Relative concentrations of the nine IPR-based (isolated-pentagon-rule) isomers of Yb@C-82 are computed from the Gibbs energy derived from partition functions supplied with parameters from density functional theory calculations. A good agreement with experiment is found at elevated temperatures where the Yb-endohedrals based on the C-2v;9 and C-s (c);6 C-82 cages exhibit comparable concentrations while the third observed species based on the C-2(c);5 cage has about one half of their populations though still a significant presence.
The result is somewhat sensitive to the partition-function description.