Monte Carlo method is a stochastic method that consists in evaluate a sequence of random perturbations to the system.
In function of the difference in energy in those changes, they are kept or not with a certain probability given by Boltzmann distribution.
This method is usually much faster than molecular dynamics since it is not necessary to calculate the atomic forces, however only statistical (i. e. thermodynamical) information can be extracted.
Montecarlo Method is designed to give approximate solutions to very complex problems which is not necessary to obtain the exact solution. In science this method is used to simulate large systems, too big to be simulated by Molecular Dynamics, get the lowest energy conformation of proteins and other macromolecules, simulate the colloids aggregation and other process that involve large number of degrees of freedom.
- N. Metropolis, & S. Ulam, "The monte carlo method" J. Am. Statist. Assoc. 44(247), 335-341, (1949). DOI: 10.1080/01621459.1949.10483310