Molecular Dynamics Simulation

Abstract

Abstract So far most of our discussion of energy storage and energy transport has been built on the reciprocal space: the dispersion relations between wavevectors and frequencies. We discarded the history of the motion of individual particles (electrons and atoms) and focused on their collective modal behavior. However, the approximate trajectory of individual particles can be traced if the computational power is sufficient, and from the calculated trajectory of all the particles we can evaluate the desired macroscopic properties or examine the microscopic processes in real space. When the particles are individual molecules or atoms, the approach is typically called molecular dynamics simulation. In classical molecular dynamics, the equations of motion for each individual atom in the system are established on the basis of an empirical interatomic force (or potential) and Newton’s second law. These equations for all the atoms in the system are coupled through the interatomic potential and solved numerically. A quantum molecular dynamics simulation solves the coupled time-dependent Schrodinger equations for all the particles in the system. Exact direct numerical solution of the Schrodinger equations for a system comprising a large number of particles is impractical, and so various approximations have been used. For example, Car and Parrinello (1985) combined the classical atomistic simulation for atomic ions with the density function theory for electrons. Both classical and quantum molecular dynamic simulations require extensive computation but are becoming increasingly useful as computers become faster. The simulation results are usually analyzed on the basis of statistical mechanics principles. In this chapter, we focus on classical molecular dynamic simulations, since quantum molecular dynamics is still limited to a small number of atoms. Molecular dynamic simulation methods have been used as a basic tool in a wide range of fields. A single chapter will not be able to cover even a small number of potential applications.