Atomistic potential for graphene and other sp2 carbon systems

We introduce a torsional force field for sp(2) carbon to augment an in-plane atomistic potential of a previous work [G. Kalosakas et al., J. Appl. Phys., 2013, 113, 134307] so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce density-functional-theory calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp(2) carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane acoustic and optical modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1000 cm(-1).