The interactions of several H-2 molecules [(H-2)(n), n = 1-5] within C-60, C-70, and C-82 have been studied with several DFT methods as well as with MP2 and SCS-MP2. As expected, B3LYP significantly underestimates dispersion interactions, while the M05-2X and M06-2X methods are in much better agreement with MP2 and SCS-MP2 results. Degenerate hydrogen exchange reactions were calculated for 3H(2) --> 3H(2) inside C-60, C-70, and C-82. The free-energy barrier at 298 K for the hydrogen exchange reaction 3H(2) --> 3H(2) is reduced from 88.8 kcal/mol for the free reaction to 36.2 kcal/mol for the reaction within C-60, corresponding to a k(cat)/k(uncat) ratio of 10(36). Steric compression, dispersion, and a favorable entropy contribute similar increments to the reduction in the free-energy barrier.