Endohedral motions inside capped single-walled carbon nanotubes

B3LYP/6-311G* electronic structure calculations reveal that the dependence of the complexation energy Ecmpl(z) on the longitudinal displacement z of the guest in endohedral complexes of the Na+ cation with capped [5,5] armchair single-walled carbon nanotubes stems from an interplay between the polarization of the host by the electric field of the guest and the guest–host steric repulsion. Overall, Ecmpl(z) is characterized by the presence of a periodic pattern of local minima and maxima that reflect the discrete nature of the tube and of a pair of global minima located at fixed distances from the tube termini. Because of the large barrier height/zero-point energy ratio, the endohedral motion of the Na+ cation at T=0 [K] is largely confined to a surface that internally follows the contour of the tube. Vibrations perpendicular to the surface give rise to transitions in the vicinity of 100 [cm−1], whereas the unimpeded motions within the surface result in a plethora of transitions with onsets as low as 0.1 [cm−1].