Systematic study of structures and stabilities of fullerenes

Abstract

We describe a scheme to generate the ground-state network for carbon clusters. Combining ' it is reported that structures for Cs2 and Cs4 always contain seven-member ring defects although we now know that a much more stable structure exists with only five-and six-membered rings. The energy to break the carbon bonds and rearrange the network is so high that it is difficult to reach the ground state unless one starts from a structure which already has the correct topology.To overcome the difficulties mentioned above, we devised a scheme for generating energetically favorable structures for large fullerenes. In this scheme, we first focus on generating the correct topological networks for energetically favorable structures. Instead of looking at the network connecting individual atoms, we focus our attention on the "face-dual" network obtained by linking the centers of each of the polygonal face of the cage structure. Since each atom of the fullerene is threefold coordinated, the face-dual network consists of a triangular mesh. For a fullerene with N atoms, the number of polygonal faces is N/2+2. We represent each of the faces by a point lying on a predetermined surface (a sphere for example) and obtain the ground-state network by simulated annealing. Initially these points are placed at random and interact with one another through a two-body repulsive potential. The face-dual network obtained can then be inverted to obtain the fullerene structure. In this scheme, whether a face is pentagonal or hexagonal is determined by the number of nearest-neighboring faces. Thus the change from pentagon to hexagon can occur easily with a small energy barrier and even for quite large number of atoms, the system does not get trapped in local metastable states. Also, this scheme distributes the faces as evenly as possible on the constrained surface and the resultant topological networks tend to separate the pentagonal faces as far apart as possible which makes the structures generated good candidates for low-energy fullerene structures. By varying the shape of the constraining surface (changing 7333

Theoretical studies of zirconium and carbon clusters with molecular dynamics simulations

“…But if we consider the proposed growth mechanism [114,115], fuUerenes can grow by adding two carbon atoms each time or can shrink by losing two carbon atoms, then only the stability of a fuUerene relative to its neighbours really matters. In our previous study [47], we did find that CgQ, Cjq and Cg4, the three most abundant fuUerene members, are more stable than their neighbors. Though the growth mechanism of the carbon network is stiU not clear, by analogy to the fuUerene, we searched the possible structures of networks with 214 atoms and 218 atoms per unit ceU for the P surface.…”

“…In this dissertation, we will present a systematic study of structures of fuUerenes ranging from C20 to Cjoo t)y introducing a novel scheme [47]. Using our new scheme, we not only reproduce aU known fuUerene structures but also successfuUy predicted several other fuUerene structures which were confirmed by experi ments [48,49,50].…”

“…In our previous TBMD simulations [46,47,48,49], the electrons always occupy the lowest energy states. In the other words, the electron temperature Tg^ is set to zero.…”

“…To overcome the difficulties mentioned above, we devised a scheme for generating energetically favorable structures for fuUerenes [47]. In this scheme, we first try to generate the correct topological networks for energetically favourable structures.…”

“…In the fuUerene family, Cgg is not special in the sense of binding energy since every fuUerene larger than 68 has a larger binding energy [47]. But if we consider the proposed growth mechanism [114,115], fuUerenes can grow by adding two carbon atoms each time or can shrink by losing two carbon atoms, then only the stability of a fuUerene relative to its neighbours really matters.…”