A general force field can be written as a series of terms representing the interactions between increasingly large sets of atoms [34,35]:

where is the total number of atoms, and the two-body term , for instance, describes the interaction of two atoms and .

Three-body and higher order terms in Equation 1.1 are often neglected, such as, for example, in the Lennard-Jones (LJ) pair potential [36,9], which takes the form

where is the distance between atoms and , is the depth of the potential energy well, and is the pair equilibrium separation. This is an approximate potential as its form is a trade-off between the accurate reproduction of the interaction between closed-shell atoms and mathematical and computational simplicity. In this thesis we will use it to describe atomic clusters of various sizes.