High Temperature Accelerated Stone-Wales Transformation and the Threshold Temperature of IPR-C₆₀ Formation

The Stone-Wales bond rotation isomerization of nonicosahedral C₆₀ (C_2v-C₆₀) into isolated-pentagon rule following icosahedral C₆₀ (I_h-C₆₀ or IPR-C₆₀) is a limiting step in the synthesis of I_h-C₆₀. However, extensive previous studies indicate that the potential energy barrier of the Stone-Wales bond rotation is between 6 and 8 eV, extremely high to allow for bond rotation at the temperatures used to produce fullerenes conventionally. This is also despite data indicating a possible fullerene road mechanism that necessitates low-temperature annealing. However, these previous investigations often have limiting factors, such as using the harmonic approximation to determine free energies at high temperatures or considering only the reverse I_h-C₆₀ to C_2v-C₆₀ transition as a basis. Indeed, when the difference in energy between I_h-C₆₀ and C_2v-C₆₀ is accounted for, this barrier is generally reduced by ∼1.5 eV. Thus, utilizing the recently developed density functional tight binding metadynamics (DFTB-MTD) interface, the effects of temperature on the bond rotation in the conversion of C_2v-C₆₀ to I_h-C₆₀ have been investigated. We found that Stone-Wales bond rotations are complex processes with both in-plane and out-of-plane transition states, and which transition path dominates depends on temperature. Our results clearly show that at temperatures of 2000 K, the free energy for a C_2v-C₆₀ to I_h-C₆₀ transition is only ∼4.21 eV and further reduces to ∼3.77 eV at 3000 K. This translates to transition times of ∼971 μs at 2000 K and ∼34 ns at 3000 K, indicating that defect healing is a fast process at temperatures typical of arc jet or laser ablation experiments. Conversely, below ∼2000 K, bond rotation becomes prohibitively slow, putting a lower threshold limit on the temperature of fullerene formation and subsequent annealing.