Penultimate Intermediates to C60 and C70

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.

Local Modifications of Single-Wall Carbon Nanotubes Induced by Bond Formation with Encapsulated Fullerenes

Defected fullerenes in nanopeapods form bonds with the encapsulating single-walled carbon nanotubes when irradiated by an electron beam leading to changes in the guest (fullerene) and the host (nanotube). Intrinsic reaction coordinate (IRC) analysis based on B3LYP hybrid density functional theory shows that a C1-C59 defect with a single protruding C atom is initially formed from the C60(Ih) cage. The high activation energy for this step (8.37 eV (193.0 kcal/mol)), being assumed to be accessible during irradiation, is lower than that of the Stone-Wales rearrangement on the sp2 network. The binding of the defected fullerene to the nanotube is preferential, orthogonal bonds relative to the tube axis being slightly preferred. Because of the covalent bonds formed between the guest and host, the carbon network on the nanotube is locally perturbed in the vicinity of the binding site. As a result of the new bonds, bisnorcaradiene-like as well as quinonoid-like patterns appear near the binding site. These results are interpreted using orbital interaction and Clar diagram arguments. The changes in the bonding pattern on the nanotube should be significant in further functionalization of carbon nanotubes.

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.

Scratching the surface of buckminsterfullerene: the barriers for Stone-Wales transformation through symmetric and asymmetric transition states

General-gradient approximation (PBE) and hybrid Hartree-Fock density functional theories (B3LYP) in conjunction with basis sets of up to polarized triple-zeta quality have been applied to study the Stone-Wales transformation of buckminsterfullerene (BF) to yield a C(60) isomer of C(2)(v) symmetry with two adjacent pentagons (#1809). In agreement with earlier investigations, two different transition states and reaction pathways could be identified for the rearrangement from BF to C(60)-C(2)(v) on the C(60) potential energy surface (PES). One has C(2) molecular point group symmetry with the two migrating carbon atoms remaining close to the fullerene surface. The other one has a high-energy carbene-like (sp(3)) structure where a single carbon atom is significantly moved away from the C(60) surface. The carbene intermediate and the second transition state along the stepwise reaction path characterized previously at lower levels of theory do not exist as stationary points with the density functionals utilized here. The classical barriers of both mechanisms are essentially identical, 6.9 eV using PBE and 7.3 eV with B3LYP.