Endohedral motions inside capped single-walled carbon nanotubes

B3LYP/6-311G* electronic structure calculations reveal that the dependence of the complexation energy E-cmpl(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, E-cmpl(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)]. (C) 2003 American Institute of Physics.