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

Abstract

The Stone–Wales bond rotation isomerization of nonicosahedral C60 (C2v-C60) into isolated-pentagon rule following icosahedral C60 (Ih-C60 or IPR-C60) is a limiting step in the synthesis of Ih-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 Ih-C60 to C2v-C60 transition as a basis. Indeed, when the difference in energy between Ih-C60 and C2v-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 C2v-C60 to Ih-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 C2v-C60 to Ih-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.

Carbon Condensation via [4 + 2] Cycloaddition of Highly Unsaturated Carbon Chains

“…One mode of cyclization of a cyclooctane derivative may generate a bicyclo[3.3.0]octane structure, which consists of fused 5-membered rings. Although fullerenes do not contain fused 5-membered rings (the 'isolated pentagon rule'), 20,51,52 the Stone−Wales rearrangement or other rearrangement reactions allow 5-membered rings to migrate in a sheet of carbon. 52,53 In the current study, the cyclodecane skeleton was derived from a dehydronaphthalene precursor (Scheme 4).…”

“…Although fullerenes do not contain fused 5-membered rings (the 'isolated pentagon rule'), 20,51,52 the Stone−Wales rearrangement or other rearrangement reactions allow 5-membered rings to migrate in a sheet of carbon. 52,53 In the current study, the cyclodecane skeleton was derived from a dehydronaphthalene precursor (Scheme 4). Depending on the nature of substituents and substitution pattern, a cyclodecane derivative may afford the possibility for structural rearrangement and to permute the substituents on a dehydronaphthalene skeleton.…”

Role of Graphitic Bowls in Temperature Dependent Fullerene Formation

“…All calculations were conducted with second order, self-consistent charge density functional tight binding (SCC-DFTB) via the DFTB+ package , with the PLUMED2 library was included as previously described. , These calculations utilized the mio-1-1 Slater–Koster files which contain tabulated Hamiltonian and overlap matrix values along with repulsive terms . This set of parameters has been tested extensively alone and with other Slater–Koster parameter sets and has been used by us previously for fullerene systems specifically . The velocity–Verlet method was used to integrate the equations of motion with a 1 fs time step .…”

“…45 This set of parameters has been tested extensively alone 46 and with other Slater−Koster parameter sets 47 and has been used by us previously for fullerene systems specifically. 48 The velocity− Verlet method was used to integrate the equations of motion with a 1 fs time step. 49 A Nose−Hoover chain thermostat with a chain length of 3 and coupling strength of 500 cm −1 (6.67 ps −1 ) was used to maintain a NVT ensemble.…”