# Introduction to Molecular Dynamics

Monday, July 23, 2007 - 9:30am - 10:30am

EE/CS 3-180

Robert Skeel (Purdue University)

Computer simulations of molecular dynamics find many applications in physical chemistry, materials science, biophysics, and structural biology. The basic idea is to simulate the motion of a set of atoms, typically (but not necessarily) in full atomic detail. For this, Newton's equations of motion are used with the forces defined by gradients of a potential energy function that is a rough approximation to that defined by quantum mechanics. A remarkably effective numerical integrator is the simple leapfrog/Stormer/Verlet method. Modeling the boundary of the simulation domain is problematic. Typically, periodicity is assumed, though spherical restraints are sometimes used. The boundary may or may not permit the exchange of energy, momentum, or mass. For the canonical ensemble, only energy is permitted to be exchanged across the boundary. This can be modeled by stochastic boundary conditions. The micro(scopic) state of a system is largely unknown, so initial conditions are chosen at random from a stationary probability distribution of the dynamics. Such a distribution can be obtained for the canonical ensemble by equilibration using Langevin dynamics. Indeed, most quantities of interest are defined only in terms of a stationary distribution and the purpose of the dynamics is to sample configuration space. In some cases, kinetic quantities are of interest and realistic Newtonian dynamics must be used. The practicalities of doing such calculations involves three steps: structure building, simulation, analysis.