  Energies of graphene nanocones with 1 to 5 pentagonal disclinations are
studied on an atomically detailed level. The numerical results are interpreted
in terms of three different contributions to the cone energy: the core
disclination energy, the bending energy of the cone surface, and the ''line
tension'' energy of the cone edge that is related to different coordination of
carbon atoms situated at the edge. This continuum description allows for a
construction of analytic expressions for the cone energetics and indicates
different regimes of cone sizes in which cones with a particular number of
disclinations are preferred energywise. An important result of the study is
that the energetics of various types of cones profoundly depends upon whether
the dangling carbon bonds at the cone basis are saturated by hydrogen atoms or
not. This may be of use for explaining the differences in the yields of various
cone types in different production processes.
