On the Structures and Growing Mechanisms of the Ti@C2n (2n = 26 - 50) Endohedral Fullerenes

During the last years, several mechanisms have been suggested in relation to the formation of fullerenes. One of them involves the ingestion of a C₂ unit by an already formed fullerene. In this communication, we summarize the theoretical investigations carried out for the series of Ti@C_2n endohedral fullerenes, with 2n = 26 to 50.  After a thorough exploration of the most favorable isomers, potential energy surfaces associated with the C₂ addition, and the topology of the involved structures we have concluded that in contrast to large endohedral metallofullerenes (2n>60) in which the empty cage is different to the optimal cage that hosts a metal ion or a small cluster, in small endohedral fullerenes encapsulating a tetravalent ion the empty and hosting cage often coincides. The addition of a C₂ unit to an already formed Ti@C_2n fullerene is always an exergonic reaction. Most of the lowest in energy isomers are formally linked by a C₂ addition and a Stone-Wales transformation.  Car-Parrinello Molecular Dynamics calculations show that after the attack of a C₂ unit to one of the C atoms of the Ti@C_2n system, the formation of the second C-C bond that closes the cage is an improbable event and must be accelerated using Metadynamics or via an external collision, for example with He atoms that are present in the sample.