerenes Lu$_3$N@C$_{80}$ and Y$_3$N@C$_{80}$.