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

A technique using causal Green’s function is proposed for extending and bridging multiple time scales in molecular dynamics for modeling time-dependent processes at the atomistic level in nanomaterials and other physical, chemical, and biological systems. The technique is applied to model propagation of a pulse in a one-dimensional lattice of nonlinear oscillators and ripples in graphene from femtoseconds to microseconds. It is shown that, at least in the vibration problems, the technique can accelerate the convergence of molecular dynamics and extend the time scales by eight orders of magnitude.

Figure 1

(Color online) Atomic displacement of the central atom in a one-dimensional lattice as function of time calculated by using GFMD with $\Delta t=100$ femtoseconds and compared with the exact result. The two curves almost overlap. The displacements are normalized with respect to the initial displacement of the central atom.

Figure 2

(Color online) Same calculations as in Fig. 1 compared with results obtained by using basic MD for time step $\Delta t=1\text{fs}$. The agreement between the two curves becomes increasing worse at longer times and/or for longer $\Delta t$.

Figure 3

(Color online) Atomic displacements as function of time in the picoseconds range for the central atom (solid line) and the atom located at about 1.9 nm along the $+X$ axis (dotted line) in graphene. The displacements are normalized as in Fig. 1.

Figure 4

(Color online) Same as in Fig. 3 for the central atom in the microseconds time range.

Figure 5

(Color online) Snapshot of normalized atomic displacements in graphene at about 20 ms. Coordinates $X$ and $Y$ are in units of half lattice constant.