Monte Carlo Simulations of Adsorbed Molecules on Ionic Surfaces

Abstract

Monte Carlo (MC) method [1-10] refers to all calculations that involve the use of random numbers for sampling processes of approximate solutions to quantitative problems. It can be applied for application domains range from economics to physics to chemistry to surface science to medicine. The Monte Carlo (MC) method is usually Linked to Comte de Buffon a French eighteenthcentury naturalist, who performed an experiment by throwing a needle of length ` at random onto a board marked with parallel lines a distance d apart to infer the probability p that the needle will intersect one of those lines. Buffon’s subsequent experiments enabled him to make an accurate estimation of π. Following the procedure of Buffon, Laplace, and then In 1864, Captain O. C. Fox and in 1873, A. Hall [8] used Monte Carlo method calculate π. Early 1940’s marked the beginning of the modern history of Monte Carlo when scientists at Los Alamos systematically used them as a research tool in their work on developing nuclear weapons. Stanislaw Ulam was the first one to realize the potential of using computers to automate the statistical sampling process. Stanislaw Ulam, John von Neuman and Nicolas Metropolis developed algorithms and explored the means to convert non-random problems into random forms so that statistical sampling can be used for their solution. The name “Monte Carlo” was suggested by Metropolis after the famous Monaco casino. One of the first published papers on this topic was by Metropolis and Ulam in 1949 [9].