Relative populations of the four energy-lowest isolated-pentagon-rule (IPR) isomers of Y@C(82) under the high-temperature synthetic conditions are computed using the Gibbs energy based on characteristics from the density functional theory calculations (B3LYP/6-31G*-SDD entropy, B3LYP/6-31G*-SDD and B2PLYPD/6-31 +G*-SDD energetics). Two major species are predicted, Y@C(2v); 9-C(82) and Y@C-s(c); 6-C(82), their calculated equilibrium relative populations agreeing with observations.