To quantitatively compare the binding strength between various cyclocarbons and C60 fullerene, we calculated binding energies based on electronic energies (Ebind) as well as binding free energies of gas-phase (G°bind(gas)) and aqueous-phase (G°bind(aq)) at respective standard states. Ebind was calculated using standard definition, that is Ebind = E(C60@Cn) -[E(C60) + E(Cn)], where E represents electronic energy evaluated at the respective optimized geometry. G°bind(gas) and G°bind(aq) were calculated by a similar way, but using free energies in the corresponding phases instead. The results of binding energies are collectively plotted in Fig. , and the raw data are given in Table .