Off-lattice pattern recognition scheme for kinetic Monte Carlo simulations

We report the development of a pattern-recognition scheme for the off-lattice self-learning kinetic Monte Carlo (KMC) method, one that is simple and flexible enough that it can be applied to all types of surfaces. In this scheme, to uniquely identify the local environment and associated processes involving three-dimensional (3D) motion of an atom or atoms, space around a central atom is divided into 3D rectangular boxes. The dimensions and the number of 3D boxes are determined by the accuracy with which a process needs to be identified and a process is described as central atom moving to a neighboring vacant box accompanied by the motion of any other atom or atoms in its surrounding boxes. As a test of this method we apply it to 3D Cu island decay on the Cu(100) surface and to 2D diffusion of a Cu monomer and a dimer on the (111) surface, and results and computational efficiency to those available in the literature.