Calculated relative populations for the Eu@C82 isomers

Formation of the icosahedral C60 fullerene via migration of single sp atoms and annihilation of sp-atom pairs

The disappearance of sp2 structural defects during abundant fullerene isomer formation is considered within the framework of the atomistic mechanism with participation of carbon atoms with sp hybridization. The study is carried out using the example of the icosahedral C60-Ih fullerene formation from the appropriate C58-C2v fullerene with a 7-ring. In this case the studied atomistic mechanism includes the following stages: (1) insertion of single carbon atoms into the fullerene from carbon vapor as an sp-atom instead of or above a bond, (2) directional migration of the sp-atom positions towards the 7-ring with decrease of energy, and (3) meeting of two sp atoms near the 7-ring with annihilation of the sp-atom pair and formation of the sp2 structure of the C60-Ih fullerene. The probabilities of all possible sp-atom positions on the appropriate C58-C2v fullerene shell are estimated as a function of temperature using the total energies of these positions obtained by spin-polarized density functional theory calculations using the PBE functional. Based on these estimations, it is shown that formation of the C60-Ih isomer is the most probable within the framework of the considered mechanism relative to other C60 isomers. The energetics of sp-atom pair annihilation in the formation of the C60-Ih isomer is also studied via DFT calculations. The advantages of the considered atomistic mechanism of the abundant fullerene isomer formation are discussed.