Chapter 1 Introduction 1 General Introduction

Two common functions used to represent the van der Waals potential in empirical force fields are the Lennard-Jones 12-6 potential (Equation 7-2) and the Buckingham exponential-6 potential(Equation 7-3). These functions reproduce the general behaviour of real interactions as described above, in an empirical way. For both functions, the long ranged attractive component which models the dispersion interactions, decays with a r⁶ relationship. For the short-ranged steric component, the two potentials differ in their representation. The more common Lennard-Jones potentials utilizes a R¹² function while the Buckingham potential uses a exponential relationship. Although, the Lennard-Jones potential is often considered more computationally efficient, its representation of the repulsive wall is sometimes too steep. Oppositely, whereas the Buckingham potential is more computationally demanding, it also more correctly models the exponential behaviour of the steric wall.

The van der Waals potential is characterized by the well position, R_o, and the well depth, D_o. In a typical molecular mechanics force field, values are assigned to each atom type and are fit to generate results consistent with the rest of the force field. The atom type is generally defined in terms of the atomic element, its hybridization and the functional group it is contained within. Table 7.1 shows some values from the AMBER95⁷⁷ molecular mechanics force field. When the van der Waals potential is required for two atoms of differing type, say between CT and O, they are generated from the two homonuclear parameters using some kind of combination rule such at that expressed in Equations 7-4 and 7-5.