Chapter 9: Molecular Dynamics

Lecture 1: Friday February 1

• The Molecular Dynamics Method
• Approximations in Molecular Dynamics
• The Verlet Integration Algorithms
• The Two-dimensional Lennard-Jones System
• Program to simulate the 2D Lennard-Jones System

Lecture 2: Monday February 4

• Molecular Dynamics Simulation of Argon
• Simple model of interacting Argon atoms
• A simple MD program

Lecture 3: Wednesday February 6

• Improving the MD program
• Position particles on a face-centered cubic lattice
• Draw initial velocities from a Maxwell-Boltzmann distribution
• Solving Newton's equations of motion
• Velocity Verlet Integration Algorithm
• Output of the program

Lecture 4: Friday February 8

• Making the MD simulation more efficient
• Improved program md3.cpp
• Variables and functions for cut-off and neighbor list
• Compute separation between two particles
• Find all pairs with separation less than $r_{\rm max}$
• Find and store all pair separations less than $r_{\rm max}$
• Compute accelerations
• Velocity-Verlet integration algorithm
• Steering the simulation
• Functions repeated from md2.cpp
• Output of the neighbor list program
• Correcting for the cut-off

Lecture 5: Monday February 11

• Physical Observables in Molecular Dynamics
• Total Energy
• Temperature
• Heat Capacity
• Pressure
• Compressibility
• Radial Distribution Function
• Animating the Argon MD Simulation
• New variables and functions for OpenGL animation
• Functions repeated from md3.cpp
• Dev-C++ and OpenGL

Lecture 6: Monday February 18

• The Melting Transition
• Mermin-Wagner Theorem
• Theories of Melting in Two Dimensions
• Simulating 2-D Melting
• Equipartition and the Fermi-Pasta-Ulam Problem
• Fermi-Pasta-Ulam Code