Molecular Dynamics

Thus far we have studied the dynamics behavior of systems with only a few particles. However, many systems in nature such as gases, liquids and solids contain many mutually interacting particles. A typical problem involves $% 10^{23}-10^{25}$ molecules which, to a good approximation, obey the laws of classical physics. Although the intermolecular forces produce a complicated trajectory for each particle, the observable properties of the whole are averages that do not depend on the individual behavior. The motion is completely determined by the classical equations of motion, and all the physics is contained in the intramolecular potential, i.e. the interactions.

The problem consists in understanding the properties of the whole, starting from the known interactions.. The most direct approach is to simulate the problem with a computer. The problem of simulating a system with $% 10^{23}-10^{25}$ particles requires the power of a supercomputer, and using parallelization techniques. However we can learn the principles using a fraction of that number, say $10^{4}$ particles, that is tractable in a PC. Not only we can learn about about many of the instead of statistical mechanics, but also the basic simulation techniques. The technique that we will learn in this section does not differ in essence from that used in supercomputers, and it is called ``molecular dynamics''.