Energy spectrum and optical properties of fullerene C$_{80}(I_{h})$ within the Hubbard model

The anticommutative Green's functions were derived in an analytical form, and the energy spectra of C$_{80}$ fullerene and endohedral Y$_3$N@C$_{80}$ fullerene of symmetry group Ih 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$_{80}$ and Y$_3$N@C$_{80}$ molecules of symmetry group Ih were determined.