Theoretical calculations on the mechanism of local polymerization and depolymerization of C$_{60}$

A reversible chemical reaction between C$_{60}$ molecules, polymerization/depolymerization, has been realized and controlled using an STM tip: the polymerization and depolymerization occur at negative and positive sample bias conditions, respectively. Using a first-principles calculation method, we investigated the mechanism responsible for the experimental results. The electronic structures were calculated for polymerized and depolymerized structures of C$_{60}$ dimers under negatively and positively ionized conditions as well as neutral condition. When a couple of C$_{60}$ is negatively ionized, the added electron occupies the initially unoccupied bonding orbital between C$_{60}$ molecules. Then the activation barrier of a polymerization is reduced. When a C$_{60}$ dimer is positively ionized, the bonding orbital energetically approaches to Fermi level and the activation barrier of depolymerization process is reduced.