Energy spectrum and optical absorption of endohedral complexes Er$_{2}$C$_{2}$@C$_{90}$ based on isomers no. 21 and no. 44

Optical absorption spectra (OASs) of endohedral Er$_{2}$C$_{2}$@C$_{90}$ complexes, based on isomers nos. 44 (C2) and 21 (C1) of fullerene C$_{90}$, have been simulated. To this end, the energy spectra of these isomers have been calculated. The calculations have been performed within two models. Within the first (conventional) model, only hoppings of $\pi$ electrons between sites (nearest-neighbor hopping integral $B\sim$ -2.6 eV) has been taken into account. Within the second model, intrasite Coulomb interaction (ISCI) of $\pi$ electrons (Coulomb-interaction integral $U\sim$ 7.0 eV) has been also taken into account along with intersite hoppings (nearest-neighbor hopping integral $B\sim$ -1.0 eV). Comparison of the obtained OAS curves with the experimental data c-onvincingly indicates that the second model describes adequately the OASs of endohedral Er$_{2}$C$_{2}$@C$_{90}$ complexes, based on the isomers under investigation. Charge transfer from the Er$_{2}$C$_{2}$ system to the fullerene shell was -4$e$.