Eur. Phys. J. B (2018) 91: 11
https://doi.org/10.1140/epjb/e2017-80444-5

Regular Article

A torsional potential for graphene derived from fitting to DFT results

¹ Department of Physics, National Technical University of Athens, 15780 Athens, Greece
² Materials Science Department, University of Patras, 26504 Rio, Greece
³ Crete Center for Quantum Complexity and Nanotechnology (CCQCN), Physics Department, University of Crete, 71003 Heraklion, Greece
⁴ Institute of Electronic Structure and Laser, FORTH, Heraklion, Greece
⁵ Department of Physics, University of South Florida, Tampa, FL 33620, USA
⁶ Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, 11635 Athens, Greece

^a e-mail: lathiot@eie.gr

Received: 29 July 2017
Received in final form: 31 October 2017
Published online: 17 January 2018

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 Å. The presented potential is applicable to other sp² carbon structures.