Abstract

This chapter introduces the Molecular Dynamics (MD) method, probably the most frequently used method to simulate classical many-body systems. As the idea behind MD is simply to solve Newton's equations of motion for a (large) number of interacting particles, we start by discussing the structure of a very simple MD program. We pay attention to the initialization of the simulation, the computation of the forces, and the so-called “position Verlet algorithm” to solve Newton's equation of motion in discretized form. After that, we look more critically at the approximate solutions of the equation of motion. We consider the time-reversibility, numerical accuracy, the possible drift in energy and the exponentially divergence of trajectories that are initially close. Subsequently, we discuss other forms of the Verlet algorithm and some common pitfalls. We then dive a bit deeper and approach the problem of solving discretized equations of motion using the so-called Trotter expansion. This formalism allows us to explain why the Verlet algorithm, though simple, is better suited for Molecular Simulations than many, more sophisticated algorithms. We end with a discussion of the Verlet algorithm from the perspective of the principle of least action.

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