‹ Abrams Group

Teaching Molecular Simulations Modern Molecular Simulations

1 Introduction
1.1 Course Objectives
1.2 Course Outline
1.3 Prerequisites
1.4 Introductory Remarks
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 Linux and Scientific Computing
3.1 The Linux Ecosystem
3.2 Running Programs at the Command-Line
4 Monte Carlo Simulation
4.1 The Metropolis Monte Carlo Method
4.2 Case Study 1: The 2D Ising Magnet
4.3 Elements of a Continuous-Space MC program
4.4 Case Study 2: MC of Hard Disks
4.5 Case Study 3: Hard-Disk Dumbbells in 2D
4.6 Case Study 4: Equation of State of the Lennard-Jones Fluid
5 Molecular Dynamics Simulation
5.1 MD: Theoretical Background
5.2 Case Study 1: An MD Code for the Lennard-Jones Fluid
5.3 Case Study 2: Static Properties of the Lennard-Jones Fluid
5.4 Case Study 3: Transport Properties: The Self-Diffusion Coefficient
6 Ensembles
6.1 Monte Carlo Simulations in the Isothermal-Isobaric and Grand Canonical Ensembles
6.2 Molecular Dynamics at Constant Temperature
6.3 Molecular Dynamics at Constant Pressure: The Berendsen Barostat
7 Long-Range Interactions: The Ewald Summation
7.1 The Ewald Coulombic energy
7.2 Ewald Forces
7.3 Implementation and Evaluation
8 All-atom Potential Energy Functions
8.1 Class-I Potentials
8.2 Reactive Potentials
8.3 Case Study: Stillinger-Weber Silicon
9 Open-source Production MD: Gromacs and NAMD
9.1 Gromacs
9.2 NAMD
10 Free Energy Methods
10.1 Excess Chemical Potential via the Widom Method
10.2 Thermodynamic Integration
10.3 The Method of Overlapping Distributions
10.4 Histogram Reweighting
10.5 Adaptive Free-Energy Methods
References

¹One modification of this code is a necessary one: the implementation of the real-space energy was left as an exercise. Other modifications made easily include embedding the main program inside a double loop over desired \(\alpha \) and \(k_{\rm max}\) values.