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.

The algorithms and capabilities of the pDynamo library discussed in this book represent only a portion of those that are available. The choice of which to include has been highly subjective and, due to space restrictions and the perseverance of the author (!), relatively small. The topics that I most regret omitting or skimping upon include density functional theory, the calculation of surfaces and volumes, continuum methods for including solvation effects, non-equilibrium methods, especially those for the determination of free energies, and enhanced methods, such as transition path sampling, for the investigation of chemical reactions and other rare events. In any case, readers are encouraged to investigate these and alternative methods themselves, for many of the techniques presented in the book are the subject of active research and are undergoing continual improvement.

pDynamo itself and the example programs described in the text are available on the World Wide Web. At the time of publication, the appropriate addresses were www.ibs.fr and www.pdynamo.org. The websites give full details about how to download, install and use the library and the types of machines upon which it has been tested.

For convenience, we include here tables of the methods and attributes of the System class and of the other classes and functions that were encountered in the book along with the section in which they were first described or in which significant new capabilities were introduced. These are in Tables A1.1, A1.2 and A1.3, respectively. The System class is, in many ways, the central class of the library although it has several other important features which could not be treated in the text.