INTRODUCTION TO THE KINETIC MONTE CARLO METHOD

Abstract

Monte Carlo refers to a broad class of algorithms that solve problems through the use of random numbers. They .rst emerged in the late 1940’s and 1950’s as electronic computers came into use [1], and the name means just what it sounds like, whimsically referring to the random nature of the gambling at Monte Carlo, Monaco. The most famous of the Monte Carlo methods is the Metropolis algorithm [2], invented just over 50 years ago at Los Alamos National Laboratory. Metropolis Monte Carlo (which is not the subject of this chapter) offers an elegant and powerful way to generate a sampling of geometries appropriate for a desired physical ensemble, such as a thermal ensemble. This is accomplished through surprisingly simple rules, involving almost nothing more than moving one atom at a time by a small random displacement. The Metropolis algorithm and the numerous methods built on it are at the heart of many, if not most, of the simulations studies of equilibrium properties of physical systems.