|| We present a Stochastic-Difference-Equation (SDE) approach to long time-scale molecular dynamics (MD) simulations, which are required for nanosecond-scale phenomena. In this method, the MD trajectory in a fixed time period is obtained as a stationary solution of an action functional
based on an error accumulation of the equation of motion along the path, thus reducing the problem to a boundary-value problem, instead of an initial-value problem in the ordinary MD method. We apply the method to formation processes of Cu thin film via nanocluster deposition onto a substrate.
The applicability of the SDE algorithm to the problem and the effects of the choice of SDE parameters on the optimization processes of configuration pathway are examined.