Parametric interatomic potential for graphene

A parametric interatomic potential is constructed for graphene. The potential energy consists of two parts: a bond energy function and a radial interaction energy function. The bond energy function is based on the Tersoff-Brenner potential model. It includes angular terms and explicitly accounts for flexural deformation of the lattice normal to the plane of graphene. It determines the cohesive energy of graphene and its equilibrium lattice constant. The radial energy function has been chosen such that it does not contribute to the binding energy or the equilibrium lattice constant but contributes to the interatomic force constants. The range of interaction of each atom extends up to its fourth-neighbor atoms in contrast to the Tersoff-Brenner potential, which extends only up to second neighbors. The parameters of the potential are obtained by fitting the calculated values to the cohesive energy, lattice constant, elastic constants, and phonon frequencies of graphene. The values of the force constants between an atom and other atoms that are within its fourth-neighbor distance are calculated. Analytical expressions are given for the elastic constants and the flexural rigidity of graphene. The flexural rigidity of the graphene lattice is found to be 2.13 eV, which is much higher than 0.797 eV calculated earlier using the Tersoff-Brenner potential.