Monte Carlo simulations for the free energies of C₆₀ and C ₇₀ fullerene crystals by acceptance ratio method and expanded ensemble method

Accurate values of the free energies of C₆₀ and C₇₀ fullerene crystals are obtained using expanded ensemble method and acceptance ratio method combined with the Einstein-molecule approach. Both simulation methods, when tested for Lennard-Jones crystals, give accurate results of the free energy differing from each other in the fifth significant digit. The solid-solid phase transition temperature of C₆₀ crystal is determined from free energy profiles, and found to be 260 K, which is in good agreement with experiment. For C₇₀ crystal, using the potential model of Sprik et al. [Phys. Rev. Lett. 69, 1660 (1992)], low-temperature solid-solid phase transition temperature is found to be 160 K determined from the free energy profiles. Whereas this is somewhat lower than the experimental value, it is in agreement with conventional molecular simulations, which validates the methodological consistency of the present simulation method. From the calculations of the free energies of C₆₀ and C₇₀ crystals, we note the significance of symmetry number for crystal phase needed to properly account for the indistinguishability of orientationally disordered states.