Relative populations of the IPR (isolated-pentagon-rule) isomers of Ce@C-82 under the high-temperature synthetic conditions are computed using the Gibbs energy based on characteristics from the density functional theory calculations (B3LYP/3-21G - SDD entropy term, B2PLYPD/6-31G* - SDD energetics). In agreement with observation, Ce@C-2v(9)-C82 (major isomer) and Ce@C-s(c; 6)-C-82 (minor isomer) endohedrals are the most populated species.
Their observed ratio is in the computational modeling reached at a temperature of about 1225 K (under a presumption of the same solubility of the isomers).