Extending the time scale in molecular dynamics simulations: Propagation of ripples in graphene

Abstract

We show that it gives an exact solution of the temporal part of the MD equations for up to quadratic terms in atomic displacements in the interatomic potential. Higher-order terms are then included by iteration. We will refer to our technique as Green’s function in molecular dynamics GFMD. This technique should be applicable to all physical, chemical, and biological systems where MD is used. In certain class of problems in which the atoms vibrate about an equilibrium site, GFMD gives exact results in the harmonic approximation. Examples of such class of problems are phonon transport, thermal conduction etc., in disordered or finite solids and low-dimensional material systems for which MD has to be used because analytical solutions are not available even in the harmonic approximation. For nonlinear vibration problems, depending upon the anharmonicity, GFMD can accelerate MD by about 8 orders of magnitude, and model processes at microseconds. In other classes of problems in which the atoms are itinerant, such as diffusion or crystal growth, GFMD can be used iteratively and should still accelerate MD by a significant amount. Consider a set of N interacting atoms. We label the atoms by indices L and L. We assume a Cartesian frame of reference and denote the position vector of atom L by rL at t = 0. We denote the displacement and velocity of atom L at time t by uL ,t and cL ,t, respectively. As in classical MD, we need to solve the following equation for u: