A Torsional potential for graphene derived from fitting to DFT results

TL;DR

This paper introduces a simple torsional potential for graphene, fitted to DFT data, to accurately model out-of-plane deformations up to large angles and displacements, applicable to other sp2 carbon structures.

Contribution

A new torsional potential for graphene derived from DFT fitting that accurately models large out-of-plane deformations and can be applied to other sp2 carbon materials.

Findings

Accurately fits deformation energy for torsional angles up to 0.5 rad.

Replicates DFT results for vertical displacement of a carbon atom.

Applicable to other sp2 carbon structures.

Abstract

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.