  Many calculations require a simple classical model for the interactions
between sp^2-bonded carbon atoms, as in graphene or carbon nanotubes. Here we
present a new valence force model to describe these interactions. The
calculated phonon spectrum of graphene and the nanotube breathing-mode energy
agree well with experimental measurements and with ab initio calculations. The
model does not assume an underlying lattice, so it can also be directly applied
to distorted structures. The characteristics and limitations of the model are
discussed.
