Modeling zigzag CNT: dependence of structural and electronic properties on length, and application to encapsulation of HCN and C 2 H 2 .

Density functional theory (B3LYP, B3LYP-D2 and wB97XD functionals) was used in finite models of zigzag carbon nanotubes (CNT), (n,0)×k with n = 6-9 and k = 2-4, to systematically investigate the effects of size on their structural and electronic properties. We found that the ratio between the length (Lt ) and the diameter (dt ) of the pristine CNT has to be larger than 2, i.e., Lt /dt  > 2, in order to provide the observed experimental trends of C=C bond distances, as well as to maintain the atomic charges nearly constant and zero around the center of the tube. Therefore, the concepts of useful length and volume were developed and tested for the encapsulation process of HCN and C2 H2 into CNTs. The energies involved in these processes, as well as the changes in molecular structure and electronic properties of the dopants and the CNTs are discussed and rationalized by the amount of charge transferred between dopant and CNT. Graphical Abstract Illustration of zigzag CNT length and diameter ratio in order to represent C=C bond experimental trend.