Combining an efficient simulated annealing scheme for generating closed, hollow, spheroidal cage structures with a tight-binding molecular-dynamics method for energy optimization, the ground-state structure of every even-numbered carbon fullerene from C72 to C102 is determined. As a general trend, most ground-state structures of the large fullerenes have relatively low symmetries. In many cases, several isomers of a fullerene are found to have competitively low energies, which suggests that a mixture of these isomers can be observed in experimental prepared samples.

The ground-state structures of small fullerenes below C70 were determined by tight-binding molecular-dynamics total energy optimization. An efficient simulated annealing scheme was used to generate closed, hollow, spheroidal cage structures for all even-numbered carbon clusters from C20 to C70. As a general trend, fullerenes prefer geometries which separate the pentagonal rings as far apart as possible. Except for C60, C70, and C50, most fullerenes have relatively low symmetries.

The vibrational frequencies of three C84 fullerene isomers are calculated with a tight-binding potential model. The differences between the vibrational properties of these isomers are discussed.Following the breakthrough in producing macroscopic quantities of C6o, ' a number of higher fullerenes have also been recently synthesized.The study of structural and dynamical properties of these higher fullerenes has attracted considerable theoretical as well as experimental interests. Among the higher fullerenes, C84 is one of the more abundant species. Although experimental e8'orts have produced detailed information on the ' C nuclear magnetic-resonance spectrum, infrared (IR) spectrum, and ultraviolet photoemission spectrum of C84, ' ' ' many chemical and physical properties of this molecule remain unclear. Three isomers of C84 with Td, D6I"and helical D2 symmetries first proposed by Fowler have been widely studied ' and the helical D2 isomer was preferred by simple Hiickel theory. However, more recent calculations' ' showed that the helical D2 isomer is, in fact, energetically very unfavorable. In our previous work' based on tight-binding calculations for all 24 isolated-pentagon isomers of C84, ' we found that two isomers with D2 and D2d symmetries are energetically most stable. Moreover, these two isomers are so close in energy and structure that they may form an inseparable mixture in the synthesis of C84. Similar results were also obtained from modified neglect of difFerential overlap calculations' and first-principles total-energy calculations. i4'~6In this paper, we present a study of the vibrational properties of the low-energy Dz and D2d isomers of C84 using a tight-binding potential. We also studied the lessstable helical D2 isomer for comparison. Although several theoretical studies on the vibrational properties of C84 have been reported, " the calculations have been performed for the less-stable T", D6~, and helical D2 geometries and not for the low-energy D2 and D2d structures. The tight-binding (TB) potential model used in the present calculation is taken from the previous work of Xu et al. ' In this model, the total energy contains two terms, of various structural and dynamical properties of carbon fullerenes, including the predictions of low-energy structures of C84 and the study of vibrational properties of 18 C6o.The structures of the two low-energy isomers and the helical D2 isomer of C84 used in the present calculation are shown in Fig. 1. The coordinates of the isomers have been optimized by the tight-binding potential. As one can see from Fig. 1, the two low-energy D2 and D2d isomers are quite spherical while the helical D2 isomer has an elongated shape. It is also interesting to note that the two low-energy isomers can be transformed from one to (a) D2 (b) D2d (c) DZ(Helical) occupied E(Ir, I)= g (P"~II&B(Ir;I)~P")+E"&(Ir,j) . The first term in (I) is the electronic energy calculated by a parametrized TB Hamiltonian HrB(Ir; I), and the second term is a short-ranged repulsive energy. This tight-b...