Monte Carlo Methods

This page will cover Monte Carlo methods used in computational chemistry, statistical mechanics, and materials modeling. It will eventually connect probability sampling, configuration-space exploration, free-energy estimation, and practical workflows for equilibrium simulations and stochastic numerical integration.

Planned Scope

This chapter should eventually explain:

• how random sampling is used to estimate high-dimensional integrals
• how Metropolis-style algorithms generate equilibrium ensembles
• how Monte Carlo differs from deterministic dynamics methods
• how importance sampling, acceptance criteria, and move design affect efficiency
• where Monte Carlo methods are especially useful in chemistry and physics

Status

This page is currently a placeholder so the theory navigation is complete. A full chapter outline and the first completed section can be added next.