Fullerene molecules are nowadays routinely produced with high yields in the range of 20% or higher per produced carbon in oxygen-rich hydrocarbon flames. This fact clearly indicates that the formation of fullerene molecules is not a stochastic and rare event but follows a certain formation pathway. However, since intermediate structures along this pathway remain undetectable in experiments, the formation mechanism of fullerene molecules has long been subject to speculation. Moreover, the high dimensionality of the problem makes it impossible to study all the possible intermediate and transition state structures using quantum chemical methods, although several studies based on semi-empirical or ab initio approaches were attempted. Common to these studies with fixed system sizes is that a very large energetic barrier has to be overcome prior to energy release due to cage closure and fullerene formation, independent of shape or form of the intermediates which makes the folding of curved carbon cluster structures into fullerenes by themselves highly unlikely even under harsh experimental conditions.
In this work we present a new quantum chemical molecular dynamics approach towards fullerene formation using the density functional tight binding (DFTB) method by which energies and gradients are computed and various types of kinetic energy thermostats. First, we demonstrate how open-ended carbon nanotubes can easily close to form cage structures by reducing the number of dangling bounds at the edges. Temperatures are kept in the range between 2000 and 4000 K with 3000 K giving the best results .
Second, we take into account the fact that fullerene molecules are always formed in an open environment where both thermal and chemical energy are supplied in excess quantities. We are starting with ensembles of 30 C2 units randomly positioned in a 30 Å cubic periodic boundary box. and new C2 units are randomly placed into the box at a constant rate, which is varied among different trajectories. We find that at under certain conditions nucleation of larger carbon complexes with a high pentagon/hexagon ratio can occur within about 6 ps simulation time. This is the crucial step. Once a curved carbon cluster has formed, additional C2's are added to its borders, releasing energy by annihilation of dangling bonds, which enables larger cumulenic chains attached to the edges to fold themselves onto the border and thereby increasing the numbers of hexagons and pentagons along the reaction pathway. Finally, cage closure occurs naturally when the system's curvature is large enough. Subsequent annealing leads eventually to perfectly symmetrical structures by Stone-Wales rearrangements. The entire process is energetically downhill throughout.
 S. Irle, G. Zheng, M. Elstner, and K. Morokuma, "Formation of Fullerene Molecules from Carbon Nanotubes: A Quantum Chemical Molecular Dynamics Study", Nano Lett. 3, 465-470 (2003).
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