Calculations of the relative populations of Lu@C82 isomers

Relative populations of five IPR (isolated-pentagon-rule) isomers of Lu@C82 are computed using the Gibbs energy based on characteristics from density functional theory calculations (B3LYP/6-31G*∼SDD entropy term, B2PLYPD/6-31G*∼SDD energetics). In agreement with observations, the major isomer has the C2v;9 cage.