Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table

Abstract

We present a method for carrying out long time scale dynamics simulations within the harmonic transition state theory approximation. For each state of the system, characterized by a local minimum on the potential energy surface, multiple searches for saddle points are carried out using random initial directions. The dimer method is used for the saddle point searches and the rate for each transition mechanism is estimated using harmonic transition state theory. Transitions are selected and the clock advanced according to the kinetic Monte Carlo algorithm. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assumed to sit on lattice sites and a list of all possible transitions need not be specified beforehand. Rather, the relevant transitions are found on the fly during the simulation. A multiple time scale simulation of Al(100) crystal growth is presented where the deposition event, occurring on the time scale of picoseconds, is simulated by ordinary classical dynamics, but the time interval in between deposition events, on the order of milliseconds, is simulated by the long time scale algorithm. The Al(100) surface is found to grow remarkably smooth, even at 30 K because of concerted displacements of multiple atoms with significantly lower activation energy than adatom diffusion on the flat terrace.