# Quantum mechanical studies on formation mechanisms of fullerenes

## Xinlei Hua, Tahir Cagin*, Jianwei Che, William A. Goddard, III

Materials and Process simulation Center, California Institute of Technology,
*tahir@wag.caltech.edu
http://www.wag.caltech.edu/home/tahir/

## Abstract

One of the most puzzling aspects of fullerenes is how such complicated symmetric molecules are formed from a gas of atomic carbons [1], namely, the atomistic or chemical mechanisms. Are the atoms added one by one or as molecules (C2, C3)? Is there a critical nucleus beyond which formation proceeds at gas kinetic rates? What determines the balance between forming buckyballs, buckytubes, graphite and soot? The answer to these questions is extremely important in manipulating the systems to achieve particular products.

A difficulty in current experiments [2-4] is that the products can only be detected on time scales of $\mu$s, long after many of the important formation steps have been completed. Consequently, it is necessary to use simulations, quantum mechanics and molecular dynamics, to determine these initial states. Experiments serve to provide the boundary conditions that severely limit the

In the original laser evaporation experiments of Kroto and Smalley [5], in the electric arc experiments of Kratchmer and Huffman [6], and in the geological fullerenes found in the Precambrian Russian rock [7] which might have resulted from lightening, there is a common condition: pressure and temperature gradient. Thus in fullerene formation the intricate balance between pressure and time played an important role. Pressure determines the density of carbon atoms in a given space, thus available source of growth. While time in terms of temperature, determines how long a metastable state would last in existence. Howard [8] produces fullerenes from benzene flame. The crucial difference here is the existence of H atoms. Because the H atoms are agents to terminate dangling bonds, the energetics in the flame set-up is quite different. The fact that this method gives lower yield than arc method indicates the existence of dangling bonds is actually helpful in the process of finding fullerene minima. The presence of buckytubes[9] suggest that cylinders are also competetive in energy, so are the bucky onions.

All the above demonstrate that kinetic pathways, the temporal sequence for the formation of carbon clusters, more than the energy of the equilibrium states, need to be carefully examined to elucidate the mexhanisms by which buckyballs, buckytubes, onions, and graphite form.

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