Chapter 3 - Monte Carlo Simulations

Abstract

This chapter describes the basic principles of the Monte Carlo (MC) method. Random sampling is the simplest MC technique. In general, it is not possible to evaluate an integral by direct MC sampling. However, in many cases, one is not interested in the configurational part of the partition function itself but in averages. Metropolis method allows the study of the ratio of two integrals. It is difficult to talk about MC or Molecular Dynamics (MD) programs in abstract terms. The best way to explain how such programs work is to write them down. Most MC or MD programs are only a few hundred to several thousand lines long. This is very short compared to, for instance, a typical quantum-chemistry code. For this reason, it is not uncommon that a simulator will write many different programs that are tailor made for specific applications. The result is that there is no such thing as a standard MC or MD program. However, the cores of most MD/MC programs are, if not identical, at least very similar.