Atomistic Simulation of Materials

This course lays the groundwork for using “atomistic” simulation tools—that is, those based on microscopic interactions between constituents. Primarily, it lays the foundation for simulations known as “Molecular Dynamics” and “Monte Carlo.”

It covers the underlying theoretical concepts to build a solid understanding of the methods, as well as the practical implementation of the corresponding code.

The critical and reasoned analysis of data is also discussed.

Understand the classical molecular dynamics approach and know how to use it; understand the Monte Carlo approach and know how to use it; know how to implement these approaches for systems of interacting particles with periodic boundary conditions; appreciate the challenges involved in generating pseudorandom numbers; be able to interpret statistical physics data for simple static observables or structural properties derived from simulations, including the assessment of statistical errors; be aware of the difficulties associated with equilibrium, correlations, etc.; be able to implement all of these methods using a compiled language (C, C++, or Fortran).

knowledge of a programming language; a course in statistical physics

Recommended prerequisites:

a compiled programming language (C, C++, or Fortran) that uses imperative programming

Continuous Integral Control

Introduction to the atomistic approach and the modeling of interactions; Overview of molecular dynamics and Monte Carlo methods; Fundamentals of the molecular dynamics method; Integration algorithms and criteria for evaluating them; Verification of an implementation via energy conservation; Handling periodic boundary conditions; adaptation of pair potentials: truncation, offset, and associated corrections; Use of periodic boundary conditions and the nearest-neighbor periodic image convention; Simple static thermodynamic observables (temperature, pressure, chemical potential); Assessment of statistical uncertainties; Structural analysis in terms of the density-density correlation function g(r) and the static structure factor S(q); Computer-generated pseudorandom numbers: generators, subtleties, non-uniform distributions; Theory underlying the Monte Carlo method: Markov chains and detailed balance; Metropolis algorithm; Thermodynamic ensembles in molecular dynamics and Monte Carlo simulations: thermostats and barostats.

Practical application of the methods covered in class to simple models (Lennard-Jones, hard spheres, Ising models, etc.) by implementing them in a compiled language.