| Summary: | The recently synthetically prepared endohedral CH<sub>4</sub>@C<sub>60</sub> was characterized here using calculations—namely its structure, energetics, thermodynamics, and vibrational spectrum. The calculations were carried out with DFT (density-functional theory) methods, namely by the DFT M06-2X functional and MP2, as well as B2PLYPD advanced correlated, treatments with the standard 6-31++G** and 6-311++G** basis sets, corrected for the basis set superposition error evaluated using the approximative Boys–Bernardi counterpoise method. The symmetry of the endohedral obtained in the geometry optimizations was tetrahedral T. The energetics of CH<sub>4</sub> encapsulation into C<sub>60</sub> was attractive (i.e., with a negative encapsulation-energy term), producing a substantial energy gain of −13.94 kcal/mol at the most advanced computational level, B2PLYPD/6-311++G**. The encapsulation equilibrium constants for CH<sub>4</sub>@C<sub>60</sub> were somewhat higher than previously found with the CO@C<sub>60</sub> system. For example at 500 K, the encapsulation equilibrium constant for CH<sub>4</sub>@C<sub>60</sub> had a value one order of magnitude larger than for CO@C<sub>60</sub>. The encapsulation thermodynamic characteristics suggest that high-pressure and high-temperature synthesis could in principle also be possible for CH<sub>4</sub>@C<sub>60</sub>.
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