The aim of this course is to provide the student with an understanding of the methods, capabilities, and limitations of molecular simulation. This should enable the student to: (1) make sound judgements regarding the quality of molecular simulation studies reported in the literature; (2) decide whether molecular simulation is suited for application to their research, and if so, to know how to begin developing a simulation program applicable to their problems; (3) understand the workings and limitations of commercial molecular simulation software. Further, it is expected that completion of this course will leave the student with a much deeper understanding of the molecular basis of physical behavior.
Outline of course content
Molecular dynamics of hard spheres, demonstrating elementary concepts of temperature, ensemble averaging, error estimation, periodic boundaries. Structure of a simulation program and introduction to programming methods used in the course.
Elementary classical statistical mechanics. Ensembles and fluctuations.
Monte Carlo integration, importance sampling, Markov chains. Monte Carlo simulation, and extension to other ensembles.
Equilibrium molecular dynamics simulations of continuous potentials. Integration algorithms. Extended Lagrangians and simulations in other ensembles. Evaluation of transport coefficients. Hybrid molecular dynamics/Monte Carlo methods.
Modeling of molecules, including hard potentials, soft potentials, multiatomic models. Torsion, stretch and bend potentials. Electrostatics and polarizability. Ewald sum and reaction field methods for treating long-range electrostatic interactions.
Free energy calculations. Examination of several methods: thermodynamic integration, free-energy perturbation (including umbrella sampling), and histogram methods.
Phase equilibria calculations. Gibbs ensemble and Gibbs-Duhem integration methods. Interfacial properties.
Advanced molecular dynamics methods, including constraints and non-equilibrium molecular dynamics.
Rare events and evaluation of kinetic properties.
Complex fluids and biased-sampling techniques. Hydrogen-bonding molecules. Chain molecules. Rosenbluth sampling and configurational bias methods.