Introduction

In the last chapter we discussed quantum chemical methods for calculating the potential energy of a system whereas in this chapter we present an alternative class of approaches, those that use empirical energy functions. To start, though, a point of notation will be clarified. Several different terms are employed to denote empirical energy functions in the literature and, no doubt, inadvertently, in this book. Common terms, which all refer to the same thing, include empirical energy function, potential energy function, empirical potential and force field. The use of empirical potentials to study molecular conformations is often termed molecular mechanics (MM).

Some of the earliest empirical potentials were derived by vibrational spectroscopists interested in interpreting their spectra (this was, in fact, the origin of the term ‘force field’), but the type of empirical potential that is described here was developed at the end of the 1960s and the beginning of the 1970s. Two prominent proponents of this approach were S. Lifson and N. Allinger. These types of force field are usually designed for studying conformations of molecules close to their equilibrium positions and so would be inappropriate for studying processes, such as chemical reactions, in which this is not the case.

Typical empirical energy functions

This section presents the general form of the empirical energy functions that are used in molecular simulations. A diversity exists, because the form of an empirical potential function is, to some extent, arbitrary, but most functions have two categories of terms that deal with the bonding and the non-bonding interactions between atoms, respectively. These will be discussed separately.