Collective dynamics of Ca atoms encapsulated in C₆₀ endohedral fullerenes

Endohedral C₆₀ fullerenes with up to four encapsulated Ca atoms were investigated by ab initio molecular dynamics simulations (AIMD). The relatively long runs allow us to describe the correlated movement of the Ca atoms inside the fullerene cage. For the systems with one or two Ca atoms a relatively unimpeded rotation was conjectured by earlier nuclear magnetic resonance experiments and supported by previous ab initio calculations used to sample the potential energy landscape. Here, by AIMD calculations, we confirm not only the circular motion, but also the correlated movement of the two Ca atoms, which is due to electric dipole interactions on the inner surface of the C₆₀ molecule. Furthermore, systems with three and four Ca atoms present highly symmetric configurations of the embedded atoms, which are shown to rotate consistently within the fullerene cage, while more complex charge density patterns emerge. Employing artificial neural network models we perform a force-field mapping, which enables us to reproduce the main characteristics of the actual dynamics, such as the circular motion and the correlated movement of the Ca atoms.