Structure and formation energy of carbon nanotube caps

We present a detailed study of the geometry, structure, and energetics of carbon nanotube caps. We show that the structure of a cap uniquely determines the chirality of the nanotube that can be attached to it. The structure of the cap is specified in a geometrical way by defining the position of six pentagons on a hexagonal lattice. Moving one (or more) pentagons systematically creates caps for other nanotube chiralities. For the example of the (10,0) tube we study the formation energy of different nanotube caps using ab initio calculations. The caps with isolated pentagons have an average formation energy $(0.29\ifmmode\pm\else\textpm\fi{}0.01)\mathrm{eV}$/atom. A pair of adjacent pentagons requires a much larger formation energy of $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. We show that the formation energy of adjacent pentagon pairs explains the diameter distribution in small-diameter nanotube samples grown by chemical vapor deposition.