Atomistic Scale Simulations

by Antonia Statt

This is a digitized collection of course notes and problems developed for MSE 485 “Atomistic Scale Simulations” at University of Illinois Urbana Champaign.

Table of contents

• 1. Introduction
  • 1.1. Why are we interested in the atomistic scale?
  • 1.2. What are Simulations?
• 2. Molecular Models and Interactions
  • 2.1. Introduction
  • 2.2. Molecular Models
  • 2.3. Periodic Boundary Conditions
  • 2.4. Intermolecular Potentials
  • 2.5. Short-Ranged Intramolecular Potentials
  • 2.6. Long-Range Potentials
• 3. Statistical Mechanics and Thermodynamics
  • 3.1. Introduction
  • 3.2. Thermodyanmics and Ensembles
  • 3.3. Statistical Mechanics: Ensembles, Ergodicity and other Stuff
  • 3.4. Thermodyanmics Properties
  • 3.5. Entropy and Temperature
  • 3.6. Structural Correlations
  • 3.7. Transport Coefficients
  • 3.8. Statistical Errors
• 4. Molecular Dynamics
  • 4.1. Introduction
  • 4.2. Verlet Integration
  • 4.3. Thermostats
  • 4.4. Langevin Dynamics
  • 4.5. Using MD Packages
  • 4.6. Initialization and Neighbor Searching
  • 4.7. HPC (High-Performance Computing)
• 5. Monte Carlo Simulations
  • 5.1. Introduction
  • 5.2. Random Numbers
  • 5.3. Monte Carlo Methods
  • 5.4. Sampling Methods
  • 5.5. Gibbs Ensemble and Phase Coexistence
  • 5.6. Phase Transitions, Finite-size Scaling and Renormalization Group
  • 5.7. Variance Reduction Techniques
  • 5.8. Metropolis Method
  • 5.9. The Ising Model
  • 5.10. Directed Monte Carlo
  • 5.11. Kinetic Monte Carlo
  • 5.12. Free Energy Estimation in Simulations
• 6. References
• 7. Credits