The paper surveys ongoing computations on endohedral fullerene systems, combining the treatments of quantum chemistry and statistical mechanics. Relative concentrations of four isomers of Ca@C 72 , six isomers of Ca@C 74 , nine isomers of Ca@C 82 , and four isomers of La@C 82 are evaluated using the Gibbs energy based on density-functional theory (DFT) computations. The results illustrate the enthalpy -entropy interplay in the systems produced under high temperatures. Approximations for description of the encapsulate motions are analyzed.