Energy and optical absorption spectra of endohedral metallofullerenes with Gd or Ho as strongly correlated $\pi$-electron systems

Isomerically pure endohedral metallofullerenes Gd@C$_{82}$(C$_{2v}$), Ho@C$_{82}$(C$_{2v})$, and their monoanions have been synthesized and separated. The optical absorption spectra of solutions of obtained compounds in $o$-dichlorobenzene have been studied. Within the Hubbard model, the energy spectrum of isomer of C$_{2v}$ symmetry (no. 9) of fullerene С$_{82}$ has been calculated. Based on the obtained spectrum, optical absorption spectra of endohedral metallofullerenes Gd@C$_{82}$ and Ho@C$_{82}$ and their monoanions have been simulated. The calculated optical absorption spectra have been compared with experimental ones; it has been found that qualitative agreement between them is observed.