Mads R. Sørensen and Arthur F. Voter
Theoretical Division, Los Alamos National Laboratory
A severe obstacle to the application of computational methods in materials science is the so-called time scale problem. The problem is that many relevant processes in materials occur on a time scale that is inaccessible to conventional, computational methods. The standard method for simulation of materials at the atomic level, molecular dynamics, is generally limited to nanoseconds, whereas in real materials, many interesting processes take place on a time scale of milliseconds or seconds. An important class of processes in materials are the so-called rare events (or infrequent events), for which the dynamical evolution of a system can be described as a sequence of transitions between distinct states. Since the system may spend a long time in a state before making a transition to another state, rare events are difficult, or sometimes even impossible, to simulate directly with molecular dynamics.
We have developed a new accelerated dynamics method for simulation of rare events, that can extend the simulation time scale by orders of magnitude compared to ordinary molecular dynamics [1,2]. The method uses first derivatives only and has the advantage of being relatively simple to implement. The basic idea in the method is to carry out a molecular dynamics simulation at a higher temperature with the system confined to a state while detecting attempted transitions out of the state. The observed escape time at the higher temperature is extrapolated to an escape time at the (lower) temperature of interest using a calculated activation energy. When the high temperature molecular dynamics simulation has evolved sufficiently long, the transition corresponding to the shortest escape time at the low temperature is accepted, and the clock at the low temperature is advanced by this escape time. Given certain assumptions, the time extrapolation assures that the method gives the correct rates for transitions at the low temperature, while the state-to-state progression is accelerated because events occur faster at a higher temperature. The method has been extended in a way that significantly reduces the problem of trapping in a subset of states separated by low activation energies (sometimes referred to as the low barrier problem). This problem may often completely block the state-to-state progression in other simulation methods.
The method has been applied to systems relevant to surface diffusion. Simulation of a model system shows that the method reproduces rates in good agreement with harmonic transition state theory. The method has also been applied to more complicated alloy systems with atoms of one metal adsorbed on a surface of another metal. Preliminary simulations of metallic nanowires show that there are processes with very low activation energies, implying that the wires switch between different structures even at a very low temperature.
 M. R. Sørensen and A. F. Voter (to be published).
 A. F. Voter and M. R. Sørensen, 1998 MRS Fall Meeting Symposium Proceedings,
Symposium J: Multiscale Modeling of Materials.