$C_{24}$ fullerene within the Hubbard model

Background. The Hubbard model is widely used for theoretical description of strongly correlated electronic systems. Investigations of carbon nanosystems within the Hubbard model demonstrate that theoretical results agree with experimental data. The purpose of this paper is to obtain and to investigate the energy spectrum of $C_{24}$ fullerene within the Hubbard model. Materials and methods. Methods of quantum theoretical field were used to obtain the Green's functions. The Green's functions were found by the method of the motion equations for creation operators. Approximation of the mean field was used to obtain a closed system of differential equations for finding the creation operators. Results. The energy spectrum and the degree of degeneracy of each energy level in $C_{24}$ fullerene were found by the Green's functions. A classification of the energy levels in fullerene $C_{24}$ was realized by the group theory. Conclusions. This work demonstrates that $C_{24}$ fullerene has ten energy levels and ten symmetrically enabled transitions between energy levels.