Theoretical investigation on isomer formation probability and free energy of small C clusters

Molecular dynamics simulations and free energy calculations are employed to investigate the evolution, formation probability, detailed balance, and isomerization rate of small C cluster isomer at 2500 K. For C₁₀, the isomer formation probability predicted by free energy is in good agreement with molecular dynamics simulation. However, for C₂₀, C₃₀, and C₃₆, the formation probabilities predicted by free energy are not in agreement with molecular dynamics simulations. Although the cluster systems are in equilibrium, detailed balance is not reached. Such results may be attributed to high transformation barriers between cage, bowl, and sheet isomers. In summary, for mesoscopic nanosystems the free energy criterion, which commonly holds for macroscopic systems in dynamic equilibrium, may not provide a good prediction for isomer formation probability. New theoretical criterion should be further investigated for predicting the isomer formation probability of a mesoscopic nanosystem.