Diffusion of Various Molecules through Crystalline C$_{60}$ Solid and their Electronic and Vibrational Properties

First-principles density functional theory is used to study the diffusion of various molecules including diatomic molecules, inert gas molecules , and small metal atoms, and so on, through the C$_{60}$ solid. For each case, the energy surface of a diffusion path is calculated while performing full geometry relaxation of the whole system. Such studies are performed while changing the concentrations of diffusing molecules. The effects of these molecules on the electronic properties of C$_ {60}$ solid are also examined. Especially for diatomic molecules, such as H$_2$, N$_2$, and O$_2$, their frequency shifts are calculated relative to their corresponding counterparts.