Lecture: Monte Carlo

 

Welcome to the Monte Carlo lecture. If you want to follow on with what I am saying during the lecture, please download this PDF file. It contains a copy of the slides together with the full text of what I am going to say. You can use this to keep up with the lecture, or to review the material at a later point.


During the lecture I will talk about the Boltzmann distribution, and how this is used to derive the Monte Carlo acceptance test. If you are interested, here are a couple of documents that provide the mathematics underlying the methods;


  1. boltzmann_equation.pdf - provides a full derivation of the canonical Boltzmann distribution

  2. monte_carlo.pdf - provides a full derivation of a variety of Monte Carlo acceptance tests


In addition, the Monte Carlo movies shown in the lecture are taken from real Monte Carlo simulations. The file mc_examples.tgz contains a copy of all of the input files and short Sire python scripts that were used to make these movies. If you are interested, download this file and take a look at the enclosed README for a full description of the contents.


Also, if you are interested in the movies in the lecture, you can view them all here.


If you want to learn more about Monte Carlo, you can also take a look at a web-based workshop that I produced a few years ago. Note that the section on “intramolecular moves” is now outdated, as it is based on older Monte Carlo software that uses a z-matrix to move the bonds, angles and dihedrals of a molecule. Z-matrix moves are an older and now outdated way of moving molecules in Monte Carlo simulations. While interesting from an historical perspective, modern Monte Carlo software no longer uses z-matrices, and now uses the bond, angle and dihedral moves that I present in the lecture.