  We present a simple torsional potential for graphene to accurately describe
its out-of-plane deformations. The parameters of the potential are derived
through appropriate fitting with suitable DFT calculations regarding the
deformation energy of graphene sheets folded around two different folding axes,
along an armchair or along a zig-zag direction. Removing the energetic
contribution of bending angles, using a previously introduced angle bending
potential, we isolate the purely torsional deformation energy, which is then
fitted to simple torsional force fields. The presented out-of-plane torsional
potential can accurately fit the deformation energy for relatively large
torsional angles up to 0.5 rad. To test our proposed potential, we apply it to
the problem of the vertical displacement of a single carbon atom out of the
graphene plane and compare the obtained deformation energy with corresponding
DFT calculations. The dependence of the deformation energy on the vertical
displacement of the pulled carbon atom is indistinguishable in these two cases,
for displacements up to about 0.5 $\AA$. The presented potential is applicable
to other sp$^2$ carbon structures.
