Swarm intelligence unravels the confinement effects for tiny noble gas clusters within carbon nanotubes

Inspired by the myriad manifestations of confinement effects for atoms and molecules encapsulated within carbon nanotubes (CNTs), herein, we explore the role of the physical dimensions of the CNTs in controlling the optimal configurations of confined noble gas clusters. We utilize the particle swarm optimization (PSO) technique together with the continuum approximation for CNTs to arrive at the minimum energy configurations of the encapsulated He, Ne and Ar clusters in the size range 2–10. The ease with which a global search technique such as PSO can track down the minima on complex potential energy surfaces within reasonable computational times enables probing a wide spectrum of CNTs covering nanotubes with lengths in the 10–50 A  range and possessing radii of 3–6 A. Our findings indicate a strong correlation between the most stable cluster configuration and the physical dimensions of the CNT within which it is confined. Notably, the confined cluster geometries encompass linear, zigzag and spiral configurations, in striking contrast to their isolated geometries. Guided by the chemical intuition, we have further expanded the search space and examined the possibility of exohedral binding in necessary cases. The implementation of the PSO along with the continuum approximation can generate excellent starting geometries amenable for further analysis using highly accurate first-principles calculations.