Ab initio study of small graphitic cones with triangle, square, and pentagon apex

Accurate geometries of carbon nanocones of different sizes with a triangle, square or pentagon at the apex have been determined for the first time using a quantum chemical optimization method. The structure close to the apex is distorted from an ideal conical surface. The charging effect of the central defect is quite different from that predicted by tight-binding calculations. The symmetry behavior of the frontier orbitals and the size of the highest occupied molecular orbital-lowest unoccupied molecular orbital gap versus cone type and size is explained. The density of states quickly converges towards that of graphite when the size of the cone increases. In comparison to previous results in the literature it is found that the local densities of states of cones, that are locally different but belong to the same topo-combinatoric class, share common features.