‹ Abrams Group
Teaching
Molecular Simulations
Modern Molecular Simulations
Contents
1
Introduction
2
Statistical Mechanics: A Brief Introduction
2.1
Microstates and Degeneracy
2.2
Making Observations: The Ergodic Hypothesis
2.3
Entropy and Temperature
2.4
Classical Statistical Mechanics
3
Monte Carlo Simulation
3.1
The Metropolis Monte Carlo Method
3.2
Case Study 1: The 2D Ising Magnet
3.3
Elements of a Continuous-Space MC program
3.4
Case Study 2: MC of Hard Disks
3.5
Case Study 3: Hard-Disk Dumbbells in 2D
3.6
Case Study 4 (F&S Case Study 1): Equation of State of the Lennard-Jones Fluid
3.7
Suggest Project: Lennard-Jones Dumbbells
4
Molecular Dynamics Simulation
4.1
MD: Theoretical Background
4.2
Case Study 1: An MD Code for the Lennard-Jones Fluid
4.3
Case Study 2: Static Properties of the Lennard-Jones Fluid (Case Study 4 in F&S)
4.4
Case Study 3: Dynamical Properties: The Self-Diffusion Coefficient
5
Ensembles
5.1
Monte Carlo Simulations in the Isothermal-Isobaric (NPT) and Grand Canonical (
\(\mu \)
VT) Ensembles
5.2
Molecular Dynamics at Constant Temperature
5.3
Molecular Dynamics at Constant Pressure: The Berendsen Barostat
6
Free Energy Methods
6.1
Excess Chemical Potential via the Widom Method
6.2
Thermodynamic Integration
7
Advanced Topics
7.1
Case Study: Stillinger-Weber Silicon and the Tersoff Potential
7.2
Rare Events: Path-Sampling Monte Carlo
7.3
Long-Range Interactions: The Ewald Summation
7.4
Densities of States: The Wang-Landau Monte Carlo Method
8
Course Projects
8.1
Suggested Topics
8.2
Schedule of Presentations
9
Concluding Remarks
10
Odds and Ends
10.1
Lennard-Jones on a Line
References
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5
Ensembles
5.1
Monte Carlo Simulations in the Isothermal-Isobaric (NPT) and Grand Canonical (
\(\mu \)
VT) Ensembles
5.2
Molecular Dynamics at Constant Temperature
5.2.1
Velocity Scaling: Isokinetics and the Berendsen Thermostat
5.2.2
Stochastic NVT Thermostats: Andersen, Langevin, and Dissipative Particle Dynamics
5.2.3
The Nosé-Hoover Chain
5.3
Molecular Dynamics at Constant Pressure: The Berendsen Barostat
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