A swarm intelligence modeling approach reveals noble gas cluster configurations confined within carbon nanotubes

Confinement of atoms and molecules brings forth fascinating properties to chemical systems that are otherwise not known in the bulk. Carbon nanotubes (CNTs) and fullerenes are excellent hosts for probing the confinement effects. Herein, we explore the potential energy surfaces of large noble gas clusters, Ngn (Ng = He, Ne and Ar; n = 10, 20, 30, 40, and 50), in the confines of CNTs of various lengths. Our implementation involves integrating the continuum approximation for CNTs with the well-known swarm intelligence technique, particle swarm optimization (PSO), followed by a deterministic local optimization. Global search techniques such as PSO have been increasingly utilized in recent times to track down minimum energy configurations on highly rugged potential energy surfaces. Aside from the position vectors of the noble gas atoms, we have considered the radius of the CNTs as a design variable. Such an approach enabled us to predict the optimal CNT radii for the encapsulation of each of the clusters. Confined cluster geometries ranging from linear, zig-zag, and double-helical to spiral configurations are obtained on encapsulation, in sharp contrast to their bare cluster geometries. On increasing the CNT length, our approach yielded quasi-linear geometries, suggesting that the length of the CNTs plays a crucial role in determining the stable cluster configurations on confinement.