# NM1: Monte Carlo and molecular dynamics

Module title: Monte Carlo and molecular dynamics (NM1)

Module convenor: Prof. Michael Allen (Warwick)

Outline Syllabus

This module will cover computer simulation methods applied to condensed matter systems. The emphasis will be on classical systems (i.e. *no* electronic structure or quantum mechanics), on understanding how these methods work, and on understanding how they connect with experimentally measurable quantities. I shall rely on some prior understanding of undergraduate-level statistical mechanics concepts such as the Boltzmann distribution, the statistical ensemble, the microscopic interpretation of entropy, free energy etc. An understanding of undergraduate-level mathematics such as Fourier transforms, probabilities, and some ideas lifted from quantum mechanics such as operators will also be needed. However, the course is intended to suit students from experimental groups as well as theoretical groups, and in particular it will not require too much in the way of computer programming skills.

The list of topics below is a guide only, and does not necessarily indicate the order in which they will be presented.

- Part 1: Molecular Dynamics
- 1. The aims of molecular simulation
- 2. Interactions: non-bonded potentials, intramolecular force fields
- 3. The molecular dynamics algorithm and the Liouville equation
- 4. Correlation times and statistical errors. Constraints and blue-moon ensemble.
- Part 2: Monte Carlo
- 5. Importance sampling and Markov chains
- 6. Biased sampling, barrier crossing, exploring configuration space,
- 7. Kinetic Monte Carlo and crystal growth
- 8. Phase transitions and finite-size effects.
- Part 3: Connecting with experiment
- 9. Time correlation functions, scattering and spectroscopy
- 10. Nonequilibrium simulations and transport coefficients

Assessment

Assessment will be through problems, and through a short written review of a topic in molecular simulation. The problems sheet is **NM1-assessment.pdf** available below. The deadline is Friday 13 March. Here is the list of topics for question 7. None of them have been discussed in detail during the lectures, but they should all be tractable.

- Hyperdynamics
- Pruned Enriched Rosenbluth Monte Carlo (PERM)
- Cluster-update Monte Carlo
- Renormalization Group Monte Carlo
- The Jarzinsky Relation
- Gibbs Ensemble Monte Carlo
- Nonequilibrium molecular dynamics
- A topic of your own choice

If you choose this last option, you must get my approval of the topic by email before starting it. In all cases you should email me at m.p.allen@warwick.ac.uk to let me know your choice of topic and paper to review, so that I can prevent overlaps between students.