Module 3 : Classical Molecular Dynamics
Chapter 28 : Montecarlo Simulations
 
 28.1. Introduction

In the earlier two chapters (Chapter 26 and 27) you have learnt how to construct a molecular dynamics (MD) simulation methodology for simple atomic/molecular systems. The generated trajectories by the MD technique are, in a sense, deterministic. This means, given a potential function of a system, one can choose a convenient time step, usually a few fs(femtoseconds), to generate the real time trajectories. But this time step is too small to probe real physical processes which call for very long MD simulations. When computation of an exact result by simulations appear infeasible, one can make use of the Monte Carlo methods.

 

28.2. The Monte Carlo methods

The Monte Carlo (MC) methods were developed during the fifties of the last century by von Neumann, Ulam and Metropolis. The name ‘Monte Carlo’ was chosen by Metropolis, because of the extensive use of the random numbers in the method. Prior to the development of the Monte Carlo methods, statisticians had used model sampling experiments to investigate complex problems. The model sampling experiments involve the generation of random numbers which were used in several arithmetic and logical operations. The use of computers have made these exercises easy and in the literature, one comes across many anecdotes narrating the efforts of the pioneers to make the Monte Carlo methods to be the most powerful and commonly used technique for analyzing complex problems.