Introduction

In this chapter we consider the motion of nuclei in the classical limit. The laws of classical mechanics apply, and the nuclei move in a conservative potential, determined by the electrons in the Born–Oppenheimer approximation. The electrons are assumed to be in the ground state, and the energy is the ground-state solution of the time-independent Schrödinger equation, with all nuclear positions as parameters. This is similar to the assumptions of Car–Parrinello dynamics (see Section 6.3.1), but the derivation of the potential on the fly by quantum-mechanical methods is far too compute-intensive to be useful in general. In order to be able to treat large systems over reasonable time spans, a simple description of the potential energy surface is required to enable the simulation of motion on that surface. This is the first task: design a suitable force field from which the forces on each atom, as well as the total energy, can be efficiently computed, given the positions of each atom. Section 6.3 describes the principles behind force fields, and emphasizes the difficulties and insufficiencies of simple force field descriptions. But before considering force fields, we must define the system with its boundary conditions (Section 6.2). The way the interactions over the boundary of the simulated systems are treated is in fact part of the total potential energy description.