Energetics and Electronic Structures of Encapsulated $C_{60}$ in a Carbon Nanotube

We report total-energy electronic structure calculations that provide energetics of encapsulation of ${\mathrm{C}}_{60}$ in the carbon nanotube and electronic structures of the resulting carbon peapods. We find that the encapsulating process is exothermic for the $(10,10)$ nanotube, whereas the processes are endothermic for the $(8,8)$ and $(9,9)$ nanotubes, indicative that the minimum radius of the nanotube for the encapsulation is 6.4 Å. We also find that the ${\mathrm{C}}_{60}@(10,10)$ is a metal with multicarriers each of which distributes either along the nanotube or on the ${\mathrm{C}}_{60}$ chain. This unusual feature is due to the nearly free electron state that is inherent to hierarchical solids with sufficient space inside.