Calculation of the structure of carbon clusters based on fullerene-like С$_{24}$ and С$_{48}$ molecules

Equilibrium structures obtained by linking with valence bonds the carbon carcasses of two fullerene-like molecules have been studied by molecular dynamics simulation. In free fullerene, carbon atoms form $sp^2$ hybridized bonds, but at places of links between fullerenes, $sp^3$ hybridized bonds are formed, which determines the changes in the properties of such structures. In the literature, the topology of diamond-like phases is described, but equilibrium clusters based on fullerene-like molecules are underexplored. The right angles between the C–C bonds are energetically unfavorable, and the reduction in the energy of clusters in the process of relaxation is connected with the optimization of valence angles, which leads to a reduction in the symmetry of clusters and, in a number of cases, even to disruption of some valence bonds. It is shown that different fashions of linking two fullerenes result in the formation of clusters with different structures and energies. Different initial conditions can lead to different configurations of clusters with the same topology. Among the analyzed clusters, a structure with the minimum potential energy per atom was found. The results of this work contribute to the study of the real structure of carbon clusters.