A study of carbon nanotubes energetics using orbital free method in the frame-work of the density functional theory

Dependence of the binding energy of carbon atoms in nanotubes on the tube diameter is studied. The full-electron orbital free modeling method, developed by us in the framework of the density functional theory, was used for calculation of the binding energy. Nanotubes of limited lengths with the armchair ends were investigated. The tube diameter $D$, was varied from $0,68$ nm up to $1,50$ nm; numbers of included atoms were changed from $80$ up to $320$. Three sets of tubes were studied: the tube length was $0,87$ nm in the first set, $1,36$ nm in second set, and $1,86$ nm in the third set. For the first set the energy minimum ($-7.50$ eV) was found at $D_{min} = 1,22$ nm, for the second set ($-7.62$ eV) at $D_{min} = 1.00$ nm, and for the third set ($-8.01$ eV) at $D_{min} = 1.06$ eV.