Path Integral Monte Carlo Study of X@C₅₀ X=H₂, He, Ne, Ar

Path integral Monte Carlo (PIMC) method is employed to study the thermal properties of the X@C₅₀ X=H₂, He, Ne, Ar system at temperatures from 5 K to 300 K. The interaction energies and probability distribution functions of one noble gas atom or H₂ inside D_5h-symmetry C₅₀ are obtained. A rough sphere model is used in calculating interaction energies, as a comparison. This model gives much lower interaction energy than PIMC calculations on all X@C₅₀, except He@C₅₀. The PIMC method and the sphere model get nearly the same values of interaction energies on He@C₅₀. The spatial distributions are enlarged by the increase in temperature, while the interaction energies change slowly in a wide range of temperature. Temperature is not the major reason for the stability of the system. It is impossible to trap an X atom into C₅₀, except H₂ because only the H₂@C₅₀ has positive interaction energies from the PIMC calculations.